\newcommand{\bclosed}{243}
\newcommand{\bopen}{293}
\newcommand{\btotal}{536}
\newcommand{\bgrouptable}{$\O_4(\F_{5})$ & reflections & 15 \\
$\Sp_4(\F_{3})$ & transvections & 67 \\
$\Sp_4(\F_{5})$ & transvections & 161 \\}
\newcommand{\bclosedlist}{$13\mathrm{a}_{69}$, $13\mathrm{a}_{70}$, $13\mathrm{a}_{72}$, $13\mathrm{a}_{73}$, $13\mathrm{a}_{74}$, $13\mathrm{a}_{76}$, $13\mathrm{a}_{79}$, $13\mathrm{a}_{96}$, $13\mathrm{a}_{104}$, $13\mathrm{a}_{106}$, $13\mathrm{a}_{107}$, $13\mathrm{a}_{108}$, $13\mathrm{a}_{156}$, $13\mathrm{a}_{157}$, $13\mathrm{a}_{160}$, $13\mathrm{a}_{171}$, $13\mathrm{a}_{235}$, $13\mathrm{a}_{343}$, $13\mathrm{a}_{353}$, $13\mathrm{a}_{354}$, $13\mathrm{a}_{355}$, $13\mathrm{a}_{358}$, $13\mathrm{a}_{359}$, $13\mathrm{a}_{360}$, $13\mathrm{a}_{388}$, $13\mathrm{a}_{390}$, $13\mathrm{a}_{396}$, $13\mathrm{a}_{399}$, $13\mathrm{a}_{400}$, $13\mathrm{a}_{402}$, $13\mathrm{a}_{403}$, $13\mathrm{a}_{408}$, $13\mathrm{a}_{413}$, $13\mathrm{a}_{414}$, $13\mathrm{a}_{505}$, $13\mathrm{a}_{524}$, $13\mathrm{a}_{525}$, $13\mathrm{a}_{526}$, $13\mathrm{a}_{527}$, $13\mathrm{a}_{528}$, $13\mathrm{a}_{529}$, $13\mathrm{a}_{535}$, $13\mathrm{a}_{536}$, $13\mathrm{a}_{541}$, $13\mathrm{a}_{542}$, $13\mathrm{a}_{543}$, $13\mathrm{a}_{544}$, $13\mathrm{a}_{545}$, $13\mathrm{a}_{554}$, $13\mathrm{a}_{555}$, $13\mathrm{a}_{557}$, $13\mathrm{a}_{558}$, $13\mathrm{a}_{596}$, $13\mathrm{a}_{597}$, $13\mathrm{a}_{601}$, $13\mathrm{a}_{621}$, $13\mathrm{a}_{630}$, $13\mathrm{a}_{631}$, $13\mathrm{a}_{632}$, $13\mathrm{a}_{636}$, $13\mathrm{a}_{637}$, $13\mathrm{a}_{657}$, $13\mathrm{a}_{664}$, $13\mathrm{a}_{665}$, $13\mathrm{a}_{815}$, $13\mathrm{a}_{867}$, $13\mathrm{a}_{1392}$, $13\mathrm{a}_{1538}$, $13\mathrm{a}_{1995}$, $13\mathrm{a}_{2006}$, $13\mathrm{a}_{2008}$, $13\mathrm{a}_{2613}$, $13\mathrm{a}_{2614}$, $13\mathrm{a}_{2615}$, $13\mathrm{a}_{2616}$, $13\mathrm{a}_{2617}$, $13\mathrm{a}_{2619}$, $13\mathrm{a}_{2620}$, $13\mathrm{a}_{2800}$, $13\mathrm{a}_{2801}$, $13\mathrm{a}_{3038}$, $13\mathrm{a}_{3040}$, $13\mathrm{a}_{3107}$, $13\mathrm{a}_{3144}$, $13\mathrm{a}_{3146}$, $13\mathrm{a}_{3179}$, $13\mathrm{a}_{3257}$, $13\mathrm{a}_{3333}$, $13\mathrm{a}_{3334}$, $13\mathrm{a}_{3343}$, $13\mathrm{a}_{3344}$, $13\mathrm{a}_{3376}$, $13\mathrm{a}_{3377}$, $13\mathrm{a}_{3378}$, $13\mathrm{a}_{3380}$, $13\mathrm{a}_{3381}$, $13\mathrm{n}_{160}$, $13\mathrm{n}_{161}$, $13\mathrm{n}_{162}$, $13\mathrm{n}_{163}$, $13\mathrm{n}_{164}$, $13\mathrm{n}_{165}$, $13\mathrm{n}_{166}$, $13\mathrm{n}_{167}$, $13\mathrm{n}_{168}$, $13\mathrm{n}_{169}$, $13\mathrm{n}_{173}$, $13\mathrm{n}_{174}$, $13\mathrm{n}_{175}$, $13\mathrm{n}_{176}$, $13\mathrm{n}_{177}$, $13\mathrm{n}_{178}$, $13\mathrm{n}_{179}$, $13\mathrm{n}_{180}$, $13\mathrm{n}_{181}$, $13\mathrm{n}_{182}$, $13\mathrm{n}_{211}$, $13\mathrm{n}_{429}$, $13\mathrm{n}_{430}$, $13\mathrm{n}_{431}$, $13\mathrm{n}_{432}$, $13\mathrm{n}_{433}$, $13\mathrm{n}_{434}$, $13\mathrm{n}_{435}$, $13\mathrm{n}_{440}$, $13\mathrm{n}_{441}$, $13\mathrm{n}_{442}$, $13\mathrm{n}_{449}$, $13\mathrm{n}_{467}$, $13\mathrm{n}_{601}$, $13\mathrm{n}_{609}$, $13\mathrm{n}_{610}$, $13\mathrm{n}_{929}$, $13\mathrm{n}_{930}$, $13\mathrm{n}_{931}$, $13\mathrm{n}_{932}$, $13\mathrm{n}_{933}$, $13\mathrm{n}_{957}$, $13\mathrm{n}_{958}$, $13\mathrm{n}_{959}$, $13\mathrm{n}_{960}$, $13\mathrm{n}_{961}$, $13\mathrm{n}_{962}$, $13\mathrm{n}_{963}$, $13\mathrm{n}_{964}$, $13\mathrm{n}_{965}$, $13\mathrm{n}_{966}$, $13\mathrm{n}_{967}$, $13\mathrm{n}_{968}$, $13\mathrm{n}_{977}$, $13\mathrm{n}_{978}$, $13\mathrm{n}_{979}$, $13\mathrm{n}_{980}$, $13\mathrm{n}_{981}$, $13\mathrm{n}_{982}$, $13\mathrm{n}_{983}$, $13\mathrm{n}_{1042}$, $13\mathrm{n}_{1058}$, $13\mathrm{n}_{1059}$, $13\mathrm{n}_{1060}$, $13\mathrm{n}_{1061}$, $13\mathrm{n}_{1062}$, $13\mathrm{n}_{1063}$, $13\mathrm{n}_{1064}$, $13\mathrm{n}_{1072}$, $13\mathrm{n}_{1073}$, $13\mathrm{n}_{1074}$, $13\mathrm{n}_{1075}$, $13\mathrm{n}_{1076}$, $13\mathrm{n}_{1077}$, $13\mathrm{n}_{1078}$, $13\mathrm{n}_{1082}$, $13\mathrm{n}_{1083}$, $13\mathrm{n}_{1084}$, $13\mathrm{n}_{1103}$, $13\mathrm{n}_{1104}$, $13\mathrm{n}_{1105}$, $13\mathrm{n}_{1106}$, $13\mathrm{n}_{1239}$, $13\mathrm{n}_{1280}$, $13\mathrm{n}_{1281}$, $13\mathrm{n}_{1282}$, $13\mathrm{n}_{1283}$, $13\mathrm{n}_{1284}$, $13\mathrm{n}_{1285}$, $13\mathrm{n}_{1286}$, $13\mathrm{n}_{1287}$, $13\mathrm{n}_{1288}$, $13\mathrm{n}_{1289}$, $13\mathrm{n}_{1290}$, $13\mathrm{n}_{1291}$, $13\mathrm{n}_{1292}$, $13\mathrm{n}_{1293}$, $13\mathrm{n}_{1294}$, $13\mathrm{n}_{1295}$, $13\mathrm{n}_{1305}$, $13\mathrm{n}_{1306}$, $13\mathrm{n}_{1307}$, $13\mathrm{n}_{1308}$, $13\mathrm{n}_{1309}$, $13\mathrm{n}_{1310}$, $13\mathrm{n}_{1311}$, $13\mathrm{n}_{1312}$, $13\mathrm{n}_{1313}$, $13\mathrm{n}_{1314}$, $13\mathrm{n}_{1315}$, $13\mathrm{n}_{1316}$, $13\mathrm{n}_{1317}$, $13\mathrm{n}_{1318}$, $13\mathrm{n}_{1319}$, $13\mathrm{n}_{1320}$, $13\mathrm{n}_{1321}$, $13\mathrm{n}_{1322}$, $13\mathrm{n}_{1323}$, $13\mathrm{n}_{1324}$, $13\mathrm{n}_{1332}$, $13\mathrm{n}_{1333}$, $13\mathrm{n}_{1334}$, $13\mathrm{n}_{1363}$, $13\mathrm{n}_{1377}$, $13\mathrm{n}_{1378}$, $13\mathrm{n}_{1379}$, $13\mathrm{n}_{1380}$, $13\mathrm{n}_{1381}$, $13\mathrm{n}_{1385}$, $13\mathrm{n}_{1386}$, $13\mathrm{n}_{2933}$, $13\mathrm{n}_{2934}$, $13\mathrm{n}_{2935}$, $13\mathrm{n}_{2936}$, $13\mathrm{n}_{2937}$, $13\mathrm{n}_{2954}$, $13\mathrm{n}_{2955}$, $13\mathrm{n}_{2956}$, $13\mathrm{n}_{3390}$, $13\mathrm{n}_{3505}$, $13\mathrm{n}_{3723}$, $13\mathrm{n}_{3725}$, $13\mathrm{n}_{3726}$, $13\mathrm{n}_{3727}$, $13\mathrm{n}_{3763}$, $13\mathrm{n}_{3838}$, $13\mathrm{n}_{3915}$}
\newcommand{\bopenlist}{$13\mathrm{a}_{129}$, $13\mathrm{a}_{135}$, $13\mathrm{a}_{136}$, $13\mathrm{a}_{137}$, $13\mathrm{a}_{194}$, $13\mathrm{a}_{196}$, $13\mathrm{a}_{197}$, $13\mathrm{a}_{198}$, $13\mathrm{a}_{233}$, $13\mathrm{a}_{234}$, $13\mathrm{a}_{239}$, $13\mathrm{a}_{242}$, $13\mathrm{a}_{243}$, $13\mathrm{a}_{244}$, $13\mathrm{a}_{253}$, $13\mathrm{a}_{265}$, $13\mathrm{a}_{268}$, $13\mathrm{a}_{269}$, $13\mathrm{a}_{270}$, $13\mathrm{a}_{271}$, $13\mathrm{a}_{272}$, $13\mathrm{a}_{304}$, $13\mathrm{a}_{309}$, $13\mathrm{a}_{338}$, $13\mathrm{a}_{362}$, $13\mathrm{a}_{365}$, $13\mathrm{a}_{366}$, $13\mathrm{a}_{369}$, $13\mathrm{a}_{373}$, $13\mathrm{a}_{375}$, $13\mathrm{a}_{387}$, $13\mathrm{a}_{391}$, $13\mathrm{a}_{392}$, $13\mathrm{a}_{471}$, $13\mathrm{a}_{483}$, $13\mathrm{a}_{487}$, $13\mathrm{a}_{516}$, $13\mathrm{a}_{518}$, $13\mathrm{a}_{530}$, $13\mathrm{a}_{623}$, $13\mathrm{a}_{629}$, $13\mathrm{a}_{3145}$, $13\mathrm{a}_{3147}$, $13\mathrm{a}_{3148}$, $13\mathrm{a}_{3149}$, $13\mathrm{a}_{3167}$, $13\mathrm{a}_{3168}$, $13\mathrm{a}_{3169}$, $13\mathrm{a}_{3170}$, $13\mathrm{a}_{3188}$, $13\mathrm{a}_{3189}$, $13\mathrm{a}_{3190}$, $13\mathrm{a}_{3191}$, $13\mathrm{a}_{3204}$, $13\mathrm{a}_{3205}$, $13\mathrm{a}_{3207}$, $13\mathrm{a}_{3208}$, $13\mathrm{a}_{3209}$, $13\mathrm{a}_{3210}$, $13\mathrm{a}_{3213}$, $13\mathrm{a}_{3216}$, $13\mathrm{a}_{3219}$, $13\mathrm{a}_{3220}$, $13\mathrm{a}_{3221}$, $13\mathrm{a}_{3222}$, $13\mathrm{a}_{3223}$, $13\mathrm{a}_{3232}$, $13\mathrm{a}_{3234}$, $13\mathrm{a}_{3248}$, $13\mathrm{a}_{3259}$, $13\mathrm{a}_{3261}$, $13\mathrm{a}_{3262}$, $13\mathrm{a}_{3263}$, $13\mathrm{a}_{3264}$, $13\mathrm{a}_{3266}$, $13\mathrm{a}_{3274}$, $13\mathrm{a}_{3275}$, $13\mathrm{a}_{3276}$, $13\mathrm{a}_{3291}$, $13\mathrm{a}_{3292}$, $13\mathrm{a}_{3293}$, $13\mathrm{a}_{3294}$, $13\mathrm{a}_{3295}$, $13\mathrm{a}_{3298}$, $13\mathrm{a}_{3301}$, $13\mathrm{a}_{3302}$, $13\mathrm{a}_{3303}$, $13\mathrm{a}_{3317}$, $13\mathrm{a}_{3320}$, $13\mathrm{a}_{3323}$, $13\mathrm{a}_{3330}$, $13\mathrm{a}_{3331}$, $13\mathrm{a}_{3335}$, $13\mathrm{a}_{3345}$, $13\mathrm{a}_{3346}$, $13\mathrm{a}_{3347}$, $13\mathrm{a}_{3348}$, $13\mathrm{a}_{3351}$, $13\mathrm{a}_{3354}$, $13\mathrm{a}_{3355}$, $13\mathrm{a}_{3356}$, $13\mathrm{a}_{3363}$, $13\mathrm{a}_{3365}$, $13\mathrm{a}_{3368}$, $13\mathrm{a}_{3374}$, $13\mathrm{a}_{3375}$, $13\mathrm{a}_{3388}$, $13\mathrm{a}_{3390}$, $13\mathrm{a}_{3393}$, $13\mathrm{a}_{3394}$, $13\mathrm{a}_{3395}$, $13\mathrm{a}_{3396}$, $13\mathrm{a}_{3399}$, $13\mathrm{a}_{3400}$, $13\mathrm{a}_{3401}$, $13\mathrm{a}_{3402}$, $13\mathrm{a}_{3403}$, $13\mathrm{a}_{3404}$, $13\mathrm{a}_{3405}$, $13\mathrm{a}_{3407}$, $13\mathrm{a}_{3409}$, $13\mathrm{a}_{3410}$, $13\mathrm{a}_{3411}$, $13\mathrm{a}_{3412}$, $13\mathrm{a}_{3413}$, $13\mathrm{a}_{3415}$, $13\mathrm{a}_{3417}$, $13\mathrm{a}_{3418}$, $13\mathrm{a}_{3811}$, $13\mathrm{a}_{3812}$, $13\mathrm{n}_{326}$, $13\mathrm{n}_{329}$, $13\mathrm{n}_{330}$, $13\mathrm{n}_{341}$, $13\mathrm{n}_{344}$, $13\mathrm{n}_{345}$, $13\mathrm{n}_{348}$, $13\mathrm{n}_{351}$, $13\mathrm{n}_{352}$, $13\mathrm{n}_{355}$, $13\mathrm{n}_{357}$, $13\mathrm{n}_{358}$, $13\mathrm{n}_{510}$, $13\mathrm{n}_{513}$, $13\mathrm{n}_{514}$, $13\mathrm{n}_{518}$, $13\mathrm{n}_{520}$, $13\mathrm{n}_{521}$, $13\mathrm{n}_{524}$, $13\mathrm{n}_{525}$, $13\mathrm{n}_{526}$, $13\mathrm{n}_{529}$, $13\mathrm{n}_{530}$, $13\mathrm{n}_{531}$, $13\mathrm{n}_{582}$, $13\mathrm{n}_{590}$, $13\mathrm{n}_{591}$, $13\mathrm{n}_{598}$, $13\mathrm{n}_{599}$, $13\mathrm{n}_{600}$, $13\mathrm{n}_{627}$, $13\mathrm{n}_{632}$, $13\mathrm{n}_{633}$, $13\mathrm{n}_{644}$, $13\mathrm{n}_{647}$, $13\mathrm{n}_{648}$, $13\mathrm{n}_{651}$, $13\mathrm{n}_{652}$, $13\mathrm{n}_{661}$, $13\mathrm{n}_{662}$, $13\mathrm{n}_{663}$, $13\mathrm{n}_{694}$, $13\mathrm{n}_{695}$, $13\mathrm{n}_{696}$, $13\mathrm{n}_{704}$, $13\mathrm{n}_{705}$, $13\mathrm{n}_{706}$, $13\mathrm{n}_{707}$, $13\mathrm{n}_{708}$, $13\mathrm{n}_{709}$, $13\mathrm{n}_{712}$, $13\mathrm{n}_{713}$, $13\mathrm{n}_{716}$, $13\mathrm{n}_{717}$, $13\mathrm{n}_{718}$, $13\mathrm{n}_{834}$, $13\mathrm{n}_{838}$, $13\mathrm{n}_{839}$, $13\mathrm{n}_{857}$, $13\mathrm{n}_{926}$, $13\mathrm{n}_{991}$, $13\mathrm{n}_{992}$, $13\mathrm{n}_{993}$, $13\mathrm{n}_{1000}$, $13\mathrm{n}_{1001}$, $13\mathrm{n}_{1004}$, $13\mathrm{n}_{1005}$, $13\mathrm{n}_{1006}$, $13\mathrm{n}_{1007}$, $13\mathrm{n}_{1011}$, $13\mathrm{n}_{1012}$, $13\mathrm{n}_{1013}$, $13\mathrm{n}_{1039}$, $13\mathrm{n}_{1040}$, $13\mathrm{n}_{1041}$, $13\mathrm{n}_{1043}$, $13\mathrm{n}_{1044}$, $13\mathrm{n}_{1045}$, $13\mathrm{n}_{1046}$, $13\mathrm{n}_{1047}$, $13\mathrm{n}_{1048}$, $13\mathrm{n}_{1175}$, $13\mathrm{n}_{1178}$, $13\mathrm{n}_{1179}$, $13\mathrm{n}_{1200}$, $13\mathrm{n}_{1201}$, $13\mathrm{n}_{1202}$, $13\mathrm{n}_{1210}$, $13\mathrm{n}_{1211}$, $13\mathrm{n}_{1212}$, $13\mathrm{n}_{1270}$, $13\mathrm{n}_{1276}$, $13\mathrm{n}_{1296}$, $13\mathrm{n}_{1367}$, $13\mathrm{n}_{1370}$, $13\mathrm{n}_{1371}$, $13\mathrm{n}_{1374}$, $13\mathrm{n}_{1375}$, $13\mathrm{n}_{1376}$, $13\mathrm{n}_{3739}$, $13\mathrm{n}_{3742}$, $13\mathrm{n}_{3745}$, $13\mathrm{n}_{3748}$, $13\mathrm{n}_{3770}$, $13\mathrm{n}_{3773}$, $13\mathrm{n}_{3776}$, $13\mathrm{n}_{3779}$, $13\mathrm{n}_{3814}$, $13\mathrm{n}_{3840}$, $13\mathrm{n}_{3842}$, $13\mathrm{n}_{3844}$, $13\mathrm{n}_{3854}$, $13\mathrm{n}_{3855}$, $13\mathrm{n}_{3856}$, $13\mathrm{n}_{3870}$, $13\mathrm{n}_{3871}$, $13\mathrm{n}_{3872}$, $13\mathrm{n}_{3873}$, $13\mathrm{n}_{3874}$, $13\mathrm{n}_{3897}$, $13\mathrm{n}_{3898}$, $13\mathrm{n}_{3899}$, $13\mathrm{n}_{3900}$, $13\mathrm{n}_{3901}$, $13\mathrm{n}_{3903}$, $13\mathrm{n}_{3904}$, $13\mathrm{n}_{3905}$, $13\mathrm{n}_{3911}$, $13\mathrm{n}_{3914}$, $13\mathrm{n}_{3916}$, $13\mathrm{n}_{3918}$, $13\mathrm{n}_{3919}$, $13\mathrm{n}_{3920}$, $13\mathrm{n}_{3921}$, $13\mathrm{n}_{3922}$, $13\mathrm{n}_{3924}$, $13\mathrm{n}_{3925}$, $13\mathrm{n}_{3928}$, $13\mathrm{n}_{3929}$, $13\mathrm{n}_{3931}$, $13\mathrm{n}_{3932}$, $13\mathrm{n}_{3933}$, $13\mathrm{n}_{3934}$, $13\mathrm{n}_{3935}$, $13\mathrm{n}_{3936}$, $13\mathrm{n}_{3937}$, $13\mathrm{n}_{3938}$, $13\mathrm{n}_{3939}$, $13\mathrm{n}_{3940}$, $13\mathrm{n}_{3941}$, $13\mathrm{n}_{4587}$, $13\mathrm{n}_{4589}$, $13\mathrm{n}_{4633}$, $13\mathrm{n}_{4634}$, $13\mathrm{n}_{4637}$, $13\mathrm{n}_{4638}$, $13\mathrm{n}_{4639}$, $13\mathrm{n}_{4640}$, $13\mathrm{n}_{4641}$, $13\mathrm{n}_{4642}$, $13\mathrm{n}_{4643}$, $13\mathrm{n}_{4644}$, $13\mathrm{n}_{4645}$}