Extensions 1→N→G→Q→1 with N=C10 and Q=2- 1+4

Direct product G=N×Q with N=C10 and Q=2- 1+4
dρLabelID
C10×2- 1+4160C10xES-(2,2)320,1633

Semidirect products G=N:Q with N=C10 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C1012- 1+4 = C2×Q8.10D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10:1ES-(2,2)320,1617
C1022- 1+4 = C2×D4.10D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10:2ES-(2,2)320,1620

Non-split extensions G=N.Q with N=C10 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C10.12- 1+4 = C10.12- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.1ES-(2,2)320,1172
C10.22- 1+4 = C10.82+ 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.2ES-(2,2)320,1176
C10.32- 1+4 = C10.2- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.3ES-(2,2)320,1179
C10.42- 1+4 = C10.2+ 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.4ES-(2,2)320,1182
C10.52- 1+4 = C10.52- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.5ES-(2,2)320,1185
C10.62- 1+4 = C10.62- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.6ES-(2,2)320,1187
C10.72- 1+4 = C42.122D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.7ES-(2,2)320,1240
C10.82- 1+4 = Q85Dic10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10320C10.8ES-(2,2)320,1241
C10.92- 1+4 = C42.125D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.9ES-(2,2)320,1244
C10.102- 1+4 = C42.126D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.10ES-(2,2)320,1246
C10.112- 1+4 = Q85D20φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.11ES-(2,2)320,1248
C10.122- 1+4 = C42.132D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.12ES-(2,2)320,1253
C10.132- 1+4 = C42.133D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.13ES-(2,2)320,1254
C10.142- 1+4 = C42.134D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.14ES-(2,2)320,1255
C10.152- 1+4 = C10.152- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.15ES-(2,2)320,1297
C10.162- 1+4 = C10.162- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.16ES-(2,2)320,1300
C10.172- 1+4 = C10.172- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.17ES-(2,2)320,1301
C10.182- 1+4 = D2022D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.18ES-(2,2)320,1303
C10.192- 1+4 = Dic1022D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.19ES-(2,2)320,1305
C10.202- 1+4 = C10.202- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.20ES-(2,2)320,1310
C10.212- 1+4 = C10.212- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.21ES-(2,2)320,1311
C10.222- 1+4 = C10.222- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.22ES-(2,2)320,1312
C10.232- 1+4 = C10.232- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.23ES-(2,2)320,1313
C10.242- 1+4 = C10.242- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.24ES-(2,2)320,1315
C10.252- 1+4 = C10.582+ 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.25ES-(2,2)320,1318
C10.262- 1+4 = C10.262- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.26ES-(2,2)320,1319
C10.272- 1+4 = C42.147D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10320C10.27ES-(2,2)320,1358
C10.282- 1+4 = C42.150D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.28ES-(2,2)320,1364
C10.292- 1+4 = C42.151D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.29ES-(2,2)320,1365
C10.302- 1+4 = C42.154D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.30ES-(2,2)320,1368
C10.312- 1+4 = C42.157D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.31ES-(2,2)320,1371
C10.322- 1+4 = C42.158D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.32ES-(2,2)320,1372
C10.332- 1+4 = Dic108Q8φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10320C10.33ES-(2,2)320,1393
C10.342- 1+4 = C42.171D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.34ES-(2,2)320,1396
C10.352- 1+4 = D2012D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.35ES-(2,2)320,1398
C10.362- 1+4 = D208Q8φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.36ES-(2,2)320,1399
C10.372- 1+4 = C42.174D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.37ES-(2,2)320,1401
C10.382- 1+4 = C42.176D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.38ES-(2,2)320,1403
C10.392- 1+4 = C42.177D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.39ES-(2,2)320,1404
C10.402- 1+4 = C42.178D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.40ES-(2,2)320,1405
C10.412- 1+4 = C42.180D10φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.41ES-(2,2)320,1407
C10.422- 1+4 = C10.422- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.42ES-(2,2)320,1484
C10.432- 1+4 = Q8×C5⋊D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.43ES-(2,2)320,1487
C10.442- 1+4 = C10.442- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.44ES-(2,2)320,1488
C10.452- 1+4 = C10.452- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C10160C10.45ES-(2,2)320,1489
C10.462- 1+4 = C42.87D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.46ES-(2,2)320,1188
C10.472- 1+4 = C42.89D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.47ES-(2,2)320,1190
C10.482- 1+4 = C42.90D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.48ES-(2,2)320,1191
C10.492- 1+4 = C42.91D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.49ES-(2,2)320,1195
C10.502- 1+4 = C42.92D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.50ES-(2,2)320,1198
C10.512- 1+4 = C42.94D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.51ES-(2,2)320,1201
C10.522- 1+4 = C42.96D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.52ES-(2,2)320,1203
C10.532- 1+4 = C42.98D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.53ES-(2,2)320,1205
C10.542- 1+4 = C42.99D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.54ES-(2,2)320,1206
C10.552- 1+4 = D4×Dic10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.55ES-(2,2)320,1209
C10.562- 1+4 = C42.105D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.56ES-(2,2)320,1213
C10.572- 1+4 = C42.106D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.57ES-(2,2)320,1214
C10.582- 1+4 = C42.108D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.58ES-(2,2)320,1218
C10.592- 1+4 = D2024D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.59ES-(2,2)320,1223
C10.602- 1+4 = Dic1023D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.60ES-(2,2)320,1224
C10.612- 1+4 = D46D20φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.61ES-(2,2)320,1227
C10.622- 1+4 = C42.115D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.62ES-(2,2)320,1233
C10.632- 1+4 = C42.118D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.63ES-(2,2)320,1236
C10.642- 1+4 = Dic1010Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C10320C10.64ES-(2,2)320,1239
C10.652- 1+4 = Q86Dic10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10320C10.65ES-(2,2)320,1242
C10.662- 1+4 = Q8×D20φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.66ES-(2,2)320,1247
C10.672- 1+4 = C42.135D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.67ES-(2,2)320,1256
C10.682- 1+4 = C10.682- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.68ES-(2,2)320,1269
C10.692- 1+4 = Dic1019D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.69ES-(2,2)320,1270
C10.702- 1+4 = C10.352+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.70ES-(2,2)320,1274
C10.712- 1+4 = C10.362+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.71ES-(2,2)320,1275
C10.722- 1+4 = C10.392+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.72ES-(2,2)320,1280
C10.732- 1+4 = C10.732- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.73ES-(2,2)320,1283
C10.742- 1+4 = C10.742- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.74ES-(2,2)320,1293
C10.752- 1+4 = C10.502+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.75ES-(2,2)320,1295
C10.762- 1+4 = Dic1021D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.76ES-(2,2)320,1304
C10.772- 1+4 = C10.772- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.77ES-(2,2)320,1314
C10.782- 1+4 = C10.572+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.78ES-(2,2)320,1317
C10.792- 1+4 = C10.792- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.79ES-(2,2)320,1320
C10.802- 1+4 = C10.802- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.80ES-(2,2)320,1322
C10.812- 1+4 = C10.812- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.81ES-(2,2)320,1323
C10.822- 1+4 = C10.822- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.82ES-(2,2)320,1327
C10.832- 1+4 = C10.632+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.83ES-(2,2)320,1332
C10.842- 1+4 = C10.842- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.84ES-(2,2)320,1334
C10.852- 1+4 = C10.852- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.85ES-(2,2)320,1337
C10.862- 1+4 = C10.692+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.86ES-(2,2)320,1339
C10.872- 1+4 = C42.137D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.87ES-(2,2)320,1341
C10.882- 1+4 = C42.139D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.88ES-(2,2)320,1343
C10.892- 1+4 = C42.140D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.89ES-(2,2)320,1344
C10.902- 1+4 = C42.141D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.90ES-(2,2)320,1347
C10.912- 1+4 = Dic1010D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.91ES-(2,2)320,1349
C10.922- 1+4 = C42.144D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.92ES-(2,2)320,1354
C10.932- 1+4 = C42.145D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.93ES-(2,2)320,1356
C10.942- 1+4 = Dic107Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C10320C10.94ES-(2,2)320,1357
C10.952- 1+4 = C42.148D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.95ES-(2,2)320,1361
C10.962- 1+4 = C42.152D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.96ES-(2,2)320,1366
C10.972- 1+4 = C42.155D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.97ES-(2,2)320,1369
C10.982- 1+4 = C42.159D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.98ES-(2,2)320,1373
C10.992- 1+4 = C42.160D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.99ES-(2,2)320,1374
C10.1002- 1+4 = C42.161D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.100ES-(2,2)320,1379
C10.1012- 1+4 = C42.162D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.101ES-(2,2)320,1380
C10.1022- 1+4 = C42.164D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.102ES-(2,2)320,1382
C10.1032- 1+4 = C42.165D10φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.103ES-(2,2)320,1384
C10.1042- 1+4 = C10.1042- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.104ES-(2,2)320,1496
C10.1052- 1+4 = C10.1052- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.105ES-(2,2)320,1497
C10.1062- 1+4 = C10.1062- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.106ES-(2,2)320,1499
C10.1072- 1+4 = C10.1072- 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.107ES-(2,2)320,1503
C10.1082- 1+4 = C10.1472+ 1+4φ: 2- 1+4/C4○D4C2 ⊆ Aut C10160C10.108ES-(2,2)320,1505
C10.1092- 1+4 = C5×C23.32C23central extension (φ=1)160C10.109ES-(2,2)320,1521
C10.1102- 1+4 = C5×C23.33C23central extension (φ=1)160C10.110ES-(2,2)320,1522
C10.1112- 1+4 = C5×C23.38C23central extension (φ=1)160C10.111ES-(2,2)320,1538
C10.1122- 1+4 = C5×C22.31C24central extension (φ=1)160C10.112ES-(2,2)320,1539
C10.1132- 1+4 = C5×C22.33C24central extension (φ=1)160C10.113ES-(2,2)320,1541
C10.1142- 1+4 = C5×C22.35C24central extension (φ=1)160C10.114ES-(2,2)320,1543
C10.1152- 1+4 = C5×C22.36C24central extension (φ=1)160C10.115ES-(2,2)320,1544
C10.1162- 1+4 = C5×C23.41C23central extension (φ=1)160C10.116ES-(2,2)320,1546
C10.1172- 1+4 = C5×D46D4central extension (φ=1)160C10.117ES-(2,2)320,1549
C10.1182- 1+4 = C5×Q85D4central extension (φ=1)160C10.118ES-(2,2)320,1550
C10.1192- 1+4 = C5×D4×Q8central extension (φ=1)160C10.119ES-(2,2)320,1551
C10.1202- 1+4 = C5×C22.46C24central extension (φ=1)160C10.120ES-(2,2)320,1554
C10.1212- 1+4 = C5×C22.50C24central extension (φ=1)160C10.121ES-(2,2)320,1558
C10.1222- 1+4 = C5×Q83Q8central extension (φ=1)320C10.122ES-(2,2)320,1559
C10.1232- 1+4 = C5×C22.56C24central extension (φ=1)160C10.123ES-(2,2)320,1564
C10.1242- 1+4 = C5×C22.57C24central extension (φ=1)160C10.124ES-(2,2)320,1565
C10.1252- 1+4 = C5×C22.58C24central extension (φ=1)320C10.125ES-(2,2)320,1566

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