Extensions 1→N→G→Q→1 with N=C4×D5 and Q=D4

Direct product G=N×Q with N=C4×D5 and Q=D4
dρLabelID
C4×D4×D580C4xD4xD5320,1216

Semidirect products G=N:Q with N=C4×D5 and Q=D4
extensionφ:Q→Out NdρLabelID
(C4×D5)⋊1D4 = C10.382+ 1+4φ: D4/C2C22 ⊆ Out C4×D580(C4xD5):1D4320,1279
(C4×D5)⋊2D4 = C10.392+ 1+4φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5):2D4320,1280
(C4×D5)⋊3D4 = C10.172- 1+4φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5):3D4320,1301
(C4×D5)⋊4D4 = C4218D10φ: D4/C2C22 ⊆ Out C4×D580(C4xD5):4D4320,1346
(C4×D5)⋊5D4 = C4226D10φ: D4/C2C22 ⊆ Out C4×D580(C4xD5):5D4320,1387
(C4×D5)⋊6D4 = C42.233D10φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5):6D4320,1340
(C4×D5)⋊7D4 = D5×C41D4φ: D4/C4C2 ⊆ Out C4×D580(C4xD5):7D4320,1386
(C4×D5)⋊8D4 = C42.238D10φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5):8D4320,1388
(C4×D5)⋊9D4 = C42.240D10φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5):9D4320,1397
(C4×D5)⋊10D4 = C42.228D10φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5):10D4320,1220
(C4×D5)⋊11D4 = D5×C4⋊D4φ: D4/C22C2 ⊆ Out C4×D580(C4xD5):11D4320,1276
(C4×D5)⋊12D4 = C4⋊C421D10φ: D4/C22C2 ⊆ Out C4×D580(C4xD5):12D4320,1278
(C4×D5)⋊13D4 = C4⋊C426D10φ: D4/C22C2 ⊆ Out C4×D580(C4xD5):13D4320,1299
(C4×D5)⋊14D4 = C4212D10φ: D4/C22C2 ⊆ Out C4×D580(C4xD5):14D4320,1219

Non-split extensions G=N.Q with N=C4×D5 and Q=D4
extensionφ:Q→Out NdρLabelID
(C4×D5).1D4 = D5×C4.D4φ: D4/C2C22 ⊆ Out C4×D5408+(C4xD5).1D4320,371
(C4×D5).2D4 = D5×C4.10D4φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).2D4320,377
(C4×D5).3D4 = (D4×D5)⋊C4φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).3D4320,397
(C4×D5).4D4 = D4⋊(C4×D5)φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).4D4320,398
(C4×D5).5D4 = (Q8×D5)⋊C4φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).5D4320,429
(C4×D5).6D4 = Q8⋊(C4×D5)φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).6D4320,430
(C4×D5).7D4 = D16⋊D5φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).7D4320,538
(C4×D5).8D4 = C16⋊D10φ: D4/C2C22 ⊆ Out C4×D5804+(C4xD5).8D4320,541
(C4×D5).9D4 = SD32⋊D5φ: D4/C2C22 ⊆ Out C4×D51604-(C4xD5).9D4320,542
(C4×D5).10D4 = Q32⋊D5φ: D4/C2C22 ⊆ Out C4×D51604(C4xD5).10D4320,545
(C4×D5).11D4 = C10.162- 1+4φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).11D4320,1300
(C4×D5).12D4 = C42.141D10φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).12D4320,1347
(C4×D5).13D4 = C42.171D10φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).13D4320,1396
(C4×D5).14D4 = C2×D8⋊D5φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).14D4320,1427
(C4×D5).15D4 = C2×D40⋊C2φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).15D4320,1431
(C4×D5).16D4 = C2×SD16⋊D5φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).16D4320,1432
(C4×D5).17D4 = C2×Q16⋊D5φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).17D4320,1436
(C4×D5).18D4 = D10.18D8φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).18D4320,212
(C4×D5).19D4 = C20.C42φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).19D4320,213
(C4×D5).20D4 = D10.D8φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).20D4320,241
(C4×D5).21D4 = D5.D16φ: D4/C2C22 ⊆ Out C4×D5808+(C4xD5).21D4320,242
(C4×D5).22D4 = D8.F5φ: D4/C2C22 ⊆ Out C4×D51608-(C4xD5).22D4320,243
(C4×D5).23D4 = D40.C4φ: D4/C2C22 ⊆ Out C4×D5808+(C4xD5).23D4320,244
(C4×D5).24D4 = D401C4φ: D4/C2C22 ⊆ Out C4×D5808+(C4xD5).24D4320,245
(C4×D5).25D4 = D5.Q32φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).25D4320,246
(C4×D5).26D4 = Q16.F5φ: D4/C2C22 ⊆ Out C4×D51608+(C4xD5).26D4320,247
(C4×D5).27D4 = Dic20.C4φ: D4/C2C22 ⊆ Out C4×D51608-(C4xD5).27D4320,248
(C4×D5).28D4 = C4⋊C4.9F5φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).28D4320,1046
(C4×D5).29D4 = C20⋊(C4⋊C4)φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).29D4320,1050
(C4×D5).30D4 = M4(2)⋊1F5φ: D4/C2C22 ⊆ Out C4×D5408(C4xD5).30D4320,1065
(C4×D5).31D4 = M4(2).1F5φ: D4/C2C22 ⊆ Out C4×D5808(C4xD5).31D4320,1067
(C4×D5).32D4 = C2×D20⋊C4φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).32D4320,1104
(C4×D5).33D4 = (D4×C10)⋊C4φ: D4/C2C22 ⊆ Out C4×D5408+(C4xD5).33D4320,1105
(C4×D5).34D4 = C2×D4⋊F5φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).34D4320,1106
(C4×D5).35D4 = (C2×D4)⋊6F5φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).35D4320,1107
(C4×D5).36D4 = (C2×D4)⋊8F5φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).36D4320,1109
(C4×D5).37D4 = (C2×D4).8F5φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).37D4320,1114
(C4×D5).38D4 = D5⋊(C4.D4)φ: D4/C2C22 ⊆ Out C4×D5408+(C4xD5).38D4320,1116
(C4×D5).39D4 = C2.(D4×F5)φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).39D4320,1118
(C4×D5).40D4 = C2×Q8⋊F5φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).40D4320,1119
(C4×D5).41D4 = (C2×Q8)⋊4F5φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).41D4320,1120
(C4×D5).42D4 = C2×Q82F5φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).42D4320,1121
(C4×D5).43D4 = (C2×Q8)⋊6F5φ: D4/C2C22 ⊆ Out C4×D5808+(C4xD5).43D4320,1122
(C4×D5).44D4 = (C2×Q8)⋊7F5φ: D4/C2C22 ⊆ Out C4×D5808+(C4xD5).44D4320,1123
(C4×D5).45D4 = (C2×Q8).5F5φ: D4/C2C22 ⊆ Out C4×D5160(C4xD5).45D4320,1125
(C4×D5).46D4 = (C2×Q8).7F5φ: D4/C2C22 ⊆ Out C4×D5808-(C4xD5).46D4320,1127
(C4×D5).47D4 = (C2×F5)⋊Q8φ: D4/C2C22 ⊆ Out C4×D580(C4xD5).47D4320,1128
(C4×D5).48D4 = C804C4φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).48D4320,185
(C4×D5).49D4 = C805C4φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).49D4320,186
(C4×D5).50D4 = C423F5φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).50D4320,201
(C4×D5).51D4 = C20.24C42φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).51D4320,233
(C4×D5).52D4 = C20.25C42φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).52D4320,235
(C4×D5).53D4 = C23⋊F55C2φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).53D4320,1083
(C4×D5).54D4 = (C4×D5).D4φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).54D4320,1099
(C4×D5).55D4 = (C2×C8)⋊F5φ: D4/C2C22 ⊆ Out C4×D5804(C4xD5).55D4320,232
(C4×D5).56D4 = C4○D20⋊C4φ: D4/C2C22 ⊆ Out C4×D5808(C4xD5).56D4320,1132
(C4×D5).57D4 = D5×D16φ: D4/C4C2 ⊆ Out C4×D5804+(C4xD5).57D4320,537
(C4×D5).58D4 = D163D5φ: D4/C4C2 ⊆ Out C4×D51604-(C4xD5).58D4320,539
(C4×D5).59D4 = D5×SD32φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).59D4320,540
(C4×D5).60D4 = SD323D5φ: D4/C4C2 ⊆ Out C4×D51604(C4xD5).60D4320,543
(C4×D5).61D4 = D5×Q32φ: D4/C4C2 ⊆ Out C4×D51604-(C4xD5).61D4320,544
(C4×D5).62D4 = D805C2φ: D4/C4C2 ⊆ Out C4×D51604+(C4xD5).62D4320,546
(C4×D5).63D4 = D5×C4.4D4φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).63D4320,1345
(C4×D5).64D4 = D5×C4⋊Q8φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).64D4320,1395
(C4×D5).65D4 = C2×D5×D8φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).65D4320,1426
(C4×D5).66D4 = C2×D83D5φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).66D4320,1428
(C4×D5).67D4 = C2×D5×SD16φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).67D4320,1430
(C4×D5).68D4 = C2×SD163D5φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).68D4320,1433
(C4×D5).69D4 = C2×D5×Q16φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).69D4320,1435
(C4×D5).70D4 = C2×Q8.D10φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).70D4320,1437
(C4×D5).71D4 = D5×C4≀C2φ: D4/C4C2 ⊆ Out C4×D5404(C4xD5).71D4320,447
(C4×D5).72D4 = C205M4(2)φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).72D4320,464
(C4×D5).73D4 = D5×C8.C4φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).73D4320,519
(C4×D5).74D4 = C802C4φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).74D4320,187
(C4×D5).75D4 = C803C4φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).75D4320,188
(C4×D5).76D4 = C16.F5φ: D4/C4C2 ⊆ Out C4×D51604(C4xD5).76D4320,189
(C4×D5).77D4 = C80.2C4φ: D4/C4C2 ⊆ Out C4×D51604(C4xD5).77D4320,190
(C4×D5).78D4 = C203M4(2)φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).78D4320,1019
(C4×D5).79D4 = C42.14F5φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).79D4320,1020
(C4×D5).80D4 = C428F5φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).80D4320,1026
(C4×D5).81D4 = C429F5φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).81D4320,1027
(C4×D5).82D4 = C2×C40⋊C4φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).82D4320,1057
(C4×D5).83D4 = C2×D5.D8φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).83D4320,1058
(C4×D5).84D4 = C2×C40.C4φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).84D4320,1060
(C4×D5).85D4 = C2×D10.Q8φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).85D4320,1061
(C4×D5).86D4 = C426F5φ: D4/C4C2 ⊆ Out C4×D5404(C4xD5).86D4320,200
(C4×D5).87D4 = C42.11F5φ: D4/C4C2 ⊆ Out C4×D5160(C4xD5).87D4320,1017
(C4×D5).88D4 = C4×C4⋊F5φ: D4/C4C2 ⊆ Out C4×D580(C4xD5).88D4320,1025
(C4×D5).89D4 = (C2×C8)⋊6F5φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).89D4320,1059
(C4×D5).90D4 = (C8×D5).C4φ: D4/C4C2 ⊆ Out C4×D5804(C4xD5).90D4320,1062
(C4×D5).91D4 = M4(2).19D10φ: D4/C22C2 ⊆ Out C4×D5808-(C4xD5).91D4320,372
(C4×D5).92D4 = M4(2).21D10φ: D4/C22C2 ⊆ Out C4×D5808+(C4xD5).92D4320,378
(C4×D5).93D4 = D5×D4⋊C4φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).93D4320,396
(C4×D5).94D4 = D42D5⋊C4φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).94D4320,399
(C4×D5).95D4 = D5×Q8⋊C4φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).95D4320,428
(C4×D5).96D4 = Q82D5⋊C4φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).96D4320,431
(C4×D5).97D4 = D5×C22⋊Q8φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).97D4320,1298
(C4×D5).98D4 = D5×C8⋊C22φ: D4/C22C2 ⊆ Out C4×D5408+(C4xD5).98D4320,1444
(C4×D5).99D4 = SD16⋊D10φ: D4/C22C2 ⊆ Out C4×D5808-(C4xD5).99D4320,1445
(C4×D5).100D4 = D5×C8.C22φ: D4/C22C2 ⊆ Out C4×D5808-(C4xD5).100D4320,1448
(C4×D5).101D4 = D40⋊C22φ: D4/C22C2 ⊆ Out C4×D5808+(C4xD5).101D4320,1449
(C4×D5).102D4 = D107M4(2)φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).102D4320,353
(C4×D5).103D4 = C22⋊C8⋊D5φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).103D4320,354
(C4×D5).104D4 = C42⋊D10φ: D4/C22C2 ⊆ Out C4×D5804(C4xD5).104D4320,448
(C4×D5).105D4 = C42.30D10φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).105D4320,466
(C4×D5).106D4 = M4(2).25D10φ: D4/C22C2 ⊆ Out C4×D5804(C4xD5).106D4320,520
(C4×D5).107D4 = Q16⋊D10φ: D4/C22C2 ⊆ Out C4×D5804(C4xD5).107D4320,1440
(C4×D5).108D4 = D10.10D8φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).108D4320,231
(C4×D5).109D4 = C20.10C42φ: D4/C22C2 ⊆ Out C4×D5160(C4xD5).109D4320,234
(C4×D5).110D4 = M4(2)⋊F5φ: D4/C22C2 ⊆ Out C4×D5408(C4xD5).110D4320,237
(C4×D5).111D4 = M4(2)⋊4F5φ: D4/C22C2 ⊆ Out C4×D5808(C4xD5).111D4320,240
(C4×D5).112D4 = D1010M4(2)φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).112D4320,1094
(C4×D5).113D4 = D106(C4⋊C4)φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).113D4320,1103
(C4×D5).114D4 = C4○D4⋊F5φ: D4/C22C2 ⊆ Out C4×D5408(C4xD5).114D4320,1131
(C4×D5).115D4 = D4⋊F5⋊C2φ: D4/C22C2 ⊆ Out C4×D5808(C4xD5).115D4320,1133
(C4×D5).116D4 = D10.3M4(2)φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).116D4320,230
(C4×D5).117D4 = M4(2)⋊3F5φ: D4/C22C2 ⊆ Out C4×D5408(C4xD5).117D4320,238
(C4×D5).118D4 = M4(2).F5φ: D4/C22C2 ⊆ Out C4×D5808(C4xD5).118D4320,239
(C4×D5).119D4 = D10.11M4(2)φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).119D4320,1091
(C4×D5).120D4 = C4×C22⋊F5φ: D4/C22C2 ⊆ Out C4×D580(C4xD5).120D4320,1101
(C4×D5).121D4 = D5⋊C4≀C2φ: D4/C22C2 ⊆ Out C4×D5408(C4xD5).121D4320,1130
(C4×D5).122D4 = D5×C22⋊C8φ: trivial image80(C4xD5).122D4320,351
(C4×D5).123D4 = D5×C4⋊C8φ: trivial image160(C4xD5).123D4320,459
(C4×D5).124D4 = D5×C4○D8φ: trivial image804(C4xD5).124D4320,1439

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