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Extensions 1→N→G→Q→1 with N=C4×D5 and Q=D6

Direct product G=N×Q with N=C4×D5 and Q=D6
dρLabelID
S3×C2×C4×D5120S3xC2xC4xD5480,1086

Semidirect products G=N:Q with N=C4×D5 and Q=D6
extensionφ:Q→Out NdρLabelID
(C4×D5)⋊1D6 = D20⋊26D6φ: D6/C3 → C22 ⊆ Out C4×D51204(C4xD5):1D6480,1094
(C4×D5)⋊2D6 = D20⋊29D6φ: D6/C3 → C22 ⊆ Out C4×D51204+(C4xD5):2D6480,1095
(C4×D5)⋊3D6 = D20⋊13D6φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5):3D6480,1101
(C4×D5)⋊4D6 = D20⋊14D6φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5):4D6480,1102
(C4×D5)⋊5D6 = D12⋊14D10φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5):5D6480,1103
(C4×D5)⋊6D6 = D20⋊17D6φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5):6D6480,1111
(C4×D5)⋊7D6 = S3×D4×D5φ: D6/S3 → C2 ⊆ Out C4×D5608+(C4xD5):7D6480,1097
(C4×D5)⋊8D6 = S3×D4⋊2D5φ: D6/S3 → C2 ⊆ Out C4×D51208-(C4xD5):8D6480,1099
(C4×D5)⋊9D6 = D30.C23φ: D6/S3 → C2 ⊆ Out C4×D51208+(C4xD5):9D6480,1100
(C4×D5)⋊10D6 = S3×Q8⋊2D5φ: D6/S3 → C2 ⊆ Out C4×D51208+(C4xD5):10D6480,1109
(C4×D5)⋊11D6 = D20⋊16D6φ: D6/S3 → C2 ⊆ Out C4×D51208-(C4xD5):11D6480,1110
(C4×D5)⋊12D6 = S3×C4○D20φ: D6/S3 → C2 ⊆ Out C4×D51204(C4xD5):12D6480,1091
(C4×D5)⋊13D6 = D20⋊24D6φ: D6/S3 → C2 ⊆ Out C4×D51204(C4xD5):13D6480,1092
(C4×D5)⋊14D6 = C2×D12⋊5D5φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5):14D6480,1084
(C4×D5)⋊15D6 = C2×C12.28D10φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5):15D6480,1085
(C4×D5)⋊16D6 = C2×D5×D12φ: D6/C6 → C2 ⊆ Out C4×D5120(C4xD5):16D6480,1087
(C4×D5)⋊17D6 = D5×C4○D12φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5):17D6480,1090
(C4×D5)⋊18D6 = C2×D6.D10φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5):18D6480,1083

Non-split extensions G=N.Q with N=C4×D5 and Q=D6
extensionφ:Q→Out NdρLabelID
(C4×D5).1D6 = C24⋊D10φ: D6/C3 → C22 ⊆ Out C4×D51204+(C4xD5).1D6480,325
(C4×D5).2D6 = D24⋊D5φ: D6/C3 → C22 ⊆ Out C4×D51204(C4xD5).2D6480,326
(C4×D5).3D6 = Dic60⋊C2φ: D6/C3 → C22 ⊆ Out C4×D52404-(C4xD5).3D6480,336
(C4×D5).4D6 = C24.2D10φ: D6/C3 → C22 ⊆ Out C4×D52404(C4xD5).4D6480,337
(C4×D5).5D6 = Dic10⋊3D6φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).5D6480,554
(C4×D5).6D6 = C60.8C23φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).6D6480,560
(C4×D5).7D6 = D12⋊10D10φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).7D6480,565
(C4×D5).8D6 = D20.9D6φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).8D6480,567
(C4×D5).9D6 = D20⋊D6φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).9D6480,578
(C4×D5).10D6 = D20.13D6φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).10D6480,584
(C4×D5).11D6 = D12.27D10φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).11D6480,589
(C4×D5).12D6 = C60.39C23φ: D6/C3 → C22 ⊆ Out C4×D52408+(C4xD5).12D6480,591
(C4×D5).13D6 = D20.38D6φ: D6/C3 → C22 ⊆ Out C4×D52404(C4xD5).13D6480,1076
(C4×D5).14D6 = D20.39D6φ: D6/C3 → C22 ⊆ Out C4×D52404-(C4xD5).14D6480,1077
(C4×D5).15D6 = C15⋊2- 1+4φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).15D6480,1096
(C4×D5).16D6 = D20.29D6φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).16D6480,1104
(C4×D5).17D6 = C30.33C24φ: D6/C3 → C22 ⊆ Out C4×D52408+(C4xD5).17D6480,1105
(C4×D5).18D6 = D12.29D10φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).18D6480,1106
(C4×D5).19D6 = D60⋊C4φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).19D6480,227
(C4×D5).20D6 = D12⋊F5φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).20D6480,228
(C4×D5).21D6 = Dic6⋊F5φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).21D6480,229
(C4×D5).22D6 = Dic30⋊C4φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).22D6480,230
(C4×D5).23D6 = D12⋊4F5φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).23D6480,231
(C4×D5).24D6 = D12⋊2F5φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).24D6480,232
(C4×D5).25D6 = D60⋊2C4φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).25D6480,233
(C4×D5).26D6 = D60⋊5C4φ: D6/C3 → C22 ⊆ Out C4×D51208+(C4xD5).26D6480,234
(C4×D5).27D6 = D20⋊Dic3φ: D6/C3 → C22 ⊆ Out C4×D51208(C4xD5).27D6480,312
(C4×D5).28D6 = Dic10⋊Dic3φ: D6/C3 → C22 ⊆ Out C4×D51208(C4xD5).28D6480,313
(C4×D5).29D6 = Dic10⋊2Dic3φ: D6/C3 → C22 ⊆ Out C4×D51208(C4xD5).29D6480,314
(C4×D5).30D6 = D20⋊2Dic3φ: D6/C3 → C22 ⊆ Out C4×D51208(C4xD5).30D6480,315
(C4×D5).31D6 = F5×Dic6φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).31D6480,982
(C4×D5).32D6 = Dic6⋊5F5φ: D6/C3 → C22 ⊆ Out C4×D51208-(C4xD5).32D6480,984
(C4×D5).33D6 = D12.2F5φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).33D6480,987
(C4×D5).34D6 = D12.F5φ: D6/C3 → C22 ⊆ Out C4×D52408-(C4xD5).34D6480,989
(C4×D5).35D6 = D60.C4φ: D6/C3 → C22 ⊆ Out C4×D52408+(C4xD5).35D6480,990
(C4×D5).36D6 = Dic6.F5φ: D6/C3 → C22 ⊆ Out C4×D52408+(C4xD5).36D6480,992
(C4×D5).37D6 = F5×D12φ: D6/C3 → C22 ⊆ Out C4×D5608+(C4xD5).37D6480,995
(C4×D5).38D6 = D60⋊3C4φ: D6/C3 → C22 ⊆ Out C4×D5608+(C4xD5).38D6480,997
(C4×D5).39D6 = Dic10.Dic3φ: D6/C3 → C22 ⊆ Out C4×D52408(C4xD5).39D6480,1066
(C4×D5).40D6 = D4×C3⋊F5φ: D6/C3 → C22 ⊆ Out C4×D5608(C4xD5).40D6480,1067
(C4×D5).41D6 = D20.Dic3φ: D6/C3 → C22 ⊆ Out C4×D52408(C4xD5).41D6480,1068
(C4×D5).42D6 = Q8×C3⋊F5φ: D6/C3 → C22 ⊆ Out C4×D51208(C4xD5).42D6480,1069
(C4×D5).43D6 = D5×D4⋊S3φ: D6/S3 → C2 ⊆ Out C4×D51208+(C4xD5).43D6480,553
(C4×D5).44D6 = D5×D4.S3φ: D6/S3 → C2 ⊆ Out C4×D51208-(C4xD5).44D6480,559
(C4×D5).45D6 = D12.24D10φ: D6/S3 → C2 ⊆ Out C4×D52408-(C4xD5).45D6480,566
(C4×D5).46D6 = C60.16C23φ: D6/S3 → C2 ⊆ Out C4×D52408+(C4xD5).46D6480,568
(C4×D5).47D6 = D5×Q8⋊2S3φ: D6/S3 → C2 ⊆ Out C4×D51208+(C4xD5).47D6480,577
(C4×D5).48D6 = D5×C3⋊Q16φ: D6/S3 → C2 ⊆ Out C4×D52408-(C4xD5).48D6480,583
(C4×D5).49D6 = D20.14D6φ: D6/S3 → C2 ⊆ Out C4×D52408-(C4xD5).49D6480,590
(C4×D5).50D6 = D20.D6φ: D6/S3 → C2 ⊆ Out C4×D52408+(C4xD5).50D6480,592
(C4×D5).51D6 = D5×D4⋊2S3φ: D6/S3 → C2 ⊆ Out C4×D51208-(C4xD5).51D6480,1098
(C4×D5).52D6 = S3×Q8×D5φ: D6/S3 → C2 ⊆ Out C4×D51208-(C4xD5).52D6480,1107
(C4×D5).53D6 = D5×Q8⋊3S3φ: D6/S3 → C2 ⊆ Out C4×D51208+(C4xD5).53D6480,1108
(C4×D5).54D6 = S3×C8⋊D5φ: D6/S3 → C2 ⊆ Out C4×D51204(C4xD5).54D6480,321
(C4×D5).55D6 = C40⋊D6φ: D6/S3 → C2 ⊆ Out C4×D51204(C4xD5).55D6480,322
(C4×D5).56D6 = C40.55D6φ: D6/S3 → C2 ⊆ Out C4×D52404(C4xD5).56D6480,343
(C4×D5).57D6 = C40.35D6φ: D6/S3 → C2 ⊆ Out C4×D52404(C4xD5).57D6480,344
(C4×D5).58D6 = D20.3Dic3φ: D6/S3 → C2 ⊆ Out C4×D52404(C4xD5).58D6480,359
(C4×D5).59D6 = D20.2Dic3φ: D6/S3 → C2 ⊆ Out C4×D52404(C4xD5).59D6480,360
(C4×D5).60D6 = Dic5.Dic6φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).60D6480,235
(C4×D5).61D6 = Dic5.4Dic6φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).61D6480,236
(C4×D5).62D6 = D10.Dic6φ: D6/S3 → C2 ⊆ Out C4×D52408(C4xD5).62D6480,237
(C4×D5).63D6 = D10.2Dic6φ: D6/S3 → C2 ⊆ Out C4×D52408(C4xD5).63D6480,238
(C4×D5).64D6 = C4⋊F5⋊3S3φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).64D6480,983
(C4×D5).65D6 = S3×C4.F5φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).65D6480,988
(C4×D5).66D6 = D15⋊M4(2)φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).66D6480,991
(C4×D5).67D6 = S3×C4⋊F5φ: D6/S3 → C2 ⊆ Out C4×D5608(C4xD5).67D6480,996
(C4×D5).68D6 = F5×C3⋊C8φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).68D6480,223
(C4×D5).69D6 = C30.C42φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).69D6480,224
(C4×D5).70D6 = C30.3C42φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).70D6480,225
(C4×D5).71D6 = C30.4C42φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).71D6480,226
(C4×D5).72D6 = (C4×S3)⋊F5φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).72D6480,985
(C4×D5).73D6 = S3×D5⋊C8φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).73D6480,986
(C4×D5).74D6 = C5⋊C8⋊D6φ: D6/S3 → C2 ⊆ Out C4×D51208(C4xD5).74D6480,993
(C4×D5).75D6 = C4×S3×F5φ: D6/S3 → C2 ⊆ Out C4×D5608(C4xD5).75D6480,994
(C4×D5).76D6 = D5×C24⋊C2φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).76D6480,323
(C4×D5).77D6 = D5×D24φ: D6/C6 → C2 ⊆ Out C4×D51204+(C4xD5).77D6480,324
(C4×D5).78D6 = D5×Dic12φ: D6/C6 → C2 ⊆ Out C4×D52404-(C4xD5).78D6480,335
(C4×D5).79D6 = C40.31D6φ: D6/C6 → C2 ⊆ Out C4×D52404(C4xD5).79D6480,345
(C4×D5).80D6 = D24⋊7D5φ: D6/C6 → C2 ⊆ Out C4×D52404-(C4xD5).80D6480,346
(C4×D5).81D6 = D120⋊C2φ: D6/C6 → C2 ⊆ Out C4×D52404+(C4xD5).81D6480,347
(C4×D5).82D6 = C2×D5×Dic6φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5).82D6480,1073
(C4×D5).83D6 = C40.54D6φ: D6/C6 → C2 ⊆ Out C4×D52404(C4xD5).83D6480,341
(C4×D5).84D6 = C40.34D6φ: D6/C6 → C2 ⊆ Out C4×D52404(C4xD5).84D6480,342
(C4×D5).85D6 = C2×C20.32D6φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5).85D6480,369
(C4×D5).86D6 = C120⋊C4φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).86D6480,298
(C4×D5).87D6 = D5.D24φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).87D6480,299
(C4×D5).88D6 = C40.Dic3φ: D6/C6 → C2 ⊆ Out C4×D52404(C4xD5).88D6480,300
(C4×D5).89D6 = C24.1F5φ: D6/C6 → C2 ⊆ Out C4×D52404(C4xD5).89D6480,301
(C4×D5).90D6 = C2×C12.F5φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5).90D6480,1061
(C4×D5).91D6 = C2×C60⋊C4φ: D6/C6 → C2 ⊆ Out C4×D5120(C4xD5).91D6480,1064
(C4×D5).92D6 = (C2×C12)⋊6F5φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).92D6480,1065
(C4×D5).93D6 = C8×C3⋊F5φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).93D6480,296
(C4×D5).94D6 = C24⋊F5φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).94D6480,297
(C4×D5).95D6 = C2×C60.C4φ: D6/C6 → C2 ⊆ Out C4×D5240(C4xD5).95D6480,1060
(C4×D5).96D6 = C60.59(C2×C4)φ: D6/C6 → C2 ⊆ Out C4×D51204(C4xD5).96D6480,1062
(C4×D5).97D6 = C2×C4×C3⋊F5φ: D6/C6 → C2 ⊆ Out C4×D5120(C4xD5).97D6480,1063
(C4×D5).98D6 = S3×C8×D5φ: trivial image1204(C4xD5).98D6480,319
(C4×D5).99D6 = D5×C8⋊S3φ: trivial image1204(C4xD5).99D6480,320
(C4×D5).100D6 = C2×D5×C3⋊C8φ: trivial image240(C4xD5).100D6480,357
(C4×D5).101D6 = D5×C4.Dic3φ: trivial image1204(C4xD5).101D6480,358

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