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Extensions 1→N→G→Q→1 with N=C2×C4×D5 and Q=C4

Direct product G=N×Q with N=C2×C4×D5 and Q=C4
dρLabelID
D5×C2×C42160D5xC2xC4^2320,1143

Semidirect products G=N:Q with N=C2×C4×D5 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C4×D5)⋊1C4 = C23⋊C4⋊5D5φ: C4/C1 → C4 ⊆ Out C2×C4×D5808-(C2xC4xD5):1C4320,367
(C2×C4×D5)⋊2C4 = D5×C23⋊C4φ: C4/C1 → C4 ⊆ Out C2×C4×D5408+(C2xC4xD5):2C4320,370
(C2×C4×D5)⋊3C4 = (C2×D20)⋊25C4φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5):3C4320,633
(C2×C4×D5)⋊4C4 = (C2×D4)⋊7F5φ: C4/C1 → C4 ⊆ Out C2×C4×D5408+(C2xC4xD5):4C4320,1108
(C2×C4×D5)⋊5C4 = (C2×Q8)⋊7F5φ: C4/C1 → C4 ⊆ Out C2×C4×D5808+(C2xC4xD5):5C4320,1123
(C2×C4×D5)⋊6C4 = C23⋊F5⋊5C2φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5):6C4320,1083
(C2×C4×D5)⋊7C4 = D10⋊4(C4⋊C4)φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):7C4320,614
(C2×C4×D5)⋊8C4 = C2×D5×C4⋊C4φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):8C4320,1173
(C2×C4×D5)⋊9C4 = C2×C4⋊C4⋊7D5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):9C4320,1174
(C2×C4×D5)⋊10C4 = D5×C42⋊C2φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):10C4320,1192
(C2×C4×D5)⋊11C4 = D5×C2.C42φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):11C4320,290
(C2×C4×D5)⋊12C4 = C22.58(D4×D5)φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):12C4320,291
(C2×C4×D5)⋊13C4 = D10⋊2C42φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):13C4320,293
(C2×C4×D5)⋊14C4 = D10⋊2(C4⋊C4)φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):14C4320,294
(C2×C4×D5)⋊15C4 = C4×D10⋊C4φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):15C4320,565
(C2×C4×D5)⋊16C4 = C2×D10.3Q8φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):16C4320,1100
(C2×C4×D5)⋊17C4 = C4×C22⋊F5φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):17C4320,1101
(C2×C4×D5)⋊18C4 = (C22×C4)⋊7F5φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):18C4320,1102
(C2×C4×D5)⋊19C4 = C2×C42⋊D5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5):19C4320,1144
(C2×C4×D5)⋊20C4 = D10⋊6(C4⋊C4)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):20C4320,1103
(C2×C4×D5)⋊21C4 = C22×C4⋊F5φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):21C4320,1591
(C2×C4×D5)⋊22C4 = C2×D10.C23φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):22C4320,1592
(C2×C4×D5)⋊23C4 = C22×C4×F5φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5):23C4320,1590

Non-split extensions G=N.Q with N=C2×C4×D5 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C4×D5).1C4 = C8.25D20φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5).1C4320,72
(C2×C4×D5).2C4 = D5×C4.10D4φ: C4/C1 → C4 ⊆ Out C2×C4×D5808-(C2xC4xD5).2C4320,377
(C2×C4×D5).3C4 = M4(2).21D10φ: C4/C1 → C4 ⊆ Out C2×C4×D5808+(C2xC4xD5).3C4320,378
(C2×C4×D5).4C4 = M4(2).31D10φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5).4C4320,759
(C2×C4×D5).5C4 = (C2×D4).9F5φ: C4/C1 → C4 ⊆ Out C2×C4×D5808-(C2xC4xD5).5C4320,1115
(C2×C4×D5).6C4 = (C2×Q8).7F5φ: C4/C1 → C4 ⊆ Out C2×C4×D5808-(C2xC4xD5).6C4320,1127
(C2×C4×D5).7C4 = C20.10M4(2)φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5).7C4320,229
(C2×C4×D5).8C4 = (C4×D5).D4φ: C4/C1 → C4 ⊆ Out C2×C4×D5804(C2xC4xD5).8C4320,1099
(C2×C4×D5).9C4 = D5×C4⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).9C4320,459
(C2×C4×D5).10C4 = C42.200D10φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).10C4320,460
(C2×C4×D5).11C4 = C20⋊5M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).11C4320,464
(C2×C4×D5).12C4 = D5×M5(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D5804(C2xC4xD5).12C4320,533
(C2×C4×D5).13C4 = D10⋊8M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).13C4320,753
(C2×C4×D5).14C4 = C2×D5×M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).14C4320,1415
(C2×C4×D5).15C4 = D10⋊1C16φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).15C4320,65
(C2×C4×D5).16C4 = C42.282D10φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).16C4320,312
(C2×C4×D5).17C4 = C4×C8⋊D5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).17C4320,314
(C2×C4×D5).18C4 = D5×C8⋊C4φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).18C4320,331
(C2×C4×D5).19C4 = C42.182D10φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).19C4320,332
(C2×C4×D5).20C4 = D10.6C42φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).20C4320,334
(C2×C4×D5).21C4 = D5×C22⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).21C4320,351
(C2×C4×D5).22C4 = D10⋊7M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).22C4320,353
(C2×C4×D5).23C4 = C42.202D10φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).23C4320,462
(C2×C4×D5).24C4 = C2×C80⋊C2φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).24C4320,527
(C2×C4×D5).25C4 = C2×D10⋊1C8φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).25C4320,735
(C2×C4×D5).26C4 = C42.5F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).26C4320,1014
(C2×C4×D5).27C4 = C42.6F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).27C4320,1016
(C2×C4×D5).28C4 = C42.11F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).28C4320,1017
(C2×C4×D5).29C4 = C42.14F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).29C4320,1020
(C2×C4×D5).30C4 = C42.15F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).30C4320,1021
(C2×C4×D5).31C4 = C42.7F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).31C4320,1022
(C2×C4×D5).32C4 = C2×D10⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).32C4320,1089
(C2×C4×D5).33C4 = D10.11M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).33C4320,1091
(C2×C4×D5).34C4 = D10⋊9M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).34C4320,1093
(C2×C4×D5).35C4 = C22×C8⋊D5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).35C4320,1409
(C2×C4×D5).36C4 = C20⋊3M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).36C4320,1019
(C2×C4×D5).37C4 = D10⋊10M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).37C4320,1094
(C2×C4×D5).38C4 = C22×C4.F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).38C4320,1588
(C2×C4×D5).39C4 = D5⋊M5(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D5804(C2xC4xD5).39C4320,1053
(C2×C4×D5).40C4 = C2×D5⋊M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4×D580(C2xC4xD5).40C4320,1589
(C2×C4×D5).41C4 = D10⋊C16φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).41C4320,225
(C2×C4×D5).42C4 = C4×D5⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).42C4320,1013
(C2×C4×D5).43C4 = C4×C4.F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).43C4320,1015
(C2×C4×D5).44C4 = C42.12F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).44C4320,1018
(C2×C4×D5).45C4 = C2×D5⋊C16φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).45C4320,1051
(C2×C4×D5).46C4 = C2×C8.F5φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).46C4320,1052
(C2×C4×D5).47C4 = C22×D5⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4×D5160(C2xC4xD5).47C4320,1587
(C2×C4×D5).48C4 = D5×C4×C8φ: trivial image160(C2xC4xD5).48C4320,311
(C2×C4×D5).49C4 = D5×C2×C16φ: trivial image160(C2xC4xD5).49C4320,526
(C2×C4×D5).50C4 = D5×C22×C8φ: trivial image160(C2xC4xD5).50C4320,1408

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