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Extensions 1→N→G→Q→1 with N=C2×C5⋊D4 and Q=C4

Direct product G=N×Q with N=C2×C5⋊D4 and Q=C4
dρLabelID
C2×C4×C5⋊D4160C2xC4xC5:D4320,1460

Semidirect products G=N:Q with N=C2×C5⋊D4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C5⋊D4)⋊1C4 = C23⋊C4⋊5D5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4808-(C2xC5:D4):1C4320,367
(C2×C5⋊D4)⋊2C4 = D5×C23⋊C4φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4408+(C2xC5:D4):2C4320,370
(C2×C5⋊D4)⋊3C4 = (C2×D4)⋊7F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4408+(C2xC5:D4):3C4320,1108
(C2×C5⋊D4)⋊4C4 = (C2×F5)⋊D4φ: C4/C1 → C4 ⊆ Out C2×C5⋊D440(C2xC5:D4):4C4320,1117
(C2×C5⋊D4)⋊5C4 = C2.(D4×F5)φ: C4/C1 → C4 ⊆ Out C2×C5⋊D480(C2xC5:D4):5C4320,1118
(C2×C5⋊D4)⋊6C4 = C2×D4×F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D440(C2xC5:D4):6C4320,1595
(C2×C5⋊D4)⋊7C4 = D10.C24φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4408+(C2xC5:D4):7C4320,1596
(C2×C5⋊D4)⋊8C4 = C2×C23.1D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D480(C2xC5:D4):8C4320,581
(C2×C5⋊D4)⋊9C4 = C24.12D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4):9C4320,583
(C2×C5⋊D4)⋊10C4 = C24.13D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4):10C4320,584
(C2×C5⋊D4)⋊11C4 = C23.45D20φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4):11C4320,585
(C2×C5⋊D4)⋊12C4 = C24.65D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4):12C4320,840
(C2×C5⋊D4)⋊13C4 = C2×Dic5⋊4D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4):13C4320,1157
(C2×C5⋊D4)⋊14C4 = C24.24D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D480(C2xC5:D4):14C4320,1158
(C2×C5⋊D4)⋊15C4 = C23⋊F5⋊5C2φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4804(C2xC5:D4):15C4320,1083
(C2×C5⋊D4)⋊16C4 = C2×C23⋊F5φ: C4/C2 → C2 ⊆ Out C2×C5⋊D480(C2xC5:D4):16C4320,1134

Non-split extensions G=N.Q with N=C2×C5⋊D4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C5⋊D4).1C4 = D5×C4.D4φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4408+(C2xC5:D4).1C4320,371
(C2×C5⋊D4).2C4 = M4(2).19D10φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4808-(C2xC5:D4).2C4320,372
(C2×C5⋊D4).3C4 = C5⋊C8⋊8D4φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).3C4320,1030
(C2×C5⋊D4).4C4 = C5⋊C8⋊D4φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).4C4320,1031
(C2×C5⋊D4).5C4 = D10⋊M4(2)φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).5C4320,1032
(C2×C5⋊D4).6C4 = Dic5⋊M4(2)φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).6C4320,1033
(C2×C5⋊D4).7C4 = (C2×D4).7F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).7C4320,1113
(C2×C5⋊D4).8C4 = (C2×D4).8F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).8C4320,1114
(C2×C5⋊D4).9C4 = (C2×D4).9F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4808-(C2xC5:D4).9C4320,1115
(C2×C5⋊D4).10C4 = C2×D4.F5φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4160(C2xC5:D4).10C4320,1593
(C2×C5⋊D4).11C4 = Dic5.C24φ: C4/C1 → C4 ⊆ Out C2×C5⋊D4808-(C2xC5:D4).11C4320,1594
(C2×C5⋊D4).12C4 = C5⋊5(C8×D4)φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).12C4320,352
(C2×C5⋊D4).13C4 = C22⋊C8⋊D5φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).13C4320,354
(C2×C5⋊D4).14C4 = D10⋊4M4(2)φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).14C4320,355
(C2×C5⋊D4).15C4 = Dic5⋊2M4(2)φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).15C4320,356
(C2×C5⋊D4).16C4 = C5⋊2C8⋊26D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).16C4320,357
(C2×C5⋊D4).17C4 = (C22×C8)⋊D5φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).17C4320,737
(C2×C5⋊D4).18C4 = C40⋊32D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).18C4320,738
(C2×C5⋊D4).19C4 = C40⋊D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).19C4320,754
(C2×C5⋊D4).20C4 = C40⋊18D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).20C4320,755
(C2×C5⋊D4).21C4 = C4.89(C2×D20)φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).21C4320,756
(C2×C5⋊D4).22C4 = M4(2).31D10φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4804(C2xC5:D4).22C4320,759
(C2×C5⋊D4).23C4 = C2×D20.2C4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4160(C2xC5:D4).23C4320,1416
(C2×C5⋊D4).24C4 = C40.47C23φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4804(C2xC5:D4).24C4320,1417
(C2×C5⋊D4).25C4 = (C4×D5).D4φ: C4/C2 → C2 ⊆ Out C2×C5⋊D4804(C2xC5:D4).25C4320,1099
(C2×C5⋊D4).26C4 = C2×C23.F5φ: C4/C2 → C2 ⊆ Out C2×C5⋊D480(C2xC5:D4).26C4320,1137
(C2×C5⋊D4).27C4 = C8×C5⋊D4φ: trivial image160(C2xC5:D4).27C4320,736
(C2×C5⋊D4).28C4 = C2×D20.3C4φ: trivial image160(C2xC5:D4).28C4320,1410

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