# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5⋊C8

Direct product G=N×Q with N=C2×C4 and Q=C5⋊C8
dρLabelID
C2×C4×C5⋊C8320C2xC4xC5:C8320,1084

Semidirect products G=N:Q with N=C2×C4 and Q=C5⋊C8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C5⋊C8) = (C2×C20)⋊1C8φ: C5⋊C8/C10C4 ⊆ Aut C2×C4160(C2xC4):(C5:C8)320,251
(C2×C4)⋊2(C5⋊C8) = C10.(C4⋊C8)φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4320(C2xC4):2(C5:C8)320,256
(C2×C4)⋊3(C5⋊C8) = C2×C20⋊C8φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4320(C2xC4):3(C5:C8)320,1085
(C2×C4)⋊4(C5⋊C8) = Dic5.12M4(2)φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4160(C2xC4):4(C5:C8)320,1086

Non-split extensions G=N.Q with N=C2×C4 and Q=C5⋊C8
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C5⋊C8) = C20.29M4(2)φ: C5⋊C8/C10C4 ⊆ Aut C2×C4804(C2xC4).(C5:C8)320,250
(C2×C4).2(C5⋊C8) = C42.4F5φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4320(C2xC4).2(C5:C8)320,197
(C2×C4).3(C5⋊C8) = C10.6M5(2)φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4160(C2xC4).3(C5:C8)320,249
(C2×C4).4(C5⋊C8) = C20⋊C16φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4320(C2xC4).4(C5:C8)320,196
(C2×C4).5(C5⋊C8) = C5⋊M6(2)φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C41604(C2xC4).5(C5:C8)320,215
(C2×C4).6(C5⋊C8) = C2×C20.C8φ: C5⋊C8/Dic5C2 ⊆ Aut C2×C4160(C2xC4).6(C5:C8)320,1081
(C2×C4).7(C5⋊C8) = C4×C5⋊C16central extension (φ=1)320(C2xC4).7(C5:C8)320,195
(C2×C4).8(C5⋊C8) = C2×C5⋊C32central extension (φ=1)320(C2xC4).8(C5:C8)320,214
(C2×C4).9(C5⋊C8) = C22×C5⋊C16central extension (φ=1)320(C2xC4).9(C5:C8)320,1080

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