# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5⋊2C8

Direct product G=N×Q with N=C2×C4 and Q=C52C8
dρLabelID
C2×C4×C52C8320C2xC4xC5:2C8320,547

Semidirect products G=N:Q with N=C2×C4 and Q=C52C8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C52C8) = (C2×C20)⋊C8φ: C52C8/C10C4 ⊆ Aut C2×C4160(C2xC4):(C5:2C8)320,86
(C2×C4)⋊2(C52C8) = (C2×C20)⋊8C8φ: C52C8/C20C2 ⊆ Aut C2×C4320(C2xC4):2(C5:2C8)320,82
(C2×C4)⋊3(C52C8) = C2×C203C8φ: C52C8/C20C2 ⊆ Aut C2×C4320(C2xC4):3(C5:2C8)320,550
(C2×C4)⋊4(C52C8) = C42.6Dic5φ: C52C8/C20C2 ⊆ Aut C2×C4160(C2xC4):4(C5:2C8)320,552

Non-split extensions G=N.Q with N=C2×C4 and Q=C52C8
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C52C8) = C40.D4φ: C52C8/C10C4 ⊆ Aut C2×C4804(C2xC4).(C5:2C8)320,111
(C2×C4).2(C52C8) = C40.10C8φ: C52C8/C20C2 ⊆ Aut C2×C4320(C2xC4).2(C5:2C8)320,19
(C2×C4).3(C52C8) = C203C16φ: C52C8/C20C2 ⊆ Aut C2×C4320(C2xC4).3(C5:2C8)320,20
(C2×C4).4(C52C8) = C40.91D4φ: C52C8/C20C2 ⊆ Aut C2×C4160(C2xC4).4(C5:2C8)320,107
(C2×C4).5(C52C8) = C80.9C4φ: C52C8/C20C2 ⊆ Aut C2×C41602(C2xC4).5(C5:2C8)320,57
(C2×C4).6(C52C8) = C2×C20.4C8φ: C52C8/C20C2 ⊆ Aut C2×C4160(C2xC4).6(C5:2C8)320,724
(C2×C4).7(C52C8) = C4×C52C16central extension (φ=1)320(C2xC4).7(C5:2C8)320,18
(C2×C4).8(C52C8) = C2×C52C32central extension (φ=1)320(C2xC4).8(C5:2C8)320,56
(C2×C4).9(C52C8) = C22×C52C16central extension (φ=1)320(C2xC4).9(C5:2C8)320,723

׿
×
𝔽