Extensions 1→N→G→Q→1 with N=C2xC4 and Q=C40

Direct product G=NxQ with N=C2xC4 and Q=C40
dρLabelID
C2xC4xC40320C2xC4xC40320,903

Semidirect products G=N:Q with N=C2xC4 and Q=C40
extensionφ:Q→Aut NdρLabelID
(C2xC4):C40 = C5xC22.M4(2)φ: C40/C10C4 ⊆ Aut C2xC4160(C2xC4):C40320,129
(C2xC4):2C40 = C5xC22.7C42φ: C40/C20C2 ⊆ Aut C2xC4320(C2xC4):2C40320,141
(C2xC4):3C40 = C10xC4:C8φ: C40/C20C2 ⊆ Aut C2xC4320(C2xC4):3C40320,923
(C2xC4):4C40 = C5xC42.12C4φ: C40/C20C2 ⊆ Aut C2xC4160(C2xC4):4C40320,932

Non-split extensions G=N.Q with N=C2xC4 and Q=C40
extensionφ:Q→Aut NdρLabelID
(C2xC4).C40 = C5xC23.C8φ: C40/C10C4 ⊆ Aut C2xC4804(C2xC4).C40320,154
(C2xC4).2C40 = C5xC16:5C4φ: C40/C20C2 ⊆ Aut C2xC4320(C2xC4).2C40320,151
(C2xC4).3C40 = C5xC22:C16φ: C40/C20C2 ⊆ Aut C2xC4160(C2xC4).3C40320,153
(C2xC4).4C40 = C5xC4:C16φ: C40/C20C2 ⊆ Aut C2xC4320(C2xC4).4C40320,168
(C2xC4).5C40 = C5xM6(2)φ: C40/C20C2 ⊆ Aut C2xC41602(C2xC4).5C40320,175
(C2xC4).6C40 = C10xM5(2)φ: C40/C20C2 ⊆ Aut C2xC4160(C2xC4).6C40320,1004

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