Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅×M₄(2)

Direct product G=N×Q with N=C₄ and Q=C₅×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₂₀		160		M4(2)xC20	320,905

Semidirect products G=N:Q with N=C₄ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₅×M₄(2)) = C₅×C₈⋊₆D₄	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₄	160		C4:1(C5xM4(2))	320,937
C₄⋊₂(C₅×M₄(2)) = C₅×C₄⋊M₄(2)	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4:2(C5xM4(2))	320,924

Non-split extensions G=N.Q with N=C₄ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₅×M₄(2)) = C₅×D₄⋊C₈	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₄	160		C4.1(C5xM4(2))	320,130
C₄.₂(C₅×M₄(2)) = C₅×Q₈⋊C₈	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₄	320		C4.2(C5xM4(2))	320,131
C₄.₃(C₅×M₄(2)) = C₅×C₈⋊₄Q₈	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₄	320		C4.3(C5xM4(2))	320,947
C₄.₄(C₅×M₄(2)) = C₅×C₈⋊₂C₈	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.4(C5xM4(2))	320,139
C₄.₅(C₅×M₄(2)) = C₅×C₈⋊₁C₈	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.5(C5xM4(2))	320,140
C₄.₆(C₅×M₄(2)) = C₅×C₁₆⋊C₄	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	80	4	C4.6(C5xM4(2))	320,152
C₄.₇(C₅×M₄(2)) = C₅×C₂³.C₈	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	80	4	C4.7(C5xM4(2))	320,154
C₄.₈(C₅×M₄(2)) = C₅×C₄².₆C₄	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.8(C5xM4(2))	320,933
C₄.₉(C₅×M₄(2)) = C₅×C₈⋊C₈	central extension (φ=1)	320		C4.9(C5xM4(2))	320,127
C₄.₁₀(C₅×M₄(2)) = C₅×C₂²⋊C₁₆	central extension (φ=1)	160		C4.10(C5xM4(2))	320,153
C₄.₁₁(C₅×M₄(2)) = C₅×C₄⋊C₁₆	central extension (φ=1)	320		C4.11(C5xM4(2))	320,168
C₄.₁₂(C₅×M₄(2)) = C₅×C₄².₁₂C₄	central extension (φ=1)	160		C4.12(C5xM4(2))	320,932

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