Extensions 1→N→G→Q→1 with N=C₆ and Q=C₅×M₄(2)

Direct product G=N×Q with N=C₆ and Q=C₅×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₃₀		240		M4(2)xC30	480,935

Semidirect products G=N:Q with N=C₆ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₅×M₄(2)) = C₁₀×C₈⋊S₃	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₆	240		C6:1(C5xM4(2))	480,779
C₆⋊₂(C₅×M₄(2)) = C₁₀×C₄.Dic₃	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6:2(C5xM4(2))	480,800

Non-split extensions G=N.Q with N=C₆ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₅×M₄(2)) = C₅×Dic₃⋊C₈	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₆	480		C6.1(C5xM4(2))	480,133
C₆.₂(C₅×M₄(2)) = C₅×C₂₄⋊C₄	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₆	480		C6.2(C5xM4(2))	480,134
C₆.₃(C₅×M₄(2)) = C₅×D₆⋊C₈	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₆	240		C6.3(C5xM4(2))	480,139
C₆.₄(C₅×M₄(2)) = C₅×C₄².S₃	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₆	480		C6.4(C5xM4(2))	480,122
C₆.₅(C₅×M₄(2)) = C₅×C₁₂⋊C₈	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₆	480		C6.5(C5xM4(2))	480,123
C₆.₆(C₅×M₄(2)) = C₅×C₁₂.₅₅D₄	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₆	240		C6.6(C5xM4(2))	480,149
C₆.₇(C₅×M₄(2)) = C₁₅×C₈⋊C₄	central extension (φ=1)	480		C6.7(C5xM4(2))	480,200
C₆.₈(C₅×M₄(2)) = C₁₅×C₂²⋊C₈	central extension (φ=1)	240		C6.8(C5xM4(2))	480,201
C₆.₉(C₅×M₄(2)) = C₁₅×C₄⋊C₈	central extension (φ=1)	480		C6.9(C5xM4(2))	480,208

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