Extensions 1→N→G→Q→1 with N=C₆ and Q=C₄.F₅

Direct product G=N×Q with N=C₆ and Q=C₄.F₅

		d	ρ	Label	ID
C₆×C₄.F₅		240		C6xC4.F5	480,1048

Semidirect products G=N:Q with N=C₆ and Q=C₄.F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₄.F₅) = C₂×Dic₃.F₅	φ: C₄.F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	240		C6:1(C4.F5)	480,1009
C₆⋊₂(C₄.F₅) = C₂×C₁₂.F₅	φ: C₄.F₅/C₄×D₅ → C₂ ⊆ Aut C₆	240		C6:2(C4.F5)	480,1061

Non-split extensions G=N.Q with N=C₆ and Q=C₄.F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₄.F₅) = C₃₀.M₄(2)	φ: C₄.F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	480		C6.1(C4.F5)	480,245
C₆.₂(C₄.F₅) = D₃₀⋊C₈	φ: C₄.F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	240		C6.2(C4.F5)	480,247
C₆.₃(C₄.F₅) = C₃₀.₄M₄(2)	φ: C₄.F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	480		C6.3(C4.F5)	480,252
C₆.₄(C₄.F₅) = C₆₀⋊C₈	φ: C₄.F₅/C₄×D₅ → C₂ ⊆ Aut C₆	480		C6.4(C4.F5)	480,306
C₆.₅(C₄.F₅) = C₃₀.₁₁C₄²	φ: C₄.F₅/C₄×D₅ → C₂ ⊆ Aut C₆	480		C6.5(C4.F5)	480,307
C₆.₆(C₄.F₅) = C₃₀.₇M₄(2)	φ: C₄.F₅/C₄×D₅ → C₂ ⊆ Aut C₆	240		C6.6(C4.F5)	480,308
C₆.₇(C₄.F₅) = C₃×C₂₀⋊C₈	central extension (φ=1)	480		C6.7(C4.F5)	480,281
C₆.₈(C₄.F₅) = C₃×C₁₀.C₄²	central extension (φ=1)	480		C6.8(C4.F5)	480,282
C₆.₉(C₄.F₅) = C₃×D₁₀⋊C₈	central extension (φ=1)	240		C6.9(C4.F5)	480,283

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