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
F₅×C₂×C₁₂		120		F5xC2xC12	480,1050

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×C₄×C₃⋊F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	120		C6:1(C4xF5)	480,1063
C₆⋊₂(C₄×F₅) = C₂×Dic₃×F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120		C6:2(C4xF5)	480,998

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) = C₈×C₃⋊F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	120	4	C6.1(C4xF5)	480,296
C₆.₂(C₄×F₅) = C₂₄⋊F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	120	4	C6.2(C4xF5)	480,297
C₆.₃(C₄×F₅) = C₄×C₁₅⋊C₈	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	480		C6.3(C4xF5)	480,305
C₆.₄(C₄×F₅) = C₃₀.₁₁C₄²	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	480		C6.4(C4xF5)	480,307
C₆.₅(C₄×F₅) = D₁₀.₁₀D₁₂	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₆	120		C6.5(C4xF5)	480,311
C₆.₆(C₄×F₅) = F₅×C₃⋊C₈	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.6(C4xF5)	480,223
C₆.₇(C₄×F₅) = C₃₀.C₄²	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.7(C4xF5)	480,224
C₆.₈(C₄×F₅) = C₃₀.₃C₄²	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.8(C4xF5)	480,225
C₆.₉(C₄×F₅) = C₃₀.₄C₄²	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120	8	C6.9(C4xF5)	480,226
C₆.₁₀(C₄×F₅) = D₁₀.₂₀D₁₂	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	120		C6.10(C4xF5)	480,243
C₆.₁₁(C₄×F₅) = Dic₃×C₅⋊C₈	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	480		C6.11(C4xF5)	480,244
C₆.₁₂(C₄×F₅) = C₃₀.M₄(2)	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₆	480		C6.12(C4xF5)	480,245
C₆.₁₃(C₄×F₅) = F₅×C₂₄	central extension (φ=1)	120	4	C6.13(C4xF5)	480,271
C₆.₁₄(C₄×F₅) = C₃×C₈⋊F₅	central extension (φ=1)	120	4	C6.14(C4xF5)	480,272
C₆.₁₅(C₄×F₅) = C₁₂×C₅⋊C₈	central extension (φ=1)	480		C6.15(C4xF5)	480,280
C₆.₁₆(C₄×F₅) = C₃×C₁₀.C₄²	central extension (φ=1)	480		C6.16(C4xF5)	480,282
C₆.₁₇(C₄×F₅) = C₃×D₁₀.₃Q₈	central extension (φ=1)	120		C6.17(C4xF5)	480,286

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