Extensions 1→N→G→Q→1 with N=C₄×C₁₂ and Q=D₅

Direct product G=N×Q with N=C₄×C₁₂ and Q=D₅

		d	ρ	Label	ID
D₅×C₄×C₁₂		240		D5xC4xC12	480,664

Semidirect products G=N:Q with N=C₄×C₁₂ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₁₂)⋊₁D₅ = C₃×C₄²⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):1D5	480,665
(C₄×C₁₂)⋊₂D₅ = C₃×C₄²⋊₂D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):2D5	480,669
(C₄×C₁₂)⋊₃D₅ = C₄²⋊₃D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):3D5	480,841
(C₄×C₁₂)⋊₄D₅ = C₄²⋊₆D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):4D5	480,839
(C₄×C₁₂)⋊₅D₅ = C₄²⋊₇D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):5D5	480,840
(C₄×C₁₂)⋊₆D₅ = D₆₀⋊₇C₄	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	120	2	(C4xC12):6D5	480,165
(C₄×C₁₂)⋊₇D₅ = C₄×D₆₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):7D5	480,838
(C₄×C₁₂)⋊₈D₅ = C₄²×D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):8D5	480,836
(C₄×C₁₂)⋊₉D₅ = C₄²⋊₂D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):9D5	480,837
(C₄×C₁₂)⋊₁₀D₅ = C₃×D₂₀⋊₄C₄	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	120	2	(C4xC12):10D5	480,83
(C₄×C₁₂)⋊₁₁D₅ = C₁₂×D₂₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):11D5	480,666
(C₄×C₁₂)⋊₁₂D₅ = C₃×C₂₀⋊₄D₄	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):12D5	480,667
(C₄×C₁₂)⋊₁₃D₅ = C₃×C₄.D₂₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	240		(C4xC12):13D5	480,668

Non-split extensions G=N.Q with N=C₄×C₁₂ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₁₂).₁D₅ = C₃×C₄².D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).1D5	480,81
(C₄×C₁₂).₂D₅ = C₆₀⋊₈Q₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).2D5	480,834
(C₄×C₁₂).₃D₅ = C₆₀.₂₄Q₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).3D5	480,835
(C₄×C₁₂).₄D₅ = C₆₀⋊₅C₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).4D5	480,164
(C₄×C₁₂).₅D₅ = C₄×Dic₃₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).5D5	480,833
(C₄×C₁₂).₆D₅ = C₄×C₁₅⋊₃C₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).6D5	480,162
(C₄×C₁₂).₇D₅ = C₄².D₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).7D5	480,163
(C₄×C₁₂).₈D₅ = C₃×C₂₀⋊₃C₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).8D5	480,82
(C₄×C₁₂).₉D₅ = C₁₂×Dic₁₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).9D5	480,661
(C₄×C₁₂).₁₀D₅ = C₃×C₂₀⋊₂Q₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).10D5	480,662
(C₄×C₁₂).₁₁D₅ = C₃×C₂₀.₆Q₈	φ: D₅/C₅ → C₂ ⊆ Aut C₄×C₁₂	480		(C4xC12).11D5	480,663
(C₄×C₁₂).₁₂D₅ = C₁₂×C₅⋊₂C₈	central extension (φ=1)	480		(C4xC12).12D5	480,80

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