Extensions 1→N→G→Q→1 with N=C₁₀×A₄ and Q=C₄

Direct product G=N×Q with N=C₁₀×A₄ and Q=C₄

		d	ρ	Label	ID
A₄×C₂×C₂₀		120		A4xC2xC20	480,1126

Semidirect products G=N:Q with N=C₁₀×A₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₁₀×A₄)⋊₁C₄ = C₂×A₄⋊F₅	φ: C₄/C₁ → C₄ ⊆ Out C₁₀×A₄	30	12+	(C10xA4):1C4	480,1191
(C₁₀×A₄)⋊₂C₄ = C₂×A₄×F₅	φ: C₄/C₁ → C₄ ⊆ Out C₁₀×A₄	30	12+	(C10xA4):2C4	480,1192
(C₁₀×A₄)⋊₃C₄ = C₂×A₄⋊Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120		(C10xA4):3C4	480,1033
(C₁₀×A₄)⋊₄C₄ = C₂×A₄×Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120		(C10xA4):4C4	480,1044
(C₁₀×A₄)⋊₅C₄ = C₁₀×A₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120		(C10xA4):5C4	480,1022

Non-split extensions G=N.Q with N=C₁₀×A₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₁₀×A₄).₁C₄ = Dic₅.S₄	φ: C₄/C₁ → C₄ ⊆ Out C₁₀×A₄	120	12-	(C10xA4).1C4	480,963
(C₁₀×A₄).₂C₄ = A₄×C₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Out C₁₀×A₄	120	12-	(C10xA4).2C4	480,966
(C₁₀×A₄).₃C₄ = C₂₀.S₄	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120	6	(C10xA4).3C4	480,259
(C₁₀×A₄).₄C₄ = A₄×C₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120	6	(C10xA4).4C4	480,265
(C₁₀×A₄).₅C₄ = C₅×A₄⋊C₈	φ: C₄/C₂ → C₂ ⊆ Out C₁₀×A₄	120	3	(C10xA4).5C4	480,255
(C₁₀×A₄).₆C₄ = A₄×C₄₀	φ: trivial image	120	3	(C10xA4).6C4	480,659

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