Extensions 1→N→G→Q→1 with N=C₂³×D₅ and Q=C₆

Direct product G=N×Q with N=C₂³×D₅ and Q=C₆

		d	ρ	Label	ID
D₅×C₂³×C₆		240		D5xC2^3xC6	480,1210

Semidirect products G=N:Q with N=C₂³×D₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×D₅)⋊₁C₆ = A₄×D₂₀	φ: C₆/C₁ → C₆ ⊆ Out C₂³×D₅	60	6+	(C2^3xD5):1C6	480,1037
(C₂³×D₅)⋊₂C₆ = A₄×C₅⋊D₄	φ: C₆/C₁ → C₆ ⊆ Out C₂³×D₅	60	6	(C2^3xD5):2C6	480,1045
(C₂³×D₅)⋊₃C₆ = C₂²×D₅×A₄	φ: C₆/C₂ → C₃ ⊆ Out C₂³×D₅	60		(C2^3xD5):3C6	480,1202
(C₂³×D₅)⋊₄C₆ = C₃×C₂²⋊D₂₀	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):4C6	480,675
(C₂³×D₅)⋊₅C₆ = C₃×C₂³⋊D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):5C6	480,730
(C₂³×D₅)⋊₆C₆ = C₂×C₆×D₂₀	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5):6C6	480,1137
(C₂³×D₅)⋊₇C₆ = C₆×D₄×D₅	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):7C6	480,1139
(C₂³×D₅)⋊₈C₆ = C₂×C₆×C₅⋊D₄	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5):8C6	480,1149

Non-split extensions G=N.Q with N=C₂³×D₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×D₅).C₆ = C₂×A₄×F₅	φ: C₆/C₁ → C₆ ⊆ Out C₂³×D₅	30	12+	(C2^3xD5).C6	480,1192
(C₂³×D₅).₂C₆ = C₄×D₅×A₄	φ: C₆/C₂ → C₃ ⊆ Out C₂³×D₅	60	6	(C2^3xD5).2C6	480,1036
(C₂³×D₅).₃C₆ = C₃×D₅×C₂²⋊C₄	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).3C6	480,673
(C₂³×D₅).₄C₆ = C₆×D₁₀⋊C₄	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5).4C6	480,720
(C₂³×D₅).₅C₆ = C₆×C₂²⋊F₅	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).5C6	480,1059
(C₂³×D₅).₆C₆ = F₅×C₂²×C₆	φ: C₆/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).6C6	480,1205
(C₂³×D₅).₇C₆ = D₅×C₂²×C₁₂	φ: trivial image	240		(C2^3xD5).7C6	480,1136

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