Extensions 1→N→G→Q→1 with N=C₂³×C₆ and Q=C₁₀

Direct product G=N×Q with N=C₂³×C₆ and Q=C₁₀

		d	ρ	Label	ID
C₂⁴×C₃₀		480		C2^4xC30	480,1213

Semidirect products G=N:Q with N=C₂³×C₆ and Q=C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆)⋊C₁₀ = S₃×C₂⁴⋊C₅	φ: C₁₀/C₁ → C₁₀ ⊆ Aut C₂³×C₆	30	10+	(C2^3xC6):C10	480,1196
(C₂³×C₆)⋊₂C₁₀ = C₆×C₂⁴⋊C₅	φ: C₁₀/C₂ → C₅ ⊆ Aut C₂³×C₆	30	5	(C2^3xC6):2C10	480,1204
(C₂³×C₆)⋊₃C₁₀ = C₁₅×C₂²≀C₂	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	120		(C2^3xC6):3C10	480,925
(C₂³×C₆)⋊₄C₁₀ = D₄×C₂×C₃₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	240		(C2^3xC6):4C10	480,1181
(C₂³×C₆)⋊₅C₁₀ = C₅×C₂⁴⋊₄S₃	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	120		(C2^3xC6):5C10	480,832
(C₂³×C₆)⋊₆C₁₀ = C₂×C₁₀×C₃⋊D₄	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	240		(C2^3xC6):6C10	480,1164
(C₂³×C₆)⋊₇C₁₀ = S₃×C₂³×C₁₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	240		(C2^3xC6):7C10	480,1211

Non-split extensions G=N.Q with N=C₂³×C₆ and Q=C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆).₁C₁₀ = C₂²⋊C₄×C₃₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	240		(C2^3xC6).1C10	480,920
(C₂³×C₆).₂C₁₀ = C₁₀×C₆.D₄	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	240		(C2^3xC6).2C10	480,831
(C₂³×C₆).₃C₁₀ = Dic₃×C₂²×C₁₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂³×C₆	480		(C2^3xC6).3C10	480,1163

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