Extensions 1→N→G→Q→1 with N=C₂²×F₅ and Q=S₃

Direct product G=N×Q with N=C₂²×F₅ and Q=S₃

		d	ρ	Label	ID
C₂²×S₃×F₅		60		C2^2xS3xF5	480,1197

Semidirect products G=N:Q with N=C₂²×F₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×F₅)⋊S₃ = F₅×S₄	φ: S₃/C₁ → S₃ ⊆ Out C₂²×F₅	20	12+	(C2^2xF5):S3	480,1189
(C₂²×F₅)⋊₂S₃ = C₂×D₆⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₂²×F₅	120		(C2^2xF5):2S3	480,1000
(C₂²×F₅)⋊₃S₃ = F₅×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂²×F₅	60	8	(C2^2xF5):3S3	480,1010

Non-split extensions G=N.Q with N=C₂²×F₅ and Q=S₃

extension	φ:Q→Out N	d	Label	ID
(C₂²×F₅).₁S₃ = D₁₀.₂₀D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₂²×F₅	120	(C2^2xF5).1S3	480,243
(C₂²×F₅).₂S₃ = C₂×Dic₃⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₂²×F₅	120	(C2^2xF5).2S3	480,1001
(C₂²×F₅).₃S₃ = C₂×Dic₃×F₅	φ: trivial image	120	(C2^2xF5).3S3	480,998

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Extensions 1→N→G→Q→1 with N=C22×F5 and Q=S3