Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=S₃

Direct product G=N×Q with N=C₂×C₁₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₂×C₁₀		60		S3xC2xC10	120,45

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁S₃ = C₅×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₁₀	20	3	(C2xC10):1S3	120,37
(C₂×C₁₀)⋊₂S₃ = C₅⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂×C₁₀	20	6+	(C2xC10):2S3	120,38
(C₂×C₁₀)⋊₃S₃ = C₅×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₁₀	60	2	(C2xC10):3S3	120,25
(C₂×C₁₀)⋊₄S₃ = C₁₅⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₁₀	60	2	(C2xC10):4S3	120,30
(C₂×C₁₀)⋊₅S₃ = C₂²×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₁₀	60		(C2xC10):5S3	120,46

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).S₃ = C₂×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂×C₁₀	120		(C2xC10).S3	120,29
(C₂×C₁₀).₂S₃ = C₁₀×Dic₃	central extension (φ=1)	120		(C2xC10).2S3	120,24

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