Extensions 1→N→G→Q→1 with N=D₁₀ and Q=S₄

Direct product G=N×Q with N=D₁₀ and Q=S₄

		d	ρ	Label	ID
C₂×D₅×S₄		30	6+	C2xD5xS4	480,1193

Semidirect products G=N:Q with N=D₁₀ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁S₄ = D₁₀⋊S₄	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	60	6	D10:1S4	480,980
D₁₀⋊₂S₄ = A₄⋊D₂₀	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	60	6+	D10:2S4	480,981

Non-split extensions G=N.Q with N=D₁₀ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.₁S₄ = D₁₀.₁S₄	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	80	4-	D10.1S4	480,972
D₁₀.₂S₄ = D₁₀.₂S₄	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	80	4	D10.2S4	480,973
D₁₀.₃S₄ = D₁₀.S₄	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	40	8-	D10.3S4	480,962
D₁₀.₄S₄ = C₂×A₄⋊F₅	φ: S₄/A₄ → C₂ ⊆ Out D₁₀	30	12+	D10.4S4	480,1191
D₁₀.₅S₄ = D₅×CSU₂(𝔽₃)	φ: trivial image	80	4-	D10.5S4	480,971
D₁₀.₆S₄ = D₅×GL₂(𝔽₃)	φ: trivial image	40	4	D10.6S4	480,974
D₁₀.₇S₄ = D₅×A₄⋊C₄	φ: trivial image	60	6	D10.7S4	480,979

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