Extensions 1→N→G→Q→1 with N=D₄ and Q=C₃⋊F₅

Direct product G=N×Q with N=D₄ and Q=C₃⋊F₅

		d	ρ	Label	ID
D₄×C₃⋊F₅		60	8	D4xC3:F5	480,1067

Semidirect products G=N:Q with N=D₄ and Q=C₃⋊F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₃⋊F₅) = D₂₀⋊Dic₃	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Out D₄	120	8	D4:1(C3:F5)	480,312
D₄⋊₂(C₃⋊F₅) = Dic₁₀⋊Dic₃	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Out D₄	120	8	D4:2(C3:F5)	480,313

Non-split extensions G=N.Q with N=D₄ and Q=C₃⋊F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.(C₃⋊F₅) = Dic₁₀.Dic₃	φ: trivial image	240	8	D4.(C3:F5)	480,1066

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Extensions 1→N→G→Q→1 with N=D4 and Q=C3⋊F5