Extensions 1→N→G→Q→1 with N=C₄.A₄ and Q=D₅

Direct product G=N×Q with N=C₄.A₄ and Q=D₅

		d	ρ	Label	ID
D₅×C₄.A₄		80	4	D5xC4.A4	480,1042

Semidirect products G=N:Q with N=C₄.A₄ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₄⋊₁D₅ = C₂₀.₃S₄	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	80	4+	C4.A4:1D5	480,1032
C₄.A₄⋊₂D₅ = C₂₀.₆S₄	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	80	4	C4.A4:2D5	480,1031
C₄.A₄⋊₃D₅ = Dic₁₀.A₄	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	120	4+	C4.A4:3D5	480,1041
C₄.A₄⋊₄D₅ = D₂₀.A₄	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	80	4-	C4.A4:4D5	480,1043

Non-split extensions G=N.Q with N=C₄.A₄ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₄.₁D₅ = C₂₀.₂S₄	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	160	4-	C4.A4.1D5	480,1030
C₄.A₄.₂D₅ = C₅⋊₂U₂(𝔽₃)	φ: D₅/C₅ → C₂ ⊆ Out C₄.A₄	120	4	C4.A4.2D5	480,261
C₄.A₄.₃D₅ = SL₂(𝔽₃).Dic₅	φ: trivial image	160	4	C4.A4.3D5	480,267

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