Extensions 1→N→G→Q→1 with N=C₅×C₄○D₄ and Q=C₆

Direct product G=N×Q with N=C₅×C₄○D₄ and Q=C₆

		d	ρ	Label	ID
C₄○D₄×C₃₀		240		C4oD4xC30	480,1183

Semidirect products G=N:Q with N=C₅×C₄○D₄ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄○D₄)⋊₁C₆ = D₅×C₄.A₄	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	80	4	(C5xC4oD4):1C6	480,1042
(C₅×C₄○D₄)⋊₂C₆ = D₂₀.A₄	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	80	4-	(C5xC4oD4):2C6	480,1043
(C₅×C₄○D₄)⋊₃C₆ = C₅×D₄.A₄	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	80	4	(C5xC4oD4):3C6	480,1132
(C₅×C₄○D₄)⋊₄C₆ = C₁₀×C₄.A₄	φ: C₆/C₂ → C₃ ⊆ Out C₅×C₄○D₄	160		(C5xC4oD4):4C6	480,1130
(C₅×C₄○D₄)⋊₅C₆ = C₃×D₄⋊D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):5C6	480,742
(C₅×C₄○D₄)⋊₆C₆ = C₃×D₄.₈D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):6C6	480,743
(C₅×C₄○D₄)⋊₇C₆ = C₃×D₅×C₄○D₄	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):7C6	480,1145
(C₅×C₄○D₄)⋊₈C₆ = C₃×D₄⋊₈D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):8C6	480,1146
(C₅×C₄○D₄)⋊₉C₆ = C₃×D₄.₁₀D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):9C6	480,1147
(C₅×C₄○D₄)⋊₁₀C₆ = C₁₅×C₄○D₈	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	2	(C5xC4oD4):10C6	480,940
(C₅×C₄○D₄)⋊₁₁C₆ = C₁₅×C₈⋊C₂²	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):11C6	480,941
(C₅×C₄○D₄)⋊₁₂C₆ = C₁₅×2₊¹⁺⁴	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):12C6	480,1184
(C₅×C₄○D₄)⋊₁₃C₆ = C₁₅×2_-¹⁺⁴	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):13C6	480,1185

Non-split extensions G=N.Q with N=C₅×C₄○D₄ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄○D₄).₁C₆ = SL₂(𝔽₃).Dic₅	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	160	4	(C5xC4oD4).1C6	480,267
(C₅×C₄○D₄).₂C₆ = Dic₁₀.A₄	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	120	4+	(C5xC4oD4).2C6	480,1041
(C₅×C₄○D₄).₃C₆ = C₅×Q₈.A₄	φ: C₆/C₁ → C₆ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4).3C6	480,1131
(C₅×C₄○D₄).₄C₆ = C₅×C₈.A₄	φ: C₆/C₂ → C₃ ⊆ Out C₅×C₄○D₄	160	2	(C5xC4oD4).4C6	480,660
(C₅×C₄○D₄).₅C₆ = C₃×D₄⋊₂Dic₅	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4).5C6	480,115
(C₅×C₄○D₄).₆C₆ = C₃×D₄.Dic₅	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4).6C6	480,741
(C₅×C₄○D₄).₇C₆ = C₃×D₄.₉D₁₀	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4).7C6	480,744
(C₅×C₄○D₄).₈C₆ = C₁₅×C₄≀C₂	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	2	(C5xC4oD4).8C6	480,207
(C₅×C₄○D₄).₉C₆ = C₁₅×C₈.C₂²	φ: C₆/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4).9C6	480,942
(C₅×C₄○D₄).₁₀C₆ = C₁₅×C₈○D₄	φ: trivial image	240	2	(C5xC4oD4).10C6	480,936

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