Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×F₅

Direct product G=N×Q with N=D₄ and Q=C₂×F₅

		d	ρ	Label	ID
C₂×D₄×F₅		40		C2xD4xF5	320,1595

Semidirect products G=N:Q with N=D₄ and Q=C₂×F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×F₅) = D₈×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	40	8+	D4:1(C2xF5)	320,1068
D₄⋊₂(C₂×F₅) = D₄₀⋊C₄	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	40	8+	D4:2(C2xF5)	320,1069
D₄⋊₃(C₂×F₅) = C₂×D₂₀⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	80		D4:3(C2xF5)	320,1104
D₄⋊₄(C₂×F₅) = C₂×D₄⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	80		D4:4(C2xF5)	320,1106
D₄⋊₅(C₂×F₅) = D₅⋊C₄≀C₂	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	40	8	D4:5(C2xF5)	320,1130
D₄⋊₆(C₂×F₅) = C₄○D₄⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	40	8	D4:6(C2xF5)	320,1131
D₄⋊₇(C₂×F₅) = D₁₀.C₂⁴	φ: trivial image	40	8+	D4:7(C2xF5)	320,1596
D₄⋊₈(C₂×F₅) = C₄○D₄×F₅	φ: trivial image	40	8	D4:8(C2xF5)	320,1603
D₄⋊₉(C₂×F₅) = D₅.2₊¹⁺⁴	φ: trivial image	40	8	D4:9(C2xF5)	320,1604

Non-split extensions G=N.Q with N=D₄ and Q=C₂×F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×F₅) = D₈⋊₅F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	80	8-	D4.1(C2xF5)	320,1070
D₄.₂(C₂×F₅) = D₈⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	80	8-	D4.2(C2xF5)	320,1071
D₄.₃(C₂×F₅) = SD₁₆×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	40	8	D4.3(C2xF5)	320,1072
D₄.₄(C₂×F₅) = SD₁₆⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	40	8	D4.4(C2xF5)	320,1073
D₄.₅(C₂×F₅) = SD₁₆⋊₃F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	80	8	D4.5(C2xF5)	320,1074
D₄.₆(C₂×F₅) = SD₁₆⋊₂F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Out D₄	80	8	D4.6(C2xF5)	320,1075
D₄.₇(C₂×F₅) = (D₄×C₁₀)⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	40	8+	D4.7(C2xF5)	320,1105
D₄.₈(C₂×F₅) = (C₂×D₄)⋊₆F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	80	8-	D4.8(C2xF5)	320,1107
D₄.₉(C₂×F₅) = C₄○D₂₀⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	80	8	D4.9(C2xF5)	320,1132
D₄.₁₀(C₂×F₅) = D₄⋊F₅⋊C₂	φ: C₂×F₅/D₁₀ → C₂ ⊆ Out D₄	80	8	D4.10(C2xF5)	320,1133
D₄.₁₁(C₂×F₅) = C₂×D₄.F₅	φ: trivial image	160		D4.11(C2xF5)	320,1593
D₄.₁₂(C₂×F₅) = Dic₅.C₂⁴	φ: trivial image	80	8-	D4.12(C2xF5)	320,1594
D₄.₁₃(C₂×F₅) = Dic₅.₂₁C₂⁴	φ: trivial image	80	8	D4.13(C2xF5)	320,1601
D₄.₁₄(C₂×F₅) = Dic₅.₂₂C₂⁴	φ: trivial image	80	8	D4.14(C2xF5)	320,1602

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