Extensions 1→N→G→Q→1 with N=D₄ and Q=C₄×D₅

Direct product G=N×Q with N=D₄ and Q=C₄×D₅

		d	ρ	Label	ID
C₄×D₄×D₅		80		C4xD4xD5	320,1216

Semidirect products G=N:Q with N=D₄ and Q=C₄×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₄×D₅) = Dic₅⋊₄D₈	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	160		D4:1(C4xD5)	320,383
D₄⋊₂(C₄×D₅) = D₄⋊D₅⋊₆C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	160		D4:2(C4xD5)	320,412
D₄⋊₃(C₄×D₅) = C₄×D₄⋊D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	160		D4:3(C4xD5)	320,640
D₄⋊₄(C₄×D₅) = C₄².₄₈D₁₀	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	160		D4:4(C4xD5)	320,641
D₄⋊₅(C₄×D₅) = D₅×D₄⋊C₄	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	80		D4:5(C4xD5)	320,396
D₄⋊₆(C₄×D₅) = D₄⋊(C₄×D₅)	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	160		D4:6(C4xD5)	320,398
D₄⋊₇(C₄×D₅) = D₅×C₄≀C₂	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	40	4	D4:7(C4xD5)	320,447
D₄⋊₈(C₄×D₅) = C₄×D₄⋊₂D₅	φ: trivial image	160		D4:8(C4xD5)	320,1208
D₄⋊₉(C₄×D₅) = C₄²⋊₁₁D₁₀	φ: trivial image	80		D4:9(C4xD5)	320,1217
D₄⋊₁₀(C₄×D₅) = C₄².₁₀₈D₁₀	φ: trivial image	160		D4:10(C4xD5)	320,1218

Non-split extensions G=N.Q with N=D₄ and Q=C₄×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₄×D₅) = D₄.D₅⋊₅C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	160		D4.1(C4xD5)	320,384
D₄.₂(C₄×D₅) = Dic₅⋊₆SD₁₆	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	160		D4.2(C4xD5)	320,385
D₄.₃(C₄×D₅) = M₄(2).₂₂D₁₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	80	4	D4.3(C4xD5)	320,450
D₄.₄(C₄×D₅) = C₄².₁₉₆D₁₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Out D₄	80	4	D4.4(C4xD5)	320,451
D₄.₅(C₄×D₅) = C₄×D₄.D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	160		D4.5(C4xD5)	320,644
D₄.₆(C₄×D₅) = C₄².₅₁D₁₀	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	160		D4.6(C4xD5)	320,645
D₄.₇(C₄×D₅) = C₄₀.₉₃D₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.7(C4xD5)	320,771
D₄.₈(C₄×D₅) = C₄₀.₅₀D₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.8(C4xD5)	320,772
D₄.₉(C₄×D₅) = (D₄×D₅)⋊C₄	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	80		D4.9(C4xD5)	320,397
D₄.₁₀(C₄×D₅) = D₄⋊₂D₅⋊C₄	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	160		D4.10(C4xD5)	320,399
D₄.₁₁(C₄×D₅) = C₄²⋊D₁₀	φ: C₄×D₅/D₁₀ → C₂ ⊆ Out D₄	80	4	D4.11(C4xD5)	320,448
D₄.₁₂(C₄×D₅) = D₅×C₈○D₄	φ: trivial image	80	4	D4.12(C4xD5)	320,1421
D₄.₁₃(C₄×D₅) = C₂₀.₇₂C₂⁴	φ: trivial image	80	4	D4.13(C4xD5)	320,1422

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