Extensions 1→N→G→Q→1 with N=D₄ and Q=D₂₀

Direct product G=N×Q with N=D₄ and Q=D₂₀

		d	ρ	Label	ID
D₄×D₂₀		80		D4xD20	320,1221

Semidirect products G=N:Q with N=D₄ and Q=D₂₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁D₂₀ = C₂₀⋊₇D₈	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4:1D20	320,642
D₄⋊₂D₂₀ = D₄⋊D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	80		D4:2D20	320,400
D₄⋊₃D₂₀ = D₄⋊₃D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	160		D4:3D20	320,408
D₄⋊₄D₂₀ = D₄⋊₄D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	40	4+	D4:4D20	320,449
D₄⋊₅D₂₀ = D₄⋊₅D₂₀	φ: trivial image	80		D4:5D20	320,1226
D₄⋊₆D₂₀ = D₄⋊₆D₂₀	φ: trivial image	160		D4:6D20	320,1227

Non-split extensions G=N.Q with N=D₄ and Q=D₂₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁D₂₀ = D₄.₁D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4.1D20	320,643
D₄.₂D₂₀ = D₄.₂D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4.2D20	320,646
D₄.₃D₂₀ = D₄.₃D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.3D20	320,768
D₄.₄D₂₀ = D₄.₄D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	80	4+	D4.4D20	320,769
D₄.₅D₂₀ = D₄.₅D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Out D₄	160	4-	D4.5D20	320,770
D₄.₆D₂₀ = D₂₀.₈D₄	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	80		D4.6D20	320,403
D₄.₇D₂₀ = D₄.D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	160		D4.7D20	320,410
D₄.₈D₂₀ = M₄(2)⋊D₁₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	80	4	D4.8D20	320,452
D₄.₉D₂₀ = D₄.₉D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	80	4-	D4.9D20	320,453
D₄.₁₀D₂₀ = D₄.₁₀D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Out D₄	80	4	D4.10D20	320,454
D₄.₁₁D₂₀ = D₄.₁₁D₂₀	φ: trivial image	80	4	D4.11D20	320,1423
D₄.₁₂D₂₀ = D₄.₁₂D₂₀	φ: trivial image	80	4+	D4.12D20	320,1424
D₄.₁₃D₂₀ = D₄.₁₃D₂₀	φ: trivial image	160	4-	D4.13D20	320,1425

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