Extensions 1→N→G→Q→1 with N=C₄○D₂₀ and Q=C₂

Direct product G=N×Q with N=C₄○D₂₀ and Q=C₂

		d	ρ	Label	ID
C₂×C₄○D₂₀		80		C2xC4oD20	160,216

Semidirect products G=N:Q with N=C₄○D₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₂₀⋊₁C₂ = D₄₀⋊₇C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	2	C4oD20:1C2	160,125
C₄○D₂₀⋊₂C₂ = C₈⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4+	C4oD20:2C2	160,129
C₄○D₂₀⋊₃C₂ = D₄.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4	C4oD20:3C2	160,153
C₄○D₂₀⋊₄C₂ = D₄.₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4	C4oD20:4C2	160,171
C₄○D₂₀⋊₅C₂ = D₄⋊₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4	C4oD20:5C2	160,219
C₄○D₂₀⋊₆C₂ = Q₈.₁₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4	C4oD20:6C2	160,222
C₄○D₂₀⋊₇C₂ = D₅×C₄○D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4	C4oD20:7C2	160,223
C₄○D₂₀⋊₈C₂ = D₄⋊₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4+	C4oD20:8C2	160,224
C₄○D₂₀⋊₉C₂ = D₄.₁₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4-	C4oD20:9C2	160,225

Non-split extensions G=N.Q with N=C₄○D₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₂₀.₁C₂ = D₂₀⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	2	C4oD20.1C2	160,12
C₄○D₂₀.₂C₂ = D₂₀⋊₇C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	40	4	C4oD20.2C2	160,32
C₄○D₂₀.₃C₂ = D₂₀.₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4	C4oD20.3C2	160,128
C₄○D₂₀.₄C₂ = C₈.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4-	C4oD20.4C2	160,130
C₄○D₂₀.₅C₂ = C₂₀.C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄○D₂₀	80	4	C4oD20.5C2	160,163
C₄○D₂₀.₆C₂ = D₂₀.₃C₄	φ: trivial image	80	2	C4oD20.6C2	160,122

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁