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

Direct product G=NxQ with N=D₂₀ and Q=C₄

		d	ρ	Label	ID
C₄xD₂₀		80		C4xD20	160,94

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₂₀:₁C₄ = D₂₀:C₄	φ: C₄/C₁ → C₄ ⊆ Out D₂₀	40	8+	D20:1C4	160,82
D₂₀:₂C₄ = Q₈:₂F₅	φ: C₄/C₁ → C₄ ⊆ Out D₂₀	40	8+	D20:2C4	160,85
D₂₀:₃C₄ = D₄xF₅	φ: C₄/C₁ → C₄ ⊆ Out D₂₀	20	8+	D20:3C4	160,207
D₂₀:₄C₄ = D₂₀:₄C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	40	2	D20:4C4	160,12
D₂₀:₅C₄ = D₂₀:₅C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	80		D20:5C4	160,28
D₂₀:₆C₄ = D₂₀:₆C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	80		D20:6C4	160,16
D₂₀:₇C₄ = D₂₀:₇C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	40	4	D20:7C4	160,32
D₂₀:₈C₄ = D₂₀:₈C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	80		D20:8C4	160,114

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₂₀.C₄ = Q₈.F₅	φ: C₄/C₁ → C₄ ⊆ Out D₂₀	80	8+	D20.C4	160,208
D₂₀.₂C₄ = D₂₀.₂C₄	φ: C₄/C₂ → C₂ ⊆ Out D₂₀	80	4	D20.2C4	160,128
D₂₀.₃C₄ = D₂₀.₃C₄	φ: trivial image	80	2	D20.3C4	160,122

׿

x

:

Z

F

o

wr

Q

<