Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₄

Direct product G=N×Q with N=C₂₀ and Q=C₄

		d	ρ	Label	ID
C₄×C₂₀		80		C4xC20	80,20

Semidirect products G=N:Q with N=C₂₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊₁C₄ = C₄⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₂₀	20	4	C20:1C4	80,31
C₂₀⋊₂C₄ = C₄×F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₂₀	20	4	C20:2C4	80,30
C₂₀⋊₃C₄ = C₄⋊Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	80		C20:3C4	80,13
C₂₀⋊₄C₄ = C₄×Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	80		C20:4C4	80,11
C₂₀⋊₅C₄ = C₅×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	80		C20:5C4	80,22

Non-split extensions G=N.Q with N=C₂₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₄ = C₄.F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₂₀	40	4	C20.1C4	80,29
C₂₀.₂C₄ = C₅⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₂₀	80	4	C20.2C4	80,3
C₂₀.₃C₄ = D₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂₀	40	4	C20.3C4	80,28
C₂₀.₄C₄ = C₄.Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.4C4	80,10
C₂₀.₅C₄ = C₅⋊₂C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	80	2	C20.5C4	80,1
C₂₀.₆C₄ = C₂×C₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	80		C20.6C4	80,9
C₂₀.₇C₄ = C₅×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.7C4	80,24

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