Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=C₂₀

Direct product G=N×Q with N=C₂×C₄ and Q=C₂₀

		d	ρ	Label	ID
C₂×C₄×C₂₀		160		C2xC4xC20	160,175

Semidirect products G=N:Q with N=C₂×C₄ and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊C₂₀ = C₅×C₂³⋊C₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂×C₄	40	4	(C2xC4):C20	160,49
(C₂×C₄)⋊₂C₂₀ = C₅×C₂.C₄²	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4):2C20	160,45
(C₂×C₄)⋊₃C₂₀ = C₁₀×C₄⋊C₄	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4):3C20	160,177
(C₂×C₄)⋊₄C₂₀ = C₅×C₄²⋊C₂	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	80		(C2xC4):4C20	160,178

Non-split extensions G=N.Q with N=C₂×C₄ and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).C₂₀ = C₅×C₄.₁₀D₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂×C₄	80	4	(C2xC4).C20	160,51
(C₂×C₄).₂C₂₀ = C₅×C₈⋊C₄	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4).2C20	160,47
(C₂×C₄).₃C₂₀ = C₅×C₂²⋊C₈	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).3C20	160,48
(C₂×C₄).₄C₂₀ = C₅×C₄⋊C₈	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4).4C20	160,55
(C₂×C₄).₅C₂₀ = C₅×M₅(2)	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	80	2	(C2xC4).5C20	160,60
(C₂×C₄).₆C₂₀ = C₁₀×M₄(2)	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).6C20	160,191

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁