Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂×C₂₀

Direct product G=N×Q with N=C₅ and Q=C₂×C₂₀

		d	ρ	Label	ID
C₁₀×C₂₀		200		C10xC20	200,37

Semidirect products G=N:Q with N=C₅ and Q=C₂×C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂×C₂₀) = C₁₀×F₅	φ: C₂×C₂₀/C₁₀ → C₄ ⊆ Aut C₅	40	4	C5:(C2xC20)	200,45
C₅⋊₂(C₂×C₂₀) = D₅×C₂₀	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Aut C₅	40	2	C5:2(C2xC20)	200,28
C₅⋊₃(C₂×C₂₀) = C₁₀×Dic₅	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Aut C₅	40		C5:3(C2xC20)	200,30

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁