Extensions 1→N→G→Q→1 with N=C₅ and Q=C₄×D₅

Direct product G=N×Q with N=C₅ and Q=C₄×D₅

		d	ρ	Label	ID
D₅×C₂₀		40	2	D5xC20	200,28

Semidirect products G=N:Q with N=C₅ and Q=C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₄×D₅) = D₅×F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₅	20	8+	C5:(C4xD5)	200,41
C₅⋊₂(C₄×D₅) = Dic₅⋊₂D₅	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₅	20	4+	C5:2(C4xD5)	200,23
C₅⋊₃(C₄×D₅) = C₄×C₅⋊D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₅	100		C5:3(C4xD5)	200,33
C₅⋊₄(C₄×D₅) = D₅×Dic₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₅	40	4-	C5:4(C4xD5)	200,22

Non-split extensions G=N.Q with N=C₅ and Q=C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₄×D₅) = C₄×D₂₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₅	100	2	C5.(C4xD5)	200,5

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=C4×D5