Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂²×D₅

Direct product G=N×Q with N=C₅ and Q=C₂²×D₅

		d	ρ	Label	ID
D₅×C₂×C₁₀		40		D5xC2xC10	200,50

Semidirect products G=N:Q with N=C₅ and Q=C₂²×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂²×D₅) = C₂×D₅²	φ: C₂²×D₅/D₁₀ → C₂ ⊆ Aut C₅	20	4+	C5:1(C2^2xD5)	200,49
C₅⋊₂(C₂²×D₅) = C₂²×C₅⋊D₅	φ: C₂²×D₅/C₂×C₁₀ → C₂ ⊆ Aut C₅	100		C5:2(C2^2xD5)	200,51

Non-split extensions G=N.Q with N=C₅ and Q=C₂²×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₂²×D₅) = C₂²×D₂₅	φ: C₂²×D₅/C₂×C₁₀ → C₂ ⊆ Aut C₅	100		C5.(C2^2xD5)	200,13

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=C22×D5