Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×D₈

Direct product G=N×Q with N=C₅ and Q=C₅×D₈

		d	ρ	Label	ID
D₈×C₅²		200		D8xC5^2	400,113

Semidirect products G=N:Q with N=C₅ and Q=C₅×D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₅×D₈) = C₅×D₄₀	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₅	80	2	C5:1(C5xD8)	400,79
C₅⋊₂(C₅×D₈) = C₅×D₄⋊D₅	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₅	40	4	C5:2(C5xD8)	400,87

Non-split extensions G=N.Q with N=C₅ and Q=C₅×D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅×D₈) = D₈×C₂₅	central extension (φ=1)	200	2	C5.(C5xD8)	400,25

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=C5×D8