Extensions 1→N→G→Q→1 with N=C₂×He₅ and Q=C₂

Direct product G=N×Q with N=C₂×He₅ and Q=C₂

		d	ρ	Label	ID
C₂²×He₅		100		C2^2xHe5	500,35

Semidirect products G=N:Q with N=C₂×He₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×He₅)⋊₁C₂ = C₂×C₅²⋊C₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂×He₅	50	10+	(C2xHe5):1C2	500,30
(C₂×He₅)⋊₂C₂ = C₂×He₅⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂×He₅	50	5	(C2xHe5):2C2	500,33

Non-split extensions G=N.Q with N=C₂×He₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×He₅).₁C₂ = He₅⋊₅C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂×He₅	100	10-	(C2xHe5).1C2	500,8
(C₂×He₅).₂C₂ = He₅⋊₆C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂×He₅	100	5	(C2xHe5).2C2	500,11
(C₂×He₅).₃C₂ = C₄×He₅	φ: trivial image	100	5	(C2xHe5).3C2	500,13

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C2×He5 and Q=C2