Extensions 1→N→G→Q→1 with N=C₂×D₅² and Q=C₂

Direct product G=N×Q with N=C₂×D₅² and Q=C₂

		d	ρ	Label	ID
C₂²×D₅²		40		C2^2xD5^2	400,218

Semidirect products G=N:Q with N=C₂×D₅² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×D₅²)⋊₁C₂ = D₅×D₂₀	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	40	4+	(C2xD5^2):1C2	400,170
(C₂×D₅²)⋊₂C₂ = C₂₀⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	40	4	(C2xD5^2):2C2	400,171
(C₂×D₅²)⋊₃C₂ = D₅×C₅⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	40	4	(C2xD5^2):3C2	400,179
(C₂×D₅²)⋊₄C₂ = D₁₀⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	20	4+	(C2xD5^2):4C2	400,180
(C₂×D₅²)⋊₅C₂ = C₂×D₅≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	20	4+	(C2xD5^2):5C2	400,211

Non-split extensions G=N.Q with N=C₂×D₅² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×D₅²).₁C₂ = D₅.D₂₀	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	40	8+	(C2xD5^2).1C2	400,118
(C₂×D₅²).₂C₂ = D₁₀⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	20	8+	(C2xD5^2).2C2	400,125
(C₂×D₅²).₃C₂ = D₅²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	20	4+	(C2xD5^2).3C2	400,129
(C₂×D₅²).₄C₂ = C₂×D₅×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	40	8+	(C2xD5^2).4C2	400,209
(C₂×D₅²).₅C₂ = C₂×D₅⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₂×D₅²	20	8+	(C2xD5^2).5C2	400,210
(C₂×D₅²).₆C₂ = C₄×D₅²	φ: trivial image	40	4	(C2xD5^2).6C2	400,169

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁