Extensions 1→N→G→Q→1 with N=C₅²⋊C₄ and Q=C₄

Direct product G=N×Q with N=C₅²⋊C₄ and Q=C₄

		d	ρ	Label	ID
C₄×C₅²⋊C₄		40	4	C4xC5^2:C4	400,158

Semidirect products G=N:Q with N=C₅²⋊C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊C₄⋊C₄ = F₅²	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊C₄	20	16+	C5^2:C4:C4	400,205
C₅²⋊C₄⋊₂C₄ = C₅²⋊₃C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊C₄	20	8+	C5^2:C4:2C4	400,124
C₅²⋊C₄⋊₃C₄ = C₂.D₅≀C₂	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊C₄	20	4	C5^2:C4:3C4	400,130
C₅²⋊C₄⋊₄C₄ = (C₅×C₁₀).Q₈	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊C₄	20	8+	C5^2:C4:4C4	400,134

Non-split extensions G=N.Q with N=C₅²⋊C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊C₄.C₄ = C₅²⋊M₄(2)	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊C₄	10	8+	C5^2:C4.C4	400,206

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C52⋊C4 and Q=C4