Extensions 1→N→G→Q→1 with N=C₅² and Q=C₂₀

Direct product G=N×Q with N=C₅² and Q=C₂₀

		d	ρ	Label	ID
C₅²×C₂₀		500		C5^2xC20	500,40

Semidirect products G=N:Q with N=C₅² and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅²⋊C₂₀ = C₅²⋊C₂₀	φ: C₂₀/C₁ → C₂₀ ⊆ Aut C₅²	25	20+	C5^2:C20	500,17
C₅²⋊₂C₂₀ = He₅⋊₅C₄	φ: C₂₀/C₂ → C₁₀ ⊆ Aut C₅²	100	10-	C5^2:2C20	500,8
C₅²⋊₃C₂₀ = C₄×He₅	φ: C₂₀/C₄ → C₅ ⊆ Aut C₅²	100	5	C5^2:3C20	500,13
C₅²⋊₄C₂₀ = F₅×C₅²	φ: C₂₀/C₅ → C₄ ⊆ Aut C₅²	100		C5^2:4C20	500,41
C₅²⋊₅C₂₀ = C₅×D₅.D₅	φ: C₂₀/C₅ → C₄ ⊆ Aut C₅²	20	4	C5^2:5C20	500,42
C₅²⋊₆C₂₀ = C₅×C₅⋊F₅	φ: C₂₀/C₅ → C₄ ⊆ Aut C₅²	100		C5^2:6C20	500,43
C₅²⋊₇C₂₀ = C₅×C₅²⋊C₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₅²	20	4	C5^2:7C20	500,44
C₅²⋊₈C₂₀ = Dic₅×C₅²	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₅²	100		C5^2:8C20	500,37
C₅²⋊₉C₂₀ = C₅×C₅²⋊₆C₄	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₅²	100		C5^2:9C20	500,38

Non-split extensions G=N.Q with N=C₅² and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅².C₂₀ = C₄×5_-¹⁺²	φ: C₂₀/C₄ → C₅ ⊆ Aut C₅²	100	5	C5^2.C20	500,14
C₅².₂C₂₀ = F₅×C₂₅	φ: C₂₀/C₅ → C₄ ⊆ Aut C₅²	100	4	C5^2.2C20	500,15
C₅².₃C₂₀ = Dic₅×C₂₅	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₅²	100	2	C5^2.3C20	500,7

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