Extensions 1→N→G→Q→1 with N=C₁₀ and Q=F₅

Direct product G=N×Q with N=C₁₀ and Q=F₅

		d	ρ	Label	ID
C₁₀×F₅		40	4	C10xF5	200,45

Semidirect products G=N:Q with N=C₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁F₅ = C₂×C₅⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	50		C10:1F5	200,47
C₁₀⋊₂F₅ = C₂×C₅²⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	20	4+	C10:2F5	200,48
C₁₀⋊₃F₅ = C₂×D₅.D₅	φ: F₅/D₅ → C₂ ⊆ Aut C₁₀	40	4	C10:3F5	200,46

Non-split extensions G=N.Q with N=C₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁F₅ = C₂₅⋊C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	200	4-	C10.1F5	200,3
C₁₀.₂F₅ = C₂×C₂₅⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	50	4+	C10.2F5	200,12
C₁₀.₃F₅ = C₅²⋊₄C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	200		C10.3F5	200,20
C₁₀.₄F₅ = C₅²⋊₅C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₁₀	40	4-	C10.4F5	200,21
C₁₀.₅F₅ = C₅²⋊₃C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₁₀	40	4	C10.5F5	200,19
C₁₀.₆F₅ = C₅×C₅⋊C₈	central extension (φ=1)	40	4	C10.6F5	200,18

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