Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅⋊F₅

Direct product G=N×Q with N=C₄ and Q=C₅⋊F₅

		d	ρ	Label	ID
C₄×C₅⋊F₅		100		C4xC5:F5	400,151

Semidirect products G=N:Q with N=C₄ and Q=C₅⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₅⋊F₅) = C₂₀⋊F₅	φ: C₅⋊F₅/C₅⋊D₅ → C₂ ⊆ Aut C₄	100		C4:(C5:F5)	400,152

Non-split extensions G=N.Q with N=C₄ and Q=C₅⋊F₅

extension	φ:Q→Aut N	d	Label	ID
C₄.(C₅⋊F₅) = C₅²⋊₇M₄(2)	φ: C₅⋊F₅/C₅⋊D₅ → C₂ ⊆ Aut C₄	200	C4.(C5:F5)	400,150
C₄.₂(C₅⋊F₅) = C₅²⋊₄C₁₆	central extension (φ=1)	400	C4.2(C5:F5)	400,58
C₄.₃(C₅⋊F₅) = C₂₀.F₅	central extension (φ=1)	200	C4.3(C5:F5)	400,149

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Extensions 1→N→G→Q→1 with N=C4 and Q=C5⋊F5