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

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

		d	ρ	Label	ID
C₅×C₅⋊F₅		100		C5xC5:F5	500,43

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

extension	φ:Q→Aut N	d	Label	ID
C₅⋊₁(C₅⋊F₅) = C₅³⋊₈C₄	φ: C₅⋊F₅/C₅² → C₄ ⊆ Aut C₅	125	C5:1(C5:F5)	500,48
C₅⋊₂(C₅⋊F₅) = C₅³⋊₉C₄	φ: C₅⋊F₅/C₅² → C₄ ⊆ Aut C₅	50	C5:2(C5:F5)	500,49
C₅⋊₃(C₅⋊F₅) = C₅³⋊₇C₄	φ: C₅⋊F₅/C₅⋊D₅ → C₂ ⊆ Aut C₅	100	C5:3(C5:F5)	500,47

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅⋊F₅) = C₂₅⋊F₅	φ: C₅⋊F₅/C₅² → C₄ ⊆ Aut C₅	125		C5.(C5:F5)	500,22
C₅.₂(C₅⋊F₅) = C₅²⋊F₅	φ: C₅⋊F₅/C₅⋊D₅ → C₂ ⊆ Aut C₅	25	10+	C5.2(C5:F5)	500,23

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