Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅⋊S₄

Direct product G=N×Q with N=C₄ and Q=C₅⋊S₄

		d	ρ	Label	ID
C₄×C₅⋊S₄		60	6	C4xC5:S4	480,1025

Semidirect products G=N:Q with N=C₄ and Q=C₅⋊S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₅⋊S₄) = C₂₀⋊S₄	φ: C₅⋊S₄/C₅×A₄ → C₂ ⊆ Aut C₄	60	6+	C4:(C5:S4)	480,1026

Non-split extensions G=N.Q with N=C₄ and Q=C₅⋊S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₅⋊S₄) = C₂₀.₁S₄	φ: C₅⋊S₄/C₅×A₄ → C₂ ⊆ Aut C₄	120	6-	C4.1(C5:S4)	480,1024
C₄.₂(C₅⋊S₄) = C₂₀.₂S₄	φ: C₅⋊S₄/C₅×A₄ → C₂ ⊆ Aut C₄	160	4-	C4.2(C5:S4)	480,1030
C₄.₃(C₅⋊S₄) = C₂₀.₃S₄	φ: C₅⋊S₄/C₅×A₄ → C₂ ⊆ Aut C₄	80	4+	C4.3(C5:S4)	480,1032
C₄.₄(C₅⋊S₄) = C₂₀.S₄	central extension (φ=1)	120	6	C4.4(C5:S4)	480,259
C₄.₅(C₅⋊S₄) = C₅⋊₂U₂(𝔽₃)	central extension (φ=1)	120	4	C4.5(C5:S4)	480,261
C₄.₆(C₅⋊S₄) = C₂₀.₆S₄	central extension (φ=1)	80	4	C4.6(C5:S4)	480,1031

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