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
C₂₀×S₄		60	3	C20xS4	480,1014

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₅×S₄) = C₅×C₄⋊S₄	φ: C₅×S₄/C₅×A₄ → C₂ ⊆ Aut C₄	60	6	C4:(C5xS4)	480,1015

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) = C₅×A₄⋊Q₈	φ: C₅×S₄/C₅×A₄ → C₂ ⊆ Aut C₄	120	6	C4.1(C5xS4)	480,1013
C₄.₂(C₅×S₄) = C₅×C₄.S₄	φ: C₅×S₄/C₅×A₄ → C₂ ⊆ Aut C₄	160	4	C4.2(C5xS4)	480,1019
C₄.₃(C₅×S₄) = C₅×C₄.₃S₄	φ: C₅×S₄/C₅×A₄ → C₂ ⊆ Aut C₄	80	4	C4.3(C5xS4)	480,1021
C₄.₄(C₅×S₄) = C₅×A₄⋊C₈	central extension (φ=1)	120	3	C4.4(C5xS4)	480,255
C₄.₅(C₅×S₄) = C₅×U₂(𝔽₃)	central extension (φ=1)	120	2	C4.5(C5xS4)	480,257
C₄.₆(C₅×S₄) = C₅×C₄.₆S₄	central extension (φ=1)	80	2	C4.6(C5xS4)	480,1020

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