Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×C₂²⋊C₄

Direct product G=N×Q with N=C₅ and Q=C₅×C₂²⋊C₄

		d	ρ	Label	ID
C₂²⋊C₄×C₅²		200		C2^2:C4xC5^2	400,109

Semidirect products G=N:Q with N=C₅ and Q=C₅×C₂²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅×C₂²⋊C₄) = C₅×C₂²⋊F₅	φ: C₅×C₂²⋊C₄/C₂×C₁₀ → C₄ ⊆ Aut C₅	40	4	C5:(C5xC2^2:C4)	400,141
C₅⋊₂(C₅×C₂²⋊C₄) = C₅×D₁₀⋊C₄	φ: C₅×C₂²⋊C₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	80		C5:2(C5xC2^2:C4)	400,86
C₅⋊₃(C₅×C₂²⋊C₄) = C₅×C₂³.D₅	φ: C₅×C₂²⋊C₄/C₂²×C₁₀ → C₂ ⊆ Aut C₅	40		C5:3(C5xC2^2:C4)	400,91

Non-split extensions G=N.Q with N=C₅ and Q=C₅×C₂²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅×C₂²⋊C₄) = C₂²⋊C₄×C₂₅	central extension (φ=1)	200		C5.(C5xC2^2:C4)	400,21

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Extensions 1→N→G→Q→1 with N=C5 and Q=C5×C22⋊C4