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

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

		d	ρ	Label	ID
C₄⋊C₄×C₅²		400		C4:C4xC5^2	400,110

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅×C₄⋊C₄) = C₅×C₄⋊F₅	φ: C₅×C₄⋊C₄/C₂₀ → C₄ ⊆ Aut C₅	80	4	C5:(C5xC4:C4)	400,138
C₅⋊₂(C₅×C₄⋊C₄) = C₅×C₁₀.D₄	φ: C₅×C₄⋊C₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	80		C5:2(C5xC4:C4)	400,84
C₅⋊₃(C₅×C₄⋊C₄) = C₅×C₄⋊Dic₅	φ: C₅×C₄⋊C₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	80		C5:3(C5xC4:C4)	400,85

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅×C₄⋊C₄) = C₄⋊C₄×C₂₅	central extension (φ=1)	400		C5.(C5xC4:C4)	400,22

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