Extensions 1→N→G→Q→1 with N=C₅ and Q=C₄²⋊₆C₄

Direct product G=N×Q with N=C₅ and Q=C₄²⋊₆C₄

		d	ρ	Label	ID
C₅×C₄²⋊₆C₄		80		C5xC4^2:6C4	320,144

Semidirect products G=N:Q with N=C₅ and Q=C₄²⋊₆C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₄²⋊₆C₄) = C₄²⋊₆F₅	φ: C₄²⋊₆C₄/C₄² → C₄ ⊆ Aut C₅	40	4	C5:1(C4^2:6C4)	320,200
C₅⋊₂(C₄²⋊₆C₄) = C₂₀.C₄²	φ: C₄²⋊₆C₄/C₄⋊C₄ → C₄ ⊆ Aut C₅	80		C5:2(C4^2:6C4)	320,213
C₅⋊₃(C₄²⋊₆C₄) = M₄(2)⋊₃F₅	φ: C₄²⋊₆C₄/M₄(2) → C₄ ⊆ Aut C₅	40	8	C5:3(C4^2:6C4)	320,238
C₅⋊₄(C₄²⋊₆C₄) = C₄²⋊₆Dic₅	φ: C₄²⋊₆C₄/C₂×C₄² → C₂ ⊆ Aut C₅	80		C5:4(C4^2:6C4)	320,81
C₅⋊₅(C₄²⋊₆C₄) = C₂₀.₃₂C₄²	φ: C₄²⋊₆C₄/C₄²⋊C₂ → C₂ ⊆ Aut C₅	80		C5:5(C4^2:6C4)	320,90
C₅⋊₆(C₄²⋊₆C₄) = C₂₀.₃₃C₄²	φ: C₄²⋊₆C₄/C₂×M₄(2) → C₂ ⊆ Aut C₅	80		C5:6(C4^2:6C4)	320,113

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