Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅²⋊C₄

Direct product G=N×Q with N=C₄ and Q=C₅²⋊C₄

		d	ρ	Label	ID
C₄×C₅²⋊C₄		40	4	C4xC5^2:C4	400,158

Semidirect products G=N:Q with N=C₄ and Q=C₅²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₅²⋊C₄) = C₂₀⋊₂F₅	φ: C₅²⋊C₄/C₅⋊D₅ → C₂ ⊆ Aut C₄	40	4	C4:(C5^2:C4)	400,159

Non-split extensions G=N.Q with N=C₄ and Q=C₅²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₅²⋊C₄) = C₅²⋊₈M₄(2)	φ: C₅²⋊C₄/C₅⋊D₅ → C₂ ⊆ Aut C₄	40	4	C4.(C5^2:C4)	400,157
C₄.₂(C₅²⋊C₄) = C₅²⋊₅C₁₆	central extension (φ=1)	80	4	C4.2(C5^2:C4)	400,59
C₄.₃(C₅²⋊C₄) = C₂₀.₁₁F₅	central extension (φ=1)	40	4	C4.3(C5^2:C4)	400,156

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Extensions 1→N→G→Q→1 with N=C4 and Q=C52⋊C4