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

Direct product G=NxQ with N=C₄ and Q=C₅²:C₄

		d	ρ	Label	ID
C₄xC₅²: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

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