Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅×F₅

Direct product G=N×Q with N=C₄ and Q=C₅×F₅

		d	ρ	Label	ID
C₂₀×F₅		80	4	C20xF5	400,137

Semidirect products G=N:Q with N=C₄ and Q=C₅×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₅×F₅) = C₅×C₄⋊F₅	φ: C₅×F₅/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4:(C5xF5)	400,138

Non-split extensions G=N.Q with N=C₄ and Q=C₅×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₅×F₅) = C₅×C₄.F₅	φ: C₅×F₅/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4.(C5xF5)	400,136
C₄.₂(C₅×F₅) = C₅×C₅⋊C₁₆	central extension (φ=1)	80	4	C4.2(C5xF5)	400,56
C₄.₃(C₅×F₅) = C₅×D₅⋊C₈	central extension (φ=1)	80	4	C4.3(C5xF5)	400,135

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Extensions 1→N→G→Q→1 with N=C4 and Q=C5×F5