Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅×C₁₀

Direct product G=N×Q with N=C₄ and Q=D₅×C₁₀

		d	ρ	Label	ID
D₅×C₂×C₂₀		80		D5xC2xC20	400,182

Semidirect products G=N:Q with N=C₄ and Q=D₅×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(D₅×C₁₀) = C₅×D₄×D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	40	4	C4:1(D5xC10)	400,185
C₄⋊₂(D₅×C₁₀) = C₁₀×D₂₀	φ: D₅×C₁₀/C₅×C₁₀ → C₂ ⊆ Aut C₄	80		C4:2(D5xC10)	400,183

Non-split extensions G=N.Q with N=C₄ and Q=D₅×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(D₅×C₁₀) = C₅×D₄⋊D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	40	4	C4.1(D5xC10)	400,87
C₄.₂(D₅×C₁₀) = C₅×D₄.D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	40	4	C4.2(D5xC10)	400,88
C₄.₃(D₅×C₁₀) = C₅×Q₈⋊D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4.3(D5xC10)	400,89
C₄.₄(D₅×C₁₀) = C₅×C₅⋊Q₁₆	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4.4(D5xC10)	400,90
C₄.₅(D₅×C₁₀) = C₅×D₄⋊₂D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	40	4	C4.5(D5xC10)	400,186
C₄.₆(D₅×C₁₀) = C₅×Q₈×D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4.6(D5xC10)	400,187
C₄.₇(D₅×C₁₀) = C₅×Q₈⋊₂D₅	φ: D₅×C₁₀/C₅×D₅ → C₂ ⊆ Aut C₄	80	4	C4.7(D5xC10)	400,188
C₄.₈(D₅×C₁₀) = C₅×C₄₀⋊C₂	φ: D₅×C₁₀/C₅×C₁₀ → C₂ ⊆ Aut C₄	80	2	C4.8(D5xC10)	400,78
C₄.₉(D₅×C₁₀) = C₅×D₄₀	φ: D₅×C₁₀/C₅×C₁₀ → C₂ ⊆ Aut C₄	80	2	C4.9(D5xC10)	400,79
C₄.₁₀(D₅×C₁₀) = C₅×Dic₂₀	φ: D₅×C₁₀/C₅×C₁₀ → C₂ ⊆ Aut C₄	80	2	C4.10(D5xC10)	400,80
C₄.₁₁(D₅×C₁₀) = C₁₀×Dic₁₀	φ: D₅×C₁₀/C₅×C₁₀ → C₂ ⊆ Aut C₄	80		C4.11(D5xC10)	400,181
C₄.₁₂(D₅×C₁₀) = D₅×C₄₀	central extension (φ=1)	80	2	C4.12(D5xC10)	400,76
C₄.₁₃(D₅×C₁₀) = C₅×C₈⋊D₅	central extension (φ=1)	80	2	C4.13(D5xC10)	400,77
C₄.₁₄(D₅×C₁₀) = C₁₀×C₅⋊₂C₈	central extension (φ=1)	80		C4.14(D5xC10)	400,81
C₄.₁₅(D₅×C₁₀) = C₅×C₄.Dic₅	central extension (φ=1)	40	2	C4.15(D5xC10)	400,82
C₄.₁₆(D₅×C₁₀) = C₅×C₄○D₂₀	central extension (φ=1)	40	2	C4.16(D5xC10)	400,184

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