Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₅×D₄

Direct product G=N×Q with N=C₁₀ and Q=C₅×D₄

		d	ρ	Label	ID
D₄×C₅×C₁₀		200		D4xC5xC10	400,202

Semidirect products G=N:Q with N=C₁₀ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁(C₅×D₄) = C₁₀×D₂₀	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₁₀	80		C10:1(C5xD4)	400,183
C₁₀⋊₂(C₅×D₄) = C₁₀×C₅⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	40		C10:2(C5xD4)	400,190

Non-split extensions G=N.Q with N=C₁₀ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₅×D₄) = C₅×C₄₀⋊C₂	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₁₀	80	2	C10.1(C5xD4)	400,78
C₁₀.₂(C₅×D₄) = C₅×D₄₀	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₁₀	80	2	C10.2(C5xD4)	400,79
C₁₀.₃(C₅×D₄) = C₅×Dic₂₀	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₁₀	80	2	C10.3(C5xD4)	400,80
C₁₀.₄(C₅×D₄) = C₅×C₄⋊Dic₅	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₁₀	80		C10.4(C5xD4)	400,85
C₁₀.₅(C₅×D₄) = C₅×C₁₀.D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	80		C10.5(C5xD4)	400,84
C₁₀.₆(C₅×D₄) = C₅×D₁₀⋊C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	80		C10.6(C5xD4)	400,86
C₁₀.₇(C₅×D₄) = C₅×D₄⋊D₅	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	40	4	C10.7(C5xD4)	400,87
C₁₀.₈(C₅×D₄) = C₅×D₄.D₅	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	40	4	C10.8(C5xD4)	400,88
C₁₀.₉(C₅×D₄) = C₅×Q₈⋊D₅	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.9(C5xD4)	400,89
C₁₀.₁₀(C₅×D₄) = C₅×C₅⋊Q₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.10(C5xD4)	400,90
C₁₀.₁₁(C₅×D₄) = C₅×C₂³.D₅	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₁₀	40		C10.11(C5xD4)	400,91
C₁₀.₁₂(C₅×D₄) = C₂²⋊C₄×C₂₅	central extension (φ=1)	200		C10.12(C5xD4)	400,21
C₁₀.₁₃(C₅×D₄) = C₄⋊C₄×C₂₅	central extension (φ=1)	400		C10.13(C5xD4)	400,22
C₁₀.₁₄(C₅×D₄) = D₈×C₂₅	central extension (φ=1)	200	2	C10.14(C5xD4)	400,25
C₁₀.₁₅(C₅×D₄) = SD₁₆×C₂₅	central extension (φ=1)	200	2	C10.15(C5xD4)	400,26
C₁₀.₁₆(C₅×D₄) = Q₁₆×C₂₅	central extension (φ=1)	400	2	C10.16(C5xD4)	400,27
C₁₀.₁₇(C₅×D₄) = D₄×C₅₀	central extension (φ=1)	200		C10.17(C5xD4)	400,46
C₁₀.₁₈(C₅×D₄) = C₂²⋊C₄×C₅²	central extension (φ=1)	200		C10.18(C5xD4)	400,109
C₁₀.₁₉(C₅×D₄) = C₄⋊C₄×C₅²	central extension (φ=1)	400		C10.19(C5xD4)	400,110
C₁₀.₂₀(C₅×D₄) = D₈×C₅²	central extension (φ=1)	200		C10.20(C5xD4)	400,113
C₁₀.₂₁(C₅×D₄) = SD₁₆×C₅²	central extension (φ=1)	200		C10.21(C5xD4)	400,114
C₁₀.₂₂(C₅×D₄) = Q₁₆×C₅²	central extension (φ=1)	400		C10.22(C5xD4)	400,115

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Extensions 1→N→G→Q→1 with N=C10 and Q=C5×D4

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₅×D₄