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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊(C₄×D₅) = C₂×D₅×F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	40	8+	C10:(C4xD5)	400,209
C₁₀⋊₂(C₄×D₅) = C₂×Dic₅⋊₂D₅	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₁₀	40		C10:2(C4xD5)	400,175
C₁₀⋊₃(C₄×D₅) = C₂×C₄×C₅⋊D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10:3(C4xD5)	400,192
C₁₀⋊₄(C₄×D₅) = C₂×D₅×Dic₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10:4(C4xD5)	400,172

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₄×D₅) = Dic₅×F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.1(C4xD5)	400,117
C₁₀.₂(C₄×D₅) = D₅.D₂₀	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	40	8+	C10.2(C4xD5)	400,118
C₁₀.₃(C₄×D₅) = D₅.Dic₁₀	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.3(C4xD5)	400,119
C₁₀.₄(C₄×D₅) = D₅×C₅⋊C₈	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.4(C4xD5)	400,120
C₁₀.₅(C₄×D₅) = Dic₅.₄F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	40	8+	C10.5(C4xD5)	400,121
C₁₀.₆(C₄×D₅) = D₁₀.F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	80	8-	C10.6(C4xD5)	400,122
C₁₀.₇(C₄×D₅) = Dic₅.F₅	φ: C₄×D₅/D₅ → C₄ ⊆ Aut C₁₀	40	8+	C10.7(C4xD5)	400,123
C₁₀.₈(C₄×D₅) = C₂₀.₂₉D₁₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₁₀	40	4	C10.8(C4xD5)	400,61
C₁₀.₉(C₄×D₅) = C₂₀.₃₁D₁₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₁₀	40	4	C10.9(C4xD5)	400,63
C₁₀.₁₀(C₄×D₅) = C₁₀.D₂₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₁₀	40		C10.10(C4xD5)	400,73
C₁₀.₁₁(C₄×D₅) = C₁₀.Dic₁₀	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₁₀	80		C10.11(C4xD5)	400,75
C₁₀.₁₂(C₄×D₅) = C₈×D₂₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200	2	C10.12(C4xD5)	400,5
C₁₀.₁₃(C₄×D₅) = C₈⋊D₂₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200	2	C10.13(C4xD5)	400,6
C₁₀.₁₄(C₄×D₅) = C₄×Dic₂₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.14(C4xD5)	400,11
C₁₀.₁₅(C₄×D₅) = C₅₀.D₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.15(C4xD5)	400,12
C₁₀.₁₆(C₄×D₅) = D₅₀⋊C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.16(C4xD5)	400,14
C₁₀.₁₇(C₄×D₅) = C₂×C₄×D₂₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.17(C4xD5)	400,36
C₁₀.₁₈(C₄×D₅) = C₈×C₅⋊D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.18(C4xD5)	400,92
C₁₀.₁₉(C₄×D₅) = C₄₀⋊D₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.19(C4xD5)	400,93
C₁₀.₂₀(C₄×D₅) = C₄×C₅²⋊₆C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.20(C4xD5)	400,99
C₁₀.₂₁(C₄×D₅) = C₁₀².₂₂C₂²	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.21(C4xD5)	400,100
C₁₀.₂₂(C₄×D₅) = C₁₀.₁₁D₂₀	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.22(C4xD5)	400,102
C₁₀.₂₃(C₄×D₅) = D₅×C₅⋊₂C₈	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.23(C4xD5)	400,60
C₁₀.₂₄(C₄×D₅) = C₂₀.₃₀D₁₀	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80	4	C10.24(C4xD5)	400,62
C₁₀.₂₅(C₄×D₅) = Dic₅²	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.25(C4xD5)	400,71
C₁₀.₂₆(C₄×D₅) = D₁₀⋊Dic₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.26(C4xD5)	400,72
C₁₀.₂₇(C₄×D₅) = Dic₅⋊Dic₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.27(C4xD5)	400,74
C₁₀.₂₈(C₄×D₅) = D₅×C₄₀	central extension (φ=1)	80	2	C10.28(C4xD5)	400,76
C₁₀.₂₉(C₄×D₅) = C₅×C₈⋊D₅	central extension (φ=1)	80	2	C10.29(C4xD5)	400,77
C₁₀.₃₀(C₄×D₅) = Dic₅×C₂₀	central extension (φ=1)	80		C10.30(C4xD5)	400,83
C₁₀.₃₁(C₄×D₅) = C₅×C₁₀.D₄	central extension (φ=1)	80		C10.31(C4xD5)	400,84
C₁₀.₃₂(C₄×D₅) = C₅×D₁₀⋊C₄	central extension (φ=1)	80		C10.32(C4xD5)	400,86

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

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