Extensions 1→N→G→Q→1 with N=C₁₀ and Q=D₂₀

Direct product G=N×Q with N=C₁₀ and Q=D₂₀

		d	ρ	Label	ID
C₁₀×D₂₀		80		C10xD20	400,183

Semidirect products G=N:Q with N=C₁₀ and Q=D₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁D₂₀ = C₂×C₂₀⋊D₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10:1D20	400,193
C₁₀⋊₂D₂₀ = C₂×C₅⋊D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	40		C10:2D20	400,177

Non-split extensions G=N.Q with N=C₁₀ and Q=D₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁D₂₀ = Dic₁₀₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	400	2-	C10.1D20	400,4
C₁₀.₂D₂₀ = C₂₀₀⋊C₂	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200	2	C10.2D20	400,7
C₁₀.₃D₂₀ = D₂₀₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200	2+	C10.3D20	400,8
C₁₀.₄D₂₀ = C₄⋊Dic₂₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.4D20	400,13
C₁₀.₅D₂₀ = D₅₀⋊C₄	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.5D20	400,14
C₁₀.₆D₂₀ = C₂×D₁₀₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.6D20	400,37
C₁₀.₇D₂₀ = C₄₀⋊₂D₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.7D20	400,94
C₁₀.₈D₂₀ = C₅²⋊₅D₈	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.8D20	400,95
C₁₀.₉D₂₀ = C₄₀.D₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.9D20	400,96
C₁₀.₁₀D₂₀ = C₂₀⋊₃Dic₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	400		C10.10D20	400,101
C₁₀.₁₁D₂₀ = C₁₀.₁₁D₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₁₀	200		C10.11D20	400,102
C₁₀.₁₂D₂₀ = C₅⋊D₄₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	40	4+	C10.12D20	400,65
C₁₀.₁₃D₂₀ = C₅²⋊₃SD₁₆	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	80	4-	C10.13D20	400,67
C₁₀.₁₄D₂₀ = C₅²⋊₄SD₁₆	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	40	4+	C10.14D20	400,68
C₁₀.₁₅D₂₀ = C₅²⋊₃Q₁₆	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	80	4-	C10.15D20	400,70
C₁₀.₁₆D₂₀ = D₁₀⋊Dic₅	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.16D20	400,72
C₁₀.₁₇D₂₀ = C₁₀.D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	40		C10.17D20	400,73
C₁₀.₁₈D₂₀ = Dic₅⋊Dic₅	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₁₀	80		C10.18D20	400,74
C₁₀.₁₉D₂₀ = C₅×C₄₀⋊C₂	central extension (φ=1)	80	2	C10.19D20	400,78
C₁₀.₂₀D₂₀ = C₅×D₄₀	central extension (φ=1)	80	2	C10.20D20	400,79
C₁₀.₂₁D₂₀ = C₅×Dic₂₀	central extension (φ=1)	80	2	C10.21D20	400,80
C₁₀.₂₂D₂₀ = C₅×C₄⋊Dic₅	central extension (φ=1)	80		C10.22D20	400,85
C₁₀.₂₃D₂₀ = C₅×D₁₀⋊C₄	central extension (φ=1)	80		C10.23D20	400,86

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C10 and Q=D20

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=D₂₀