Extensions 1→N→G→Q→1 with N=C₄ and Q=D₁₀

Direct product G=N×Q with N=C₄ and Q=D₁₀

		d	ρ	Label	ID
C₂×C₄×D₅		40		C2xC4xD5	80,36

Semidirect products G=N:Q with N=C₄ and Q=D₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₁₀ = D₄×D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	20	4+	C4:1D10	80,39
C₄⋊₂D₁₀ = C₂×D₂₀	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₄	40		C4:2D10	80,37

Non-split extensions G=N.Q with N=C₄ and Q=D₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₁₀ = D₄⋊D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4+	C4.1D10	80,15
C₄.₂D₁₀ = D₄.D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4-	C4.2D10	80,16
C₄.₃D₁₀ = Q₈⋊D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4+	C4.3D10	80,17
C₄.₄D₁₀ = C₅⋊Q₁₆	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	80	4-	C4.4D10	80,18
C₄.₅D₁₀ = D₄⋊₂D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4-	C4.5D10	80,40
C₄.₆D₁₀ = Q₈×D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4-	C4.6D10	80,41
C₄.₇D₁₀ = Q₈⋊₂D₅	φ: D₁₀/D₅ → C₂ ⊆ Aut C₄	40	4+	C4.7D10	80,42
C₄.₈D₁₀ = C₄₀⋊C₂	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₄	40	2	C4.8D10	80,6
C₄.₉D₁₀ = D₄₀	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₄	40	2+	C4.9D10	80,7
C₄.₁₀D₁₀ = Dic₂₀	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₄	80	2-	C4.10D10	80,8
C₄.₁₁D₁₀ = C₂×Dic₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₄	80		C4.11D10	80,35
C₄.₁₂D₁₀ = C₈×D₅	central extension (φ=1)	40	2	C4.12D10	80,4
C₄.₁₃D₁₀ = C₈⋊D₅	central extension (φ=1)	40	2	C4.13D10	80,5
C₄.₁₄D₁₀ = C₂×C₅⋊₂C₈	central extension (φ=1)	80		C4.14D10	80,9
C₄.₁₅D₁₀ = C₄.Dic₅	central extension (φ=1)	40	2	C4.15D10	80,10
C₄.₁₆D₁₀ = C₄○D₂₀	central extension (φ=1)	40	2	C4.16D10	80,38

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