Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂³

Direct product G=N×Q with N=C₁₀ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₁₀		80		C2^3xC10	80,52

Semidirect products G=N:Q with N=C₁₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊C₂³ = C₂³×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40		C10:C2^3	80,51

Non-split extensions G=N.Q with N=C₁₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁C₂³ = C₂×Dic₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	80		C10.1C2^3	80,35
C₁₀.₂C₂³ = C₂×C₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40		C10.2C2^3	80,36
C₁₀.₃C₂³ = C₂×D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40		C10.3C2^3	80,37
C₁₀.₄C₂³ = C₄○D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40	2	C10.4C2^3	80,38
C₁₀.₅C₂³ = D₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	20	4+	C10.5C2^3	80,39
C₁₀.₆C₂³ = D₄⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40	4-	C10.6C2^3	80,40
C₁₀.₇C₂³ = Q₈×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40	4-	C10.7C2^3	80,41
C₁₀.₈C₂³ = Q₈⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40	4+	C10.8C2^3	80,42
C₁₀.₉C₂³ = C₂²×Dic₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	80		C10.9C2^3	80,43
C₁₀.₁₀C₂³ = C₂×C₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₁₀	40		C10.10C2^3	80,44
C₁₀.₁₁C₂³ = D₄×C₁₀	central extension (φ=1)	40		C10.11C2^3	80,46
C₁₀.₁₂C₂³ = Q₈×C₁₀	central extension (φ=1)	80		C10.12C2^3	80,47
C₁₀.₁₃C₂³ = C₅×C₄○D₄	central extension (φ=1)	40	2	C10.13C2^3	80,48

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