Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₅⋊D₅

Direct product G=N×Q with N=C₁₀ and Q=C₅⋊D₅

		d	ρ	Label	ID
C₁₀×C₅⋊D₅		100		C10xC5:D5	500,54

Semidirect products G=N:Q with N=C₁₀ and Q=C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊(C₅⋊D₅) = C₂×C₅³⋊C₂	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₁₀	250		C10:(C5:D5)	500,55

Non-split extensions G=N.Q with N=C₁₀ and Q=C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₅⋊D₅) = C₅₀.D₅	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₁₀	500		C10.1(C5:D5)	500,10
C₁₀.₂(C₅⋊D₅) = C₂×C₂₅⋊D₅	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₁₀	250		C10.2(C5:D5)	500,32
C₁₀.₃(C₅⋊D₅) = C₅³⋊₁₂C₄	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₁₀	500		C10.3(C5:D5)	500,39
C₁₀.₄(C₅⋊D₅) = He₅⋊₆C₄	central extension (φ=1)	100	5	C10.4(C5:D5)	500,11
C₁₀.₅(C₅⋊D₅) = C₂×He₅⋊C₂	central extension (φ=1)	50	5	C10.5(C5:D5)	500,33
C₁₀.₆(C₅⋊D₅) = C₅×C₅²⋊₆C₄	central extension (φ=1)	100		C10.6(C5:D5)	500,38

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