Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂×C₅⋊D₅

Direct product G=N×Q with N=C₅ and Q=C₂×C₅⋊D₅

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

Semidirect products G=N:Q with N=C₅ and Q=C₂×C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂×C₅⋊D₅) = D₅×C₅⋊D₅	φ: C₂×C₅⋊D₅/C₅⋊D₅ → C₂ ⊆ Aut C₅	50		C5:1(C2xC5:D5)	500,51
C₅⋊₂(C₂×C₅⋊D₅) = C₂×C₅³⋊C₂	φ: C₂×C₅⋊D₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	250		C5:2(C2xC5:D5)	500,55

Non-split extensions G=N.Q with N=C₅ and Q=C₂×C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₂×C₅⋊D₅) = C₂×C₂₅⋊D₅	φ: C₂×C₅⋊D₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	250		C5.(C2xC5:D5)	500,32
C₅.₂(C₂×C₅⋊D₅) = C₂×He₅⋊C₂	central stem extension (φ=1)	50	5	C5.2(C2xC5:D5)	500,33

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Extensions 1→N→G→Q→1 with N=C5 and Q=C2×C5⋊D5