Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅⋊C₈

Direct product G=N×Q with N=C₂³ and Q=C₅⋊C₈

		d	ρ	Label	ID
C₂³×C₅⋊C₈		320		C2^3xC5:C8	320,1605

Semidirect products G=N:Q with N=C₂³ and Q=C₅⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₅⋊C₈) = C₂⁴.F₅	φ: C₅⋊C₈/C₁₀ → C₄ ⊆ Aut C₂³	80		C2^3:(C5:C8)	320,271
C₂³⋊₂(C₅⋊C₈) = C₂×C₂³.₂F₅	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₂³	160		C2^3:2(C5:C8)	320,1135

Non-split extensions G=N.Q with N=C₂³ and Q=C₅⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₅⋊C₈) = C₂₀.₂₉M₄(2)	φ: C₅⋊C₈/C₁₀ → C₄ ⊆ Aut C₂³	80	4	C2^3.(C5:C8)	320,250
C₂³.₂(C₅⋊C₈) = C₁₀.₆M₅(2)	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₂³	160		C2^3.2(C5:C8)	320,249
C₂³.₃(C₅⋊C₈) = C₂×C₂₀.C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₂³	160		C2^3.3(C5:C8)	320,1081
C₂³.₄(C₅⋊C₈) = C₂²×C₅⋊C₁₆	central extension (φ=1)	320		C2^3.4(C5:C8)	320,1080

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