Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂²×C₄²

Direct product G=N×Q with N=C₅ and Q=C₂²×C₄²

		d	ρ	Label	ID
C₂²×C₄×C₂₀		320		C2^2xC4xC20	320,1513

Semidirect products G=N:Q with N=C₅ and Q=C₂²×C₄²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂²×C₄²) = C₂²×C₄×F₅	φ: C₂²×C₄²/C₂²×C₄ → C₄ ⊆ Aut C₅	80		C5:(C2^2xC4^2)	320,1590
C₅⋊₂(C₂²×C₄²) = D₅×C₂×C₄²	φ: C₂²×C₄²/C₂×C₄² → C₂ ⊆ Aut C₅	160		C5:2(C2^2xC4^2)	320,1143
C₅⋊₃(C₂²×C₄²) = C₂²×C₄×Dic₅	φ: C₂²×C₄²/C₂³×C₄ → C₂ ⊆ Aut C₅	320		C5:3(C2^2xC4^2)	320,1454

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁