Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂×C₄²⋊C₂

Direct product G=N×Q with N=C₅ and Q=C₂×C₄²⋊C₂

		d	ρ	Label	ID
C₁₀×C₄²⋊C₂		160		C10xC4^2:C2	320,1516

Semidirect products G=N:Q with N=C₅ and Q=C₂×C₄²⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂×C₄²⋊C₂) = C₂×D₁₀.C₂³	φ: C₂×C₄²⋊C₂/C₂²×C₄ → C₄ ⊆ Aut C₅	80		C5:(C2xC4^2:C2)	320,1592
C₅⋊₂(C₂×C₄²⋊C₂) = C₂×C₄²⋊D₅	φ: C₂×C₄²⋊C₂/C₂×C₄² → C₂ ⊆ Aut C₅	160		C5:2(C2xC4^2:C2)	320,1144
C₅⋊₃(C₂×C₄²⋊C₂) = C₂×C₂³.₁₁D₁₀	φ: C₂×C₄²⋊C₂/C₂×C₂²⋊C₄ → C₂ ⊆ Aut C₅	160		C5:3(C2xC4^2:C2)	320,1152
C₅⋊₄(C₂×C₄²⋊C₂) = C₂×C₄⋊C₄⋊₇D₅	φ: C₂×C₄²⋊C₂/C₂×C₄⋊C₄ → C₂ ⊆ Aut C₅	160		C5:4(C2xC4^2:C2)	320,1174
C₅⋊₅(C₂×C₄²⋊C₂) = D₅×C₄²⋊C₂	φ: C₂×C₄²⋊C₂/C₄²⋊C₂ → C₂ ⊆ Aut C₅	80		C5:5(C2xC4^2:C2)	320,1192
C₅⋊₆(C₂×C₄²⋊C₂) = C₂×C₂³.₂₁D₁₀	φ: C₂×C₄²⋊C₂/C₂³×C₄ → C₂ ⊆ Aut C₅	160		C5:6(C2xC4^2:C2)	320,1458

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁