Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂³×C₁₀

Direct product G=N×Q with N=C₄ and Q=C₂³×C₁₀

		d	ρ	Label	ID
C₂⁴×C₂₀		320		C2^4xC20	320,1628

Semidirect products G=N:Q with N=C₄ and Q=C₂³×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂³×C₁₀) = D₄×C₂²×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4:(C2^3xC10)	320,1629

Non-split extensions G=N.Q with N=C₄ and Q=C₂³×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂³×C₁₀) = D₈×C₂×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.1(C2^3xC10)	320,1571
C₄.₂(C₂³×C₁₀) = SD₁₆×C₂×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.2(C2^3xC10)	320,1572
C₄.₃(C₂³×C₁₀) = Q₁₆×C₂×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	320		C4.3(C2^3xC10)	320,1573
C₄.₄(C₂³×C₁₀) = C₁₀×C₄○D₈	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.4(C2^3xC10)	320,1574
C₄.₅(C₂³×C₁₀) = C₁₀×C₈⋊C₂²	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.5(C2^3xC10)	320,1575
C₄.₆(C₂³×C₁₀) = C₁₀×C₈.C₂²	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.6(C2^3xC10)	320,1576
C₄.₇(C₂³×C₁₀) = C₅×D₈⋊C₂²	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.7(C2^3xC10)	320,1577
C₄.₈(C₂³×C₁₀) = C₅×D₄○D₈	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.8(C2^3xC10)	320,1578
C₄.₉(C₂³×C₁₀) = C₅×D₄○SD₁₆	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.9(C2^3xC10)	320,1579
C₄.₁₀(C₂³×C₁₀) = C₅×Q₈○D₈	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160	4	C4.10(C2^3xC10)	320,1580
C₄.₁₁(C₂³×C₁₀) = Q₈×C₂²×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	320		C4.11(C2^3xC10)	320,1630
C₄.₁₂(C₂³×C₁₀) = C₄○D₄×C₂×C₁₀	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.12(C2^3xC10)	320,1631
C₄.₁₃(C₂³×C₁₀) = C₁₀×2₊¹⁺⁴	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80		C4.13(C2^3xC10)	320,1632
C₄.₁₄(C₂³×C₁₀) = C₁₀×2_-¹⁺⁴	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	160		C4.14(C2^3xC10)	320,1633
C₄.₁₅(C₂³×C₁₀) = C₅×C₂.C₂⁵	φ: C₂³×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₄	80	4	C4.15(C2^3xC10)	320,1634
C₄.₁₆(C₂³×C₁₀) = M₄(2)×C₂×C₁₀	central extension (φ=1)	160		C4.16(C2^3xC10)	320,1568
C₄.₁₇(C₂³×C₁₀) = C₁₀×C₈○D₄	central extension (φ=1)	160		C4.17(C2^3xC10)	320,1569
C₄.₁₈(C₂³×C₁₀) = C₅×Q₈○M₄(2)	central extension (φ=1)	80	4	C4.18(C2^3xC10)	320,1570

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