Extensions 1→N→G→Q→1 with N=D₄×C₂×C₁₀ and Q=C₂

Direct product G=N×Q with N=D₄×C₂×C₁₀ and Q=C₂

		d	ρ	Label	ID
D₄×C₂²×C₁₀		160		D4xC2^2xC10	320,1629

Semidirect products G=N:Q with N=D₄×C₂×C₁₀ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₄×C₂×C₁₀)⋊₁C₂ = (C₂×C₁₀)⋊₈D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):1C2	320,844
(D₄×C₂×C₁₀)⋊₂C₂ = C₂²×D₄⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):2C2	320,1464
(D₄×C₂×C₁₀)⋊₃C₂ = C₂×D₄.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):3C2	320,1465
(D₄×C₂×C₁₀)⋊₄C₂ = C₂×C₂₀⋊₂D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):4C2	320,1472
(D₄×C₂×C₁₀)⋊₅C₂ = D₄×C₅⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):5C2	320,1473
(D₄×C₂×C₁₀)⋊₆C₂ = C₂×C₂₀⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):6C2	320,1475
(D₄×C₂×C₁₀)⋊₇C₂ = C₂⁴.₄₁D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):7C2	320,1477
(D₄×C₂×C₁₀)⋊₈C₂ = C₂⁴.₄₂D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):8C2	320,1478
(D₄×C₂×C₁₀)⋊₉C₂ = C₂²×D₄×D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):9C2	320,1612
(D₄×C₂×C₁₀)⋊₁₀C₂ = C₂²×D₄⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):10C2	320,1613
(D₄×C₂×C₁₀)⋊₁₁C₂ = C₂×D₄⋊₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):11C2	320,1614
(D₄×C₂×C₁₀)⋊₁₂C₂ = C₂⁴.₂₁D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):12C2	320,850
(D₄×C₂×C₁₀)⋊₁₃C₂ = C₅×C₂³⋊₂D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):13C2	320,893
(D₄×C₂×C₁₀)⋊₁₄C₂ = C₅×C₂²⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):14C2	320,948
(D₄×C₂×C₁₀)⋊₁₅C₂ = C₂×C₂³⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):15C2	320,1471
(D₄×C₂×C₁₀)⋊₁₆C₂ = C₂×Dic₅⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):16C2	320,1474
(D₄×C₂×C₁₀)⋊₁₇C₂ = C₂⁴⋊₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):17C2	320,1476
(D₄×C₂×C₁₀)⋊₁₈C₂ = C₁₀×C₂²≀C₂	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):18C2	320,1523
(D₄×C₂×C₁₀)⋊₁₉C₂ = C₁₀×C₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):19C2	320,1524
(D₄×C₂×C₁₀)⋊₂₀C₂ = C₁₀×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):20C2	320,1532
(D₄×C₂×C₁₀)⋊₂₁C₂ = C₅×C₂³⋊₃D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):21C2	320,1536
(D₄×C₂×C₁₀)⋊₂₂C₂ = C₅×C₂².₂₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):22C2	320,1537
(D₄×C₂×C₁₀)⋊₂₃C₂ = C₅×D₄²	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):23C2	320,1547
(D₄×C₂×C₁₀)⋊₂₄C₂ = C₅×D₄⋊₅D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):24C2	320,1548
(D₄×C₂×C₁₀)⋊₂₅C₂ = D₈×C₂×C₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10):25C2	320,1571
(D₄×C₂×C₁₀)⋊₂₆C₂ = C₁₀×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):26C2	320,1575
(D₄×C₂×C₁₀)⋊₂₇C₂ = C₁₀×2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10):27C2	320,1632
(D₄×C₂×C₁₀)⋊₂₈C₂ = C₄○D₄×C₂×C₁₀	φ: trivial image	160	(D4xC2xC10):28C2	320,1631

Non-split extensions G=N.Q with N=D₄×C₂×C₁₀ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₄×C₂×C₁₀).₁C₂ = C₂×D₄⋊Dic₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).1C2	320,841
(D₄×C₂×C₁₀).₂C₂ = (D₄×C₁₀)⋊₁₈C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).2C2	320,842
(D₄×C₂×C₁₀).₃C₂ = C₂×C₂₀.D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).3C2	320,843
(D₄×C₂×C₁₀).₄C₂ = (C₅×D₄).₃₁D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).4C2	320,845
(D₄×C₂×C₁₀).₅C₂ = C₂⁴.₁₉D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).5C2	320,848
(D₄×C₂×C₁₀).₆C₂ = C₂²×D₄.D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).6C2	320,1466
(D₄×C₂×C₁₀).₇C₂ = C₂×D₄×Dic₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).7C2	320,1467
(D₄×C₂×C₁₀).₈C₂ = C₂×C₂₀.₁₇D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).8C2	320,1469
(D₄×C₂×C₁₀).₉C₂ = C₂⁴.₃₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).9C2	320,1470
(D₄×C₂×C₁₀).₁₀C₂ = C₂×C₂³⋊Dic₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).10C2	320,846
(D₄×C₂×C₁₀).₁₁C₂ = C₂⁴.₁₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).11C2	320,847
(D₄×C₂×C₁₀).₁₂C₂ = C₂⁴.₂₀D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).12C2	320,849
(D₄×C₂×C₁₀).₁₃C₂ = C₅×C₂³.₂₃D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).13C2	320,887
(D₄×C₂×C₁₀).₁₄C₂ = C₅×C₂⁴.₃C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).14C2	320,891
(D₄×C₂×C₁₀).₁₅C₂ = C₅×C₂³.₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).15C2	320,895
(D₄×C₂×C₁₀).₁₆C₂ = C₁₀×C₂³⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).16C2	320,910
(D₄×C₂×C₁₀).₁₇C₂ = C₁₀×C₄.D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).17C2	320,912
(D₄×C₂×C₁₀).₁₈C₂ = C₁₀×D₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).18C2	320,915
(D₄×C₂×C₁₀).₁₉C₂ = C₅×C₂³.₃₇D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).19C2	320,919
(D₄×C₂×C₁₀).₂₀C₂ = C₅×C₂²⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).20C2	320,951
(D₄×C₂×C₁₀).₂₁C₂ = C₂×C₂³.₁₈D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).21C2	320,1468
(D₄×C₂×C₁₀).₂₂C₂ = C₅×C₂².₁₁C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	80	(D4xC2xC10).22C2	320,1520
(D₄×C₂×C₁₀).₂₃C₂ = C₁₀×C₂².D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).23C2	320,1526
(D₄×C₂×C₁₀).₂₄C₂ = C₁₀×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).24C2	320,1528
(D₄×C₂×C₁₀).₂₅C₂ = SD₁₆×C₂×C₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂×C₁₀	160	(D4xC2xC10).25C2	320,1572
(D₄×C₂×C₁₀).₂₆C₂ = D₄×C₂×C₂₀	φ: trivial image	160	(D4xC2xC10).26C2	320,1517

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Extensions 1→N→G→Q→1 with N=D4×C2×C10 and Q=C2

Extensions 1→N→G→Q→1 with N=D₄×C₂×C₁₀ and Q=C₂