Extensions 1→N→G→Q→1 with N=C₄⋊D₄ and Q=C₁₀

Direct product G=N×Q with N=C₄⋊D₄ and Q=C₁₀

		d	ρ	Label	ID
C₁₀×C₄⋊D₄		160		C10xC4:D4	320,1524

Semidirect products G=N:Q with N=C₄⋊D₄ and Q=C₁₀

extension	φ:Q→Out N	d	Label	ID
C₄⋊D₄⋊₁C₁₀ = C₅×C₂²⋊D₈	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:1C10	320,948
C₄⋊D₄⋊₂C₁₀ = C₅×D₄⋊D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:2C10	320,950
C₄⋊D₄⋊₃C₁₀ = C₅×C₈⋊₇D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:3C10	320,967
C₄⋊D₄⋊₄C₁₀ = C₅×C₈⋊₂D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:4C10	320,970
C₄⋊D₄⋊₅C₁₀ = C₅×C₂³⋊₃D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:5C10	320,1536
C₄⋊D₄⋊₆C₁₀ = C₅×C₂².₂₉C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:6C10	320,1537
C₄⋊D₄⋊₇C₁₀ = C₅×C₂².₃₁C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:7C10	320,1539
C₄⋊D₄⋊₈C₁₀ = C₅×C₂².₃₂C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:8C10	320,1540
C₄⋊D₄⋊₉C₁₀ = C₅×C₂².₃₄C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:9C10	320,1542
C₄⋊D₄⋊₁₀C₁₀ = C₅×D₄²	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:10C10	320,1547
C₄⋊D₄⋊₁₁C₁₀ = C₅×D₄⋊₅D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:11C10	320,1548
C₄⋊D₄⋊₁₂C₁₀ = C₅×D₄⋊₆D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:12C10	320,1549
C₄⋊D₄⋊₁₃C₁₀ = C₅×Q₈⋊₅D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:13C10	320,1550
C₄⋊D₄⋊₁₄C₁₀ = C₅×Q₈⋊₆D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:14C10	320,1552
C₄⋊D₄⋊₁₅C₁₀ = C₅×C₂².₄₇C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:15C10	320,1555
C₄⋊D₄⋊₁₆C₁₀ = C₅×C₂².₄₉C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:16C10	320,1557
C₄⋊D₄⋊₁₇C₁₀ = C₅×C₂².₅₄C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4:17C10	320,1562
C₄⋊D₄⋊₁₈C₁₀ = C₅×C₂².₅₆C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4:18C10	320,1564
C₄⋊D₄⋊₁₉C₁₀ = C₅×C₂².₁₉C₂⁴	φ: trivial image	80	C4:D4:19C10	320,1527
C₄⋊D₄⋊₂₀C₁₀ = C₅×C₂².₂₆C₂⁴	φ: trivial image	160	C4:D4:20C10	320,1534

Non-split extensions G=N.Q with N=C₄⋊D₄ and Q=C₁₀

extension	φ:Q→Out N	d	Label	ID
C₄⋊D₄.₁C₁₀ = C₅×C₂².SD₁₆	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	80	C4:D4.1C10	320,132
C₄⋊D₄.₂C₁₀ = C₅×Q₈⋊D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.2C10	320,949
C₄⋊D₄.₃C₁₀ = C₅×C₈⋊₈D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.3C10	320,966
C₄⋊D₄.₄C₁₀ = C₅×C₈⋊D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.4C10	320,969
C₄⋊D₄.₅C₁₀ = C₅×C₂².D₈	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.5C10	320,981
C₄⋊D₄.₆C₁₀ = C₅×C₂³.₄₆D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.6C10	320,982
C₄⋊D₄.₇C₁₀ = C₅×C₂³.₁₉D₄	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.7C10	320,983
C₄⋊D₄.₈C₁₀ = C₅×C₂².₃₃C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.8C10	320,1541
C₄⋊D₄.₉C₁₀ = C₅×C₂².₃₆C₂⁴	φ: C₁₀/C₅ → C₂ ⊆ Out C₄⋊D₄	160	C4:D4.9C10	320,1544
C₄⋊D₄.₁₀C₁₀ = C₅×C₂³.₃₆C₂³	φ: trivial image	160	C4:D4.10C10	320,1531

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4⋊D4 and Q=C10

Extensions 1→N→G→Q→1 with N=C₄⋊D₄ and Q=C₁₀