Extensions 1→N→G→Q→1 with N=C₅⋊Q₁₆ and Q=C₂²

Direct product G=N×Q with N=C₅⋊Q₁₆ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₅⋊Q₁₆		320		C2^2xC5:Q16	320,1481

Semidirect products G=N:Q with N=C₅⋊Q₁₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊Q₁₆⋊₁C₂² = D₂₀.₂₉D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	80	4	C5:Q16:1C2^2	320,1434
C₅⋊Q₁₆⋊₂C₂² = D₈⋊₁₁D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	80	4	C5:Q16:2C2^2	320,1442
C₅⋊Q₁₆⋊₃C₂² = SD₁₆⋊D₁₀	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	80	8-	C5:Q16:3C2^2	320,1445
C₅⋊Q₁₆⋊₄C₂² = D₅×C₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	80	8-	C5:Q16:4C2^2	320,1448
C₅⋊Q₁₆⋊₅C₂² = D₄₀⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	80	8+	C5:Q16:5C2^2	320,1449
C₅⋊Q₁₆⋊₆C₂² = C₂×SD₁₆⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:6C2^2	320,1432
C₅⋊Q₁₆⋊₇C₂² = C₂×SD₁₆⋊₃D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:7C2^2	320,1433
C₅⋊Q₁₆⋊₈C₂² = C₂×D₅×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:8C2^2	320,1435
C₅⋊Q₁₆⋊₉C₂² = C₂×Q₁₆⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:9C2^2	320,1436
C₅⋊Q₁₆⋊₁₀C₂² = D₅×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	4	C5:Q16:10C2^2	320,1439
C₅⋊Q₁₆⋊₁₁C₂² = Q₁₆⋊D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	4	C5:Q16:11C2^2	320,1440
C₅⋊Q₁₆⋊₁₂C₂² = D₈⋊₅D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	8+	C5:Q16:12C2^2	320,1446
C₅⋊Q₁₆⋊₁₃C₂² = D₈⋊₆D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	8-	C5:Q16:13C2^2	320,1447
C₅⋊Q₁₆⋊₁₄C₂² = C₄₀.C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	8+	C5:Q16:14C2^2	320,1450
C₅⋊Q₁₆⋊₁₅C₂² = C₂×C₂₀.C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:15C2^2	320,1480
C₅⋊Q₁₆⋊₁₆C₂² = C₂₀.C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	4	C5:Q16:16C2^2	320,1494
C₅⋊Q₁₆⋊₁₇C₂² = C₂×D₄.₉D₁₀	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160		C5:Q16:17C2^2	320,1495
C₅⋊Q₁₆⋊₁₈C₂² = D₂₀.₃₃C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	8-	C5:Q16:18C2^2	320,1508
C₅⋊Q₁₆⋊₁₉C₂² = D₂₀.₃₄C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	80	8+	C5:Q16:19C2^2	320,1509
C₅⋊Q₁₆⋊₂₀C₂² = C₂×D₄.₈D₁₀	φ: trivial image	160		C5:Q16:20C2^2	320,1493
C₅⋊Q₁₆⋊₂₁C₂² = D₂₀.₃₂C₂³	φ: trivial image	80	8+	C5:Q16:21C2^2	320,1507

Non-split extensions G=N.Q with N=C₅⋊Q₁₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊Q₁₆.₁C₂² = D₂₀.₃₀D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	160	4	C5:Q16.1C2^2	320,1438
C₅⋊Q₁₆.₂C₂² = D₂₀.₄₇D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅⋊Q₁₆	160	4-	C5:Q16.2C2^2	320,1443
C₅⋊Q₁₆.₃C₂² = D₂₀.₄₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅⋊Q₁₆	160	8-	C5:Q16.3C2^2	320,1451
C₅⋊Q₁₆.₄C₂² = D₂₀.₃₅C₂³	φ: trivial image	160	8-	C5:Q16.4C2^2	320,1510

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5⋊Q16 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅⋊Q₁₆ and Q=C₂²