Extensions 1→N→G→Q→1 with N=C₅⋊₂C₈ and Q=C₂³

Direct product G=N×Q with N=C₅⋊₂C₈ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₅⋊₂C₈		320		C2^3xC5:2C8	320,1452

Semidirect products G=N:Q with N=C₅⋊₂C₈ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈⋊₁C₂³ = C₂×D₈⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80		C5:2C8:1C2^3	320,1427
C₅⋊₂C₈⋊₂C₂³ = C₂×D₄₀⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80		C5:2C8:2C2^3	320,1431
C₅⋊₂C₈⋊₃C₂³ = D₅×C₈⋊C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	40	8+	C5:2C8:3C2^3	320,1444
C₅⋊₂C₈⋊₄C₂³ = C₂×D₄.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80		C5:2C8:4C2^3	320,1465
C₅⋊₂C₈⋊₅C₂³ = C₂×D₄⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80		C5:2C8:5C2^3	320,1492
C₅⋊₂C₈⋊₆C₂³ = C₂×D₅×D₈	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80		C5:2C8:6C2^3	320,1426
C₅⋊₂C₈⋊₇C₂³ = C₂×D₅×SD₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80		C5:2C8:7C2^3	320,1430
C₅⋊₂C₈⋊₈C₂³ = C₂²×D₄⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8:8C2^3	320,1464
C₅⋊₂C₈⋊₉C₂³ = C₂²×D₄.D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8:9C2^3	320,1466
C₅⋊₂C₈⋊₁₀C₂³ = C₂²×Q₈⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8:10C2^3	320,1479
C₅⋊₂C₈⋊₁₁C₂³ = C₂²×C₈⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8:11C2^3	320,1409
C₅⋊₂C₈⋊₁₂C₂³ = C₂×D₅×M₄(2)	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80		C5:2C8:12C2^3	320,1415
C₅⋊₂C₈⋊₁₃C₂³ = C₂²×C₄.Dic₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8:13C2^3	320,1453
C₅⋊₂C₈⋊₁₄C₂³ = D₅×C₂²×C₈	φ: trivial image	160		C5:2C8:14C2^3	320,1408

Non-split extensions G=N.Q with N=C₅⋊₂C₈ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈.₁C₂³ = D₈⋊₁₃D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.1C2^3	320,1429
C₅⋊₂C₈.₂C₂³ = C₂×SD₁₆⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160		C5:2C8.2C2^3	320,1432
C₅⋊₂C₈.₃C₂³ = D₂₀.₂₉D₄	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.3C2^3	320,1434
C₅⋊₂C₈.₄C₂³ = C₂×Q₁₆⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160		C5:2C8.4C2^3	320,1436
C₅⋊₂C₈.₅C₂³ = D₂₀.₃₀D₄	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160	4	C5:2C8.5C2^3	320,1438
C₅⋊₂C₈.₆C₂³ = Q₁₆⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.6C2^3	320,1440
C₅⋊₂C₈.₇C₂³ = D₈⋊₁₅D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4+	C5:2C8.7C2^3	320,1441
C₅⋊₂C₈.₈C₂³ = D₈⋊₁₁D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.8C2^3	320,1442
C₅⋊₂C₈.₉C₂³ = D₂₀.₄₇D₄	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160	4-	C5:2C8.9C2^3	320,1443
C₅⋊₂C₈.₁₀C₂³ = SD₁₆⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8-	C5:2C8.10C2^3	320,1445
C₅⋊₂C₈.₁₁C₂³ = D₅×C₈.C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8-	C5:2C8.11C2^3	320,1448
C₅⋊₂C₈.₁₂C₂³ = D₄₀⋊C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8+	C5:2C8.12C2^3	320,1449
C₅⋊₂C₈.₁₃C₂³ = C₂×C₂₀.C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160		C5:2C8.13C2^3	320,1480
C₅⋊₂C₈.₁₄C₂³ = C₂₀.C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.14C2^3	320,1494
C₅⋊₂C₈.₁₅C₂³ = C₂×D₄.₉D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160		C5:2C8.15C2^3	320,1495
C₅⋊₂C₈.₁₆C₂³ = D₂₀.₃₂C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8+	C5:2C8.16C2^3	320,1507
C₅⋊₂C₈.₁₇C₂³ = D₂₀.₃₃C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8-	C5:2C8.17C2^3	320,1508
C₅⋊₂C₈.₁₈C₂³ = D₂₀.₃₄C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	80	8+	C5:2C8.18C2^3	320,1509
C₅⋊₂C₈.₁₉C₂³ = D₂₀.₃₅C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₅⋊₂C₈	160	8-	C5:2C8.19C2^3	320,1510
C₅⋊₂C₈.₂₀C₂³ = C₂×D₈⋊₃D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.20C2^3	320,1428
C₅⋊₂C₈.₂₁C₂³ = C₂×SD₁₆⋊₃D₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.21C2^3	320,1433
C₅⋊₂C₈.₂₂C₂³ = C₂×D₅×Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.22C2^3	320,1435
C₅⋊₂C₈.₂₃C₂³ = C₂×Q₈.D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.23C2^3	320,1437
C₅⋊₂C₈.₂₄C₂³ = D₅×C₄○D₈	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.24C2^3	320,1439
C₅⋊₂C₈.₂₅C₂³ = D₈⋊₅D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	8+	C5:2C8.25C2^3	320,1446
C₅⋊₂C₈.₂₆C₂³ = D₈⋊₆D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	8-	C5:2C8.26C2^3	320,1447
C₅⋊₂C₈.₂₇C₂³ = C₄₀.C₂³	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	8+	C5:2C8.27C2^3	320,1450
C₅⋊₂C₈.₂₈C₂³ = D₂₀.₄₄D₄	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160	8-	C5:2C8.28C2^3	320,1451
C₅⋊₂C₈.₂₉C₂³ = C₂²×C₅⋊Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	320		C5:2C8.29C2^3	320,1481
C₅⋊₂C₈.₃₀C₂³ = C₂×D₄.₈D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.30C2^3	320,1493
C₅⋊₂C₈.₃₁C₂³ = C₂×D₂₀.₃C₄	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.31C2^3	320,1410
C₅⋊₂C₈.₃₂C₂³ = C₄₀.₄₇C₂³	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.32C2^3	320,1417
C₅⋊₂C₈.₃₃C₂³ = C₂₀.₇₂C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.33C2^3	320,1422
C₅⋊₂C₈.₃₄C₂³ = C₂₀.₇₆C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.34C2^3	320,1491
C₅⋊₂C₈.₃₅C₂³ = C₂×D₅⋊C₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.35C2^3	320,1051
C₅⋊₂C₈.₃₆C₂³ = C₂×C₈.F₅	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.36C2^3	320,1052
C₅⋊₂C₈.₃₇C₂³ = D₅⋊M₅(2)	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.37C2^3	320,1053
C₅⋊₂C₈.₃₈C₂³ = Dic₁₀.C₈	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160	8	C5:2C8.38C2^3	320,1063
C₅⋊₂C₈.₃₉C₂³ = C₂²×C₅⋊C₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	320		C5:2C8.39C2^3	320,1080
C₅⋊₂C₈.₄₀C₂³ = C₂×C₂₀.C₈	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160		C5:2C8.40C2^3	320,1081
C₅⋊₂C₈.₄₁C₂³ = C₅⋊C₁₆.C₂²	φ: C₂³/C₂² → C₂ ⊆ Out C₅⋊₂C₈	160	8	C5:2C8.41C2^3	320,1129
C₅⋊₂C₈.₄₂C₂³ = C₂×D₂₀.₂C₄	φ: trivial image	160		C5:2C8.42C2^3	320,1416
C₅⋊₂C₈.₄₃C₂³ = D₅×C₈○D₄	φ: trivial image	80	4	C5:2C8.43C2^3	320,1421
C₅⋊₂C₈.₄₄C₂³ = C₂×D₄.Dic₅	φ: trivial image	160		C5:2C8.44C2^3	320,1490

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5⋊2C8 and Q=C23

Extensions 1→N→G→Q→1 with N=C₅⋊₂C₈ and Q=C₂³