Finite Group Databasebeta

← C23×C5×D3×C7 #13132981

Subgroups — C23×C5×D3×C7 #13132981

Order 1680.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C7C211yesmaximal, characteristic, complemented
2C22×C5×D3×C7C2114yesmaximal, direct product factor
3C24×C5×C7—31nomaximal, Hall
4C22×C3×C5×C7C2217yescomplemented
5C2×C5×D3×C7C22128yesdirect product factor
6C23×D3×C7C511yesmaximal, characteristic, direct product factor, Hall
7C23×C5×C7—314no—
8C23×C5×C7D311yescharacteristic, direct product factor
9C23×C5×D3C711yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×C7C2317yescomplemented
11C5×D3×C7C2318yesdirect product factor
12C23×C3×C7C2×C511yescharacteristic, complemented
13C22×D3×C7C2×C5114yesdirect product factor
14C22×C5×C7—328no—
15C22×C5×C7C2×D317yesdirect product factor
16C23×C3×C5C2×C711yescharacteristic, complemented
17C22×C5×D3C2×C7114yesdirect product factor
18C24×C7—31noHall
19C3×C5×C7C2411yescharacteristic, complemented, Hall
20C22×C3×C7C22×C517yescomplemented
21C2×D3×C7C22×C5128yesdirect product factor
22C24×C5—31noHall
23C2×C5×C7—38no—
24C2×C5×C7C22×D317yesdirect product factor
25C22×C3×C5C22×C717yescomplemented
26C2×C5×D3C22×C7128yesdirect product factor
27C23×C7—314no—
28C23×C7C5×D311yescharacteristic, direct product factor
29C23×D3C5×C711yescharacteristic, direct product factor, Hall
30C2×C3×C7C23×C517yescomplemented
31D3×C7C23×C518yesdirect product factor
32C23×C5—314no—
33C23×C5D3×C711yescharacteristic, direct product factor
34C5×C7C23×D311yescharacteristic, direct product factor, Hall
35C2×C3×C5C23×C717yescomplemented
36C5×D3C23×C718yesdirect product factor
37C22×C7—328no—
38C22×C7C2×C5×D317yesdirect product factor
39C23×C3C2×C5×C711yescharacteristic, complemented
40C22×D3C2×C5×C7114yesdirect product factor
41C3×C7C24×C511yescharacteristic, complemented, Hall
42C22×C5—328no—
43C22×C5C2×D3×C717yesdirect product factor
44C24—31noSylow
45C3×C5C24×C711yescharacteristic, complemented, Hall
46C2×C7—38no—
47C2×C7C22×C5×D317yesdirect product factor
48C22×C3C22×C5×C717yescomplemented
49C2×D3C22×C5×C7128yesdirect product factor
50C2×C5—38no—
51C2×C5C22×D3×C717yesdirect product factor
52C23—314no—
53C23C5×D3×C711yescharacteristic, direct product factor
54C7C23×C5×D311yescharacteristic, direct product factor, Sylow
55C2×C3C23×C5×C717yescomplemented
56D3C23×C5×C718yesdirect product factor
57C5C23×D3×C711yescharacteristic, direct product factor, Sylow
58C22—328no—
59C22C2×C5×D3×C717yesdirect product factor
60C3C24×C5×C711yescharacteristic, complemented, Sylow
61C2—38no—
62C2C22×C5×D3×C717yesdirect product factor
subgroupG/H
center, hypercenterC23×C5×C7D3
commutator, cosocle, hypocenterC3C24×C5×C7
FrattiniC1G
Fitting, socleC23×C3×C5×C7C2
LCSG ▷ C3
UCSC1 ◁ C23×C5×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C5×D3×C7C2direct (N × H)
4. C22×C3×C5×C7C22semidirect
5. C2×C5×D3×C7C22direct (N × H)
6. C23×D3×C7C5direct (N × H)
8. C23×C5×C7D3direct (N × H)
9. C23×C5×D3C7direct (N × H)
10. C2×C3×C5×C7C23semidirect
11. C5×D3×C7C23direct (N × H)
12. C23×C3×C7C2×C5semidirect
13. C22×D3×C7C2×C5direct (N × H)
15. C22×C5×C7C2×D3direct (N × H)
16. C23×C3×C5C2×C7semidirect
17. C22×C5×D3C2×C7direct (N × H)
19. C3×C5×C7C24semidirect
20. C22×C3×C7C22×C5semidirect
21. C2×D3×C7C22×C5direct (N × H)
24. C2×C5×C7C22×D3direct (N × H)
25. C22×C3×C5C22×C7semidirect
26. C2×C5×D3C22×C7direct (N × H)
28. C23×C7C5×D3direct (N × H)
29. C23×D3C5×C7direct (N × H)
30. C2×C3×C7C23×C5semidirect
31. D3×C7C23×C5direct (N × H)
33. C23×C5D3×C7direct (N × H)
34. C5×C7C23×D3direct (N × H)
35. C2×C3×C5C23×C7semidirect
36. C5×D3C23×C7direct (N × H)
38. C22×C7C2×C5×D3direct (N × H)
39. C23×C3C2×C5×C7semidirect
40. C22×D3C2×C5×C7direct (N × H)
41. C3×C7C24×C5semidirect
43. C22×C5C2×D3×C7direct (N × H)
45. C3×C5C24×C7semidirect
47. C2×C7C22×C5×D3direct (N × H)
48. C22×C3C22×C5×C7semidirect
49. C2×D3C22×C5×C7direct (N × H)
51. C2×C5C22×D3×C7direct (N × H)
53. C23C5×D3×C7direct (N × H)
54. C7C23×C5×D3direct (N × H)
55. C2×C3C23×C5×C7semidirect
56. D3C23×C5×C7direct (N × H)
57. C5C23×D3×C7direct (N × H)
59. C22C2×C5×D3×C7direct (N × H)
60. C3C24×C5×C7semidirect
62. C2C22×C5×D3×C7direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C3×C5×C72
C22×C5×D3×C72
C24×C5×C73
C23×D3×C75
C23×C5×D37