Finite Group Databasebeta

← C23×C3×C5×C7×C13 #72189463

Subgroups — C23×C3×C5×C7×C13 #72189463

Order 10920.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C7×C13C311yesmaximal, characteristic, direct product factor, Hall
2C23×C3×C7×C13C511yesmaximal, characteristic, direct product factor, Hall
3C22×C3×C5×C7×C13C217yesmaximal, direct product factor
4C2×C3×C5×C7×C13C2217yesdirect product factor
5C22×C5×C7×C13C2×C317yesdirect product factor
6C23×C3×C5×C13C711yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C7×C13C2311yescharacteristic, direct product factor, Hall
8C22×C3×C7×C13C2×C517yesdirect product factor
9C2×C5×C7×C13C22×C317yesdirect product factor
10C23×C3×C5×C7C1311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×C13C2×C717yesdirect product factor
12C23×C7×C13C3×C511yescharacteristic, direct product factor, Hall
13C2×C3×C7×C13C22×C517yesdirect product factor
14C23×C5×C13C3×C711yescharacteristic, direct product factor, Hall
15C5×C7×C13C23×C311yescharacteristic, direct product factor, Hall
16C22×C3×C5×C7C2×C1317yesdirect product factor
17C2×C3×C5×C13C22×C717yesdirect product factor
18C22×C7×C13C2×C3×C517yesdirect product factor
19C23×C3×C13C5×C711yescharacteristic, direct product factor, Hall
20C23×C5×C7C3×C1311yescharacteristic, direct product factor, Hall
21C3×C7×C13C23×C511yescharacteristic, direct product factor, Hall
22C22×C5×C13C2×C3×C717yesdirect product factor
23C2×C3×C5×C7C22×C1317yesdirect product factor
24C3×C5×C13C23×C711yescharacteristic, direct product factor, Hall
25C2×C7×C13C22×C3×C517yesdirect product factor
26C23×C3×C7C5×C1311yescharacteristic, direct product factor, Hall
27C22×C3×C13C2×C5×C717yesdirect product factor
28C22×C5×C7C2×C3×C1317yesdirect product factor
29C2×C5×C13C22×C3×C717yesdirect product factor
30C23×C3×C5C7×C1311yescharacteristic, direct product factor, Hall
31C3×C5×C7C23×C1311yescharacteristic, direct product factor, Hall
32C23×C13C3×C5×C711yescharacteristic, direct product factor, Hall
33C7×C13C23×C3×C511yescharacteristic, direct product factor, Hall
34C22×C3×C7C2×C5×C1317yesdirect product factor
35C2×C3×C13C22×C5×C717yesdirect product factor
36C2×C5×C7C22×C3×C1317yesdirect product factor
37C5×C13C23×C3×C711yescharacteristic, direct product factor, Hall
38C22×C3×C5C2×C7×C1317yesdirect product factor
39C23×C7C3×C5×C1311yescharacteristic, direct product factor, Hall
40C22×C13C2×C3×C5×C717yesdirect product factor
41C2×C3×C7C22×C5×C1317yesdirect product factor
42C23×C5C3×C7×C1311yescharacteristic, direct product factor, Hall
43C3×C13C23×C5×C711yescharacteristic, direct product factor, Hall
44C5×C7C23×C3×C1311yescharacteristic, direct product factor, Hall
45C2×C3×C5C22×C7×C1317yesdirect product factor
46C22×C7C2×C3×C5×C1317yesdirect product factor
47C2×C13C22×C3×C5×C717yesdirect product factor
48C23×C3C5×C7×C1311yescharacteristic, direct product factor, Hall
49C3×C7C23×C5×C1311yescharacteristic, direct product factor, Hall
50C22×C5C2×C3×C7×C1317yesdirect product factor
51C3×C5C23×C7×C1311yescharacteristic, direct product factor, Hall
52C2×C7C22×C3×C5×C1317yesdirect product factor
53C13C23×C3×C5×C711yescharacteristic, direct product factor, Sylow
54C22×C3C2×C5×C7×C1317yesdirect product factor
55C2×C5C22×C3×C7×C1317yesdirect product factor
56C23C3×C5×C7×C1311yescharacteristic, direct product factor, Sylow
57C7C23×C3×C5×C1311yescharacteristic, direct product factor, Sylow
58C2×C3C22×C5×C7×C1317yesdirect product factor
59C5C23×C3×C7×C1311yescharacteristic, direct product factor, Sylow
60C22C2×C3×C5×C7×C1317yesdirect product factor
61C3C23×C5×C7×C1311yescharacteristic, direct product factor, Sylow
62C2C22×C3×C5×C7×C1317yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C5×C7×C13C3direct (N × H)
2. C23×C3×C7×C13C5direct (N × H)
3. C22×C3×C5×C7×C13C2direct (N × H)
4. C2×C3×C5×C7×C13C22direct (N × H)
5. C22×C5×C7×C13C2×C3direct (N × H)
6. C23×C3×C5×C13C7direct (N × H)
7. C3×C5×C7×C13C23direct (N × H)
8. C22×C3×C7×C13C2×C5direct (N × H)
9. C2×C5×C7×C13C22×C3direct (N × H)
10. C23×C3×C5×C7C13direct (N × H)
11. C22×C3×C5×C13C2×C7direct (N × H)
12. C23×C7×C13C3×C5direct (N × H)
13. C2×C3×C7×C13C22×C5direct (N × H)
14. C23×C5×C13C3×C7direct (N × H)
15. C5×C7×C13C23×C3direct (N × H)
16. C22×C3×C5×C7C2×C13direct (N × H)
17. C2×C3×C5×C13C22×C7direct (N × H)
18. C22×C7×C13C2×C3×C5direct (N × H)
19. C23×C3×C13C5×C7direct (N × H)
20. C23×C5×C7C3×C13direct (N × H)
21. C3×C7×C13C23×C5direct (N × H)
22. C22×C5×C13C2×C3×C7direct (N × H)
23. C2×C3×C5×C7C22×C13direct (N × H)
24. C3×C5×C13C23×C7direct (N × H)
25. C2×C7×C13C22×C3×C5direct (N × H)
26. C23×C3×C7C5×C13direct (N × H)
27. C22×C3×C13C2×C5×C7direct (N × H)
28. C22×C5×C7C2×C3×C13direct (N × H)
29. C2×C5×C13C22×C3×C7direct (N × H)
30. C23×C3×C5C7×C13direct (N × H)
31. C3×C5×C7C23×C13direct (N × H)
32. C23×C13C3×C5×C7direct (N × H)
33. C7×C13C23×C3×C5direct (N × H)
34. C22×C3×C7C2×C5×C13direct (N × H)
35. C2×C3×C13C22×C5×C7direct (N × H)
36. C2×C5×C7C22×C3×C13direct (N × H)
37. C5×C13C23×C3×C7direct (N × H)
38. C22×C3×C5C2×C7×C13direct (N × H)
39. C23×C7C3×C5×C13direct (N × H)
40. C22×C13C2×C3×C5×C7direct (N × H)
41. C2×C3×C7C22×C5×C13direct (N × H)
42. C23×C5C3×C7×C13direct (N × H)
43. C3×C13C23×C5×C7direct (N × H)
44. C5×C7C23×C3×C13direct (N × H)
45. C2×C3×C5C22×C7×C13direct (N × H)
46. C22×C7C2×C3×C5×C13direct (N × H)
47. C2×C13C22×C3×C5×C7direct (N × H)
48. C23×C3C5×C7×C13direct (N × H)
49. C3×C7C23×C5×C13direct (N × H)
50. C22×C5C2×C3×C7×C13direct (N × H)
51. C3×C5C23×C7×C13direct (N × H)
52. C2×C7C22×C3×C5×C13direct (N × H)
53. C13C23×C3×C5×C7direct (N × H)
54. C22×C3C2×C5×C7×C13direct (N × H)
55. C2×C5C22×C3×C7×C13direct (N × H)
56. C23C3×C5×C7×C13direct (N × H)
57. C7C23×C3×C5×C13direct (N × H)
58. C2×C3C22×C5×C7×C13direct (N × H)
59. C5C23×C3×C7×C13direct (N × H)
60. C22C2×C3×C5×C7×C13direct (N × H)
61. C3C23×C5×C7×C13direct (N × H)
62. C2C22×C3×C5×C7×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C7×C133
C23×C3×C7×C135
C22×C3×C5×C7×C132
C23×C3×C5×C137
C23×C3×C5×C713