Finite Group Databasebeta

← C25×C3×C52×C13 #72207997

Subgroups — C25×C3×C52×C13 #72207997

Order 31200.

11968 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C52×C13C2131yesmaximal, direct product factor
2C25×C52×C13C311yesmaximal, characteristic, direct product factor, Hall
3C23×C3×C52×C13C221155yesdirect product factor
4C25×C3×C5×C13C516yesmaximal, direct product factor
5C24×C52×C13C2×C3131yesdirect product factor
6C24×C3×C5×C13C2×C51186yesdirect product factor
7C23×C52×C13C22×C31155yesdirect product factor
8C25×C3×C52C1311yesmaximal, characteristic, direct product factor, Hall
9C25×C5×C13C3×C516yesdirect product factor
10C22×C3×C52×C13C231155yesdirect product factor
11C2×C3×C52×C13C24131yesdirect product factor
12C23×C3×C5×C13C22×C51930yesdirect product factor
13C22×C52×C13C23×C31155yesdirect product factor
14C25×C3×C13C5211yescharacteristic, direct product factor, Hall
15C24×C3×C52C2×C13131yesdirect product factor
16C24×C5×C13C2×C3×C51186yesdirect product factor
17C3×C52×C13C2511yescharacteristic, direct product factor, Hall
18C25×C52C3×C1311yescharacteristic, direct product factor, Hall
19C22×C3×C5×C13C23×C51930yesdirect product factor
20C2×C52×C13C24×C3131yesdirect product factor
21C24×C3×C13C2×C52131yesdirect product factor
22C23×C3×C52C22×C131155yesdirect product factor
23C23×C5×C13C22×C3×C51930yesdirect product factor
24C25×C3×C5C5×C1316yesdirect product factor
25C25×C13C3×C5211yescharacteristic, direct product factor, Hall
26C24×C52C2×C3×C13131yesdirect product factor
27C2×C3×C5×C13C24×C51186yesdirect product factor
28C52×C13C25×C311yescharacteristic, direct product factor, Hall
29C23×C3×C13C22×C521155yesdirect product factor
30C22×C3×C52C23×C131155yesdirect product factor
31C22×C5×C13C23×C3×C51930yesdirect product factor
32C24×C3×C5C2×C5×C131186yesdirect product factor
33C24×C13C2×C3×C52131yesdirect product factor
34C23×C52C22×C3×C131155yesdirect product factor
35C3×C5×C13C25×C516yesdirect product factor
36C25×C5C3×C5×C1316yesdirect product factor
37C22×C3×C13C23×C521155yesdirect product factor
38C2×C3×C52C24×C13131yesdirect product factor
39C2×C5×C13C24×C3×C51186yesdirect product factor
40C23×C3×C5C22×C5×C131930yesdirect product factor
41C23×C13C22×C3×C521155yesdirect product factor
42C22×C52C23×C3×C131155yesdirect product factor
43C25×C3C52×C1311yescharacteristic, direct product factor, Hall
44C24×C5C2×C3×C5×C131186yesdirect product factor
45C2×C3×C13C24×C52131yesdirect product factor
46C3×C52C25×C1311yescharacteristic, direct product factor, Hall
47C5×C13C25×C3×C516yesdirect product factor
48C22×C3×C5C23×C5×C131930yesdirect product factor
49C22×C13C23×C3×C521155yesdirect product factor
50C2×C52C24×C3×C13131yesdirect product factor
51C24×C3C2×C52×C13131yesdirect product factor
52C23×C5C22×C3×C5×C131930yesdirect product factor
53C3×C13C25×C5211yescharacteristic, direct product factor, Hall
54C25C3×C52×C1311yescharacteristic, direct product factor, Sylow
55C2×C3×C5C24×C5×C131186yesdirect product factor
56C2×C13C24×C3×C52131yesdirect product factor
57C52C25×C3×C1311yescharacteristic, direct product factor, Sylow
58C23×C3C22×C52×C131155yesdirect product factor
59C22×C5C23×C3×C5×C131930yesdirect product factor
60C24C2×C3×C52×C13131yesdirect product factor
61C3×C5C25×C5×C1316yesdirect product factor
62C13C25×C3×C5211yescharacteristic, direct product factor, Sylow
63C22×C3C23×C52×C131155yesdirect product factor
64C2×C5C24×C3×C5×C131186yesdirect product factor
65C23C22×C3×C52×C131155yesdirect product factor
66C2×C3C24×C52×C13131yesdirect product factor
67C5C25×C3×C5×C1316yesdirect product factor
68C22C23×C3×C52×C131155yesdirect product factor
69C3C25×C52×C1311yescharacteristic, direct product factor, Sylow
70C2C24×C3×C52×C13131yesdirect 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. C24×C3×C52×C13C2direct (N × H)
2. C25×C52×C13C3direct (N × H)
3. C23×C3×C52×C13C22direct (N × H)
4. C25×C3×C5×C13C5direct (N × H)
5. C24×C52×C13C2×C3direct (N × H)
6. C24×C3×C5×C13C2×C5direct (N × H)
7. C23×C52×C13C22×C3direct (N × H)
8. C25×C3×C52C13direct (N × H)
9. C25×C5×C13C3×C5direct (N × H)
10. C22×C3×C52×C13C23direct (N × H)
11. C2×C3×C52×C13C24direct (N × H)
12. C23×C3×C5×C13C22×C5direct (N × H)
13. C22×C52×C13C23×C3direct (N × H)
14. C25×C3×C13C52direct (N × H)
15. C24×C3×C52C2×C13direct (N × H)
16. C24×C5×C13C2×C3×C5direct (N × H)
17. C3×C52×C13C25direct (N × H)
18. C25×C52C3×C13direct (N × H)
19. C22×C3×C5×C13C23×C5direct (N × H)
20. C2×C52×C13C24×C3direct (N × H)
21. C24×C3×C13C2×C52direct (N × H)
22. C23×C3×C52C22×C13direct (N × H)
23. C23×C5×C13C22×C3×C5direct (N × H)
24. C25×C3×C5C5×C13direct (N × H)
25. C25×C13C3×C52direct (N × H)
26. C24×C52C2×C3×C13direct (N × H)
27. C2×C3×C5×C13C24×C5direct (N × H)
28. C52×C13C25×C3direct (N × H)
29. C23×C3×C13C22×C52direct (N × H)
30. C22×C3×C52C23×C13direct (N × H)
31. C22×C5×C13C23×C3×C5direct (N × H)
32. C24×C3×C5C2×C5×C13direct (N × H)
33. C24×C13C2×C3×C52direct (N × H)
34. C23×C52C22×C3×C13direct (N × H)
35. C3×C5×C13C25×C5direct (N × H)
36. C25×C5C3×C5×C13direct (N × H)
37. C22×C3×C13C23×C52direct (N × H)
38. C2×C3×C52C24×C13direct (N × H)
39. C2×C5×C13C24×C3×C5direct (N × H)
40. C23×C3×C5C22×C5×C13direct (N × H)
41. C23×C13C22×C3×C52direct (N × H)
42. C22×C52C23×C3×C13direct (N × H)
43. C25×C3C52×C13direct (N × H)
44. C24×C5C2×C3×C5×C13direct (N × H)
45. C2×C3×C13C24×C52direct (N × H)
46. C3×C52C25×C13direct (N × H)
47. C5×C13C25×C3×C5direct (N × H)
48. C22×C3×C5C23×C5×C13direct (N × H)
49. C22×C13C23×C3×C52direct (N × H)
50. C2×C52C24×C3×C13direct (N × H)
51. C24×C3C2×C52×C13direct (N × H)
52. C23×C5C22×C3×C5×C13direct (N × H)
53. C3×C13C25×C52direct (N × H)
54. C25C3×C52×C13direct (N × H)
55. C2×C3×C5C24×C5×C13direct (N × H)
56. C2×C13C24×C3×C52direct (N × H)
57. C52C25×C3×C13direct (N × H)
58. C23×C3C22×C52×C13direct (N × H)
59. C22×C5C23×C3×C5×C13direct (N × H)
60. C24C2×C3×C52×C13direct (N × H)
61. C3×C5C25×C5×C13direct (N × H)
62. C13C25×C3×C52direct (N × H)
63. C22×C3C23×C52×C13direct (N × H)
64. C2×C5C24×C3×C5×C13direct (N × H)
65. C23C22×C3×C52×C13direct (N × H)
66. C2×C3C24×C52×C13direct (N × H)
67. C5C25×C3×C5×C13direct (N × H)
68. C22C23×C3×C52×C13direct (N × H)
69. C3C25×C52×C13direct (N × H)
70. C2C24×C3×C52×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C52×C132
C25×C52×C133
C25×C3×C5×C135
C25×C3×C5213