Finite Group Databasebeta

← C26×C34×C5 #72203119

Subgroups — C26×C34×C5 #72203119

Order 25920.

1197800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C34×C5C2163yesmaximal, direct product factor
2C26×C33×C5C3140yesmaximal, direct product factor
3C24×C34×C5C221651yesdirect product factor
4C26×C34C511yesmaximal, characteristic, direct product factor, Hall
5C25×C33×C5C2×C312520yesdirect product factor
6C23×C34×C5C2311395yesdirect product factor
7C26×C32×C5C321130yesdirect product factor
8C25×C34C2×C5163yesdirect product factor
9C24×C33×C5C22×C3126040yesdirect product factor
10C26×C33C3×C5140yesdirect product factor
11C22×C34×C5C241651yesdirect product factor
12C25×C32×C5C2×C3218190yesdirect product factor
13C24×C34C22×C51651yesdirect product factor
14C23×C33×C5C23×C3155800yesdirect product factor
15C26×C3×C5C33140yesdirect product factor
16C25×C33C2×C3×C512520yesdirect product factor
17C2×C34×C5C25163yesdirect product factor
18C24×C32×C5C22×C32184630yesdirect product factor
19C23×C34C23×C511395yesdirect product factor
20C26×C32C32×C51130yesdirect product factor
21C22×C33×C5C24×C3126040yesdirect product factor
22C25×C3×C5C2×C3312520yesdirect product factor
23C24×C33C22×C3×C5126040yesdirect product factor
24C34×C5C2611yescharacteristic, direct product factor, Hall
25C23×C32×C5C23×C321181350yesdirect product factor
26C22×C34C24×C51651yesdirect product factor
27C26×C5C3411yescharacteristic, direct product factor, Hall
28C25×C32C2×C32×C518190yesdirect product factor
29C2×C33×C5C25×C312520yesdirect product factor
30C24×C3×C5C22×C33126040yesdirect product factor
31C23×C33C23×C3×C5155800yesdirect product factor
32C26×C3C33×C5140yesdirect product factor
33C22×C32×C5C24×C32184630yesdirect product factor
34C2×C34C25×C5163yesdirect product factor
35C25×C5C2×C34163yesdirect product factor
36C24×C32C22×C32×C5184630yesdirect product factor
37C33×C5C26×C3140yesdirect product factor
38C23×C3×C5C23×C33155800yesdirect product factor
39C22×C33C24×C3×C5126040yesdirect product factor
40C25×C3C2×C33×C512520yesdirect product factor
41C2×C32×C5C25×C3218190yesdirect product factor
42C34C26×C511yescharacteristic, direct product factor, Sylow
43C24×C5C22×C341651yesdirect product factor
44C23×C32C23×C32×C51181350yesdirect product factor
45C26C34×C511yescharacteristic, direct product factor, Sylow
46C22×C3×C5C24×C33126040yesdirect product factor
47C2×C33C25×C3×C512520yesdirect product factor
48C24×C3C22×C33×C5126040yesdirect product factor
49C32×C5C26×C321130yesdirect product factor
50C23×C5C23×C3411395yesdirect product factor
51C22×C32C24×C32×C5184630yesdirect product factor
52C25C2×C34×C5163yesdirect product factor
53C2×C3×C5C25×C3312520yesdirect product factor
54C33C26×C3×C5140yesdirect product factor
55C23×C3C23×C33×C5155800yesdirect product factor
56C22×C5C24×C341651yesdirect product factor
57C2×C32C25×C32×C518190yesdirect product factor
58C24C22×C34×C51651yesdirect product factor
59C3×C5C26×C33140yesdirect product factor
60C22×C3C24×C33×C5126040yesdirect product factor
61C2×C5C25×C34163yesdirect product factor
62C32C26×C32×C51130yesdirect product factor
63C23C23×C34×C511395yesdirect product factor
64C2×C3C25×C33×C512520yesdirect product factor
65C5C26×C3411yescharacteristic, direct product factor, Sylow
66C22C24×C34×C51651yesdirect product factor
67C3C26×C33×C5140yesdirect product factor
68C2C25×C34×C5163yesdirect 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. C25×C34×C5C2direct (N × H)
2. C26×C33×C5C3direct (N × H)
3. C24×C34×C5C22direct (N × H)
4. C26×C34C5direct (N × H)
5. C25×C33×C5C2×C3direct (N × H)
6. C23×C34×C5C23direct (N × H)
7. C26×C32×C5C32direct (N × H)
8. C25×C34C2×C5direct (N × H)
9. C24×C33×C5C22×C3direct (N × H)
10. C26×C33C3×C5direct (N × H)
11. C22×C34×C5C24direct (N × H)
12. C25×C32×C5C2×C32direct (N × H)
13. C24×C34C22×C5direct (N × H)
14. C23×C33×C5C23×C3direct (N × H)
15. C26×C3×C5C33direct (N × H)
16. C25×C33C2×C3×C5direct (N × H)
17. C2×C34×C5C25direct (N × H)
18. C24×C32×C5C22×C32direct (N × H)
19. C23×C34C23×C5direct (N × H)
20. C26×C32C32×C5direct (N × H)
21. C22×C33×C5C24×C3direct (N × H)
22. C25×C3×C5C2×C33direct (N × H)
23. C24×C33C22×C3×C5direct (N × H)
24. C34×C5C26direct (N × H)
25. C23×C32×C5C23×C32direct (N × H)
26. C22×C34C24×C5direct (N × H)
27. C26×C5C34direct (N × H)
28. C25×C32C2×C32×C5direct (N × H)
29. C2×C33×C5C25×C3direct (N × H)
30. C24×C3×C5C22×C33direct (N × H)
31. C23×C33C23×C3×C5direct (N × H)
32. C26×C3C33×C5direct (N × H)
33. C22×C32×C5C24×C32direct (N × H)
34. C2×C34C25×C5direct (N × H)
35. C25×C5C2×C34direct (N × H)
36. C24×C32C22×C32×C5direct (N × H)
37. C33×C5C26×C3direct (N × H)
38. C23×C3×C5C23×C33direct (N × H)
39. C22×C33C24×C3×C5direct (N × H)
40. C25×C3C2×C33×C5direct (N × H)
41. C2×C32×C5C25×C32direct (N × H)
42. C34C26×C5direct (N × H)
43. C24×C5C22×C34direct (N × H)
44. C23×C32C23×C32×C5direct (N × H)
45. C26C34×C5direct (N × H)
46. C22×C3×C5C24×C33direct (N × H)
47. C2×C33C25×C3×C5direct (N × H)
48. C24×C3C22×C33×C5direct (N × H)
49. C32×C5C26×C32direct (N × H)
50. C23×C5C23×C34direct (N × H)
51. C22×C32C24×C32×C5direct (N × H)
52. C25C2×C34×C5direct (N × H)
53. C2×C3×C5C25×C33direct (N × H)
54. C33C26×C3×C5direct (N × H)
55. C23×C3C23×C33×C5direct (N × H)
56. C22×C5C24×C34direct (N × H)
57. C2×C32C25×C32×C5direct (N × H)
58. C24C22×C34×C5direct (N × H)
59. C3×C5C26×C33direct (N × H)
60. C22×C3C24×C33×C5direct (N × H)
61. C2×C5C25×C34direct (N × H)
62. C32C26×C32×C5direct (N × H)
63. C23C23×C34×C5direct (N × H)
64. C2×C3C25×C33×C5direct (N × H)
65. C5C26×C34direct (N × H)
66. C22C24×C34×C5direct (N × H)
67. C3C26×C33×C5direct (N × H)
68. C2C25×C34×C5direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C34×C52
C26×C33×C53
C26×C345