Finite Group Databasebeta

← C26×C3×C5×C13 #72190829

Subgroups — C26×C3×C5×C13 #72190829

Order 12480.

22600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×C5×C13C2163yesmaximal, direct product factor
2C26×C5×C13C311yesmaximal, characteristic, direct product factor, Hall
3C24×C3×C5×C13C221651yesdirect product factor
4C26×C3×C13C511yesmaximal, characteristic, direct product factor, Hall
5C25×C5×C13C2×C3163yesdirect product factor
6C23×C3×C5×C13C2311395yesdirect product factor
7C25×C3×C13C2×C5163yesdirect product factor
8C24×C5×C13C22×C31651yesdirect product factor
9C26×C3×C5C1311yesmaximal, characteristic, direct product factor, Hall
10C26×C13C3×C511yescharacteristic, direct product factor, Hall
11C22×C3×C5×C13C241651yesdirect product factor
12C24×C3×C13C22×C51651yesdirect product factor
13C23×C5×C13C23×C311395yesdirect product factor
14C25×C3×C5C2×C13163yesdirect product factor
15C25×C13C2×C3×C5163yesdirect product factor
16C2×C3×C5×C13C25163yesdirect product factor
17C26×C5C3×C1311yescharacteristic, direct product factor, Hall
18C23×C3×C13C23×C511395yesdirect product factor
19C22×C5×C13C24×C31651yesdirect product factor
20C24×C3×C5C22×C131651yesdirect product factor
21C24×C13C22×C3×C51651yesdirect product factor
22C3×C5×C13C2611yescharacteristic, direct product factor, Hall
23C26×C3C5×C1311yescharacteristic, direct product factor, Hall
24C25×C5C2×C3×C13163yesdirect product factor
25C22×C3×C13C24×C51651yesdirect product factor
26C2×C5×C13C25×C3163yesdirect product factor
27C23×C3×C5C23×C1311395yesdirect product factor
28C23×C13C23×C3×C511395yesdirect product factor
29C25×C3C2×C5×C13163yesdirect product factor
30C24×C5C22×C3×C131651yesdirect product factor
31C2×C3×C13C25×C5163yesdirect product factor
32C5×C13C26×C311yescharacteristic, direct product factor, Hall
33C26C3×C5×C1311yescharacteristic, direct product factor, Sylow
34C22×C3×C5C24×C131651yesdirect product factor
35C22×C13C24×C3×C51651yesdirect product factor
36C24×C3C22×C5×C131651yesdirect product factor
37C23×C5C23×C3×C1311395yesdirect product factor
38C3×C13C26×C511yescharacteristic, direct product factor, Hall
39C25C2×C3×C5×C13163yesdirect product factor
40C2×C3×C5C25×C13163yesdirect product factor
41C2×C13C25×C3×C5163yesdirect product factor
42C23×C3C23×C5×C1311395yesdirect product factor
43C22×C5C24×C3×C131651yesdirect product factor
44C24C22×C3×C5×C131651yesdirect product factor
45C3×C5C26×C1311yescharacteristic, direct product factor, Hall
46C13C26×C3×C511yescharacteristic, direct product factor, Sylow
47C22×C3C24×C5×C131651yesdirect product factor
48C2×C5C25×C3×C13163yesdirect product factor
49C23C23×C3×C5×C1311395yesdirect product factor
50C2×C3C25×C5×C13163yesdirect product factor
51C5C26×C3×C1311yescharacteristic, direct product factor, Sylow
52C22C24×C3×C5×C131651yesdirect product factor
53C3C26×C5×C1311yescharacteristic, direct product factor, Sylow
54C2C25×C3×C5×C13163yesdirect 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×C3×C5×C13C2direct (N × H)
2. C26×C5×C13C3direct (N × H)
3. C24×C3×C5×C13C22direct (N × H)
4. C26×C3×C13C5direct (N × H)
5. C25×C5×C13C2×C3direct (N × H)
6. C23×C3×C5×C13C23direct (N × H)
7. C25×C3×C13C2×C5direct (N × H)
8. C24×C5×C13C22×C3direct (N × H)
9. C26×C3×C5C13direct (N × H)
10. C26×C13C3×C5direct (N × H)
11. C22×C3×C5×C13C24direct (N × H)
12. C24×C3×C13C22×C5direct (N × H)
13. C23×C5×C13C23×C3direct (N × H)
14. C25×C3×C5C2×C13direct (N × H)
15. C25×C13C2×C3×C5direct (N × H)
16. C2×C3×C5×C13C25direct (N × H)
17. C26×C5C3×C13direct (N × H)
18. C23×C3×C13C23×C5direct (N × H)
19. C22×C5×C13C24×C3direct (N × H)
20. C24×C3×C5C22×C13direct (N × H)
21. C24×C13C22×C3×C5direct (N × H)
22. C3×C5×C13C26direct (N × H)
23. C26×C3C5×C13direct (N × H)
24. C25×C5C2×C3×C13direct (N × H)
25. C22×C3×C13C24×C5direct (N × H)
26. C2×C5×C13C25×C3direct (N × H)
27. C23×C3×C5C23×C13direct (N × H)
28. C23×C13C23×C3×C5direct (N × H)
29. C25×C3C2×C5×C13direct (N × H)
30. C24×C5C22×C3×C13direct (N × H)
31. C2×C3×C13C25×C5direct (N × H)
32. C5×C13C26×C3direct (N × H)
33. C26C3×C5×C13direct (N × H)
34. C22×C3×C5C24×C13direct (N × H)
35. C22×C13C24×C3×C5direct (N × H)
36. C24×C3C22×C5×C13direct (N × H)
37. C23×C5C23×C3×C13direct (N × H)
38. C3×C13C26×C5direct (N × H)
39. C25C2×C3×C5×C13direct (N × H)
40. C2×C3×C5C25×C13direct (N × H)
41. C2×C13C25×C3×C5direct (N × H)
42. C23×C3C23×C5×C13direct (N × H)
43. C22×C5C24×C3×C13direct (N × H)
44. C24C22×C3×C5×C13direct (N × H)
45. C3×C5C26×C13direct (N × H)
46. C13C26×C3×C5direct (N × H)
47. C22×C3C24×C5×C13direct (N × H)
48. C2×C5C25×C3×C13direct (N × H)
49. C23C23×C3×C5×C13direct (N × H)
50. C2×C3C25×C5×C13direct (N × H)
51. C5C26×C3×C13direct (N × H)
52. C22C24×C3×C5×C13direct (N × H)
53. C3C26×C5×C13direct (N × H)
54. C2C25×C3×C5×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C5×C132
C26×C5×C133
C26×C3×C135
C26×C3×C513