Finite Group Databasebeta

← C25×C5×C11×C13 #72200261

Subgroups — C25×C5×C11×C13 #72200261

Order 22880.

2992 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C5×C11×C13C2131yesmaximal, direct product factor
2C23×C5×C11×C13C221155yesdirect product factor
3C25×C11×C13C511yesmaximal, characteristic, direct product factor, Hall
4C24×C11×C13C2×C5131yesdirect product factor
5C25×C5×C13C1111yesmaximal, characteristic, direct product factor, Hall
6C22×C5×C11×C13C231155yesdirect product factor
7C25×C5×C11C1311yesmaximal, characteristic, direct product factor, Hall
8C2×C5×C11×C13C24131yesdirect product factor
9C23×C11×C13C22×C51155yesdirect product factor
10C24×C5×C13C2×C11131yesdirect product factor
11C24×C5×C11C2×C13131yesdirect product factor
12C5×C11×C13C2511yescharacteristic, direct product factor, Hall
13C22×C11×C13C23×C51155yesdirect product factor
14C23×C5×C13C22×C111155yesdirect product factor
15C23×C5×C11C22×C131155yesdirect product factor
16C25×C13C5×C1111yescharacteristic, direct product factor, Hall
17C25×C11C5×C1311yescharacteristic, direct product factor, Hall
18C2×C11×C13C24×C5131yesdirect product factor
19C22×C5×C13C23×C111155yesdirect product factor
20C22×C5×C11C23×C131155yesdirect product factor
21C24×C13C2×C5×C11131yesdirect product factor
22C24×C11C2×C5×C13131yesdirect product factor
23C25×C5C11×C1311yescharacteristic, direct product factor, Hall
24C11×C13C25×C511yescharacteristic, direct product factor, Hall
25C2×C5×C13C24×C11131yesdirect product factor
26C2×C5×C11C24×C13131yesdirect product factor
27C23×C13C22×C5×C111155yesdirect product factor
28C23×C11C22×C5×C131155yesdirect product factor
29C24×C5C2×C11×C13131yesdirect product factor
30C5×C13C25×C1111yescharacteristic, direct product factor, Hall
31C5×C11C25×C1311yescharacteristic, direct product factor, Hall
32C22×C13C23×C5×C111155yesdirect product factor
33C22×C11C23×C5×C131155yesdirect product factor
34C23×C5C22×C11×C131155yesdirect product factor
35C25C5×C11×C1311yescharacteristic, direct product factor, Sylow
36C2×C13C24×C5×C11131yesdirect product factor
37C2×C11C24×C5×C13131yesdirect product factor
38C22×C5C23×C11×C131155yesdirect product factor
39C24C2×C5×C11×C13131yesdirect product factor
40C13C25×C5×C1111yescharacteristic, direct product factor, Sylow
41C11C25×C5×C1311yescharacteristic, direct product factor, Sylow
42C2×C5C24×C11×C13131yesdirect product factor
43C23C22×C5×C11×C131155yesdirect product factor
44C5C25×C11×C1311yescharacteristic, direct product factor, Sylow
45C22C23×C5×C11×C131155yesdirect product factor
46C2C24×C5×C11×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×C5×C11×C13C2direct (N × H)
2. C23×C5×C11×C13C22direct (N × H)
3. C25×C11×C13C5direct (N × H)
4. C24×C11×C13C2×C5direct (N × H)
5. C25×C5×C13C11direct (N × H)
6. C22×C5×C11×C13C23direct (N × H)
7. C25×C5×C11C13direct (N × H)
8. C2×C5×C11×C13C24direct (N × H)
9. C23×C11×C13C22×C5direct (N × H)
10. C24×C5×C13C2×C11direct (N × H)
11. C24×C5×C11C2×C13direct (N × H)
12. C5×C11×C13C25direct (N × H)
13. C22×C11×C13C23×C5direct (N × H)
14. C23×C5×C13C22×C11direct (N × H)
15. C23×C5×C11C22×C13direct (N × H)
16. C25×C13C5×C11direct (N × H)
17. C25×C11C5×C13direct (N × H)
18. C2×C11×C13C24×C5direct (N × H)
19. C22×C5×C13C23×C11direct (N × H)
20. C22×C5×C11C23×C13direct (N × H)
21. C24×C13C2×C5×C11direct (N × H)
22. C24×C11C2×C5×C13direct (N × H)
23. C25×C5C11×C13direct (N × H)
24. C11×C13C25×C5direct (N × H)
25. C2×C5×C13C24×C11direct (N × H)
26. C2×C5×C11C24×C13direct (N × H)
27. C23×C13C22×C5×C11direct (N × H)
28. C23×C11C22×C5×C13direct (N × H)
29. C24×C5C2×C11×C13direct (N × H)
30. C5×C13C25×C11direct (N × H)
31. C5×C11C25×C13direct (N × H)
32. C22×C13C23×C5×C11direct (N × H)
33. C22×C11C23×C5×C13direct (N × H)
34. C23×C5C22×C11×C13direct (N × H)
35. C25C5×C11×C13direct (N × H)
36. C2×C13C24×C5×C11direct (N × H)
37. C2×C11C24×C5×C13direct (N × H)
38. C22×C5C23×C11×C13direct (N × H)
39. C24C2×C5×C11×C13direct (N × H)
40. C13C25×C5×C11direct (N × H)
41. C11C25×C5×C13direct (N × H)
42. C2×C5C24×C11×C13direct (N × H)
43. C23C22×C5×C11×C13direct (N × H)
44. C5C25×C11×C13direct (N × H)
45. C22C23×C5×C11×C13direct (N × H)
46. C2C24×C5×C11×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C5×C11×C132
C25×C11×C135
C25×C5×C1311
C25×C5×C1113