Finite Group Databasebeta

← C25×C3×C7×C37 #72202128

Subgroups — C25×C3×C7×C37 #72202128

Order 24864.

2992 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C7×C37C2131yesmaximal, direct product factor
2C25×C7×C37C311yesmaximal, characteristic, direct product factor, Hall
3C23×C3×C7×C37C221155yesdirect product factor
4C24×C7×C37C2×C3131yesdirect product factor
5C25×C3×C37C711yesmaximal, characteristic, direct product factor, Hall
6C23×C7×C37C22×C31155yesdirect product factor
7C22×C3×C7×C37C231155yesdirect product factor
8C24×C3×C37C2×C7131yesdirect product factor
9C2×C3×C7×C37C24131yesdirect product factor
10C25×C37C3×C711yescharacteristic, direct product factor, Hall
11C22×C7×C37C23×C31155yesdirect product factor
12C23×C3×C37C22×C71155yesdirect product factor
13C3×C7×C37C2511yescharacteristic, direct product factor, Hall
14C25×C3×C7C3711yesmaximal, characteristic, direct product factor, Hall
15C24×C37C2×C3×C7131yesdirect product factor
16C2×C7×C37C24×C3131yesdirect product factor
17C22×C3×C37C23×C71155yesdirect product factor
18C24×C3×C7C2×C37131yesdirect product factor
19C23×C37C22×C3×C71155yesdirect product factor
20C7×C37C25×C311yescharacteristic, direct product factor, Hall
21C25×C7C3×C3711yescharacteristic, direct product factor, Hall
22C2×C3×C37C24×C7131yesdirect product factor
23C23×C3×C7C22×C371155yesdirect product factor
24C22×C37C23×C3×C71155yesdirect product factor
25C24×C7C2×C3×C37131yesdirect product factor
26C3×C37C25×C711yescharacteristic, direct product factor, Hall
27C25×C3C7×C3711yescharacteristic, direct product factor, Hall
28C22×C3×C7C23×C371155yesdirect product factor
29C2×C37C24×C3×C7131yesdirect product factor
30C23×C7C22×C3×C371155yesdirect product factor
31C24×C3C2×C7×C37131yesdirect product factor
32C2×C3×C7C24×C37131yesdirect product factor
33C37C25×C3×C711yescharacteristic, direct product factor, Sylow
34C25C3×C7×C3711yescharacteristic, direct product factor, Sylow
35C22×C7C23×C3×C371155yesdirect product factor
36C23×C3C22×C7×C371155yesdirect product factor
37C3×C7C25×C3711yescharacteristic, direct product factor, Hall
38C24C2×C3×C7×C37131yesdirect product factor
39C2×C7C24×C3×C37131yesdirect product factor
40C22×C3C23×C7×C371155yesdirect product factor
41C23C22×C3×C7×C371155yesdirect product factor
42C7C25×C3×C3711yescharacteristic, direct product factor, Sylow
43C2×C3C24×C7×C37131yesdirect product factor
44C22C23×C3×C7×C371155yesdirect product factor
45C3C25×C7×C3711yescharacteristic, direct product factor, Sylow
46C2C24×C3×C7×C37131yesdirect 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×C7×C37C2direct (N × H)
2. C25×C7×C37C3direct (N × H)
3. C23×C3×C7×C37C22direct (N × H)
4. C24×C7×C37C2×C3direct (N × H)
5. C25×C3×C37C7direct (N × H)
6. C23×C7×C37C22×C3direct (N × H)
7. C22×C3×C7×C37C23direct (N × H)
8. C24×C3×C37C2×C7direct (N × H)
9. C2×C3×C7×C37C24direct (N × H)
10. C25×C37C3×C7direct (N × H)
11. C22×C7×C37C23×C3direct (N × H)
12. C23×C3×C37C22×C7direct (N × H)
13. C3×C7×C37C25direct (N × H)
14. C25×C3×C7C37direct (N × H)
15. C24×C37C2×C3×C7direct (N × H)
16. C2×C7×C37C24×C3direct (N × H)
17. C22×C3×C37C23×C7direct (N × H)
18. C24×C3×C7C2×C37direct (N × H)
19. C23×C37C22×C3×C7direct (N × H)
20. C7×C37C25×C3direct (N × H)
21. C25×C7C3×C37direct (N × H)
22. C2×C3×C37C24×C7direct (N × H)
23. C23×C3×C7C22×C37direct (N × H)
24. C22×C37C23×C3×C7direct (N × H)
25. C24×C7C2×C3×C37direct (N × H)
26. C3×C37C25×C7direct (N × H)
27. C25×C3C7×C37direct (N × H)
28. C22×C3×C7C23×C37direct (N × H)
29. C2×C37C24×C3×C7direct (N × H)
30. C23×C7C22×C3×C37direct (N × H)
31. C24×C3C2×C7×C37direct (N × H)
32. C2×C3×C7C24×C37direct (N × H)
33. C37C25×C3×C7direct (N × H)
34. C25C3×C7×C37direct (N × H)
35. C22×C7C23×C3×C37direct (N × H)
36. C23×C3C22×C7×C37direct (N × H)
37. C3×C7C25×C37direct (N × H)
38. C24C2×C3×C7×C37direct (N × H)
39. C2×C7C24×C3×C37direct (N × H)
40. C22×C3C23×C7×C37direct (N × H)
41. C23C22×C3×C7×C37direct (N × H)
42. C7C25×C3×C37direct (N × H)
43. C2×C3C24×C7×C37direct (N × H)
44. C22C23×C3×C7×C37direct (N × H)
45. C3C25×C7×C37direct (N × H)
46. C2C24×C3×C7×C37direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C7×C372
C25×C7×C373
C25×C3×C377
C25×C3×C737