Finite Group Databasebeta

← C24×C3×C5×C103 #72202016

Subgroups — C24×C3×C5×C103 #72202016

Order 24720.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C103C2115yesmaximal, direct product factor
2C24×C5×C103C311yesmaximal, characteristic, direct product factor, Hall
3C24×C3×C103C511yesmaximal, characteristic, direct product factor, Hall
4C23×C5×C103C2×C3115yesdirect product factor
5C23×C3×C103C2×C5115yesdirect product factor
6C22×C3×C5×C103C22135yesdirect product factor
7C2×C3×C5×C103C23115yesdirect product factor
8C22×C5×C103C22×C3135yesdirect product factor
9C24×C103C3×C511yescharacteristic, direct product factor, Hall
10C3×C5×C103C2411yescharacteristic, direct product factor, Hall
11C22×C3×C103C22×C5135yesdirect product factor
12C2×C5×C103C23×C3115yesdirect product factor
13C23×C103C2×C3×C5115yesdirect product factor
14C2×C3×C103C23×C5115yesdirect product factor
15C5×C103C24×C311yescharacteristic, direct product factor, Hall
16C22×C103C22×C3×C5135yesdirect product factor
17C3×C103C24×C511yescharacteristic, direct product factor, Hall
18C24×C3×C5C10311yesmaximal, characteristic, direct product factor, Hall
19C2×C103C23×C3×C5115yesdirect product factor
20C23×C3×C5C2×C103115yesdirect product factor
21C103C24×C3×C511yescharacteristic, direct product factor, Sylow
22C24×C5C3×C10311yescharacteristic, direct product factor, Hall
23C22×C3×C5C22×C103135yesdirect product factor
24C24×C3C5×C10311yescharacteristic, direct product factor, Hall
25C23×C5C2×C3×C103115yesdirect product factor
26C2×C3×C5C23×C103115yesdirect product factor
27C23×C3C2×C5×C103115yesdirect product factor
28C22×C5C22×C3×C103135yesdirect product factor
29C24C3×C5×C10311yescharacteristic, direct product factor, Sylow
30C3×C5C24×C10311yescharacteristic, direct product factor, Hall
31C22×C3C22×C5×C103135yesdirect product factor
32C2×C5C23×C3×C103115yesdirect product factor
33C23C2×C3×C5×C103115yesdirect product factor
34C2×C3C23×C5×C103115yesdirect product factor
35C5C24×C3×C10311yescharacteristic, direct product factor, Sylow
36C22C22×C3×C5×C103135yesdirect product factor
37C3C24×C5×C10311yescharacteristic, direct product factor, Sylow
38C2C23×C3×C5×C103115yesdirect 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. C23×C3×C5×C103C2direct (N × H)
2. C24×C5×C103C3direct (N × H)
3. C24×C3×C103C5direct (N × H)
4. C23×C5×C103C2×C3direct (N × H)
5. C23×C3×C103C2×C5direct (N × H)
6. C22×C3×C5×C103C22direct (N × H)
7. C2×C3×C5×C103C23direct (N × H)
8. C22×C5×C103C22×C3direct (N × H)
9. C24×C103C3×C5direct (N × H)
10. C3×C5×C103C24direct (N × H)
11. C22×C3×C103C22×C5direct (N × H)
12. C2×C5×C103C23×C3direct (N × H)
13. C23×C103C2×C3×C5direct (N × H)
14. C2×C3×C103C23×C5direct (N × H)
15. C5×C103C24×C3direct (N × H)
16. C22×C103C22×C3×C5direct (N × H)
17. C3×C103C24×C5direct (N × H)
18. C24×C3×C5C103direct (N × H)
19. C2×C103C23×C3×C5direct (N × H)
20. C23×C3×C5C2×C103direct (N × H)
21. C103C24×C3×C5direct (N × H)
22. C24×C5C3×C103direct (N × H)
23. C22×C3×C5C22×C103direct (N × H)
24. C24×C3C5×C103direct (N × H)
25. C23×C5C2×C3×C103direct (N × H)
26. C2×C3×C5C23×C103direct (N × H)
27. C23×C3C2×C5×C103direct (N × H)
28. C22×C5C22×C3×C103direct (N × H)
29. C24C3×C5×C103direct (N × H)
30. C3×C5C24×C103direct (N × H)
31. C22×C3C22×C5×C103direct (N × H)
32. C2×C5C23×C3×C103direct (N × H)
33. C23C2×C3×C5×C103direct (N × H)
34. C2×C3C23×C5×C103direct (N × H)
35. C5C24×C3×C103direct (N × H)
36. C22C22×C3×C5×C103direct (N × H)
37. C3C24×C5×C103direct (N × H)
38. C2C23×C3×C5×C103direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×C1032
C24×C5×C1033
C24×C3×C1035
C24×C3×C5103