Finite Group Databasebeta

← C22×C3×C5×C11×C29 #34062332

Subgroups — C22×C3×C5×C11×C29 #34062332

Order 19140.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C11×C29C213yesmaximal, direct product factor
2C22×C5×C11×C29C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C11×C29C2211yescharacteristic, direct product factor, Hall
4C22×C3×C11×C29C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C11×C29C2×C313yesdirect product factor
6C2×C3×C11×C29C2×C513yesdirect product factor
7C22×C3×C5×C29C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C29C22×C311yescharacteristic, direct product factor, Hall
9C22×C11×C29C3×C511yescharacteristic, direct product factor, Hall
10C3×C11×C29C22×C511yescharacteristic, direct product factor, Hall
11C2×C3×C5×C29C2×C1113yesdirect product factor
12C22×C3×C5×C11C2911yesmaximal, characteristic, direct product factor, Hall
13C2×C11×C29C2×C3×C513yesdirect product factor
14C22×C5×C29C3×C1111yescharacteristic, direct product factor, Hall
15C3×C5×C29C22×C1111yescharacteristic, direct product factor, Hall
16C22×C3×C29C5×C1111yescharacteristic, direct product factor, Hall
17C2×C3×C5×C11C2×C2913yesdirect product factor
18C11×C29C22×C3×C511yescharacteristic, direct product factor, Hall
19C2×C5×C29C2×C3×C1113yesdirect product factor
20C22×C5×C11C3×C2911yescharacteristic, direct product factor, Hall
21C2×C3×C29C2×C5×C1113yesdirect product factor
22C3×C5×C11C22×C2911yescharacteristic, direct product factor, Hall
23C5×C29C22×C3×C1111yescharacteristic, direct product factor, Hall
24C22×C3×C11C5×C2911yescharacteristic, direct product factor, Hall
25C22×C29C3×C5×C1111yescharacteristic, direct product factor, Hall
26C2×C5×C11C2×C3×C2913yesdirect product factor
27C3×C29C22×C5×C1111yescharacteristic, direct product factor, Hall
28C2×C3×C11C2×C5×C2913yesdirect product factor
29C22×C3×C5C11×C2911yescharacteristic, direct product factor, Hall
30C2×C29C2×C3×C5×C1113yesdirect product factor
31C5×C11C22×C3×C2911yescharacteristic, direct product factor, Hall
32C22×C11C3×C5×C2911yescharacteristic, direct product factor, Hall
33C3×C11C22×C5×C2911yescharacteristic, direct product factor, Hall
34C2×C3×C5C2×C11×C2913yesdirect product factor
35C29C22×C3×C5×C1111yescharacteristic, direct product factor, Sylow
36C2×C11C2×C3×C5×C2913yesdirect product factor
37C22×C5C3×C11×C2911yescharacteristic, direct product factor, Hall
38C3×C5C22×C11×C2911yescharacteristic, direct product factor, Hall
39C22×C3C5×C11×C2911yescharacteristic, direct product factor, Hall
40C11C22×C3×C5×C2911yescharacteristic, direct product factor, Sylow
41C2×C5C2×C3×C11×C2913yesdirect product factor
42C2×C3C2×C5×C11×C2913yesdirect product factor
43C5C22×C3×C11×C2911yescharacteristic, direct product factor, Sylow
44C22C3×C5×C11×C2911yescharacteristic, direct product factor, Sylow
45C3C22×C5×C11×C2911yescharacteristic, direct product factor, Sylow
46C2C2×C3×C5×C11×C2913yesdirect 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. C2×C3×C5×C11×C29C2direct (N × H)
2. C22×C5×C11×C29C3direct (N × H)
3. C3×C5×C11×C29C22direct (N × H)
4. C22×C3×C11×C29C5direct (N × H)
5. C2×C5×C11×C29C2×C3direct (N × H)
6. C2×C3×C11×C29C2×C5direct (N × H)
7. C22×C3×C5×C29C11direct (N × H)
8. C5×C11×C29C22×C3direct (N × H)
9. C22×C11×C29C3×C5direct (N × H)
10. C3×C11×C29C22×C5direct (N × H)
11. C2×C3×C5×C29C2×C11direct (N × H)
12. C22×C3×C5×C11C29direct (N × H)
13. C2×C11×C29C2×C3×C5direct (N × H)
14. C22×C5×C29C3×C11direct (N × H)
15. C3×C5×C29C22×C11direct (N × H)
16. C22×C3×C29C5×C11direct (N × H)
17. C2×C3×C5×C11C2×C29direct (N × H)
18. C11×C29C22×C3×C5direct (N × H)
19. C2×C5×C29C2×C3×C11direct (N × H)
20. C22×C5×C11C3×C29direct (N × H)
21. C2×C3×C29C2×C5×C11direct (N × H)
22. C3×C5×C11C22×C29direct (N × H)
23. C5×C29C22×C3×C11direct (N × H)
24. C22×C3×C11C5×C29direct (N × H)
25. C22×C29C3×C5×C11direct (N × H)
26. C2×C5×C11C2×C3×C29direct (N × H)
27. C3×C29C22×C5×C11direct (N × H)
28. C2×C3×C11C2×C5×C29direct (N × H)
29. C22×C3×C5C11×C29direct (N × H)
30. C2×C29C2×C3×C5×C11direct (N × H)
31. C5×C11C22×C3×C29direct (N × H)
32. C22×C11C3×C5×C29direct (N × H)
33. C3×C11C22×C5×C29direct (N × H)
34. C2×C3×C5C2×C11×C29direct (N × H)
35. C29C22×C3×C5×C11direct (N × H)
36. C2×C11C2×C3×C5×C29direct (N × H)
37. C22×C5C3×C11×C29direct (N × H)
38. C3×C5C22×C11×C29direct (N × H)
39. C22×C3C5×C11×C29direct (N × H)
40. C11C22×C3×C5×C29direct (N × H)
41. C2×C5C2×C3×C11×C29direct (N × H)
42. C2×C3C2×C5×C11×C29direct (N × H)
43. C5C22×C3×C11×C29direct (N × H)
44. C22C3×C5×C11×C29direct (N × H)
45. C3C22×C5×C11×C29direct (N × H)
46. C2C2×C3×C5×C11×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C292
C22×C5×C11×C293
C22×C3×C11×C295
C22×C3×C5×C2911
C22×C3×C5×C1129