Finite Group Databasebeta

← C22×C3×C53×C7 #72189113

Subgroups — C22×C3×C53×C7 #72189113

Order 10500.

1280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C53×C7C213yesmaximal, direct product factor
2C22×C53×C7C311yesmaximal, characteristic, direct product factor, Hall
3C3×C53×C7C2211yescharacteristic, direct product factor, Hall
4C22×C3×C52×C7C5131yesmaximal, direct product factor
5C2×C53×C7C2×C313yesdirect product factor
6C22×C3×C53C711yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C52×C7C2×C5193yesdirect product factor
8C53×C7C22×C311yescharacteristic, direct product factor, Hall
9C2×C3×C53C2×C713yesdirect product factor
10C22×C52×C7C3×C5131yesdirect product factor
11C3×C52×C7C22×C5131yesdirect product factor
12C22×C53C3×C711yescharacteristic, direct product factor, Hall
13C22×C3×C5×C7C52131yesdirect product factor
14C3×C53C22×C711yescharacteristic, direct product factor, Hall
15C2×C52×C7C2×C3×C5193yesdirect product factor
16C22×C3×C52C5×C7131yesdirect product factor
17C2×C53C2×C3×C713yesdirect product factor
18C2×C3×C5×C7C2×C52193yesdirect product factor
19C52×C7C22×C3×C5131yesdirect product factor
20C2×C3×C52C2×C5×C7193yesdirect product factor
21C22×C5×C7C3×C52131yesdirect product factor
22C53C22×C3×C711yescharacteristic, direct product factor, Sylow
23C3×C5×C7C22×C52131yesdirect product factor
24C22×C52C3×C5×C7131yesdirect product factor
25C22×C3×C7C5311yescharacteristic, direct product factor, Hall
26C3×C52C22×C5×C7131yesdirect product factor
27C2×C5×C7C2×C3×C52193yesdirect product factor
28C22×C3×C5C52×C7131yesdirect product factor
29C2×C52C2×C3×C5×C7193yesdirect product factor
30C2×C3×C7C2×C5313yesdirect product factor
31C5×C7C22×C3×C52131yesdirect product factor
32C2×C3×C5C2×C52×C7193yesdirect product factor
33C22×C7C3×C5311yescharacteristic, direct product factor, Hall
34C52C22×C3×C5×C7131yesdirect product factor
35C3×C7C22×C5311yescharacteristic, direct product factor, Hall
36C22×C5C3×C52×C7131yesdirect product factor
37C3×C5C22×C52×C7131yesdirect product factor
38C2×C7C2×C3×C5313yesdirect product factor
39C22×C3C53×C711yescharacteristic, direct product factor, Hall
40C2×C5C2×C3×C52×C7193yesdirect product factor
41C7C22×C3×C5311yescharacteristic, direct product factor, Sylow
42C2×C3C2×C53×C713yesdirect product factor
43C5C22×C3×C52×C7131yesdirect product factor
44C22C3×C53×C711yescharacteristic, direct product factor, Sylow
45C3C22×C53×C711yescharacteristic, direct product factor, Sylow
46C2C2×C3×C53×C713yesdirect 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×C53×C7C2direct (N × H)
2. C22×C53×C7C3direct (N × H)
3. C3×C53×C7C22direct (N × H)
4. C22×C3×C52×C7C5direct (N × H)
5. C2×C53×C7C2×C3direct (N × H)
6. C22×C3×C53C7direct (N × H)
7. C2×C3×C52×C7C2×C5direct (N × H)
8. C53×C7C22×C3direct (N × H)
9. C2×C3×C53C2×C7direct (N × H)
10. C22×C52×C7C3×C5direct (N × H)
11. C3×C52×C7C22×C5direct (N × H)
12. C22×C53C3×C7direct (N × H)
13. C22×C3×C5×C7C52direct (N × H)
14. C3×C53C22×C7direct (N × H)
15. C2×C52×C7C2×C3×C5direct (N × H)
16. C22×C3×C52C5×C7direct (N × H)
17. C2×C53C2×C3×C7direct (N × H)
18. C2×C3×C5×C7C2×C52direct (N × H)
19. C52×C7C22×C3×C5direct (N × H)
20. C2×C3×C52C2×C5×C7direct (N × H)
21. C22×C5×C7C3×C52direct (N × H)
22. C53C22×C3×C7direct (N × H)
23. C3×C5×C7C22×C52direct (N × H)
24. C22×C52C3×C5×C7direct (N × H)
25. C22×C3×C7C53direct (N × H)
26. C3×C52C22×C5×C7direct (N × H)
27. C2×C5×C7C2×C3×C52direct (N × H)
28. C22×C3×C5C52×C7direct (N × H)
29. C2×C52C2×C3×C5×C7direct (N × H)
30. C2×C3×C7C2×C53direct (N × H)
31. C5×C7C22×C3×C52direct (N × H)
32. C2×C3×C5C2×C52×C7direct (N × H)
33. C22×C7C3×C53direct (N × H)
34. C52C22×C3×C5×C7direct (N × H)
35. C3×C7C22×C53direct (N × H)
36. C22×C5C3×C52×C7direct (N × H)
37. C3×C5C22×C52×C7direct (N × H)
38. C2×C7C2×C3×C53direct (N × H)
39. C22×C3C53×C7direct (N × H)
40. C2×C5C2×C3×C52×C7direct (N × H)
41. C7C22×C3×C53direct (N × H)
42. C2×C3C2×C53×C7direct (N × H)
43. C5C22×C3×C52×C7direct (N × H)
44. C22C3×C53×C7direct (N × H)
45. C3C22×C53×C7direct (N × H)
46. C2C2×C3×C53×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C53×C72
C22×C53×C73
C22×C3×C52×C75
C22×C3×C537