Finite Group Databasebeta

← C23×C3×C7×D5 #13132979

Subgroups — C23×C3×C7×D5 #13132979

Order 1680.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C7C211yesmaximal, characteristic, complemented
2C22×C3×C7×D5C2114yesmaximal, direct product factor
3C23×C7×D5C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C5×C7C2217yescomplemented
5C2×C3×C7×D5C22128yesdirect product factor
6C24×C3×C7—51nomaximal, Hall
7C23×C5×C7C2×C311yescharacteristic, complemented
8C22×C7×D5C2×C3114yesdirect product factor
9C23×C3×D5C711yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×C7C2317yescomplemented
11C3×C7×D5C2318yesdirect product factor
12C23×C3×C7—514no—
13C23×C3×C7D511yescharacteristic, direct product factor
14C22×C5×C7C22×C317yescomplemented
15C2×C7×D5C22×C3128yesdirect product factor
16C23×C3×C5C2×C711yescharacteristic, complemented
17C22×C3×D5C2×C7114yesdirect product factor
18C24×C7—51noHall
19C3×C5×C7C2411yescharacteristic, complemented, Hall
20C22×C3×C7—528no—
21C22×C3×C7C2×D517yesdirect product factor
22C23×D5C3×C711yescharacteristic, direct product factor, Hall
23C2×C5×C7C23×C317yescomplemented
24C7×D5C23×C318yesdirect product factor
25C22×C3×C5C22×C717yescomplemented
26C2×C3×D5C22×C7128yesdirect product factor
27C23×C7—514no—
28C23×C7C3×D511yescharacteristic, direct product factor
29C24×C3—51noHall
30C2×C3×C7—58no—
31C2×C3×C7C22×D517yesdirect product factor
32C23×C5C2×C3×C711yescharacteristic, complemented
33C22×D5C2×C3×C7114yesdirect product factor
34C5×C7C24×C311yescharacteristic, complemented, Hall
35C2×C3×C5C23×C717yescomplemented
36C3×D5C23×C718yesdirect product factor
37C22×C7—528no—
38C22×C7C2×C3×D517yesdirect product factor
39C23×C3—514no—
40C23×C3C7×D511yescharacteristic, direct product factor
41C3×C7C23×D511yescharacteristic, direct product factor, Hall
42C22×C5C22×C3×C717yescomplemented
43C2×D5C22×C3×C7128yesdirect product factor
44C24—51noSylow
45C3×C5C24×C711yescharacteristic, complemented, Hall
46C2×C7—58no—
47C2×C7C22×C3×D517yesdirect product factor
48C22×C3—528no—
49C22×C3C2×C7×D517yesdirect product factor
50C2×C5C23×C3×C717yescomplemented
51D5C23×C3×C718yesdirect product factor
52C23—514no—
53C23C3×C7×D511yescharacteristic, direct product factor
54C7C23×C3×D511yescharacteristic, direct product factor, Sylow
55C2×C3—58no—
56C2×C3C22×C7×D517yesdirect product factor
57C5C24×C3×C711yescharacteristic, complemented, Sylow
58C22—528no—
59C22C2×C3×C7×D517yesdirect product factor
60C3C23×C7×D511yescharacteristic, direct product factor, Sylow
61C2—58no—
62C2C22×C3×C7×D517yesdirect product factor
subgroupG/H
center, hypercenterC23×C3×C7D5
commutator, cosocle, hypocenterC5C24×C3×C7
FrattiniC1G
Fitting, socleC23×C3×C5×C7C2
LCSG ▷ C5
UCSC1 ◁ C23×C3×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C3×C7×D5C2direct (N × H)
3. C23×C7×D5C3direct (N × H)
4. C22×C3×C5×C7C22semidirect
5. C2×C3×C7×D5C22direct (N × H)
7. C23×C5×C7C2×C3semidirect
8. C22×C7×D5C2×C3direct (N × H)
9. C23×C3×D5C7direct (N × H)
10. C2×C3×C5×C7C23semidirect
11. C3×C7×D5C23direct (N × H)
13. C23×C3×C7D5direct (N × H)
14. C22×C5×C7C22×C3semidirect
15. C2×C7×D5C22×C3direct (N × H)
16. C23×C3×C5C2×C7semidirect
17. C22×C3×D5C2×C7direct (N × H)
19. C3×C5×C7C24semidirect
21. C22×C3×C7C2×D5direct (N × H)
22. C23×D5C3×C7direct (N × H)
23. C2×C5×C7C23×C3semidirect
24. C7×D5C23×C3direct (N × H)
25. C22×C3×C5C22×C7semidirect
26. C2×C3×D5C22×C7direct (N × H)
28. C23×C7C3×D5direct (N × H)
31. C2×C3×C7C22×D5direct (N × H)
32. C23×C5C2×C3×C7semidirect
33. C22×D5C2×C3×C7direct (N × H)
34. C5×C7C24×C3semidirect
35. C2×C3×C5C23×C7semidirect
36. C3×D5C23×C7direct (N × H)
38. C22×C7C2×C3×D5direct (N × H)
40. C23×C3C7×D5direct (N × H)
41. C3×C7C23×D5direct (N × H)
42. C22×C5C22×C3×C7semidirect
43. C2×D5C22×C3×C7direct (N × H)
45. C3×C5C24×C7semidirect
47. C2×C7C22×C3×D5direct (N × H)
49. C22×C3C2×C7×D5direct (N × H)
50. C2×C5C23×C3×C7semidirect
51. D5C23×C3×C7direct (N × H)
53. C23C3×C7×D5direct (N × H)
54. C7C23×C3×D5direct (N × H)
56. C2×C3C22×C7×D5direct (N × H)
57. C5C24×C3×C7semidirect
59. C22C2×C3×C7×D5direct (N × H)
60. C3C23×C7×D5direct (N × H)
62. C2C22×C3×C7×D5direct (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×C72
C22×C3×C7×D52
C23×C7×D53
C24×C3×C75
C23×C3×D57