Finite Group Databasebeta

← C23×C7×D15 #13132983

Subgroups — C23×C7×D15 #13132983

Order 1680.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C7C211yesmaximal, characteristic, complemented
2C22×C7×D15C2114yesmaximal, direct product factor
3C23×C7×D5—31nomaximal, Hall
4C22×C3×C5×C7C2217yescomplemented
5C2×C7×D15C22128yesdirect product factor
6C23×D3×C7—51nomaximal, Hall
7C23×C5×C7D311yescharacteristic, complemented
8C22×C7×D5—314no—
9C23×D15C711yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×C7C2317yescomplemented
11C7×D15C2318yesdirect product factor
12C23×C3×C7D511yescharacteristic, complemented
13C22×D3×C7—514no—
14C22×C5×C7C2×D317yescomplemented
15C2×C7×D5—328no—
16C23×C3×C5C2×C711yescharacteristic, complemented
17C22×D15C2×C7114yesdirect product factor
18C24×C7—151noHall
19C3×C5×C7C2411yescharacteristic, complemented, Hall
20C22×C3×C7C2×D517yescomplemented
21C2×D3×C7—528no—
22C23×D5—31noHall
23C2×C5×C7C22×D317yescomplemented
24C7×D5—38no—
25C22×C3×C5C22×C717yescomplemented
26C2×D15C22×C7128yesdirect product factor
27C23×C7—1514no—
28C23×C7D1511yescharacteristic, direct product factor
29C23×D3—51noHall
30C2×C3×C7C22×D517yescomplemented
31D3×C7—58no—
32C23×C5D3×C711yescharacteristic, complemented
33C22×D5—314no—
34C5×C7C23×D311yescharacteristic, complemented, Hall
35C2×C3×C5C23×C717yescomplemented
36D15C23×C718yesdirect product factor
37C22×C7—1528no—
38C22×C7C2×D1517yesdirect product factor
39C23×C3C7×D511yescharacteristic, complemented
40C22×D3—514no—
41C3×C7C23×D511yescharacteristic, complemented, Hall
42C22×C5C2×D3×C717yescomplemented
43C2×D5—328no—
44C24—151noSylow
45C3×C5C24×C711yescharacteristic, complemented, Hall
46C2×C7—158no—
47C2×C7C22×D1517yesdirect product factor
48C22×C3C2×C7×D517yescomplemented
49C2×D3—528no—
50C2×C5C22×D3×C717yescomplemented
51D5—38no—
52C23—1514no—
53C23C7×D1511yescharacteristic, direct product factor
54C7C23×D1511yescharacteristic, direct product factor, Sylow
55C2×C3C22×C7×D517yescomplemented
56D3—58no—
57C5C23×D3×C711yescharacteristic, complemented, Sylow
58C22—1528no—
59C22C2×C7×D1517yesdirect product factor
60C3C23×C7×D511yescharacteristic, complemented, Sylow
61C2—158no—
62C2C22×C7×D1517yesdirect product factor
subgroupG/H
center, hypercenterC23×C7D15
commutator, cosocle, hypocenterC3×C5C24×C7
FrattiniC1G
Fitting, socleC23×C3×C5×C7C2
LCSG ▷ C3×C5
UCSC1 ◁ C23×C7

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C7×D15C2direct (N × H)
4. C22×C3×C5×C7C22semidirect
5. C2×C7×D15C22direct (N × H)
7. C23×C5×C7D3semidirect
9. C23×D15C7direct (N × H)
10. C2×C3×C5×C7C23semidirect
11. C7×D15C23direct (N × H)
12. C23×C3×C7D5semidirect
14. C22×C5×C7C2×D3semidirect
16. C23×C3×C5C2×C7semidirect
17. C22×D15C2×C7direct (N × H)
19. C3×C5×C7C24semidirect
20. C22×C3×C7C2×D5semidirect
23. C2×C5×C7C22×D3semidirect
25. C22×C3×C5C22×C7semidirect
26. C2×D15C22×C7direct (N × H)
28. C23×C7D15direct (N × H)
30. C2×C3×C7C22×D5semidirect
32. C23×C5D3×C7semidirect
34. C5×C7C23×D3semidirect
35. C2×C3×C5C23×C7semidirect
36. D15C23×C7direct (N × H)
38. C22×C7C2×D15direct (N × H)
39. C23×C3C7×D5semidirect
41. C3×C7C23×D5semidirect
42. C22×C5C2×D3×C7semidirect
45. C3×C5C24×C7semidirect
47. C2×C7C22×D15direct (N × H)
48. C22×C3C2×C7×D5semidirect
50. C2×C5C22×D3×C7semidirect
53. C23C7×D15direct (N × H)
54. C7C23×D15direct (N × H)
55. C2×C3C22×C7×D5semidirect
57. C5C23×D3×C7semidirect
59. C22C2×C7×D15direct (N × H)
60. C3C23×C7×D5semidirect
62. C2C22×C7×D15direct (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×C7×D152
C23×C7×D53
C23×D3×C75
C23×D157