Finite Group Databasebeta

← C3×D5×C11×D47 #44526644

Subgroups — C3×D5×C11×D47 #44526644

Order 31020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×D235C211yesmaximal, characteristic, complemented
2C3×D5×C11×C47C211yesmaximal, characteristic, complemented
3C3×C5×C11×D47C211yesmaximal, characteristic, complemented
4D5×C11×D47C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C11×C47C2211yescharacteristic, complemented, Hall
6C2×C3×C11×D47—51nomaximal, Hall
7C11×D235C2×C311yescharacteristic, complemented
8D5×C11×C47C2×C311yescharacteristic, complemented
9C5×C11×D47C2×C311yescharacteristic, complemented
10C3×C11×D47—51no—
11C3×C11×D47D511yescharacteristic, direct product factor
12C2×C3×C11×C47—51no—
13C3×D5×D47C1111yesmaximal, characteristic, direct product factor, Hall
14C5×C11×C47C22×C311yescharacteristic, complemented, Hall
15C2×C11×D47—51noHall
16C3×C11×C47C2×D511yescharacteristic, complemented, Hall
17C3×D235C2×C1111yescharacteristic, complemented
18C3×D5×C47C2×C1111yescharacteristic, complemented
19C3×C5×D47C2×C1111yescharacteristic, complemented
20C2×C11×C47—51no—
21C11×D47—51no—
22C11×D47C3×D511yescharacteristic, direct product factor
23D5×D47C3×C1111yescharacteristic, direct product factor, Hall
24C3×C5×C47C22×C1111yescharacteristic, complemented, Hall
25C2×C3×D5×C11—471nomaximal, Hall
26C2×C3×D47—51noHall
27C11×C47C2×C3×D511yescharacteristic, complemented, Hall
28D235C2×C3×C1111yescharacteristic, complemented
29C5×D47C2×C3×C1111yescharacteristic, complemented
30D5×C47C2×C3×C1111yescharacteristic, complemented
31C2×C3×C5×C11—471no—
32C3×D5×C11—471no—
33C3×D5×C11D4711yescharacteristic, direct product factor
34C2×C3×C47—51no—
35C3×D47—51no—
36C3×D47D5×C1111yescharacteristic, direct product factor
37C5×C47C22×C3×C1111yescharacteristic, complemented, Hall
38C2×D5×C11—471noHall
39C2×D47—51noHall
40C3×C5×C11C2×D4711yescharacteristic, complemented, Hall
41C3×C47C2×D5×C1111yescharacteristic, complemented, Hall
42C22×C3×C11—2351noHall
43C2×C5×C11—471no—
44D5×C11—471no—
45D5×C11C3×D4711yescharacteristic, direct product factor
46C2×C47—51no—
47D47—51no—
48D47C3×D5×C1111yescharacteristic, direct product factor
49C2×C3×C11—51no—
50C2×C3×C11—471no—
51C2×C3×C11—2351no—
52C2×C3×D5—471noHall
53C5×C11C2×C3×D4711yescharacteristic, complemented, Hall
54C47C2×C3×D5×C1111yescharacteristic, complemented, Sylow
55C22×C11—2351noHall
56C3×C11D5×D4711yescharacteristic, direct product factor, Hall
57C2×C3×C5—471no—
58C3×D5—471no—
59C3×D5C11×D4711yescharacteristic, direct product factor
60C2×C11—51no—
61C2×C11—471no—
62C2×C11—2351no—
63C2×D5—471noHall
64C3×C5C2×C11×D4711yescharacteristic, complemented, Hall
65C22×C3—2351noHall
66C11C3×D5×D4711yescharacteristic, direct product factor, Sylow
67C2×C5—471no—
68D5—471no—
69D5C3×C11×D4711yescharacteristic, direct product factor
70C2×C3—51no—
71C2×C3—471no—
72C2×C3—2351no—
73C5C2×C3×C11×D4711yescharacteristic, complemented, Sylow
74C22—2351noSylow
75C3D5×C11×D4711yescharacteristic, direct product factor, Sylow
76C2—51no—
77C2—471no—
78C2—2351no—
subgroupG/H
center, hypercenterC3×C11D5×D47
commutator, cosocle, hypocenterC5×C47C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C47C22
LCSG ▷ C5×C47
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×D235C2semidirect
2. C3×D5×C11×C47C2semidirect
3. C3×C5×C11×D47C2semidirect
4. D5×C11×D47C3direct (N × H)
5. C3×C5×C11×C47C22semidirect
7. C11×D235C2×C3semidirect
8. D5×C11×C47C2×C3semidirect
9. C5×C11×D47C2×C3semidirect
11. C3×C11×D47D5direct (N × H)
13. C3×D5×D47C11direct (N × H)
14. C5×C11×C47C22×C3semidirect
16. C3×C11×C47C2×D5semidirect
17. C3×D235C2×C11semidirect
18. C3×D5×C47C2×C11semidirect
19. C3×C5×D47C2×C11semidirect
22. C11×D47C3×D5direct (N × H)
23. D5×D47C3×C11direct (N × H)
24. C3×C5×C47C22×C11semidirect
27. C11×C47C2×C3×D5semidirect
28. D235C2×C3×C11semidirect
29. C5×D47C2×C3×C11semidirect
30. D5×C47C2×C3×C11semidirect
33. C3×D5×C11D47direct (N × H)
36. C3×D47D5×C11direct (N × H)
37. C5×C47C22×C3×C11semidirect
40. C3×C5×C11C2×D47semidirect
41. C3×C47C2×D5×C11semidirect
45. D5×C11C3×D47direct (N × H)
48. D47C3×D5×C11direct (N × H)
53. C5×C11C2×C3×D47semidirect
54. C47C2×C3×D5×C11semidirect
56. C3×C11D5×D47direct (N × H)
59. C3×D5C11×D47direct (N × H)
64. C3×C5C2×C11×D47semidirect
66. C11C3×D5×D47direct (N × H)
69. D5C3×C11×D47direct (N × H)
73. C5C2×C3×C11×D47semidirect
75. C3D5×C11×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×D2352
C3×D5×C11×C472
C3×C5×C11×D472
D5×C11×D473
C2×C3×C11×D475
C3×D5×D4711
C2×C3×D5×C1147