Finite Group Databasebeta

← C2×C11×D13×C11⋊C5 #44538201

Subgroups — C2×C11×D13×C11⋊C5 #44538201

Order 31460.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C13×C11⋊C5C211yesmaximal, characteristic, complemented
2C11×D13×C11⋊C5C212yesmaximal, direct product factor
3C11×C13×C11⋊C5C2211yescharacteristic, complemented, Hall
4C2×C112×D13C511yesmaximal, characteristic, complemented, Hall
5C112×D13C2×C512yescomplemented
6C2×C112×C13C2×C511yescharacteristic, complemented
7C2×C5×C11×D13—111nomaximal
8C2×D13×C11⋊C5C1111yesmaximal, characteristic, direct product factor
9C22×C11×C11⋊C5—131nomaximal, Hall
10C112×C13C22×C511yescharacteristic, complemented, Hall
11C2×C5×C11×C13—111no—
12C5×C11×D13—112no—
13C2×C13×C11⋊C5C2×C1111yescharacteristic, complemented
14D13×C11⋊C5C2×C1112yesdirect product factor
15C2×C11×C11⋊C5—132no—
16C2×C11×C11⋊C5D1311yescharacteristic, direct product factor
17C5×C11×C13—111no—
18C13×C11⋊C5C22×C1111yescharacteristic, complemented
19C11×C11⋊C5C2×D1311yescharacteristic, direct product factor, Hall
20C2×C11×D13—52no—
21C2×C11×D13C11⋊C511yescharacteristic, direct product factor
22C2×C11×D13C5×C1111yescharacteristic, complemented
23C22×C112—131noHall
24C2×C11×C13—52no—
25C2×C11×C13C2×C11⋊C511yescharacteristic, complemented
26C2×C11×C13C2×C5×C1111yescharacteristic, complemented
27C11×D13—54no—
28C11×D13C2×C11⋊C512yesdirect product factor
29C11×D13C2×C5×C1112yescomplemented
30C2×C5×D13—111noHall
31C2×C112—132no—
32C2×C112C5×D1311yescharacteristic, complemented
33C22×C5×C11—1431no—
34C22×C11⋊C5—131no—
35C11×C13—52no—
36C11×C13C22×C11⋊C511yescharacteristic, complemented
37C11×C13C22×C5×C1111yescharacteristic, complemented
38C2×C5×C13—111no—
39C5×D13—112no—
40C112C2×C5×D1311yescharacteristic, complemented, Sylow
41C2×C5×C11—111no—
42C2×C5×C11—1432no—
43C2×C11⋊C5—132no—
44C2×C11⋊C5C11×D1311yescharacteristic, direct product factor
45C5×C13—111noHall
46C5×C11—111no—
47C11⋊C5C2×C11×D1311yescharacteristic, direct product factor
48C2×D13C11×C11⋊C511yescharacteristic, direct product factor, Hall
49C22×C11—131no—
50C22×C11—131no—
51C22×C11—652no—
52C2×C13C2×C11×C11⋊C511yescharacteristic, complemented
53D13C2×C11×C11⋊C512yesdirect product factor
54C2×C11—52no—
55C2×C11—132no—
56C2×C11—132no—
57C2×C11—654no—
58C2×C11D13×C11⋊C511yescharacteristic, direct product factor
59C2×C11C5×C11×D1311yescharacteristic, complemented
60C22×C5—1431noHall
61C13C22×C11×C11⋊C511yescharacteristic, complemented, Sylow
62C11—52no—
63C11C2×D13×C11⋊C511yescharacteristic, direct product factor
64C11C2×C5×C11×D1311yescharacteristic, complemented
65C2×C5—111no—
66C2×C5—1432no—
67C5—111noSylow
68C22—131noSylow
69C2—132no—
70C2C11×D13×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11D13×C11⋊C5
commutator, cosocle, hypocenterC11×C13C22×C5×C11
FrattiniC1G
Fitting, socleC2×C112×C13C2×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C2×C11×C13×C11⋊C5C2semidirect
2. C11×D13×C11⋊C5C2direct (N × H)
3. C11×C13×C11⋊C5C22semidirect
4. C2×C112×D13C5semidirect
5. C112×D13C2×C5semidirect
6. C2×C112×C13C2×C5semidirect
8. C2×D13×C11⋊C5C11direct (N × H)
10. C112×C13C22×C5semidirect
13. C2×C13×C11⋊C5C2×C11semidirect
14. D13×C11⋊C5C2×C11direct (N × H)
16. C2×C11×C11⋊C5D13direct (N × H)
18. C13×C11⋊C5C22×C11semidirect
19. C11×C11⋊C5C2×D13direct (N × H)
21. C2×C11×D13C11⋊C5direct (N × H)
22. C2×C11×D13C5×C11semidirect
25. C2×C11×C13C2×C11⋊C5semidirect
26. C2×C11×C13C2×C5×C11semidirect
28. C11×D13C2×C11⋊C5direct (N × H)
29. C11×D13C2×C5×C11semidirect
32. C2×C112C5×D13semidirect
36. C11×C13C22×C11⋊C5semidirect
37. C11×C13C22×C5×C11semidirect
40. C112C2×C5×D13semidirect
44. C2×C11⋊C5C11×D13direct (N × H)
47. C11⋊C5C2×C11×D13direct (N × H)
48. C2×D13C11×C11⋊C5direct (N × H)
52. C2×C13C2×C11×C11⋊C5semidirect
53. D13C2×C11×C11⋊C5direct (N × H)
58. C2×C11D13×C11⋊C5direct (N × H)
59. C2×C11C5×C11×D13semidirect
61. C13C22×C11×C11⋊C5semidirect
63. C11C2×D13×C11⋊C5direct (N × H)
64. C11C2×C5×C11×D13semidirect
70. C2C11×D13×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C13×C11⋊C52
C11×D13×C11⋊C52
C2×C112×D135
C2×C5×C11×D1311
C2×D13×C11⋊C511
C22×C11×C11⋊C513