Finite Group Databasebeta

← C2×C11×(C19⋊C3)⋊D13 #45656754

Subgroups — C2×C11×(C19⋊C3)⋊D13 #45656754

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×(C19⋊C3)⋊D13C212yesmaximal, direct product factor
2C2×C11×C13×C19⋊C3C211yesmaximal, characteristic, complemented
3C2×C11×D247C311yesmaximal, characteristic, complemented, Hall
4C11×C13×C19⋊C3C2211yescharacteristic, complemented, Hall
5C11×D247C2×C312yescomplemented
6C2×C11×C13×C19C2×C311yescharacteristic, complemented
7C2×(C19⋊C3)⋊D13C1111yesmaximal, characteristic, direct product factor, Hall
8C11×C13×C19C22×C311yescharacteristic, complemented, Hall
9C2×C11×D19⋊C3—131nomaximal, Hall
10C2×C3×C11×D13—191nomaximal, Hall
11C2×C13×C19⋊C3C2×C1111yescharacteristic, complemented
12(C19⋊C3)⋊D13C2×C1112yesdirect product factor
13C2×C11×C19⋊C3D1311yescharacteristic, complemented
14C11×D19⋊C3—132no—
15C2×D247C3×C1111yescharacteristic, complemented, Hall
16C2×C3×C11×C13—191no—
17C3×C11×D13—192no—
18C2×C11×D19—131noHall
19C13×C19⋊C3C22×C1111yescharacteristic, complemented, Hall
20C11×C19⋊C3C2×D1311yescharacteristic, complemented, Hall
21C2×C11×D13—191noHall
22C2×C13×C19C2×C3×C1111yescharacteristic, complemented
23D247C2×C3×C1112yescomplemented
24C3×C11×C13—191noHall
25C2×C11×C19C3×D1311yescharacteristic, complemented
26C11×D19—132no—
27C2×C11×C13D19⋊C311yescharacteristic, complemented
28C11×D13—192no—
29C13×C19C22×C3×C1111yescharacteristic, complemented, Hall
30C2×D19⋊C3—131noHall
31C11×C19C2×C3×D1311yescharacteristic, complemented, Hall
32C2×C3×D13—191noHall
33C11×C13C2×D19⋊C311yescharacteristic, complemented, Hall
34C22×C3×C11—2471noHall
35C2×C19⋊C3C11×D1311yescharacteristic, complemented
36D19⋊C3—132no—
37C2×C3×C13—191no—
38C3×D13—192no—
39C2×D19—131noHall
40C2×C3×C11—191no—
41C2×C3×C11—2472no—
42C19⋊C3C2×C11×D1311yescharacteristic, complemented, Hall
43C2×D13—191noHall
44C22×C11—2471noHall
45C3×C13—191noHall
46C2×C19C3×C11×D1311yescharacteristic, complemented
47D19—132no—
48C3×C11—191noHall
49C2×C13C11×D19⋊C311yescharacteristic, complemented
50D13—192no—
51C2×C11—2472no—
52C2×C11(C19⋊C3)⋊D1311yescharacteristic, direct product factor
53C19C2×C3×C11×D1311yescharacteristic, complemented, Sylow
54C13C2×C11×D19⋊C311yescharacteristic, complemented, Sylow
55C22×C3—2471noHall
56C11C2×(C19⋊C3)⋊D1311yescharacteristic, direct product factor, Sylow
57C2×C3—191no—
58C2×C3—2472no—
59C22—2471noSylow
60C3—191noSylow
61C2—2472no—
62C2C11×(C19⋊C3)⋊D1311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11(C19⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C19C22×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×(C19⋊C3)⋊D13C2direct (N × H)
2. C2×C11×C13×C19⋊C3C2semidirect
3. C2×C11×D247C3semidirect
4. C11×C13×C19⋊C3C22semidirect
5. C11×D247C2×C3semidirect
6. C2×C11×C13×C19C2×C3semidirect
7. C2×(C19⋊C3)⋊D13C11direct (N × H)
8. C11×C13×C19C22×C3semidirect
11. C2×C13×C19⋊C3C2×C11semidirect
12. (C19⋊C3)⋊D13C2×C11direct (N × H)
13. C2×C11×C19⋊C3D13semidirect
15. C2×D247C3×C11semidirect
19. C13×C19⋊C3C22×C11semidirect
20. C11×C19⋊C3C2×D13semidirect
22. C2×C13×C19C2×C3×C11semidirect
23. D247C2×C3×C11semidirect
25. C2×C11×C19C3×D13semidirect
27. C2×C11×C13D19⋊C3semidirect
29. C13×C19C22×C3×C11semidirect
31. C11×C19C2×C3×D13semidirect
33. C11×C13C2×D19⋊C3semidirect
35. C2×C19⋊C3C11×D13semidirect
42. C19⋊C3C2×C11×D13semidirect
46. C2×C19C3×C11×D13semidirect
49. C2×C13C11×D19⋊C3semidirect
52. C2×C11(C19⋊C3)⋊D13direct (N × H)
53. C19C2×C3×C11×D13semidirect
54. C13C2×C11×D19⋊C3semidirect
56. C11C2×(C19⋊C3)⋊D13direct (N × H)
62. C2C11×(C19⋊C3)⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C11×(C19⋊C3)⋊D132
C2×C11×C13×C19⋊C32
C2×C11×D2473
C2×(C19⋊C3)⋊D1311
C2×C11×D19⋊C313
C2×C3×C11×D1319