Finite Group Databasebeta

← C13×C3⋊(C11⋊(D13⋊C3)) #45689600

Subgroups — C13×C3⋊(C11⋊(D13⋊C3)) #45689600

Order 33462.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×C13×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C13×D429C311yesmaximal, characteristic, complemented
3C13×C11⋊(D13⋊C3)—31nomaximal
4C11×C13×C13⋊C3—21no—
5C11×C13×C13⋊C3D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C13×D143—31noHall
8C13×C3⋊(D13⋊C3)—111nomaximal, Hall
9C3×C13×D33—131nomaximal
10C3⋊(C11⋊(D13⋊C3))C1311yesmaximal, characteristic, direct product factor
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×C13×C13⋊C3D1111yescharacteristic, complemented, Hall
13C32×C11×C13—131no—
14C3×C11×C13⋊C3C2×C1311yescharacteristic, complemented
15C13×D39—111no—
16C13×D13⋊C3—331no—
17D429C3×C1311yescharacteristic, complemented
18C13×D33—131no—
19C3×C13×D11—391no—
20C11⋊(D13⋊C3)—31no—
21C3×C132C3×D1111yescharacteristic, complemented
22C13×C13⋊C3—21no—
23C13×C13⋊C3D3311yescharacteristic, complemented
24C3×C11×C13—62no—
25C3×C11×C13—131no—
26C3×C11×C13—261no—
27C3×C11×C13D13⋊C311yescharacteristic, complemented
28C3×C11×C13C2×C3×C1311yescharacteristic, complemented
29C11×C13⋊C3—21no—
30C11×C13⋊C3D3×C1311yescharacteristic, complemented
31C13×D13—331noHall
32D143—31no—
33C13×D11—391no—
34C3×D3×C13—1431no—
35C3⋊(D13⋊C3)—111no—
36C3×D33—131noHall
37C132C3×D3311yescharacteristic, complemented, Sylow
38C11×C13—62no—
39C11×C13C3⋊(D13⋊C3)11yescharacteristic, complemented
40C11×C13C3×D3×C1311yescharacteristic, complemented
41C32×C13—131no—
42C3×C13⋊C3C13×D1111yescharacteristic, complemented
43C32×C11—131noHall
44C2×C3×C13—4291no—
45D39—111no—
46D3×C13—1431no—
47D13⋊C3—331no—
48D33—131no—
49C3×D11—391no—
50C3×C13—62no—
51C3×C13—131no—
52C3×C13—261no—
53C3×C13C11⋊(D13⋊C3)11yescharacteristic, complemented
54C3×C13C3×C13×D1111yescharacteristic, complemented
55C13⋊C3—21no—
56C13⋊C3C13×D3311yescharacteristic, complemented
57C3×C11—131no—
58C3×C11—261no—
59C3×C11C13×D13⋊C311yescharacteristic, complemented
60C2×C13—4291no—
61D13—331no—
62D11—391noHall
63C3×D3—1431noHall
64C13—62no—
65C13C3⋊(C11⋊(D13⋊C3))11yescharacteristic, direct product factor
66C13C3×C13×D3311yescharacteristic, complemented
67C11C13×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
68C32—131noSylow
69C2×C3—4291no—
70D3—1431no—
71C3—131no—
72C3—261no—
73C3C13×C11⋊(D13⋊C3)11yescharacteristic, complemented
74C2—4291noSylow
subgroupG/H
center, hypercenterC13C3⋊(C11⋊(D13⋊C3))
commutator, cosocle, hypocenterC3×C11×C13C2×C3×C13
FrattiniC1G
Fitting, socleC3×C11×C132C2×C3
LCSG ▷ C3×C11×C13
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C11×C13×C13⋊C3C2semidirect
2. C13×D429C3semidirect
5. C11×C13×C13⋊C3D3semidirect
6. C3×C11×C132C2×C3semidirect
10. C3⋊(C11⋊(D13⋊C3))C13direct (N × H)
11. C11×C132C3×D3semidirect
12. C3×C13×C13⋊C3D11semidirect
14. C3×C11×C13⋊C3C2×C13semidirect
17. D429C3×C13semidirect
21. C3×C132C3×D11semidirect
23. C13×C13⋊C3D33semidirect
27. C3×C11×C13D13⋊C3semidirect
28. C3×C11×C13C2×C3×C13semidirect
30. C11×C13⋊C3D3×C13semidirect
37. C132C3×D33semidirect
39. C11×C13C3⋊(D13⋊C3)semidirect
40. C11×C13C3×D3×C13semidirect
42. C3×C13⋊C3C13×D11semidirect
53. C3×C13C11⋊(D13⋊C3)semidirect
54. C3×C13C3×C13×D11semidirect
56. C13⋊C3C13×D33semidirect
59. C3×C11C13×D13⋊C3semidirect
65. C13C3⋊(C11⋊(D13⋊C3))direct (N × H)
66. C13C3×C13×D33semidirect
67. C11C13×C3⋊(D13⋊C3)semidirect
73. C3C13×C11⋊(D13⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C3×C11×C13×C13⋊C32
C13×D4293
C13×C11⋊(D13⋊C3)3
C13×C3⋊(D13⋊C3)11
C3×C13×D3313
C3⋊(C11⋊(D13⋊C3))13