Finite Group Databasebeta

← C11×D15×C11⋊C5 #31827663

Subgroups — C11×D15×C11⋊C5 #31827663

Order 18150.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2D5×C11×C11⋊C5—31nomaximal, Hall
3C112×D15C511yesmaximal, characteristic, complemented
4D3×C11×C11⋊C5—51nomaximal
5C5×C11×C11⋊C5D311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×C11×C11⋊C5—22no—
8C3×C11×C11⋊C5D511yescharacteristic, complemented
9C5×C11×D15—111nomaximal
10D15×C11⋊C5C1111yesmaximal, characteristic, direct product factor
11D5×C112—31no—
12C2×C11×C11⋊C5—151no—
13C3×C52×C11—111no—
14C3×C5×C11⋊C5C2×C1111yescharacteristic, complemented
15D3×C112—51noHall
16C5×C112C5×D311yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5D1511yescharacteristic, direct product factor
19C5×D5×C11—331no—
20D5×C11⋊C5—31no—
21C3×C112C5×D511yescharacteristic, complemented, Hall
22C11×D15—52no—
23C11×D15C11⋊C511yescharacteristic, direct product factor
24C11×D15C5×C1111yescharacteristic, complemented
25C5×D3×C11—551no—
26D3×C11⋊C5—51no—
27C52×C11—111no—
28C5×C11⋊C5D3×C1111yescharacteristic, complemented
29C2×C112—151noHall
30C3×C5×C11—52no—
31C3×C5×C11—111no—
32C3×C5×C11—222no—
33C3×C5×C11C2×C11⋊C511yescharacteristic, complemented
34C3×C5×C11C2×C5×C1111yescharacteristic, complemented
35C3×C11⋊C5—22no—
36C3×C11⋊C5D5×C1111yescharacteristic, complemented
37C5×D15—111noHall
38C112C5×D1511yescharacteristic, complemented, Sylow
39C2×C5×C11—1651no—
40D5×C11—31no—
41D5×C11—31no—
42D5×C11—152no—
43C2×C11⋊C5—151no—
44C3×C52—111noHall
45D3×C11—51no—
46D3×C11—51no—
47D3×C11—252no—
48C5×C11—52no—
49C5×C11—111no—
50C5×C11—222no—
51C5×C11D3×C11⋊C511yescharacteristic, complemented
52C5×C11C5×D3×C1111yescharacteristic, complemented
53C11⋊C5—22no—
54C11⋊C5C11×D1511yescharacteristic, direct product factor
55C5×D5—331noHall
56C3×C11—52no—
57C3×C11D5×C11⋊C511yescharacteristic, complemented
58C3×C11C5×D5×C1111yescharacteristic, complemented
59D15C11×C11⋊C511yescharacteristic, direct product factor
60C5×D3—551no—
61C52—111noSylow
62C2×C11—151no—
63C2×C11—151no—
64C2×C11—752no—
65C3×C5—111no—
66C3×C5—222no—
67C3×C5C2×C11×C11⋊C511yescharacteristic, complemented
68C11—52no—
69C11D15×C11⋊C511yescharacteristic, direct product factor
70C11C5×C11×D1511yescharacteristic, complemented
71C2×C5—1651no—
72D5—31no—
73D3—51noHall
74C5—111no—
75C5—222no—
76C5D3×C11×C11⋊C511yescharacteristic, complemented
77C3D5×C11×C11⋊C511yescharacteristic, complemented, Sylow
78C2—151noSylow
subgroupG/H
center, hypercenterC11D15×C11⋊C5
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C11⋊C5C2semidirect
3. C112×D15C5semidirect
5. C5×C11×C11⋊C5D3semidirect
6. C3×C5×C112C2×C5semidirect
8. C3×C11×C11⋊C5D5semidirect
10. D15×C11⋊C5C11direct (N × H)
14. C3×C5×C11⋊C5C2×C11semidirect
16. C5×C112C5×D3semidirect
18. C11×C11⋊C5D15direct (N × H)
21. C3×C112C5×D5semidirect
23. C11×D15C11⋊C5direct (N × H)
24. C11×D15C5×C11semidirect
28. C5×C11⋊C5D3×C11semidirect
33. C3×C5×C11C2×C11⋊C5semidirect
34. C3×C5×C11C2×C5×C11semidirect
36. C3×C11⋊C5D5×C11semidirect
38. C112C5×D15semidirect
51. C5×C11D3×C11⋊C5semidirect
52. C5×C11C5×D3×C11semidirect
54. C11⋊C5C11×D15direct (N × H)
57. C3×C11D5×C11⋊C5semidirect
58. C3×C11C5×D5×C11semidirect
59. D15C11×C11⋊C5direct (N × H)
67. C3×C5C2×C11×C11⋊C5semidirect
69. C11D15×C11⋊C5direct (N × H)
70. C11C5×C11×D15semidirect
76. C5D3×C11×C11⋊C5semidirect
77. C3D5×C11×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×C11⋊C52
D5×C11×C11⋊C53
C112×D155
D3×C11×C11⋊C55
C5×C11×D1511
D15×C11⋊C511