Finite Group Databasebeta

← C3×D3×C11×C11⋊C5 #24926152

Subgroups — C3×D3×C11×C11⋊C5 #24926152

Order 10890.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C2×C3×C11×C11⋊C5—31nomaximal
3D3×C11×C11⋊C5C311yesmaximal, characteristic, direct product factor
4C3×D3×C112C511yesmaximal, characteristic, complemented, Hall
5C3×C11×C11⋊C5—21no—
6C3×C11×C11⋊C5D311yescharacteristic, direct product factor
7C3×C11×C11⋊C5C2×C311yescharacteristic, complemented
8C2×C11×C11⋊C5—31noHall
9C32×C112C2×C511yescharacteristic, complemented, Hall
10C3×C5×D3×C11—111nomaximal
11C3×D3×C11⋊C5C1111yesmaximal, characteristic, direct product factor
12C2×C3×C112—31no—
13D3×C112C3×C511yescharacteristic, complemented
14C11×C11⋊C5C3×D311yescharacteristic, direct product factor, Hall
15C32×C5×C11—111no—
16C32×C11⋊C5C2×C1111yescharacteristic, complemented
17C3×C112—21no—
18C3×C112C5×D311yescharacteristic, complemented
19C3×C112C2×C3×C511yescharacteristic, complemented
20C2×C3×C5×C11—331no—
21C5×D3×C11—111no—
22C2×C3×C11⋊C5—31no—
23D3×C11⋊C5C3×C1111yescharacteristic, direct product factor
24C2×C112—31noHall
25C3×D3×C11—52no—
26C3×D3×C11C11⋊C511yescharacteristic, direct product factor
27C3×D3×C11C5×C1111yescharacteristic, complemented
28C3×C5×C11—111no—
29C3×C5×C11—111no—
30C3×C5×C11—221no—
31C3×C11⋊C5—21no—
32C3×C11⋊C5D3×C1111yescharacteristic, direct product factor
33C3×C11⋊C5C2×C3×C1111yescharacteristic, complemented
34C112C3×C5×D311yescharacteristic, complemented, Sylow
35C2×C5×C11—331no—
36C2×C11⋊C5—31no—
37C32×C11—52no—
38C32×C11C2×C11⋊C511yescharacteristic, complemented
39C32×C11C2×C5×C1111yescharacteristic, complemented
40C3×C5×D3—111noHall
41C2×C3×C11—31no—
42C2×C3×C11—31no—
43C2×C3×C11—152no—
44D3×C11—52no—
45D3×C11C3×C11⋊C511yescharacteristic, direct product factor
46D3×C11C3×C5×C1111yescharacteristic, complemented
47C5×C11—111no—
48C11⋊C5C3×D3×C1111yescharacteristic, direct product factor
49C32×C5—111noHall
50C3×C11—21no—
51C3×C11—21no—
52C3×C11—52no—
53C3×C11—52no—
54C3×C11—102no—
55C3×C11D3×C11⋊C511yescharacteristic, direct product factor
56C3×C11C2×C3×C11⋊C511yescharacteristic, complemented
57C3×C11C5×D3×C1111yescharacteristic, complemented
58C3×C11C2×C3×C5×C1111yescharacteristic, complemented
59C2×C3×C5—331no—
60C5×D3—111no—
61C2×C11—31no—
62C2×C11—31no—
63C2×C11—152no—
64C3×D3C11×C11⋊C511yescharacteristic, direct product factor, Hall
65C3×C5—111no—
66C3×C5—111no—
67C3×C5—221no—
68C11—52no—
69C11C3×D3×C11⋊C511yescharacteristic, direct product factor
70C11C3×C5×D3×C1111yescharacteristic, complemented
71C2×C5—331noHall
72C32C2×C11×C11⋊C511yescharacteristic, complemented, Sylow
73C2×C3—31no—
74D3C3×C11×C11⋊C511yescharacteristic, direct product factor
75C5—111noSylow
76C3—21no—
77C3D3×C11×C11⋊C511yescharacteristic, direct product factor
78C3C2×C3×C11×C11⋊C511yescharacteristic, complemented
79C2—31noSylow
subgroupG/H
center, hypercenterC3×C11D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×C11⋊C5C2semidirect
3. D3×C11×C11⋊C5C3direct (N × H)
4. C3×D3×C112C5semidirect
6. C3×C11×C11⋊C5D3direct (N × H)
7. C3×C11×C11⋊C5C2×C3semidirect
9. C32×C112C2×C5semidirect
11. C3×D3×C11⋊C5C11direct (N × H)
13. D3×C112C3×C5semidirect
14. C11×C11⋊C5C3×D3direct (N × H)
16. C32×C11⋊C5C2×C11semidirect
18. C3×C112C5×D3semidirect
19. C3×C112C2×C3×C5semidirect
23. D3×C11⋊C5C3×C11direct (N × H)
26. C3×D3×C11C11⋊C5direct (N × H)
27. C3×D3×C11C5×C11semidirect
32. C3×C11⋊C5D3×C11direct (N × H)
33. C3×C11⋊C5C2×C3×C11semidirect
34. C112C3×C5×D3semidirect
38. C32×C11C2×C11⋊C5semidirect
39. C32×C11C2×C5×C11semidirect
45. D3×C11C3×C11⋊C5direct (N × H)
46. D3×C11C3×C5×C11semidirect
48. C11⋊C5C3×D3×C11direct (N × H)
55. C3×C11D3×C11⋊C5direct (N × H)
56. C3×C11C2×C3×C11⋊C5semidirect
57. C3×C11C5×D3×C11semidirect
58. C3×C11C2×C3×C5×C11semidirect
64. C3×D3C11×C11⋊C5direct (N × H)
69. C11C3×D3×C11⋊C5direct (N × H)
70. C11C3×C5×D3×C11semidirect
72. C32C2×C11×C11⋊C5semidirect
74. D3C3×C11×C11⋊C5direct (N × H)
77. C3D3×C11×C11⋊C5direct (N × H)
78. C3C2×C3×C11×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C32×C11×C11⋊C52
C2×C3×C11×C11⋊C53
D3×C11×C11⋊C53
C3×D3×C1125
C3×C5×D3×C1111
C3×D3×C11⋊C511