Finite Group Databasebeta

← C3×(C5⋊D5)⋊(C11⋊D11) #49137727

Subgroups — C3×(C5⋊D5)⋊(C11⋊D11) #49137727

Order 36300.

672 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C5⋊(C11⋊D11)C212yesmaximal, complemented
2C3×C112×C5⋊D5C211yesmaximal, characteristic, complemented
3(C5⋊D5)⋊(C11⋊D11)C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5C3×D5×C11⋊D11—52nomaximal
6C112×C5⋊D5C2×C311yescharacteristic, complemented
7C5×C5⋊(C11⋊D11)C2×C312yescomplemented
8C3×C5⋊(C11⋊D11)D512yescomplemented
9C3×D5×C112—52no—
10C3×D5×C112—102no—
11C3×C5×C11⋊D11—52no—
12C3×(C5⋊D5)⋊D11—1112nomaximal
13C52×C112C22×C311yescharacteristic, complemented, Hall
14D5×C11⋊D11—52no—
15C3×C5×C112—22no—
16C3×C5×C112C2×D512yescomplemented
17C3×C11×C5⋊D5D11112yescomplemented
18C3×C5×D55—1124no—
19C2×C3×C11⋊D11—251noHall
20C5⋊(C11⋊D11)C3×D512yescomplemented
21D5×C112—52no—
22D5×C112—102no—
23C5×C11⋊D11—52no—
24(C5⋊D5)⋊D11—1112no—
25C3×C52×C11C2×D11112yescomplemented
26C2×C3×C112—251no—
27C3×C11⋊D11—52no—
28C3×D5×D11—5524no—
29C5×C112—22no—
30C5×C112C2×C3×D512yescomplemented
31C11×C5⋊D5C3×D11112yescomplemented
32C5×D55—1124no—
33C2×C11⋊D11—251noHall
34C3×C112D5211yescharacteristic, complemented, Hall
35C3×D55—1124no—
36C3×D5×C11—524no—
37C3×D5×C11—1024no—
38C3×C5×D11—5524no—
39C3×D52—1211noHall
40C52×C11C2×C3×D11112yescomplemented
41C2×C112—251no—
42C11⋊D11—52no—
43D5×D11—5524no—
44C3×C5×C11—224no—
45C3×C5×C11D5×D11124yescomplemented
46C3×C5⋊D5C11⋊D1111yescharacteristic, complemented
47C3×C5×D5—1212no—
48C2×C3×D11—27512no—
49C112C3×D5211yescharacteristic, complemented, Sylow
50D55—1124no—
51C5×D11—5524no—
52D5×C11—524no—
53D5×C11—1024no—
54D52—1211noHall
55C3×C52C2×C11⋊D1111yescharacteristic, complemented, Hall
56C2×C3×C11—2512no—
57C3×D11—5524no—
58C2×C3×D5—6052no—
59C5×C11—224no—
60C5×C11C3×D5×D11124yescomplemented
61C5⋊D5C3×C11⋊D1111yescharacteristic, complemented
62C5×D5—1212no—
63C2×D11—27512no—
64C3×C11(C5⋊D5)⋊D11112yescomplemented
65C2×C3×C5—6052no—
66C3×D5—52no—
67C3×D5—102no—
68C3×D5—1212no—
69C52C2×C3×C11⋊D1111yescharacteristic, complemented, Sylow
70C2×C11—2512no—
71D11—5524no—
72C2×D5—6052no—
73C3×C5—22no—
74C3×C5D5×C11⋊D1112yescomplemented
75C22×C3—30251noHall
76C11C3×(C5⋊D5)⋊D11112yescomplemented
77C2×C5—6052no—
78D5—52no—
79D5—102no—
80D5—1212no—
81C2×C3—251no—
82C2×C3—6052no—
83C5—22no—
84C5C3×D5×C11⋊D1112yescomplemented
85C22—30251noSylow
86C3(C5⋊D5)⋊(C11⋊D11)11yescharacteristic, direct product factor, Sylow
87C2—251no—
88C2—6052no—
subgroupG/H
center, hypercenterC3(C5⋊D5)⋊(C11⋊D11)
commutator, cosocle, hypocenterC52×C112C22×C3
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C52×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C5⋊(C11⋊D11)C2semidirect
2. C3×C112×C5⋊D5C2semidirect
3. (C5⋊D5)⋊(C11⋊D11)C3direct (N × H)
4. C3×C52×C112C22semidirect
6. C112×C5⋊D5C2×C3semidirect
7. C5×C5⋊(C11⋊D11)C2×C3semidirect
8. C3×C5⋊(C11⋊D11)D5semidirect
13. C52×C112C22×C3semidirect
16. C3×C5×C112C2×D5semidirect
17. C3×C11×C5⋊D5D11semidirect
20. C5⋊(C11⋊D11)C3×D5semidirect
25. C3×C52×C11C2×D11semidirect
30. C5×C112C2×C3×D5semidirect
31. C11×C5⋊D5C3×D11semidirect
34. C3×C112D52semidirect
40. C52×C11C2×C3×D11semidirect
45. C3×C5×C11D5×D11semidirect
46. C3×C5⋊D5C11⋊D11semidirect
49. C112C3×D52semidirect
55. C3×C52C2×C11⋊D11semidirect
60. C5×C11C3×D5×D11semidirect
61. C5⋊D5C3×C11⋊D11semidirect
64. C3×C11(C5⋊D5)⋊D11semidirect
69. C52C2×C3×C11⋊D11semidirect
74. C3×C5D5×C11⋊D11semidirect
76. C11C3×(C5⋊D5)⋊D11semidirect
84. C5C3×D5×C11⋊D11semidirect
86. C3(C5⋊D5)⋊(C11⋊D11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C5⋊(C11⋊D11)2
C3×C112×C5⋊D52
(C5⋊D5)⋊(C11⋊D11)3
C3×D5×C11⋊D115
C3×(C5⋊D5)⋊D1111