Finite Group Databasebeta

← C3⋊(C5⋊((C11⋊C5)⋊D11)) #31827671

Subgroups — C3⋊(C5⋊((C11⋊C5)⋊D11)) #31827671

Order 18150.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C5⋊((C11⋊C5)⋊D11)—31nomaximal, Hall
3C3⋊(C5⋊(C11⋊D11))C511yesmaximal, characteristic, complemented
4C3⋊((C11⋊C5)⋊D11)—51nomaximal
5C5×C11×C11⋊C5D311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×C11×C11⋊C5—22no—
8C3×C11×C11⋊C5D511yescharacteristic, complemented
9C5×D165—111nomaximal
10C3⋊(C5⋊AGL(1,𝔽11))—111nomaximal
11C5⋊(C11⋊D11)—31no—
12(C11⋊C5)⋊D11—151no—
13C3×C52×C11—221no—
14C3×C5×C11⋊C5D1111yescharacteristic, complemented
15C3⋊(C11⋊D11)—51noHall
16C5×C112C5×D311yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5D1511yescharacteristic, complemented
19C5×D55—331no—
20C5⋊AGL(1,𝔽11)—331no—
21C3×C112C5×D511yescharacteristic, complemented, Hall
22D165—111no—
23D165—111no—
24D165—552no—
25C5×D33—551no—
26C3⋊AGL(1,𝔽11)—551no—
27C52×C11—221no—
28C5×C11⋊C5D3311yescharacteristic, complemented
29C11⋊D11—151noHall
30C3×C5×C11—52no—
31C3×C5×C11—222no—
32C3×C5×C11—221no—
33C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
34C3×C5×C11C5×D1111yescharacteristic, complemented
35C3×C11⋊C5—22no—
36C3×C11⋊C5D5511yescharacteristic, complemented
37C5×D15—1211noHall
38C112C5×D1511yescharacteristic, complemented, Sylow
39D55—331no—
40D55—331no—
41D55—1652no—
42C5×D11—1651no—
43AGL(1,𝔽11)—1651no—
44C3×C52—221noHall
45D33—2752no—
46D33—551no—
47D33—551no—
48C5×C11—52no—
49C5×C11—221no—
50C5×C11—222no—
51C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
52C5×C11C5×D3311yescharacteristic, complemented
53C11⋊C5—22no—
54C11⋊C5D16511yescharacteristic, complemented
55C5×D5—3631noHall
56C3×C11—52no—
57C3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
58C3×C11C5×D5511yescharacteristic, complemented
59D15—1211no—
60C5×D3—6051no—
61C52—221noSylow
62D11—8252no—
63D11—1651no—
64D11—1651no—
65C3×C5—221no—
66C3×C5—222no—
67C3×C5(C11⋊C5)⋊D1111yescharacteristic, complemented
68C11—52no—
69C11C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic, complemented
70C11C5×D16511yescharacteristic, complemented
71C2×C5—18151no—
72D5—3631no—
73D3—6051noHall
74C5—221no—
75C5—222no—
76C5C3⋊((C11⋊C5)⋊D11)11yescharacteristic, complemented
77C3C5⋊((C11⋊C5)⋊D11)11yescharacteristic, complemented, Sylow
78C2—18151noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C2×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C11⋊C5C2semidirect
3. C3⋊(C5⋊(C11⋊D11))C5semidirect
5. C5×C11×C11⋊C5D3semidirect
6. C3×C5×C112C2×C5semidirect
8. C3×C11×C11⋊C5D5semidirect
14. C3×C5×C11⋊C5D11semidirect
16. C5×C112C5×D3semidirect
18. C11×C11⋊C5D15semidirect
21. C3×C112C5×D5semidirect
28. C5×C11⋊C5D33semidirect
33. C3×C5×C11AGL(1,𝔽11)semidirect
34. C3×C5×C11C5×D11semidirect
36. C3×C11⋊C5D55semidirect
38. C112C5×D15semidirect
51. C5×C11C3⋊AGL(1,𝔽11)semidirect
52. C5×C11C5×D33semidirect
54. C11⋊C5D165semidirect
57. C3×C11C5⋊AGL(1,𝔽11)semidirect
58. C3×C11C5×D55semidirect
67. C3×C5(C11⋊C5)⋊D11semidirect
69. C11C3⋊(C5⋊AGL(1,𝔽11))semidirect
70. C11C5×D165semidirect
76. C5C3⋊((C11⋊C5)⋊D11)semidirect
77. C3C5⋊((C11⋊C5)⋊D11)semidirect

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
C5⋊((C11⋊C5)⋊D11)3
C3⋊(C5⋊(C11⋊D11))5
C3⋊((C11⋊C5)⋊D11)5
C5×D16511
C3⋊(C5⋊AGL(1,𝔽11))11