Finite Group Databasebeta

← C2×C3⋊(C5⋊((C11⋊D11)⋊C3)) #36345271

Subgroups — C2×C3⋊(C5⋊((C11⋊D11)⋊C3)) #36345271

Order 21780.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C112⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(C5⋊((C11⋊D11)⋊C3))C212yesmaximal, direct product factor
3C2×C3⋊(C5⋊(C11⋊D11))C311yesmaximal, characteristic, complemented
4C2×C5⋊((C11⋊D11)⋊C3)—31nomaximal
5C3×C5×C112⋊C3C2211yescharacteristic, complemented, Hall
6C2×C3⋊((C11⋊D11)⋊C3)—51nomaximal, Hall
7C3⋊(C5⋊(C11⋊D11))C2×C312yescomplemented
8C2×C5×C112⋊C3—21no—
9C2×C5×C112⋊C3D311yescharacteristic, complemented
10C5⋊((C11⋊D11)⋊C3)—32no—
11C2×C3×C5×C112C2×C311yescharacteristic, complemented
12C2×C5⋊(C11⋊D11)—31noHall
13C2×C3×C112⋊C3D511yescharacteristic, complemented
14C3⋊((C11⋊D11)⋊C3)—52no—
15C3×C5×C112C22×C311yescharacteristic, complemented
16C5×C112⋊C3—21no—
17C5×C112⋊C3C2×D311yescharacteristic, complemented
18C2×C3⋊(C11⋊D11)—51no—
19C2×(C11⋊D11)⋊C3—151no—
20C2×C5×C112C3×D311yescharacteristic, complemented
21C5⋊(C11⋊D11)—32no—
22C3×C112⋊C3C2×D511yescharacteristic, complemented, Hall
23C2×C3×C112C3×D511yescharacteristic, complemented
24C3⋊(C11⋊D11)—52no—
25C2×C112⋊C3—21no—
26C2×C112⋊C3D1511yescharacteristic, complemented
27(C11⋊D11)⋊C3—152no—
28C2×D165—334no—
29C5×C112C2×C3×D311yescharacteristic, complemented, Hall
30C2×C11⋊D11—151noHall
31C3×C112C2×C3×D511yescharacteristic, complemented
32C112⋊C3—21no—
33C112⋊C3C2×D1511yescharacteristic, complemented
34C2×C3×C5×C11—34no—
35D165—338no—
36C2×C112C3×D1511yescharacteristic, complemented
37C11⋊D11—152no—
38C2×D55—994no—
39C2×C3×D15—1211nomaximal, Hall
40C3×C5×C11—34no—
41C2×D33—1654no—
42C112C2×C3×D1511yescharacteristic, complemented, Sylow
43C2×C5×C11—34no—
44D55—998no—
45C2×C32×C5—1211no—
46C3×D15—1212no—
47C2×C3×C11—34no—
48D33—1658no—
49C2×D15—1211no—
50C2×C3×D5—3631no—
51C5×C11—34no—
52C32×C5—1211noHall
53C2×D11—4954no—
54C2×C3×D3—6051noHall
55C3×C11—34no—
56C2×C3×C5—1211no—
57C2×C3×C5—2421no—
58C2×C3×C5(C11⋊D11)⋊C311yescharacteristic, complemented
59D15—1212no—
60C3×D5—3632no—
61C2×C11—34no—
62D11—4958no—
63C2×D5—3631noHall
64C2×C32—1211no—
65C3×D3—6052no—
66C3×C5—1211no—
67C3×C5—2421no—
68C3×C5C2×(C11⋊D11)⋊C311yescharacteristic, complemented
69C22×C3—18151no—
70C2×D3—6051no—
71C11—34no—
72C2×C5C3⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented
73D5—3632no—
74C32—1211noSylow
75C2×C3—18152no—
76C2×C3—1211no—
77C2×C3—2421no—
78C2×C3C5⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented
79D3—6052no—
80C5C2×C3⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented, Sylow
81C22—18151noSylow
82C3—1211no—
83C3—2421no—
84C3C2×C5⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented
85C2—18152no—
86C2C3⋊(C5⋊((C11⋊D11)⋊C3))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C5⋊((C11⋊D11)⋊C3))
commutator, cosocle, hypocenterC3×C5×C112C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2×C3
LCSG ▷ C3×C5×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C112⋊C3C2semidirect
2. C3⋊(C5⋊((C11⋊D11)⋊C3))C2direct (N × H)
3. C2×C3⋊(C5⋊(C11⋊D11))C3semidirect
5. C3×C5×C112⋊C3C22semidirect
7. C3⋊(C5⋊(C11⋊D11))C2×C3semidirect
9. C2×C5×C112⋊C3D3semidirect
11. C2×C3×C5×C112C2×C3semidirect
13. C2×C3×C112⋊C3D5semidirect
15. C3×C5×C112C22×C3semidirect
17. C5×C112⋊C3C2×D3semidirect
20. C2×C5×C112C3×D3semidirect
22. C3×C112⋊C3C2×D5semidirect
23. C2×C3×C112C3×D5semidirect
26. C2×C112⋊C3D15semidirect
29. C5×C112C2×C3×D3semidirect
31. C3×C112C2×C3×D5semidirect
33. C112⋊C3C2×D15semidirect
36. C2×C112C3×D15semidirect
42. C112C2×C3×D15semidirect
58. C2×C3×C5(C11⋊D11)⋊C3semidirect
68. C3×C5C2×(C11⋊D11)⋊C3semidirect
72. C2×C5C3⋊((C11⋊D11)⋊C3)semidirect
78. C2×C3C5⋊((C11⋊D11)⋊C3)semidirect
80. C5C2×C3⋊((C11⋊D11)⋊C3)semidirect
84. C3C2×C5⋊((C11⋊D11)⋊C3)semidirect
86. C2C3⋊(C5⋊((C11⋊D11)⋊C3))direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C112⋊C32
C3⋊(C5⋊((C11⋊D11)⋊C3))2
C2×C3⋊(C5⋊(C11⋊D11))3
C2×C5⋊((C11⋊D11)⋊C3)3
C2×C3⋊((C11⋊D11)⋊C3)5
C2×C3×D15121