Finite Group Databasebeta

← C11×D11×C3⋊(C5⋊D5) #49137787

Subgroups — C11×D11×C3⋊(C5⋊D5) #49137787

Order 36300.

480 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×C11×D11C211yesmaximal, characteristic, complemented
2C112×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊D55)C211yesmaximal, characteristic, complemented
4C11×D11×C5⋊D5—31nomaximal, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6C11×D11×D15—56nomaximal
7C11×C5⋊D55—31no—
8C112×C5⋊D5—31no—
9C52×C11×D11D311yescharacteristic, complemented
10C11×D165—56no—
11C112×D15—56no—
12C3×C5×C11×D11D516yescomplemented
13C2×C11×C3⋊(C5⋊D5)—111nomaximal
14D11×C3⋊(C5⋊D5)C1111yesmaximal, characteristic, direct product factor
15C52×C112C2×D311yescharacteristic, complemented, Hall
16D5×C11×D11—156no—
17C3×C5×C112C2×D516yescomplemented
18C2×C3×C52×C11—111no—
19C3⋊(C5⋊D55)C2×C1111yescharacteristic, complemented
20C11×C3⋊(C5⋊D5)—25no—
21C11×C3⋊(C5⋊D5)—111no—
22C11×C3⋊(C5⋊D5)D1111yescharacteristic, direct product factor
23C11×C3⋊(C5⋊D5)C2×C1111yescharacteristic, complemented
24C3×C52×D11C2×C1111yescharacteristic, complemented
25D3×C11×D11—251noHall
26C11×D55—156no—
27D5×C112—156no—
28C5×C11×D11D1516yescomplemented
29C2×C11×C5⋊D5—331no—
30D11×C5⋊D5—31no—
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C22×C1111yescharacteristic, complemented
34C11×D33—251no—
35D3×C112—251no—
36C3×C11×D11C5⋊D511yescharacteristic, complemented
37C2×C11×D15—556no—
38D11×D15—56no—
39C5×C112C2×D1516yescomplemented
40C2×C52×C11—111no—
41C5⋊D55—31no—
42C11×C5⋊D5—31no—
43C11×C5⋊D5—31no—
44C11×C5⋊D5—65no—
45C11×C5⋊D5—331no—
46C52×D11D3×C1111yescharacteristic, complemented
47C2×C11×D11—751noHall
48C3×C112C2×C5⋊D511yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50D165—56no—
51C11×D15—56no—
52C11×D15—56no—
53C11×D15—1030no—
54C11×D15—556no—
55C3×C5×D11D5×C1116yescomplemented
56C2×C3⋊(C5⋊D5)—111noHall
57C52×C11—25no—
58C52×C11D3×D1111yescharacteristic, complemented
59C52×C11C2×D3×C1111yescharacteristic, complemented
60C2×C112—751no—
61C11×D11—751no—
62C11×D11C3⋊(C5⋊D5)11yescharacteristic, direct product factor
63C2×D5×C11—1656no—
64D5×D11—156no—
65C3×C5×C11—230no—
66C3×C5×C11D5×D1116yescomplemented
67C3×C5×C11C2×D5×C1116yescomplemented
68C2×C3×C52—111no—
69C3⋊(C5⋊D5)—111no—
70C3⋊(C5⋊D5)C11×D1111yescharacteristic, direct product factor
71C2×D3×C11—2751no—
72D3×D11—251no—
73C112C2×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
74C2×C5×C11—116no—
75D55—156no—
76C5×D11C11×D1516yescomplemented
77D5×C11—156no—
78D5×C11—156no—
79D5×C11—3030no—
80D5×C11—1656no—
81C2×C5⋊D5—331noHall
82C3×C52C2×C11×D1111yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84D33—251no—
85C3×D11C11×C5⋊D511yescharacteristic, complemented
86D3×C11—2751no—
87D3×C11—251no—
88D3×C11—251no—
89D3×C11—505no—
90C2×D15—556no—
91C5×C11—230no—
92C5×C11D11×D1516yescomplemented
93C5×C11C2×C11×D1516yescomplemented
94C2×C52—111no—
95C5⋊D5—31no—
96C5⋊D5—331no—
97C22×C11—8251no—
98C2×D11—751no—
99C3×C11—25no—
100C3×C11D11×C5⋊D511yescharacteristic, complemented
101C3×C11C2×C11×C5⋊D511yescharacteristic, complemented
102C2×C3×C5—116no—
103D15—56no—
104D15—556no—
105C52D3×C11×D1111yescharacteristic, complemented, Sylow
106C2×C11—111no—
107C2×C11—8251no—
108C2×C11—751no—
109C2×C11—751no—
110C2×C11—1505no—
111D11—751no—
112D11C11×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
113C2×D5—1656no—
114C3×C5D5×C11×D1116yescomplemented
115C2×D3—2751noHall
116C11—25no—
117C11D11×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
118C11C2×C11×C3⋊(C5⋊D5)11yescharacteristic, complemented
119C2×C5—116no—
120D5—156no—
121D5—1656no—
122C2×C3—111no—
123D3—2751no—
124D3—251no—
125C5C11×D11×D1516yescomplemented
126C22—8251noSylow
127C3C11×D11×C5⋊D511yescharacteristic, complemented, Sylow
128C2—111no—
129C2—8251no—
130C2—751no—
subgroupG/H
center, hypercenterC11D11×C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C11C22×C11
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C3×C52×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C112×C3⋊(C5⋊D5)C2semidirect
3. C11×C3⋊(C5⋊D55)C2semidirect
5. C3×C52×C112C22semidirect
9. C52×C11×D11D3semidirect
12. C3×C5×C11×D11D5semidirect
14. D11×C3⋊(C5⋊D5)C11direct (N × H)
15. C52×C112C2×D3semidirect
17. C3×C5×C112C2×D5semidirect
19. C3⋊(C5⋊D55)C2×C11semidirect
22. C11×C3⋊(C5⋊D5)D11direct (N × H)
23. C11×C3⋊(C5⋊D5)C2×C11semidirect
24. C3×C52×D11C2×C11semidirect
28. C5×C11×D11D15semidirect
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C22×C11semidirect
36. C3×C11×D11C5⋊D5semidirect
39. C5×C112C2×D15semidirect
46. C52×D11D3×C11semidirect
48. C3×C112C2×C5⋊D5semidirect
55. C3×C5×D11D5×C11semidirect
58. C52×C11D3×D11semidirect
59. C52×C11C2×D3×C11semidirect
62. C11×D11C3⋊(C5⋊D5)direct (N × H)
66. C3×C5×C11D5×D11semidirect
67. C3×C5×C11C2×D5×C11semidirect
70. C3⋊(C5⋊D5)C11×D11direct (N × H)
73. C112C2×C3⋊(C5⋊D5)semidirect
76. C5×D11C11×D15semidirect
82. C3×C52C2×C11×D11semidirect
85. C3×D11C11×C5⋊D5semidirect
92. C5×C11D11×D15semidirect
93. C5×C11C2×C11×D15semidirect
100. C3×C11D11×C5⋊D5semidirect
101. C3×C11C2×C11×C5⋊D5semidirect
105. C52D3×C11×D11semidirect
112. D11C11×C3⋊(C5⋊D5)direct (N × H)
114. C3×C5D5×C11×D11semidirect
117. C11D11×C3⋊(C5⋊D5)direct (N × H)
118. C11C2×C11×C3⋊(C5⋊D5)semidirect
125. C5C11×D11×D15semidirect
127. C3C11×D11×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C112×C3⋊(C5⋊D5)2
C11×C3⋊(C5⋊D55)2
C11×D11×C5⋊D53
C11×D11×D155
C2×C11×C3⋊(C5⋊D5)11
D11×C3⋊(C5⋊D5)11