Finite Group Databasebeta

← C52×D3×C11×D11 #49137742

Subgroups — C52×D3×C11×D11 #49137742

Order 36300.

480 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 160 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
2C52×D3×C112C211yesmaximal, characteristic, complemented
3C52×C11×D33C211yesmaximal, characteristic, complemented
4C2×C52×C11×D11—31nomaximal, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6C5×D3×C11×D11C516yesmaximal, direct product factor
7C52×C11×D11—31no—
8C52×C11×D11D311yescharacteristic, direct product factor
9C2×C52×C112—31no—
10C5×C11×D33C2×C516yescomplemented
11C5×D3×C112C2×C516yescomplemented
12C3×C5×C11×D11C2×C516yescomplemented
13C2×C52×D3×C11—111nomaximal
14C52×D3×D11C1111yesmaximal, characteristic, direct product factor
15C52×C112C2×D311yescharacteristic, complemented, Hall
16C2×C5×C11×D11—36no—
17C3×C5×C112C22×C516yescomplemented
18C2×C3×C52×C11—111no—
19C52×D33C2×C1111yescharacteristic, complemented
20C52×D3×C11—25no—
21C52×D3×C11—111no—
22C52×D3×C11D1111yescharacteristic, direct product factor
23C52×D3×C11C2×C1111yescharacteristic, complemented
24C3×C52×D11C2×C1111yescharacteristic, complemented
25D3×C11×D11C5211yescharacteristic, direct product factor, Hall
26C2×C5×C112—36no—
27C5×C11×D11—36no—
28C5×C11×D11C5×D316yesdirect product factor
29C22×C52×C11—331no—
30C2×C52×D11—31no—
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C22×C1111yescharacteristic, complemented
34C11×D33C2×C5211yescharacteristic, complemented
35D3×C112C2×C5211yescharacteristic, complemented
36C3×C11×D11C2×C5211yescharacteristic, complemented
37C2×C5×D3×C11—116no—
38C5×D3×D11C5×C1116yesdirect product factor
39C5×C112C2×C5×D316yescomplemented
40C2×C52×C11—31no—
41C2×C52×C11—31no—
42C2×C52×C11—65no—
43C2×C52×C11—111no—
44C2×C52×C11—331no—
45C52×D11—31no—
46C52×D11D3×C1111yescharacteristic, direct product factor
47C2×C11×D11—31noHall
48C3×C112C22×C5211yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50C5×D33C2×C5×C1116yescomplemented
51C5×D3×C11—230no—
52C5×D3×C11—116no—
53C5×D3×C11C5×D1116yesdirect product factor
54C5×D3×C11C2×C5×C1116yescomplemented
55C3×C5×D11C2×C5×C1116yescomplemented
56C2×C52×D3—111noHall
57C52×C11—25no—
58C52×C11D3×D1111yescharacteristic, direct product factor
59C52×C11C2×D3×C1111yescharacteristic, complemented
60C2×C112—31no—
61C11×D11—31no—
62C11×D11C52×D311yescharacteristic, direct product factor
63C22×C5×C11—336no—
64C2×C5×D11—36no—
65C3×C5×C11—230no—
66C3×C5×C11C2×C5×D1116yescomplemented
67C3×C5×C11C22×C5×C1116yescomplemented
68C2×C3×C52—111no—
69C52×D3—111no—
70C52×D3C11×D1111yescharacteristic, direct product factor
71C2×D3×C11—111no—
72D3×D11C52×C1111yescharacteristic, direct product factor
73C112C2×C52×D311yescharacteristic, complemented, Sylow
74C2×C5×C11—36no—
75C2×C5×C11—36no—
76C2×C5×C11—630no—
77C2×C5×C11—116no—
78C2×C5×C11—336no—
79C5×D11—36no—
80C5×D11C5×D3×C1116yesdirect product factor
81C22×C52—331noHall
82C3×C52C2×C11×D1111yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84D33C2×C52×C1111yescharacteristic, complemented
85C3×D11C2×C52×C1111yescharacteristic, complemented
86D3×C11—25no—
87D3×C11—111no—
88D3×C11C52×D1111yescharacteristic, direct product factor
89D3×C11C2×C52×C1111yescharacteristic, complemented
90C2×C5×D3—116no—
91C5×C11—230no—
92C5×C11C5×D3×D1116yesdirect product factor
93C5×C11C2×C5×D3×C1116yescomplemented
94C2×C52—31no—
95C2×C52—111no—
96C2×C52—331no—
97C22×C11—331no—
98C2×D11—31no—
99C3×C11—25no—
100C3×C11C2×C52×D1111yescharacteristic, complemented
101C3×C11C22×C52×C1111yescharacteristic, complemented
102C2×C3×C5—116no—
103C5×D3—116no—
104C5×D3C5×C11×D1116yesdirect product factor
105C52D3×C11×D1111yescharacteristic, direct product factor, Sylow
106C2×C11—31no—
107C2×C11—31no—
108C2×C11—65no—
109C2×C11—111no—
110C2×C11—331no—
111D11—31no—
112D11C52×D3×C1111yescharacteristic, direct product factor
113C22×C5—336no—
114C3×C5C2×C5×C11×D1116yescomplemented
115C2×D3—111noHall
116C11—25no—
117C11C52×D3×D1111yescharacteristic, direct product factor
118C11C2×C52×D3×C1111yescharacteristic, complemented
119C2×C5—36no—
120C2×C5—116no—
121C2×C5—336no—
122C2×C3—111no—
123D3—111no—
124D3C52×C11×D1111yescharacteristic, direct product factor
125C5C5×D3×C11×D1116yesdirect product factor
126C22—331noSylow
127C3C2×C52×C11×D1111yescharacteristic, complemented, Sylow
128C2—31no—
129C2—111no—
130C2—331no—
subgroupG/H
center, hypercenterC52×C11D3×D11
commutator, cosocle, hypocenterC3×C11C22×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C3×C11
UCSC1 ◁ C52×C11

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C52×D3×C112C2semidirect
3. C52×C11×D33C2semidirect
5. C3×C52×C112C22semidirect
6. C5×D3×C11×D11C5direct (N × H)
8. C52×C11×D11D3direct (N × H)
10. C5×C11×D33C2×C5semidirect
11. C5×D3×C112C2×C5semidirect
12. C3×C5×C11×D11C2×C5semidirect
14. C52×D3×D11C11direct (N × H)
15. C52×C112C2×D3semidirect
17. C3×C5×C112C22×C5semidirect
19. C52×D33C2×C11semidirect
22. C52×D3×C11D11direct (N × H)
23. C52×D3×C11C2×C11semidirect
24. C3×C52×D11C2×C11semidirect
25. D3×C11×D11C52direct (N × H)
28. C5×C11×D11C5×D3direct (N × H)
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C22×C11semidirect
34. C11×D33C2×C52semidirect
35. D3×C112C2×C52semidirect
36. C3×C11×D11C2×C52semidirect
38. C5×D3×D11C5×C11direct (N × H)
39. C5×C112C2×C5×D3semidirect
46. C52×D11D3×C11direct (N × H)
48. C3×C112C22×C52semidirect
50. C5×D33C2×C5×C11semidirect
53. C5×D3×C11C5×D11direct (N × H)
54. C5×D3×C11C2×C5×C11semidirect
55. C3×C5×D11C2×C5×C11semidirect
58. C52×C11D3×D11direct (N × H)
59. C52×C11C2×D3×C11semidirect
62. C11×D11C52×D3direct (N × H)
66. C3×C5×C11C2×C5×D11semidirect
67. C3×C5×C11C22×C5×C11semidirect
70. C52×D3C11×D11direct (N × H)
72. D3×D11C52×C11direct (N × H)
73. C112C2×C52×D3semidirect
80. C5×D11C5×D3×C11direct (N × H)
82. C3×C52C2×C11×D11semidirect
84. D33C2×C52×C11semidirect
85. C3×D11C2×C52×C11semidirect
88. D3×C11C52×D11direct (N × H)
89. D3×C11C2×C52×C11semidirect
92. C5×C11C5×D3×D11direct (N × H)
93. C5×C11C2×C5×D3×C11semidirect
100. C3×C11C2×C52×D11semidirect
101. C3×C11C22×C52×C11semidirect
104. C5×D3C5×C11×D11direct (N × H)
105. C52D3×C11×D11direct (N × H)
112. D11C52×D3×C11direct (N × H)
114. C3×C5C2×C5×C11×D11semidirect
117. C11C52×D3×D11direct (N × H)
118. C11C2×C52×D3×C11semidirect
124. D3C52×C11×D11direct (N × H)
125. C5C5×D3×C11×D11direct (N × H)
127. C3C2×C52×C11×D11semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C52×D3×C1122
C52×C11×D332
C2×C52×C11×D113
C5×D3×C11×D115
C2×C52×D3×C1111
C52×D3×D1111