Finite Group Databasebeta

← C2×C3×C11×C5⋊D55 #49137822

Subgroups — C2×C3×C11×C5⋊D55 #49137822

Order 36300.

480 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 140 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×C11×C5⋊D55C212yesmaximal, direct product factor
2C2×C3×C52×C112C211yesmaximal, characteristic, complemented
3C2×C11×C5⋊D55C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5C2×C3×C11×D55—56nomaximal
6C11×C5⋊D55C2×C312yesdirect product factor
7C2×C52×C112C2×C311yescharacteristic, complemented
8C3×C11×D55—512no—
9C2×C3×C5×C112D516yescomplemented
10C2×C3×C5⋊D55C1111yesmaximal, characteristic, direct product factor
11C2×C3×C11×C5⋊D5—111nomaximal
12C52×C112C22×C311yescharacteristic, complemented, Hall
13C2×C11×D55—56no—
14C3×C5×C112C2×D516yescomplemented
15C2×C3×C52×C11—25no—
16C2×C3×C52×C11D1111yescharacteristic, complemented
17C2×C3×C52×C11C2×C1111yescharacteristic, complemented
18C3×C5⋊D55C2×C1112yesdirect product factor
19C3×C11×C5⋊D5—112no—
20C2×C3×C11×D11—251noHall
21C2×C5×C112C3×D516yescomplemented
22C11×D55—512no—
23C2×C5⋊D55C3×C1111yescharacteristic, direct product factor
24C2×C11×C5⋊D5—111no—
25C3×C52×C11—25no—
26C3×C52×C11C2×D1111yescharacteristic, complemented
27C3×C52×C11C22×C1111yescharacteristic, complemented
28C2×C3×C112C5⋊D511yescharacteristic, complemented
29C3×C11×D11—252no—
30C2×C3×D55—56no—
31C2×C3×D5×C11—556no—
32C5×C112C2×C3×D516yescomplemented
33C2×C52×C11—25no—
34C2×C52×C11C3×D1111yescharacteristic, complemented
35C2×C52×C11C2×C3×C1111yescharacteristic, complemented
36C5⋊D55C2×C3×C1112yesdirect product factor
37C11×C5⋊D5—112no—
38C2×C11×D11—251noHall
39C3×C112C2×C5⋊D511yescharacteristic, complemented, Hall
40C2×C3×C5×C11—230no—
41C2×C3×C5×C11D5×C1116yescomplemented
42C2×C3×C5×C11D5516yescomplemented
43C3×D55—512no—
44C3×D5×C11—5512no—
45C2×C3×C5⋊D5—111noHall
46C52×C11—25no—
47C52×C11C2×C3×D1111yescharacteristic, complemented
48C52×C11C22×C3×C1111yescharacteristic, complemented
49C2×C112C3×C5⋊D511yescharacteristic, complemented
50C11×D11—252no—
51C2×D55—56no—
52C2×D5×C11—556no—
53C3×C5×C11—230no—
54C3×C5×C11C2×D5×C1116yescomplemented
55C3×C5×C11C2×D5516yescomplemented
56C2×C3×C52C11×D1111yescharacteristic, complemented
57C3×C5⋊D5—112no—
58C22×C3×C11—2751no—
59C2×C3×D11—251no—
60C112C2×C3×C5⋊D511yescharacteristic, complemented, Sylow
61C2×C5×C11—230no—
62C2×C5×C11C3×D5×C1116yescomplemented
63C2×C5×C11C3×D5516yescomplemented
64D55—512no—
65D5×C11—5512no—
66C2×C5⋊D5—111noHall
67C3×C52C2×C11×D1111yescharacteristic, complemented, Hall
68C2×C3×C11—25no—
69C2×C3×C11—2752no—
70C2×C3×C11C11×C5⋊D511yescharacteristic, complemented
71C2×C3×C11C5⋊D5511yescharacteristic, direct product factor
72C3×D11—252no—
73C2×C3×D5—556no—
74C5×C11—230no—
75C5×C11C2×C3×D5×C1116yescomplemented
76C5×C11C2×C3×D5516yescomplemented
77C2×C52C3×C11×D1111yescharacteristic, complemented
78C5⋊D5—112no—
79C22×C11—2751no—
80C2×D11—251no—
81C3×C11—25no—
82C3×C11C2×C11×C5⋊D511yescharacteristic, complemented
83C3×C11C2×C5⋊D5511yescharacteristic, direct product factor
84C2×C3×C5C11×D5516yescomplemented
85C3×D5—5512no—
86C52C2×C3×C11×D1111yescharacteristic, complemented, Sylow
87C2×C11—25no—
88C2×C11—2752no—
89C2×C11C3×C11×C5⋊D511yescharacteristic, complemented
90C2×C11C3×C5⋊D5511yescharacteristic, direct product factor
91D11—252no—
92C2×D5—556no—
93C3×C5C2×C11×D5516yescomplemented
94C22×C3—2751noHall
95C11—25no—
96C11C2×C3×C11×C5⋊D511yescharacteristic, complemented
97C11C2×C3×C5⋊D5511yescharacteristic, direct product factor
98C2×C5C3×C11×D5516yescomplemented
99D5—5512no—
100C2×C3—2752no—
101C2×C3C11×C5⋊D5511yescharacteristic, direct product factor
102C5C2×C3×C11×D5516yescomplemented
103C22—2751noSylow
104C3C2×C11×C5⋊D5511yescharacteristic, direct product factor, Sylow
105C2—2752no—
106C2C3×C11×C5⋊D5511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11C5⋊D55
commutator, cosocle, hypocenterC52×C11C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C112C2
LCSG ▷ C52×C11
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×C5⋊D55C2direct (N × H)
2. C2×C3×C52×C112C2semidirect
3. C2×C11×C5⋊D55C3direct (N × H)
4. C3×C52×C112C22semidirect
6. C11×C5⋊D55C2×C3direct (N × H)
7. C2×C52×C112C2×C3semidirect
9. C2×C3×C5×C112D5semidirect
10. C2×C3×C5⋊D55C11direct (N × H)
12. C52×C112C22×C3semidirect
14. C3×C5×C112C2×D5semidirect
16. C2×C3×C52×C11D11semidirect
17. C2×C3×C52×C11C2×C11semidirect
18. C3×C5⋊D55C2×C11direct (N × H)
21. C2×C5×C112C3×D5semidirect
23. C2×C5⋊D55C3×C11direct (N × H)
26. C3×C52×C11C2×D11semidirect
27. C3×C52×C11C22×C11semidirect
28. C2×C3×C112C5⋊D5semidirect
32. C5×C112C2×C3×D5semidirect
34. C2×C52×C11C3×D11semidirect
35. C2×C52×C11C2×C3×C11semidirect
36. C5⋊D55C2×C3×C11direct (N × H)
39. C3×C112C2×C5⋊D5semidirect
41. C2×C3×C5×C11D5×C11semidirect
42. C2×C3×C5×C11D55semidirect
47. C52×C11C2×C3×D11semidirect
48. C52×C11C22×C3×C11semidirect
49. C2×C112C3×C5⋊D5semidirect
54. C3×C5×C11C2×D5×C11semidirect
55. C3×C5×C11C2×D55semidirect
56. C2×C3×C52C11×D11semidirect
60. C112C2×C3×C5⋊D5semidirect
62. C2×C5×C11C3×D5×C11semidirect
63. C2×C5×C11C3×D55semidirect
67. C3×C52C2×C11×D11semidirect
70. C2×C3×C11C11×C5⋊D5semidirect
71. C2×C3×C11C5⋊D55direct (N × H)
75. C5×C11C2×C3×D5×C11semidirect
76. C5×C11C2×C3×D55semidirect
77. C2×C52C3×C11×D11semidirect
82. C3×C11C2×C11×C5⋊D5semidirect
83. C3×C11C2×C5⋊D55direct (N × H)
84. C2×C3×C5C11×D55semidirect
86. C52C2×C3×C11×D11semidirect
89. C2×C11C3×C11×C5⋊D5semidirect
90. C2×C11C3×C5⋊D55direct (N × H)
93. C3×C5C2×C11×D55semidirect
96. C11C2×C3×C11×C5⋊D5semidirect
97. C11C2×C3×C5⋊D55direct (N × H)
98. C2×C5C3×C11×D55semidirect
101. C2×C3C11×C5⋊D55direct (N × H)
102. C5C2×C3×C11×D55semidirect
104. C3C2×C11×C5⋊D55direct (N × H)
106. C2C3×C11×C5⋊D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×C5⋊D552
C2×C3×C52×C1122
C2×C11×C5⋊D553
C2×C3×C11×D555
C2×C3×C5⋊D5511
C2×C3×C11×C5⋊D511