Finite Group Databasebeta

← C3×C11×D11×C5⋊D5 #49137729

Subgroups — C3×C11×D11×C5⋊D5 #49137729

Order 36300.

480 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 112 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
2C3×C112×C5⋊D5C211yesmaximal, characteristic, complemented
3C3×C11×C5⋊D55C211yesmaximal, characteristic, complemented
4C11×D11×C5⋊D5C311yesmaximal, characteristic, direct product factor, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6C3×D5×C11×D11—56nomaximal
7C11×C5⋊D55C2×C311yescharacteristic, complemented
8C112×C5⋊D5C2×C311yescharacteristic, complemented
9C52×C11×D11C2×C311yescharacteristic, complemented
10C3×C11×D55—56no—
11C3×D5×C112—56no—
12C3×C5×C11×D11D516yescomplemented
13C2×C3×C11×C5⋊D5—111nomaximal
14C3×D11×C5⋊D5C1111yesmaximal, characteristic, direct product factor
15C52×C112C22×C311yescharacteristic, complemented, Hall
16D5×C11×D11—56no—
17C3×C5×C112C2×D516yescomplemented
18C2×C3×C52×C11—111no—
19C3×C5⋊D55C2×C1111yescharacteristic, complemented
20C3×C11×C5⋊D5—25no—
21C3×C11×C5⋊D5—111no—
22C3×C11×C5⋊D5D1111yescharacteristic, direct product factor
23C3×C11×C5⋊D5C2×C1111yescharacteristic, complemented
24C3×C52×D11C2×C1111yescharacteristic, complemented
25C2×C3×C11×D11—251noHall
26C11×D55—56no—
27D5×C112—56no—
28C5×C11×D11C3×D516yescomplemented
29C2×C11×C5⋊D5—111no—
30D11×C5⋊D5C3×C1111yescharacteristic, direct product factor
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C22×C1111yescharacteristic, complemented
34C2×C3×C112—251no—
35C3×C11×D11—251no—
36C3×C11×D11C5⋊D511yescharacteristic, direct product factor
37C2×C3×D5×C11—556no—
38C3×D5×D11—56no—
39C5×C112C2×C3×D516yescomplemented
40C2×C52×C11—111no—
41C5⋊D55C2×C3×C1111yescharacteristic, complemented
42C11×C5⋊D5—25no—
43C11×C5⋊D5—111no—
44C11×C5⋊D5C3×D1111yescharacteristic, direct product factor
45C11×C5⋊D5C2×C3×C1111yescharacteristic, complemented
46C52×D11C2×C3×C1111yescharacteristic, complemented
47C2×C11×D11—251noHall
48C3×C112C2×C5⋊D511yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50C3×D55—56no—
51C3×D5×C11—56no—
52C3×D5×C11—56no—
53C3×D5×C11—1030no—
54C3×D5×C11—556no—
55C3×C5×D11D5×C1116yescomplemented
56C2×C3×C5⋊D5—111noHall
57C52×C11—25no—
58C52×C11C2×C3×D1111yescharacteristic, complemented
59C52×C11C22×C3×C1111yescharacteristic, complemented
60C2×C112—251no—
61C11×D11—251no—
62C11×D11C3×C5⋊D511yescharacteristic, direct product factor
63C2×D5×C11—556no—
64D5×D11—56no—
65C3×C5×C11—230no—
66C3×C5×C11D5×D1116yescomplemented
67C3×C5×C11C2×D5×C1116yescomplemented
68C2×C3×C52—111no—
69C3×C5⋊D5—111no—
70C3×C5⋊D5C11×D1111yescharacteristic, direct product factor
71C22×C3×C11—2751no—
72C2×C3×D11—251no—
73C112C2×C3×C5⋊D511yescharacteristic, complemented, Sylow
74C2×C5×C11—116no—
75D55—56no—
76C5×D11C3×D5×C1116yescomplemented
77D5×C11—56no—
78D5×C11—56no—
79D5×C11—1030no—
80D5×C11—556no—
81C2×C5⋊D5—111noHall
82C3×C52C2×C11×D1111yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84C2×C3×C11—2751no—
85C2×C3×C11—251no—
86C2×C3×C11—251no—
87C2×C3×C11—505no—
88C3×D11—251no—
89C3×D11C11×C5⋊D511yescharacteristic, direct product factor
90C2×C3×D5—556no—
91C5×C11—230no—
92C5×C11C3×D5×D1116yescomplemented
93C5×C11C2×C3×D5×C1116yescomplemented
94C2×C52—111no—
95C5⋊D5—111no—
96C5⋊D5C3×C11×D1111yescharacteristic, direct product factor
97C22×C11—2751no—
98C2×D11—251no—
99C3×C11—25no—
100C3×C11D11×C5⋊D511yescharacteristic, direct product factor
101C3×C11C2×C11×C5⋊D511yescharacteristic, complemented
102C2×C3×C5—116no—
103C3×D5—56no—
104C3×D5—556no—
105C52C2×C3×C11×D1111yescharacteristic, complemented, Sylow
106C2×C11—111no—
107C2×C11—2751no—
108C2×C11—251no—
109C2×C11—251no—
110C2×C11—505no—
111D11—251no—
112D11C3×C11×C5⋊D511yescharacteristic, direct product factor
113C2×D5—556no—
114C3×C5D5×C11×D1116yescomplemented
115C22×C3—2751noHall
116C11—25no—
117C11C3×D11×C5⋊D511yescharacteristic, direct product factor
118C11C2×C3×C11×C5⋊D511yescharacteristic, complemented
119C2×C5—116no—
120D5—56no—
121D5—556no—
122C2×C3—111no—
123C2×C3—2751no—
124C2×C3—251no—
125C5C3×D5×C11×D1116yescomplemented
126C22—2751noSylow
127C3C11×D11×C5⋊D511yescharacteristic, direct product factor, Sylow
128C2—111no—
129C2—2751no—
130C2—251no—
subgroupG/H
center, hypercenterC3×C11D11×C5⋊D5
commutator, cosocle, hypocenterC52×C11C22×C3×C11
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C52×C11
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C3×C112×C5⋊D5C2semidirect
3. C3×C11×C5⋊D55C2semidirect
4. C11×D11×C5⋊D5C3direct (N × H)
5. C3×C52×C112C22semidirect
7. C11×C5⋊D55C2×C3semidirect
8. C112×C5⋊D5C2×C3semidirect
9. C52×C11×D11C2×C3semidirect
12. C3×C5×C11×D11D5semidirect
14. C3×D11×C5⋊D5C11direct (N × H)
15. C52×C112C22×C3semidirect
17. C3×C5×C112C2×D5semidirect
19. C3×C5⋊D55C2×C11semidirect
22. C3×C11×C5⋊D5D11direct (N × H)
23. C3×C11×C5⋊D5C2×C11semidirect
24. C3×C52×D11C2×C11semidirect
28. C5×C11×D11C3×D5semidirect
30. D11×C5⋊D5C3×C11direct (N × H)
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C22×C11semidirect
36. C3×C11×D11C5⋊D5direct (N × H)
39. C5×C112C2×C3×D5semidirect
41. C5⋊D55C2×C3×C11semidirect
44. C11×C5⋊D5C3×D11direct (N × H)
45. C11×C5⋊D5C2×C3×C11semidirect
46. C52×D11C2×C3×C11semidirect
48. C3×C112C2×C5⋊D5semidirect
55. C3×C5×D11D5×C11semidirect
58. C52×C11C2×C3×D11semidirect
59. C52×C11C22×C3×C11semidirect
62. C11×D11C3×C5⋊D5direct (N × H)
66. C3×C5×C11D5×D11semidirect
67. C3×C5×C11C2×D5×C11semidirect
70. C3×C5⋊D5C11×D11direct (N × H)
73. C112C2×C3×C5⋊D5semidirect
76. C5×D11C3×D5×C11semidirect
82. C3×C52C2×C11×D11semidirect
89. C3×D11C11×C5⋊D5direct (N × H)
92. C5×C11C3×D5×D11semidirect
93. C5×C11C2×C3×D5×C11semidirect
96. C5⋊D5C3×C11×D11direct (N × H)
100. C3×C11D11×C5⋊D5direct (N × H)
101. C3×C11C2×C11×C5⋊D5semidirect
105. C52C2×C3×C11×D11semidirect
112. D11C3×C11×C5⋊D5direct (N × H)
114. C3×C5D5×C11×D11semidirect
117. C11C3×D11×C5⋊D5direct (N × H)
118. C11C2×C3×C11×C5⋊D5semidirect
125. C5C3×D5×C11×D11semidirect
127. C3C11×D11×C5⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C3×C112×C5⋊D52
C3×C11×C5⋊D552
C11×D11×C5⋊D53
C3×D5×C11×D115
C2×C3×C11×C5⋊D511
C3×D11×C5⋊D511