Finite Group Databasebeta

← C2×C3×C5×C5⋊(C11⋊D11) #49137820

Subgroups — C2×C3×C5×C5⋊(C11⋊D11) #49137820

Order 36300.

672 conjugacy classes of subgroups; only the 236 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 236 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×C5×C5⋊(C11⋊D11)C212yesmaximal, direct product factor
2C2×C3×C52×C112C211yesmaximal, characteristic, complemented
3C2×C5×C5⋊(C11⋊D11)C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5C2×C3×C5×C11⋊D11—51nomaximal
6C2×C3×C5⋊(C11⋊D11)C511yesmaximal, characteristic, direct product factor
7C5×C5⋊(C11⋊D11)C2×C312yesdirect product factor
8C2×C52×C112C2×C311yescharacteristic, complemented
9C3×C5⋊(C11⋊D11)C2×C512yesdirect product factor
10C3×C5×C11⋊D11—52no—
11C2×C3×C5×C112—22no—
12C2×C3×C5×C112D511yescharacteristic, complemented
13C2×C3×C5×C112C2×C511yescharacteristic, complemented
14C2×C3×C5×D55—1112nomaximal
15C52×C112C22×C311yescharacteristic, complemented, Hall
16C2×C5⋊(C11⋊D11)C3×C511yescharacteristic, direct product factor
17C2×C5×C11⋊D11—51no—
18C3×C5×C112—22no—
19C3×C5×C112C2×D511yescharacteristic, complemented
20C3×C5×C112C22×C511yescharacteristic, complemented
21C2×C3×C52×C11D11112yescomplemented
22C3×C5×D55—1124no—
23C2×C3×C11⋊D11—51noHall
24C2×C5×C112—22no—
25C2×C5×C112C3×D511yescharacteristic, complemented
26C2×C5×C112C2×C3×C511yescharacteristic, complemented
27C5⋊(C11⋊D11)C2×C3×C512yesdirect product factor
28C5×C11⋊D11—52no—
29C2×C5×D55—1112no—
30C3×C52×C11C2×D11112yescomplemented
31C2×C3×C112C5×D511yescharacteristic, complemented
32C3×C11⋊D11—52no—
33C2×C3×D55—1112no—
34C2×C3×C5×D11—5512no—
35C5×C112—22no—
36C5×C112C2×C3×D511yescharacteristic, complemented
37C5×C112C22×C3×C511yescharacteristic, complemented
38C2×C52×C11C3×D11112yescomplemented
39C5×D55—1124no—
40C2×C11⋊D11—51noHall
41C3×C112C2×C5×D511yescharacteristic, complemented, Hall
42C2×C3×C5×C11—224no—
43C2×C3×C5×C11C5×D11112yescomplemented
44C2×C3×C5×C11D55112yescomplemented
45C3×D55—1124no—
46C3×C5×D11—5524no—
47C2×C3×C5×D5—1211noHall
48C52×C11C2×C3×D11112yescomplemented
49C2×C112C3×C5×D511yescharacteristic, complemented
50C11⋊D11—52no—
51C2×D55—1112no—
52C2×C5×D11—5512no—
53C3×C5×C11—224no—
54C3×C5×C11C2×C5×D11112yescomplemented
55C3×C5×C11C2×D55112yescomplemented
56C2×C3×C52C11⋊D1111yescharacteristic, complemented
57C3×C5×D5—1212no—
58C2×C3×D11—5512no—
59C112C2×C3×C5×D511yescharacteristic, complemented, Sylow
60C2×C5×C11—224no—
61C2×C5×C11C3×C5×D11112yescomplemented
62C2×C5×C11C3×D55112yescomplemented
63D55—1124no—
64C5×D11—5524no—
65C2×C5×D5—1211noHall
66C3×C52C2×C11⋊D1111yescharacteristic, complemented, Hall
67C2×C3×C11C5×D55112yescomplemented
68C3×D11—5524no—
69C22×C3×C5—6051no—
70C2×C3×D5—1211no—
71C5×C11—224no—
72C5×C11C2×C3×C5×D11112yescomplemented
73C5×C11C2×C3×D55112yescomplemented
74C2×C52C3×C11⋊D1111yescharacteristic, complemented
75C5×D5—1212no—
76C2×D11—5512no—
77C3×C11C2×C5×D55112yescomplemented
78C2×C3×C5—22no—
79C2×C3×C5—6052no—
80C2×C3×C5C5×C11⋊D1111yescharacteristic, complemented
81C2×C3×C5C5⋊(C11⋊D11)11yescharacteristic, direct product factor
82C3×D5—1212no—
83C52C2×C3×C11⋊D1111yescharacteristic, complemented, Sylow
84C2×C11C3×C5×D55112yescomplemented
85D11—5524no—
86C22×C5—6051no—
87C2×D5—1211no—
88C3×C5—22no—
89C3×C5C2×C5×C11⋊D1111yescharacteristic, complemented
90C3×C5C2×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
91C22×C3—6051noHall
92C11C2×C3×C5×D55112yescomplemented
93C2×C5—22no—
94C2×C5—6052no—
95C2×C5C3×C5×C11⋊D1111yescharacteristic, complemented
96C2×C5C3×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
97D5—1212no—
98C2×C3—6052no—
99C2×C3C5×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
100C5—22no—
101C5C2×C3×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
102C5C2×C3×C5×C11⋊D1111yescharacteristic, complemented
103C22—6051noSylow
104C3C2×C5×C5⋊(C11⋊D11)11yescharacteristic, direct product factor, Sylow
105C2—6052no—
106C2C3×C5×C5⋊(C11⋊D11)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5C5⋊(C11⋊D11)
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C112C2
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C5⋊(C11⋊D11)C2direct (N × H)
2. C2×C3×C52×C112C2semidirect
3. C2×C5×C5⋊(C11⋊D11)C3direct (N × H)
4. C3×C52×C112C22semidirect
6. C2×C3×C5⋊(C11⋊D11)C5direct (N × H)
7. C5×C5⋊(C11⋊D11)C2×C3direct (N × H)
8. C2×C52×C112C2×C3semidirect
9. C3×C5⋊(C11⋊D11)C2×C5direct (N × H)
12. C2×C3×C5×C112D5semidirect
13. C2×C3×C5×C112C2×C5semidirect
15. C52×C112C22×C3semidirect
16. C2×C5⋊(C11⋊D11)C3×C5direct (N × H)
19. C3×C5×C112C2×D5semidirect
20. C3×C5×C112C22×C5semidirect
21. C2×C3×C52×C11D11semidirect
25. C2×C5×C112C3×D5semidirect
26. C2×C5×C112C2×C3×C5semidirect
27. C5⋊(C11⋊D11)C2×C3×C5direct (N × H)
30. C3×C52×C11C2×D11semidirect
31. C2×C3×C112C5×D5semidirect
36. C5×C112C2×C3×D5semidirect
37. C5×C112C22×C3×C5semidirect
38. C2×C52×C11C3×D11semidirect
41. C3×C112C2×C5×D5semidirect
43. C2×C3×C5×C11C5×D11semidirect
44. C2×C3×C5×C11D55semidirect
48. C52×C11C2×C3×D11semidirect
49. C2×C112C3×C5×D5semidirect
54. C3×C5×C11C2×C5×D11semidirect
55. C3×C5×C11C2×D55semidirect
56. C2×C3×C52C11⋊D11semidirect
59. C112C2×C3×C5×D5semidirect
61. C2×C5×C11C3×C5×D11semidirect
62. C2×C5×C11C3×D55semidirect
66. C3×C52C2×C11⋊D11semidirect
67. C2×C3×C11C5×D55semidirect
72. C5×C11C2×C3×C5×D11semidirect
73. C5×C11C2×C3×D55semidirect
74. C2×C52C3×C11⋊D11semidirect
77. C3×C11C2×C5×D55semidirect
80. C2×C3×C5C5×C11⋊D11semidirect
81. C2×C3×C5C5⋊(C11⋊D11)direct (N × H)
83. C52C2×C3×C11⋊D11semidirect
84. C2×C11C3×C5×D55semidirect
89. C3×C5C2×C5×C11⋊D11semidirect
90. C3×C5C2×C5⋊(C11⋊D11)direct (N × H)
92. C11C2×C3×C5×D55semidirect
95. C2×C5C3×C5×C11⋊D11semidirect
96. C2×C5C3×C5⋊(C11⋊D11)direct (N × H)
99. C2×C3C5×C5⋊(C11⋊D11)direct (N × H)
101. C5C2×C3×C5⋊(C11⋊D11)direct (N × H)
102. C5C2×C3×C5×C11⋊D11semidirect
104. C3C2×C5×C5⋊(C11⋊D11)direct (N × H)
106. C2C3×C5×C5⋊(C11⋊D11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C5⋊(C11⋊D11)2
C2×C3×C52×C1122
C2×C5×C5⋊(C11⋊D11)3
C2×C3×C5×C11⋊D115
C2×C3×C5⋊(C11⋊D11)5
C2×C3×C5×D5511