Finite Group Databasebeta

← #26043811

Subgroups — #26043811

Order 11700.

288 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C5×C3⋊D195C211yesmaximal, characteristic, complemented
2C5×C13×C3⋊D15C211yesmaximal, characteristic, complemented
3C32×C5⋊D65C211yesmaximal, characteristic, complemented
4D15⋊D65—34nomaximal
5C32×C52×C13C2211yescharacteristic, complemented, Hall
6D65⋊(C3⋊D3)—51nomaximal
7C3⋊D3×D65—51nomaximal
8C5×D195—34no—
9C5×C13×D15—34no—
10C3×C5⋊D65D314yescomplemented
11D5×D65—91noHall
12C3⋊D195D511yescharacteristic, complemented
13C13×C3⋊D15D511yescharacteristic, complemented
14C5×C3⋊D39—51no—
15C5×C13×C3⋊D3—51no—
16C32×D65—51no—
17C32×D65—51no—
18C32×D65—102no—
19C3×C52×C13C2×D314yescomplemented
20#11744719—131nomaximal, Hall
21D15⋊D13—154no—
22D3×D65—154no—
23C5⋊D65C3⋊D311yescharacteristic, complemented
24C5×D65—91no—
25C5×D5×C13—91no—
26C32×C5×C13—22no—
27C32×C5×C13C2×D511yescharacteristic, complemented
28C32×C5×C13C2×D511yescharacteristic, complemented
29C3⋊D3×D13—251noHall
30C5×C3⋊D15—131no—
31C5×C3⋊D15D1311yescharacteristic, complemented
32C32×C5⋊D5—131no—
33D195—34no—
34C13×D15—34no—
35C5×D39—154no—
36C5×D3×C13—154no—
37C3×D65—54no—
38C3×D65—54no—
39C3×D65—108no—
40C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
41D15⋊D5—394no—
42C2×D65—451no—
43D5×D13—451no—
44C3⋊D39—51no—
45C13×C3⋊D3—51no—
46C32×D13—251no—
47C32×C52C2×D1311yescharacteristic, complemented, Hall
48C3×C5×C13—28no—
49C3×C5×C13D3×D514yescomplemented
50C3×C5×C13D3×D514yescomplemented
51D5×C3⋊D3—651no—
52D5×C3⋊D3—651no—
53D3×D13—754no—
54C5×D15—34no—
55C5×D15—394no—
56C3×C5⋊D5—134no—
57C2×C5×C13—451no—
58D65—51no—
59D65—51no—
60D65—91no—
61D65—102no—
62C5×D13—451no—
63D5×C13—91no—
64C32×C13D5211yescharacteristic, complemented, Hall
65D52—1171noHall
66C3⋊D15—131no—
67C3⋊D15D6511yescharacteristic, complemented
68C5×C3⋊D3—51no—
69C5×C3⋊D3—651no—
70C32×D5—651no—
71C32×D5—651no—
72C32×D5—1302no—
73D39—154no—
74C3×D13—254no—
75D3×C13—154no—
76C3×C52D3×D1314yescomplemented
77C5×C13—22no—
78C5×C13D5×C3⋊D311yescharacteristic, complemented
79C5×C13D5×C3⋊D311yescharacteristic, complemented
80D3×D5—1954no—
81D3×D5—1954no—
82C2×D13—2251noHall
83C5⋊D5—131no—
84C5×D5—91no—
85C5×D5—1171no—
86C32×C5—22no—
87C32×C5D5×D1311yescharacteristic, complemented
88C32×C5C2×D6511yescharacteristic, complemented
89C3×C13D15⋊D514yescomplemented
90C2×C3⋊D3—3251noHall
91D15—34no—
92D15—394no—
93C3×D5—654no—
94C3×D5—654no—
95C3×D5—1308no—
96C5×D3—154no—
97C5×D3—1954no—
98C2×C13—451no—
99D13—251no—
100D13—451no—
101C52C3⋊D3×D1311yescharacteristic, complemented, Sylow
102C2×D5—5851no—
103C2×D5—5851no—
104C2×C32—3251no—
105C3⋊D3—51no—
106C3⋊D3—651no—
107C3×C5—28no—
108C3×C5D3×D6514yescomplemented
109C3×C5D15⋊D1314yescomplemented
110C13#1174471911yescharacteristic, complemented, Sylow
111C2×D3—9754no—
112C2×C5—451no—
113C2×C5—5851no—
114D5—91no—
115D5—651no—
116D5—651no—
117D5—1171no—
118D5—1302no—
119C32D5×D6511yescharacteristic, complemented, Sylow
120C2×C3—3254no—
121D3—154no—
122D3—1954no—
123C5—22no—
124C5C3⋊D3×D6511yescharacteristic, complemented
125C5D65⋊(C3⋊D3)11yescharacteristic, complemented
126C22—29251noSylow
127C3D15⋊D6514yescomplemented
128C2—451no—
129C2—3251no—
130C2—5851no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C13C22
LCSG ▷ C32×C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D195C2semidirect
2. C5×C13×C3⋊D15C2semidirect
3. C32×C5⋊D65C2semidirect
5. C32×C52×C13C22semidirect
10. C3×C5⋊D65D3semidirect
12. C3⋊D195D5semidirect
13. C13×C3⋊D15D5semidirect
19. C3×C52×C13C2×D3semidirect
23. C5⋊D65C3⋊D3semidirect
27. C32×C5×C13C2×D5semidirect
28. C32×C5×C13C2×D5semidirect
31. C5×C3⋊D15D13semidirect
40. C52×C13C2×C3⋊D3semidirect
47. C32×C52C2×D13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13D3×D5semidirect
64. C32×C13D52semidirect
67. C3⋊D15D65semidirect
76. C3×C52D3×D13semidirect
78. C5×C13D5×C3⋊D3semidirect
79. C5×C13D5×C3⋊D3semidirect
87. C32×C5D5×D13semidirect
88. C32×C5C2×D65semidirect
89. C3×C13D15⋊D5semidirect
101. C52C3⋊D3×D13semidirect
108. C3×C5D3×D65semidirect
109. C3×C5D15⋊D13semidirect
110. C13#11744719semidirect
119. C32D5×D65semidirect
124. C5C3⋊D3×D65semidirect
125. C5D65⋊(C3⋊D3)semidirect
127. C3D15⋊D65semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D1952
C5×C13×C3⋊D152
C32×C5⋊D652
D15⋊D653
D65⋊(C3⋊D3)5
C3⋊D3×D655
#1174471913