Finite Group Databasebeta

← #13182834

Subgroups — #13182834

Order 1760.

188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×C4×C5×D11C211yesmaximal, characteristic, complemented
2C2×#89167C211yesmaximal, characteristic
3C2×D5×Dic11C211yesmaximal, characteristic, complemented
4#11724930C211yesmaximal, characteristic, complemented
5C11×#685C211yesmaximal, characteristic, complemented
6(C2×D11)⋊Dic5C211yesmaximal, characteristic, complemented
7Dic5×Dic11C211yesmaximal, characteristic, complemented
8C22×D5×C11C2211yescharacteristic
9C22×C5×D11C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×Dic55C2211yescharacteristic
12C2×Dic55C2211yescharacteristic
13C2×C11×Dic5C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15C4×C5×D11—22no—
16#89167C414yescomplemented
17D5×Dic11—22no—
18(C22⋊D11)⋊C4—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D5×C11—21no—
21C2×D5×C11—21no—
22C2×D5×C11C2×C412yescomplemented
23C2×C5×D11—21no—
24C2×C5×D11—21no—
25C2×C5×D11C2×C412yescomplemented
26C4×C5×C11—21no—
27Dic55—21no—
28Dic55C2×C412yescomplemented
29C5×Dic11D412yescomplemented
30C11×Dic5—21no—
31C2×C22⋊D11—51no—
32C22×Dic11—51no—
33C2×C4×D11D511yescharacteristic, complemented
34C11×C22⋊C4—51no—
35(C2×D11)⋊C4—51no—
36Dic11⋊C4—51no—
37C4×Dic11—51no—
38C4×C22⋊D5—111nomaximal, Hall
39C2×C5×C11C22×C411yescharacteristic
40C2×C5×C11C2×D411yescharacteristic
41C2×C5×C11#4111yescharacteristic
42C5×D11—22no—
43D5×C11—22no—
44C23×C11—51no—
45C22×D11C2×D511yescharacteristic
46C2×C4×C11—51no—
47C2×C4×C11C2×D511yescharacteristic
48C22⋊D11—54no—
49C2×Dic11—51no—
50C2×Dic11—51no—
51C2×Dic11—102no—
52C2×Dic11C2×D511yescharacteristic
53C4×D11—22no—
54C22×C4×C5—111no—
55C2×C22⋊D5—111no—
56C2×C4×D5—111no—
57C22⋊Dic5—111no—
58#685D1111yescharacteristic, complemented
59#683—111no—
60C4×Dic5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—52no—
63C22×C11—101no—
64C22×C11—101no—
65C22×C11C22×D511yescharacteristic
66C2×D11—21no—
67C2×D11—21no—
68C2×D11C4×D512yescomplemented
69C4×C11—21no—
70C4×C11—101no—
71Dic11—52no—
72Dic11—101no—
73Dic11C22⋊D512yescomplemented
74C23×C5—111no—
75C22×D5C2×D1111yescharacteristic
76C2×C4×C5—111no—
77C2×C4×C5—222no—
78C2×C4×C5C2×D1111yescharacteristic
79C22⋊D5—114no—
80C2×Dic5—111no—
81C2×Dic5—111no—
82C2×Dic5C2×D1111yescharacteristic
83C4×D5—222no—
84C4×D4—551noSylow
85C2×C11—102no—
86C2×C11C2×C4×D511yescharacteristic
87C2×C11#70911yescharacteristic
88C2×C11C2×C22⋊D511yescharacteristic
89D11—22no—
90C22×C5—112no—
91C22×C5—221no—
92C22×C5—221no—
93C22×C5C22×D1111yescharacteristic
94C2×D5—21no—
95C2×D5—21no—
96C2×D5C4×D1112yescomplemented
97C4×C5—21no—
98C4×C5—112no—
99Dic5—21no—
100Dic5—112no—
101Dic5—221no—
102C2×D4—551no—
103C22×C4—111no—
104C22×C4—551no—
105C4⋊C4—551no—
106C22⋊C4—51no—
107C22⋊C4—551no—
108C42—551no—
109C11C4×C22⋊D511yescharacteristic, complemented, Sylow
110C2×C5—222no—
111C2×C5C2×C4×D1111yescharacteristic
112C2×C5D4×D1111yescharacteristic
113C2×C5#434111yescharacteristic
114D5—22no—
115C23—51no—
116C23—111no—
117D4—554no—
118C2×C4—51no—
119C2×C4—111no—
120C2×C4—222no—
121C2×C4—551no—
122C2×C4—551no—
123C2×C4—1102no—
124C2×C4D5×D1111yescharacteristic
125C5(C22⋊D11)⋊C411yescharacteristic, complemented, Sylow
126C22—52no—
127C22—101no—
128C22—101no—
129C22—112no—
130C22—221no—
131C22—221no—
132C22C2×D5×D1111yescharacteristic
133C4—21no—
134C4—101no—
135C4—112no—
136C4—552no—
137C4—1101no—
138C2—102no—
139C2—222no—
140C2#1172498911yescharacteristic
141C2C4×D5×D1111yescharacteristic
142C2D11×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutatorC2×C5×C11C22×C4
FittingC2×C4×C5×C11C22
socle, cosocleC22×C5×C11C23
prime radicalC2×#89167C2
hypercenterC2×C4D5×D11
hypocenterC5×C11C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×D11C2semidirect
3. C2×D5×Dic11C2semidirect
4. #11724930C2semidirect
5. C11×#685C2semidirect
6. (C2×D11)⋊Dic5C2semidirect
7. Dic5×Dic11C2semidirect
16. #89167C4semidirect
22. C2×D5×C11C2×C4semidirect
25. C2×C5×D11C2×C4semidirect
28. Dic55C2×C4semidirect
29. C5×Dic11D4semidirect
33. C2×C4×D11D5semidirect
58. #685D11semidirect
61. C5×C11C4×D4semidirect
68. C2×D11C4×D5semidirect
73. Dic11C22⋊D5semidirect
96. C2×D5C4×D11semidirect
109. C11C4×C22⋊D5semidirect
125. C5(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D112
C2×#891672
C2×D5×Dic112
#117249302
C11×#6852
(C2×D11)⋊Dic52
Dic5×Dic112
(C22⋊D11)⋊C45
C4×C22⋊D511