Finite Group Databasebeta

← #13182838

Subgroups — #13182838

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×#89168C211yesmaximal, characteristic
3C2×#89166C211yesmaximal, characteristic, complemented
4#11724932C211yesmaximal, characteristic, complemented
5C11×#683C211yesmaximal, characteristic, complemented
6(C2×D11)⋊Dic5C211yesmaximal, characteristic, complemented
7Dic5×Dic11C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C22×C5×D11C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×Dic55C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C11×Dic5C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15C4×C5×D11—22no—
16#89168C414yescomplemented
17#89166—22no—
18#66946—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55—21no—
21C2×D55—21no—
22C2×D55C2×C412yescomplemented
23C2×C5×D11—21no—
24C2×C5×D11—21no—
25C2×C5×D11C2×C412yescomplemented
26C4×C5×C11—21no—
27Dic55—21no—
28C5×Dic11D412yescomplemented
29C11×Dic5—21no—
30C11×Dic5C2×C412yescomplemented
31C2×D44—51no—
32C2×C4×D11—51no—
33C2×C4×D11D511yescharacteristic, complemented
34C11×C4⋊C4—51no—
35(C2×D11)⋊C4—51no—
36(C2×D11)⋊C4—51no—
37C4×Dic11—51no—
38C4×C22⋊D5—111nomaximal, Hall
39C2×C5×C11C22×C411yescharacteristic
40C2×C5×C11C2×D411yescharacteristic
41C2×C5×C11#4111yescharacteristic
42D55—22no—
43C5×D11—22no—
44C22×D11—51no—
45C22×D11C2×D511yescharacteristic
46C2×C4×C11—51no—
47C2×C4×C11—51no—
48C2×C4×C11C2×D511yescharacteristic
49C2×Dic11—51no—
50C2×Dic11C2×D511yescharacteristic
51D44—54no—
52C4×D11—22no—
53C4×D11—102no—
54C22×C4×C5—111no—
55C2×C22⋊D5—111no—
56C2×C4×D5—111no—
57C22⋊Dic5—111no—
58#685—111no—
59#683D1111yescharacteristic, complemented
60C4×Dic5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11C22×D511yescharacteristic
63C2×D11—21no—
64C2×D11—21no—
65C2×D11—52no—
66C2×D11—101no—
67C2×D11—101no—
68C2×D11C4×D512yescomplemented
69C4×C11—21no—
70C4×C11—52no—
71C4×C11—101no—
72Dic11—101no—
73Dic11C22⋊D512yescomplemented
74C23×C5—111no—
75C22×D5—111no—
76C2×C4×C5—111no—
77C2×C4×C5—222no—
78C2×C4×C5C2×D1111yescharacteristic
79C22⋊D5—114no—
80C2×Dic5—111no—
81C2×Dic5C2×D1111yescharacteristic
82C2×Dic5C2×D1111yescharacteristic
83C4×D5—222no—
84C4×D4—551noSylow
85C2×C11C2×C4×D511yescharacteristic
86C2×C11#70911yescharacteristic
87C2×C11C2×C22⋊D511yescharacteristic
88D11—22no—
89D11—102no—
90C22×C5—112no—
91C22×C5—221no—
92C22×C5—221no—
93C22×C5C22×D1111yescharacteristic
94C2×D5—112no—
95C2×D5—221no—
96C2×D5—221no—
97C4×C5—21no—
98C4×C5—112no—
99Dic5—21no—
100Dic5—221no—
101Dic5C4×D1112yescomplemented
102C2×D4—551no—
103C22×C4—111no—
104C22×C4—551no—
105C4⋊C4—51no—
106C22⋊C4—551no—
107C22⋊C4—551no—
108C42—551no—
109C11C4×C22⋊D511yescharacteristic, complemented, Sylow
110C2×C5—222no—
111C2×C5C2×C4×D1111yescharacteristic
112C2×C5D4×D1111yescharacteristic
113C2×C5#434311yescharacteristic
114D5—222no—
115C23—111no—
116C23—551no—
117D4—554no—
118C2×C4—51no—
119C2×C4—51no—
120C2×C4—111no—
121C2×C4—222no—
122C2×C4—551no—
123C2×C4—1102no—
124C2×C4D5×D1111yescharacteristic
125C5#6694611yescharacteristic, complemented, Sylow
126C22—112no—
127C22—221no—
128C22—221no—
129C22—552no—
130C22—1101no—
131C22—1101no—
132C22C2×D5×D1111yescharacteristic
133C4—21no—
134C4—52no—
135C4—101no—
136C4—112no—
137C4—1101no—
138C2—222no—
139C2—1102no—
140C2#1172499011yescharacteristic
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×#89168C2
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×#89166C2semidirect
4. #11724932C2semidirect
5. C11×#683C2semidirect
6. (C2×D11)⋊Dic5C2semidirect
7. Dic5×Dic11C2semidirect
16. #89168C4semidirect
22. C2×D55C2×C4semidirect
25. C2×C5×D11C2×C4semidirect
28. C5×Dic11D4semidirect
30. C11×Dic5C2×C4semidirect
33. C2×C4×D11D5semidirect
59. #683D11semidirect
61. C5×C11C4×D4semidirect
68. C2×D11C4×D5semidirect
73. Dic11C22⋊D5semidirect
101. Dic5C4×D11semidirect
109. C11C4×C22⋊D5semidirect
125. C5#66946semidirect

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×#891682
C2×#891662
#117249322
C11×#6832
(C2×D11)⋊Dic52
Dic5×Dic112
#669465
C4×C22⋊D511