Finite Group Databasebeta

← #13182964

Subgroups — #13182964

Order 1760.

188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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×C22⋊D55C211yesmaximal, characteristic
2C22×C5×Dic11C211yesmaximal, characteristic, complemented
3C2×#89166C211yesmaximal, characteristic, complemented
4C11×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#11724888C211yesmaximal, characteristic, complemented
6#11724886C211yesmaximal, characteristic, complemented
7Dic5×Dic11C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic
9C22×D55C2211yescharacteristic
10C22⋊D55C414yescomplemented
11C2×Dic55C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C11×Dic5C2211yescharacteristic
14C2×C5×Dic11—22no—
15C2×C5×Dic11C2211yescharacteristic
16C2×C5×Dic11C2211yescharacteristic
17#89166—22no—
18(C22⋊D11)⋊C4—51nomaximal, Hall
19C22×C5×C11—21no—
20C22×C5×C11—21no—
21C22×C5×C11C2×C412yescomplemented
22C22×C5×C11C2311yescharacteristic
23C2×D55—21no—
24C2×D55—21no—
25C2×D55C2×C412yescomplemented
26Dic55C2×C412yescomplemented
27C5×Dic11—21no—
28C5×Dic11D412yescomplemented
29C11×Dic5—21no—
30C11×Dic5—21no—
31C2×C22⋊D11—51no—
32C22×Dic11D511yescharacteristic, complemented
33C2×C4×D11—51no—
34C11×C22⋊C4—51no—
35(C2×D11)⋊C4—51no—
36Dic11⋊C4—51no—
37C4×Dic11—51no—
38C4×C22⋊D5—111nomaximal, Hall
39C2×C5×C11—22no—
40C2×C5×C11C22×C411yescharacteristic
41C2×C5×C11C2×D411yescharacteristic
42C2×C5×C11#4111yescharacteristic
43D55—22no—
44C23×C11C2×D511yescharacteristic
45C22×D11—51no—
46C2×C4×C11—51no—
47C2×C4×C11—51no—
48C22⋊D11—54no—
49C2×Dic11—22no—
50C2×Dic11—51no—
51C2×Dic11C2×D511yescharacteristic
52C2×Dic11C2×D511yescharacteristic
53C4×D11—102no—
54C22×C4×C5—111no—
55C2×C22⋊D5—111no—
56C2×C4×D5—111no—
57C22⋊Dic5D1111yescharacteristic, complemented
58#685—111no—
59#683—111no—
60C4×Dic5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—21no—
63C22×C11—21no—
64C22×C11C4×D512yescomplemented
65C22×C11C22×D511yescharacteristic
66C2×D11—52no—
67C2×D11—101no—
68C2×D11—101no—
69C4×C11—101no—
70C4×C11—101no—
71Dic11—21no—
72Dic11—52no—
73Dic11C22⋊D512yescomplemented
74C23×C5C2×D1111yescharacteristic
75C22×D5—111no—
76C2×C4×C5—111no—
77C2×C4×C5—111no—
78C2×C4×C5—222no—
79C22⋊D5—114no—
80C2×Dic5—111no—
81C2×Dic5C2×D1111yescharacteristic
82C2×Dic5C2×D1111yescharacteristic
83C4×D5—222no—
84C4×D4—551noSylow
85C2×C11—22no—
86C2×C11C2×C4×D511yescharacteristic
87C2×C11#70911yescharacteristic
88C2×C11C2×C22⋊D511yescharacteristic
89D11—102no—
90C22×C5—21no—
91C22×C5—21no—
92C22×C5C4×D1112yescomplemented
93C22×C5C22×D1111yescharacteristic
94C2×D5—112no—
95C2×D5—221no—
96C2×D5—221no—
97C4×C5—112no—
98C4×C5—221no—
99Dic5—21no—
100Dic5—21no—
101Dic5—112no—
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—22no—
111C2×C5C2×C4×D1111yescharacteristic
112C2×C5D4×D1111yescharacteristic
113C2×C5#434111yescharacteristic
114D5—222no—
115C23—551no—
116C23D5×D1111yescharacteristic
117D4—554no—
118C2×C4—51no—
119C2×C4—51no—
120C2×C4—111no—
121C2×C4—111no—
122C2×C4—222no—
123C2×C4—551no—
124C2×C4—1102no—
125C5(C22⋊D11)⋊C411yescharacteristic, complemented, Sylow
126C22—21no—
127C22—21no—
128C22—552no—
129C22—1101no—
130C22—1101no—
131C22#8916612yescomplemented
132C22C2×D5×D1111yescharacteristic
133C4—101no—
134C4—101no—
135C4—112no—
136C4—221no—
137C4—552no—
138C2—22no—
139C2—1102no—
140C2#1172499911yescharacteristic
141C2C2×#8916611yescharacteristic
142C2D11×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutatorC2×C5×C11C22×C4
FittingC23×C5×C11C22
socle, cosocleC22×C5×C11C23
prime radicalC2×C22⋊D55C2
hypercenterC23D5×D11
hypocenterC5×C11C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C5×Dic11C2semidirect
3. C2×#89166C2semidirect
4. C11×C22⋊Dic5C2semidirect
5. #11724888C2semidirect
6. #11724886C2semidirect
7. Dic5×Dic11C2semidirect
10. C22⋊D55C4semidirect
21. C22×C5×C11C2×C4semidirect
25. C2×D55C2×C4semidirect
26. Dic55C2×C4semidirect
28. C5×Dic11D4semidirect
32. C22×Dic11D5semidirect
57. C22⋊Dic5D11semidirect
61. C5×C11C4×D4semidirect
64. C22×C11C4×D5semidirect
73. Dic11C22⋊D5semidirect
92. C22×C5C4×D11semidirect
109. C11C4×C22⋊D5semidirect
125. C5(C22⋊D11)⋊C4semidirect
131. C22#89166semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊D552
C22×C5×Dic112
C2×#891662
C11×C22⋊Dic52
#117248882
#117248862
Dic5×Dic112
(C22⋊D11)⋊C45
C4×C22⋊D511