Finite Group Databasebeta

← #13182980

Subgroups — #13182980

Order 1760.

216 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 54 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, complemented
2C2×C11×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C5×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×#89169C211yesmaximal, characteristic, complemented
5C2×#89168C211yesmaximal, characteristic, complemented
6C2×#89167C211yesmaximal, characteristic, complemented
7Dic5×Dic11C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic
9C22×D55C2211yescharacteristic
10C22×D5×C11C2211yescharacteristic
11C22×C5×D11C2211yescharacteristic
12C22⋊D55—22no—
13C2×Dic55C2211yescharacteristic
14C11×C22⋊D5—22no—
15C2×C11×Dic5C2211yescharacteristic
16C5×C22⋊D11—22no—
17C2×C5×Dic11C2211yescharacteristic
18#89169—22no—
19#89168—22no—
20#89167—22no—
21#66993—51nomaximal, Hall
22C22×C5×C11—21no—
23C22×C5×C11—21no—
24C22×C5×C11—21no—
25C22×C5×C11C2311yescharacteristic
26C2×D55—21no—
27C2×D55—21no—
28C2×D55—21no—
29C2×D5×C11—21no—
30C2×D5×C11—21no—
31C2×D5×C11—21no—
32C2×C5×D11—21no—
33C2×C5×D11—21no—
34C2×C5×D11—21no—
35Dic55D412yescomplemented
36C5×Dic11D412yescomplemented
37C11×Dic5D412yescomplemented
38C2×D4×C11—51no—
39C2×C22⋊D11—51no—
40C2×C22⋊D11—51no—
41C2×C22⋊D11—51no—
42C2×C22⋊D11D511yescharacteristic, complemented
43C2×D44—51no—
44C4×Dic11—51no—
45#4086—111nomaximal, Hall
46C2×C5×C11—41no—
47C2×C5×C11C2×D411yescharacteristic
48C2×C5×C11C2×D411yescharacteristic
49C2×C5×C11C2×D411yescharacteristic
50D55—41no—
51C5×D11—41no—
52D5×C11—41no—
53C23×C11—51no—
54C23×C11C2×D511yescharacteristic
55C22×D11—51no—
56C22×D11C2×D511yescharacteristic
57D4×C11—102no—
58C2×C4×C11—51no—
59C22⋊D11—22no—
60C22⋊D11—102no—
61C22⋊D11—102no—
62C22⋊D11—102no—
63C2×Dic11—51no—
64C2×Dic11C2×D511yescharacteristic
65D44—102no—
66C2×C5×D4—111no—
67C2×C22⋊D5—111no—
68C2×C22⋊D5—111no—
69C2×C22⋊D5—111no—
70C2×C22⋊D5D1111yescharacteristic, complemented
71C2×D20—111no—
72C4×Dic5—111no—
73C5×C11#12711yescharacteristic, complemented, Hall
74C22×C11—21no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—101no—
78C22×C11—101no—
79C22×C11—101no—
80C22×C11C22×D511yescharacteristic
81C2×D11—21no—
82C2×D11—21no—
83C2×D11—21no—
84C2×D11—101no—
85C2×D11—101no—
86C2×D11—101no—
87C4×C11—52no—
88Dic11—52no—
89Dic11C22⋊D512yescomplemented
90C23×C5—111no—
91C23×C5C2×D1111yescharacteristic
92C22×D5—111no—
93C22×D5C2×D1111yescharacteristic
94C5×D4—222no—
95C2×C4×C5—111no—
96C22⋊D5—22no—
97C22⋊D5—222no—
98C22⋊D5—222no—
99C22⋊D5—222no—
100C2×Dic5—111no—
101C2×Dic5C2×D1111yescharacteristic
102D20—222no—
103#127—551noSylow
104C2×C11—41no—
105C2×C11—201no—
106C2×C11D4×D511yescharacteristic
107C2×C11D4×D511yescharacteristic
108C2×C11C2×C22⋊D511yescharacteristic
109D11—41no—
110D11—201no—
111C22×C5—21no—
112C22×C5—21no—
113C22×C5—21no—
114C22×C5—221no—
115C22×C5—221no—
116C22×C5—221no—
117C22×C5C22×D1111yescharacteristic
118C2×D5—21no—
119C2×D5—21no—
120C2×D5—21no—
121C2×D5—221no—
122C2×D5—221no—
123C2×D5—221no—
124C4×C5—112no—
125Dic5—112no—
126Dic5C22⋊D1112yescomplemented
127C2×D4—51no—
128C2×D4—111no—
129C2×D4—551no—
130C2×D4—551no—
131C2×D4—551no—
132C2×D4—551no—
133C42—551no—
134C11#408611yescharacteristic, complemented, Sylow
135C2×C5—41no—
136C2×C5—441no—
137C2×C5D4×D1111yescharacteristic
138C2×C5D4×D1111yescharacteristic
139C2×C5C2×C22⋊D1111yescharacteristic
140D5—41no—
141D5—441no—
142C23—51no—
143C23—111no—
144C23—551no—
145C23D5×D1111yescharacteristic
146D4—102no—
147D4—222no—
148D4—1102no—
149D4—1102no—
150D4—1102no—
151D4—1102no—
152C2×C4—51no—
153C2×C4—111no—
154C2×C4—551no—
155C5#6699311yescharacteristic, complemented, Sylow
156C22—21no—
157C22—21no—
158C22—21no—
159C22—101no—
160C22—101no—
161C22—101no—
162C22—221no—
163C22—221no—
164C22—221no—
165C22—1101no—
166C22—1101no—
167C22—1101no—
168C22C2×D5×D1111yescharacteristic
169C4—52no—
170C4—112no—
171C4—552no—
172C2—41no—
173C2—201no—
174C2—441no—
175C2—2201no—
176C2D11×C22⋊D511yescharacteristic
177C2D5×C22⋊D1111yescharacteristic
178C2#1172500711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC23×C5×C11C22
hypercenterC23D5×D11
hypocenterC5×C11#127
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊D55C2semidirect
2. C2×C11×C22⋊D5C2semidirect
3. C2×C5×C22⋊D11C2semidirect
4. C2×#89169C2semidirect
5. C2×#89168C2semidirect
6. C2×#89167C2semidirect
7. Dic5×Dic11C2semidirect
35. Dic55D4semidirect
36. C5×Dic11D4semidirect
37. C11×Dic5D4semidirect
42. C2×C22⋊D11D5semidirect
70. C2×C22⋊D5D11semidirect
73. C5×C11#127semidirect
89. Dic11C22⋊D5semidirect
126. Dic5C22⋊D11semidirect
134. C11#4086semidirect
155. C5#66993semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊D552
C2×C11×C22⋊D52
C2×C5×C22⋊D112
C2×#891692
C2×#891682
C2×#891672
Dic5×Dic112
#669935
#408611