Finite Group Databasebeta

← #13182994

Subgroups — #13182994

Order 1760.

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

normal subgroups only

This group has 260 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
1C22×D5×D11C211yesmaximal, characteristic, complemented
2C2×C22⋊D55C211yesmaximal, characteristic, complemented
3C2×C11×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C5×C22⋊D11C211yesmaximal, characteristic, complemented
5#11724886C211yesmaximal, characteristic, complemented
6#11724885C211yesmaximal, characteristic, complemented
7(C2×D11)⋊Dic5C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic, complemented
9C22×D55C2211yescharacteristic
10C22×D5×C11C2211yescharacteristic
11C22×C5×D11C2211yescharacteristic
12C2×D5×D11—22no—
13C2×D5×D11—22no—
14C2×D5×D11—22no—
15C22⋊D55—22no—
16C2×Dic55C2211yescharacteristic, complemented
17C11×C22⋊D5—22no—
18C2×C11×Dic5C2211yescharacteristic, complemented
19C5×C22⋊D11—22no—
20C2×C5×Dic11C2211yescharacteristic, complemented
21#66990—51nomaximal, Hall
22C22×C5×C11—21no—
23C22×C5×C11—21no—
24C22×C5×C11—21no—
25C22×C5×C11C2311yescharacteristic
26C2×D55—21no—
27C2×D55—21no—
28C2×D55D412yescomplemented
29C2×D5×C11—21no—
30C2×D5×C11—21no—
31C2×D5×C11D412yescomplemented
32C2×C5×D11—21no—
33C2×C5×D11—21no—
34C2×C5×D11D412yescomplemented
35D5×D11—28no—
36Dic55—21no—
37C5×Dic11—21no—
38C11×Dic5—21no—
39C23×D11—51no—
40C2×D4×C11—51no—
41C2×C22⋊D11—51no—
42C2×C22⋊D11D511yescharacteristic, complemented
43C22⋊Dic11—51no—
44(C2×D11)⋊C4—51no—
45(C2×D11)⋊C4—51no—
46#4083—111nomaximal, Hall
47C2×C5×C11—41no—
48C2×C5×C11C2×D411yescharacteristic
49C2×C5×C11C2×D411yescharacteristic
50C2×C5×C11C2×D411yescharacteristic
51D55—22no—
52C5×D11—22no—
53D5×C11—22no—
54C23×C11—51no—
55C23×C11C2×D511yescharacteristic, complemented
56C22×D11—51no—
57C22×D11—102no—
58C22×D11—102no—
59C22×D11—102no—
60C22×D11C2×D511yescharacteristic
61D4×C11—102no—
62C2×C4×C11—51no—
63C22⋊D11—22no—
64C22⋊D11—102no—
65C2×Dic11—51no—
66C2×Dic11C2×D511yescharacteristic, complemented
67C23×D5—111no—
68C2×C5×D4—111no—
69C2×C22⋊D5—111no—
70C2×C22⋊D5D1111yescharacteristic, complemented
71C22⋊Dic5—111no—
72#685—111no—
73#685—111no—
74C5×C11#12011yescharacteristic, complemented, Hall
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—52no—
79C22×C11—101no—
80C22×C11—101no—
81C22×C11C22×D511yescharacteristic
82C2×D11—21no—
83C2×D11—21no—
84C2×D11—52no—
85C2×D11—108no—
86C2×D11—101no—
87C2×D11—101no—
88C2×D11C22⋊D512yescomplemented
89C4×C11—101no—
90Dic11—21no—
91Dic11—101no—
92C23×C5—111no—
93C23×C5C2×D1111yescharacteristic, complemented
94C22×D5—111no—
95C22×D5—222no—
96C22×D5—222no—
97C22×D5—222no—
98C22×D5C2×D1111yescharacteristic
99C5×D4—222no—
100C2×C4×C5—111no—
101C22⋊D5—22no—
102C22⋊D5—222no—
103C2×Dic5—111no—
104C2×Dic5C2×D1111yescharacteristic, complemented
105#120—551noSylow
106C2×C11—41no—
107C2×C11—102no—
108C2×C11D4×D511yescharacteristic
109C2×C11D4×D511yescharacteristic
110C2×C11C2×C22⋊D511yescharacteristic
111D11—22no—
112D11—102no—
113C22×C5—21no—
114C22×C5—21no—
115C22×C5—21no—
116C22×C5—112no—
117C22×C5—221no—
118C22×C5—221no—
119C22×C5C22×D1111yescharacteristic
120C2×D5—21no—
121C2×D5—21no—
122C2×D5—112no—
123C2×D5—228no—
124C2×D5—221no—
125C2×D5—221no—
126C2×D5C22⋊D1112yescomplemented
127C4×C5—221no—
128Dic5—21no—
129Dic5—221no—
130C24—551no—
131C2×D4—51no—
132C2×D4—111no—
133C2×D4—551no—
134C22⋊C4—551no—
135C22⋊C4—551no—
136C22⋊C4—551no—
137C11#408311yescharacteristic, complemented, Sylow
138C2×C5—41no—
139C2×C5—222no—
140C2×C5D4×D1111yescharacteristic
141C2×C5D4×D1111yescharacteristic
142C2×C5C2×C22⋊D1111yescharacteristic
143D5—22no—
144D5—222no—
145C23—51no—
146C23—111no—
147C23—551no—
148C23—1102no—
149C23—1102no—
150C23—1102no—
151C23D5×D1111yescharacteristic, complemented
152D4—102no—
153D4—222no—
154D4—1102no—
155C2×C4—51no—
156C2×C4—111no—
157C2×C4—551no—
158C5#6699011yescharacteristic, complemented, Sylow
159C22—21no—
160C22—21no—
161C22—21no—
162C22—52no—
163C22—101no—
164C22—101no—
165C22—112no—
166C22—221no—
167C22—221no—
168C22—552no—
169C22—1108no—
170C22—1101no—
171C22—1101no—
172C22C2×D5×D1111yescharacteristic
173C4—101no—
174C4—221no—
175C4—1101no—
176C2—41no—
177C2—102no—
178C2—222no—
179C2—1102no—
180C2D11×C22⋊D511yescharacteristic
181C2D5×C22⋊D1111yescharacteristic
182C2#1172500711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC23×C5×C11C22
hypercenterC23D5×D11
hypocenterC5×C11#120
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×D5×D11C2semidirect
2. C2×C22⋊D55C2semidirect
3. C2×C11×C22⋊D5C2semidirect
4. C2×C5×C22⋊D11C2semidirect
5. #11724886C2semidirect
6. #11724885C2semidirect
7. (C2×D11)⋊Dic5C2semidirect
8. C23×C5×C11C22semidirect
16. C2×Dic55C22semidirect
18. C2×C11×Dic5C22semidirect
20. C2×C5×Dic11C22semidirect
28. C2×D55D4semidirect
31. C2×D5×C11D4semidirect
34. C2×C5×D11D4semidirect
42. C2×C22⋊D11D5semidirect
55. C23×C11C2×D5semidirect
66. C2×Dic11C2×D5semidirect
70. C2×C22⋊D5D11semidirect
74. C5×C11#120semidirect
88. C2×D11C22⋊D5semidirect
93. C23×C5C2×D11semidirect
104. C2×Dic5C2×D11semidirect
126. C2×D5C22⋊D11semidirect
137. C11#4083semidirect
151. C23D5×D11semidirect
158. C5#66990semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D112
C2×C22⋊D552
C2×C11×C22⋊D52
C2×C5×C22⋊D112
#117248862
#117248852
(C2×D11)⋊Dic52
#669905
#408311