Finite Group Databasebeta

← #13182890

Subgroups — #13182890

Order 1760.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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
2C2×C4×D55C211yesmaximal, characteristic, complemented
3C2×#89166C211yesmaximal, characteristic, complemented
4C11×#685C211yesmaximal, characteristic, complemented
5C5×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#11724885C211yesmaximal, characteristic, complemented
7(C2×D11)⋊Dic5C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C22×D5×C11C2211yescharacteristic
10C22×C5×D11C2211yescharacteristic
11C2×D5×D11—22no—
12C2×D5×D11—22no—
13C2×D5×D11C414yescomplemented
14C2×C4×C5×C11C2211yescharacteristic, complemented
15C2×Dic55C2211yescharacteristic, complemented
16C4×D55—22no—
17C2×C11×Dic5C2211yescharacteristic, complemented
18C2×C5×Dic11C2211yescharacteristic, complemented
19#89166—22no—
20C22⋊C4×D11—51nomaximal, Hall
21C22×C5×C11C2311yescharacteristic
22C2×D55C2×C412yes—
23C2×D55D412yes—
24C2×D55D412yes—
25C2×D5×C11—21no—
26C2×D5×C11—21no—
27C2×D5×C11C2×C412yescomplemented
28C2×C5×D11—21no—
29C2×C5×D11—21no—
30C2×C5×D11C2×C412yescomplemented
31D5×D11—28no—
32C4×C5×C11—21no—
33Dic55—21no—
34C5×Dic11—21no—
35C11×Dic5—21no—
36C23×D11—51no—
37C2×C4×D11—51no—
38C2×C4×D11—51no—
39C11×C22⋊C4—51no—
40C22⋊Dic11—51no—
41(C2×D11)⋊C4—51no—
42(C2×D11)⋊C4D511yescharacteristic, complemented
43D5×C22⋊C4—111nomaximal, Hall
44C2×C5×C11C22×C411yescharacteristic
45C2×C5×C11C2×D411yescharacteristic
46C2×C5×C11C2×D411yescharacteristic
47D55C22⋊C414yescomplemented
48C5×D11—22no—
49D5×C11—22no—
50C23×C11—51no—
51C22×D11—51no—
52C22×D11—54no—
53C22×D11—102no—
54C22×D11—102no—
55C22×D11C2×D511yescharacteristic
56C2×C4×C11—51no—
57C2×C4×C11C2×D511yescharacteristic, complemented
58C2×Dic11—51no—
59C2×Dic11C2×D511yescharacteristic, complemented
60C4×D11—102no—
61C4×D11—102no—
62C23×D5—111no—
63C2×C4×D5—111no—
64C2×C4×D5—111no—
65C5×C22⋊C4—111no—
66C22⋊Dic5—111no—
67#685—111no—
68#685D1111yescharacteristic, complemented
69C5×C11C2×C22⋊C411yescharacteristic, complemented, Hall
70C22×C11—52no—
71C22×C11—101no—
72C22×C11—101no—
73C22×C11C22×D511yescharacteristic
74C2×D11—21no—
75C2×D11—21no—
76C2×D11—52no—
77C2×D11—52no—
78C2×D11—52no—
79C2×D11—108no—
80C2×D11C4×D512yescomplemented
81C4×C11—21no—
82C4×C11—101no—
83Dic11—21no—
84Dic11—101no—
85C23×C5—111no—
86C22×D5—111no—
87C22×D5—114no—
88C22×D5—222no—
89C22×D5—222no—
90C22×D5C2×D1111yescharacteristic
91C2×C4×C5—111no—
92C2×C4×C5C2×D1111yescharacteristic, complemented
93C2×Dic5—111no—
94C2×Dic5C2×D1111yescharacteristic, complemented
95C4×D5—222no—
96C4×D5—222no—
97C2×C22⋊C4—551noSylow
98C2×C11—102no—
99C2×C11C2×C4×D511yescharacteristic
100C2×C11D4×D511yescharacteristic
101C2×C11D4×D511yescharacteristic
102D11—22no—
103D11—54no—
104C22×C5—112no—
105C22×C5—221no—
106C22×C5—221no—
107C22×C5C22×D1111yescharacteristic
108C2×D5—21no—
109C2×D5—21no—
110C2×D5—112no—
111C2×D5—112no—
112C2×D5—112no—
113C2×D5—228no—
114C2×D5C4×D1112yescomplemented
115C4×C5—21no—
116C4×C5—221no—
117Dic5—21no—
118Dic5—221no—
119C24—551no—
120C22×C4—551no—
121C22×C4—551no—
122C22⋊C4—51no—
123C22⋊C4—111no—
124C22⋊C4—551no—
125C22⋊C4—551no—
126C11D5×C22⋊C411yescharacteristic, complemented, Sylow
127C2×C5—222no—
128C2×C5C2×C4×D1111yescharacteristic
129C2×C5D4×D1111yescharacteristic
130C2×C5D4×D1111yescharacteristic
131D5—22no—
132D5—114no—
133C23—51no—
134C23—111no—
135C23—554no—
136C23—551no—
137C23—1102no—
138C23—1102no—
139C2×C4—51no—
140C2×C4—111no—
141C2×C4—551no—
142C2×C4—1102no—
143C2×C4—1102no—
144C2×C4D5×D1111yescharacteristic, complemented
145C5C22⋊C4×D1111yescharacteristic, complemented, Sylow
146C22—52no—
147C22—101no—
148C22—101no—
149C22—112no—
150C22—221no—
151C22—221no—
152C22—552no—
153C22—552no—
154C22—552no—
155C22—1108no—
156C22C2×D5×D1111yescharacteristic
157C4—21no—
158C4—101no—
159C4—221no—
160C4—1101no—
161C2—102no—
162C2—222no—
163C2—554no—
164C2C4×D5×D1111yescharacteristic
165C2#1172499411yescharacteristic
166C2#1172500711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutatorC2×C5×C11C22×C4
FittingC2×C4×C5×C11C22
socle, cosocleC22×C5×C11C23
prime radicalC22×D5×D11C2
hypercenterC2×C4D5×D11
hypocenterC5×C11C2×C22⋊C4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D55C2semidirect
3. C2×#89166C2semidirect
4. C11×#685C2semidirect
5. C5×(C2×D11)⋊C4C2semidirect
6. #11724885C2semidirect
7. (C2×D11)⋊Dic5C2semidirect
13. C2×D5×D11C4semidirect
14. C2×C4×C5×C11C22semidirect
15. C2×Dic55C22semidirect
17. C2×C11×Dic5C22semidirect
18. C2×C5×Dic11C22semidirect
27. C2×D5×C11C2×C4semidirect
30. C2×C5×D11C2×C4semidirect
42. (C2×D11)⋊C4D5semidirect
47. D55C22⋊C4semidirect
57. C2×C4×C11C2×D5semidirect
59. C2×Dic11C2×D5semidirect
68. #685D11semidirect
69. C5×C11C2×C22⋊C4semidirect
80. C2×D11C4×D5semidirect
92. C2×C4×C5C2×D11semidirect
94. C2×Dic5C2×D11semidirect
114. C2×D5C4×D11semidirect
126. C11D5×C22⋊C4semidirect
144. C2×C4D5×D11semidirect
145. C5C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D112
C2×C4×D552
C2×#891662
C11×#6852
C5×(C2×D11)⋊C42
#117248852
(C2×D11)⋊Dic52
C22⋊C4×D115
D5×C22⋊C411