Finite Group Databasebeta

← #13182802

Subgroups — #13182802

Order 1760.

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

normal subgroups only

This group has 184 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
1C2×C4×D55C211yesmaximal, characteristic
2C2×#89166C211yesmaximal, characteristic
3C2×#89166C211yesmaximal, characteristic
4C11×#683C211yesmaximal, characteristic, complemented
5C5×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#11724889C211yesmaximal, characteristic, complemented
7Dic11⋊Dic5C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C2×C4×C5×C11C2211yescharacteristic
10C2×Dic55C2211yescharacteristic
11C4×D55—22no—
12C2×C11×Dic5C2211yescharacteristic
13C2×C11×Dic5C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15C2×C5×Dic11C2211yescharacteristic
16#89166—22no—
17#89166C414yescomplemented
18C4⋊C4×D11—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55C2×C412yes—
21C2×D55D412yes—
22C2×D55Q812yes—
23C4×C5×C11—21no—
24Dic55—21no—
25C5×Dic11—21no—
26C5×Dic11C2×C412yescomplemented
27C11×Dic5—21no—
28C11×Dic5C2×C412yescomplemented
29C2×C4×D11—51no—
30C2×C4×D11—51no—
31C2×C4×D11—51no—
32C11×C4⋊C4—51no—
33C4⋊Dic11—51no—
34Dic11⋊C4—51no—
35Dic11⋊C4D511yescharacteristic, complemented
36D5×C4⋊C4—111nomaximal, Hall
37C2×C5×C11C22×C411yescharacteristic
38C2×C5×C11C2×D411yescharacteristic
39C2×C5×C11C2×Q811yescharacteristic
40D55C4⋊C414yescomplemented
41C22×D11—51no—
42C2×C4×C11—51no—
43C2×C4×C11—51no—
44C2×C4×C11C2×D511yescharacteristic
45C2×Dic11—51no—
46C2×Dic11C2×D511yescharacteristic
47C2×Dic11C2×D511yescharacteristic
48C4×D11—54no—
49C4×D11—102no—
50C4×D11—102no—
51C2×C4×D5—111no—
52C2×C4×D5—111no—
53C2×C4×D5—111no—
54C5×C4⋊C4—111no—
55C4⋊Dic5—111no—
56#683—111no—
57#683D1111yescharacteristic, complemented
58C5×C11C2×C4⋊C411yescharacteristic, complemented, Hall
59C22×C11C22×D511yescharacteristic
60C2×D11—52no—
61C2×D11—52no—
62C2×D11—52no—
63C4×C11—21no—
64C4×C11—52no—
65C4×C11—101no—
66Dic11—21no—
67Dic11—101no—
68Dic11C4×D512yescomplemented
69C22×D5—111no—
70C2×C4×C5—111no—
71C2×C4×C5—111no—
72C2×C4×C5C2×D1111yescharacteristic
73C2×Dic5—111no—
74C2×Dic5C2×D1111yescharacteristic
75C2×Dic5C2×D1111yescharacteristic
76C4×D5—114no—
77C4×D5—222no—
78C4×D5—222no—
79C2×C4⋊C4—551noSylow
80C2×C11C2×C4×D511yescharacteristic
81C2×C11D4×D511yescharacteristic
82C2×C11Q8×D511yescharacteristic
83D11—54no—
84C22×C5C22×D1111yescharacteristic
85C2×D5—112no—
86C2×D5—112no—
87C2×D5—112no—
88C4×C5—21no—
89C4×C5—112no—
90C4×C5—221no—
91Dic5—21no—
92Dic5—221no—
93Dic5C4×D1112yescomplemented
94C22×C4—551no—
95C22×C4—551no—
96C22×C4—551no—
97C4⋊C4—51no—
98C4⋊C4—111no—
99C4⋊C4—551no—
100C4⋊C4—551no—
101C11D5×C4⋊C411yescharacteristic, complemented, Sylow
102C2×C5C2×C4×D1111yescharacteristic
103C2×C5D4×D1111yescharacteristic
104C2×C5Q8×D1111yescharacteristic
105D5—114no—
106C23—551no—
107C2×C4—51no—
108C2×C4—51no—
109C2×C4—111no—
110C2×C4—111no—
111C2×C4—554no—
112C2×C4—551no—
113C2×C4—1102no—
114C2×C4—1102no—
115C2×C4D5×D1111yescharacteristic
116C5C4⋊C4×D1111yescharacteristic, complemented, Sylow
117C22—552no—
118C22—552no—
119C22—552no—
120C22C2×D5×D1111yescharacteristic
121C4—21no—
122C4—52no—
123C4—101no—
124C4—112no—
125C4—221no—
126C4—1101no—
127C2—554no—
128C2D55⋊Q811yescharacteristic
129C2C4×D5×D1111yescharacteristic
130C2#1172500711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutatorC2×C5×C11C22×C4
FittingC2×C4×C5×C11C22
socle, cosocleC22×C5×C11C23
prime radicalC22×D55C22
hypercenterC2×C4D5×D11
hypocenterC5×C11C2×C4⋊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
4. C11×#683C2semidirect
5. C5×Dic11⋊C4C2semidirect
6. #11724889C2semidirect
7. Dic11⋊Dic5C2semidirect
17. #89166C4semidirect
26. C5×Dic11C2×C4semidirect
28. C11×Dic5C2×C4semidirect
35. Dic11⋊C4D5semidirect
40. D55C4⋊C4semidirect
57. #683D11semidirect
58. C5×C11C2×C4⋊C4semidirect
68. Dic11C4×D5semidirect
93. Dic5C4×D11semidirect
101. C11D5×C4⋊C4semidirect
116. C5C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D552
C2×#891662
C11×#6832
C5×Dic11⋊C42
#117248892
Dic11⋊Dic52
C4⋊C4×D115
D5×C4⋊C411