Finite Group Databasebeta

← #13182880

Subgroups — #13182880

Order 1760.

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

normal subgroups only

This group has 136 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×C5×Dic22C211yesmaximal, characteristic
2C2×#89170C211yesmaximal, characteristic
3#11724930C211yesmaximal, characteristic
4C11×#683C211yesmaximal, characteristic
5#11724889C211yesmaximal, characteristic
6#11724888C211yesmaximal, characteristic
7Dic5×Dic11C211yesmaximal, characteristic
8C2×C4×C5×C11C2211yescharacteristic
9C2×Dic55C2211yescharacteristic
10C2×Dic55C2211yescharacteristic
11C2×C11×Dic5C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C5×Dic11C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15C5×Dic22—22no—
16#89170—22no—
17#66941—51nomaximal, Hall
18C22×C5×C11C2311yescharacteristic
19C4×C5×C11—21no—
20Dic55—21no—
21Dic55Q812yescomplemented
22C5×Dic11—21no—
23C5×Dic11D412yes—
24C11×Dic5—21no—
25C11×Dic5Q812yescomplemented
26C2×Dic22—51no—
27C2×Dic22D511yescharacteristic
28C11×C4⋊C4—51no—
29C4⋊Dic11—51no—
30Dic11⋊C4—51no—
31Dic11⋊C4—51no—
32C4×Dic11—51no—
33#4090—111nomaximal, Hall
34C2×C5×C11C2×D411yescharacteristic
35C2×C5×C11C2×Q811yescharacteristic
36C2×C5×C11C2×Q811yescharacteristic
37C2×C4×C11—51no—
38C2×C4×C11—51no—
39C2×C4×C11C2×D511yescharacteristic
40C2×Dic11—51no—
41C2×Dic11—51no—
42C2×Dic11C2×D511yescharacteristic
43C2×Dic11C2×D511yescharacteristic
44Dic22—22no—
45Dic22—102no—
46C2×C5×Q8—111no—
47C2×Dic10—111no—
48#683—111no—
49#683—111no—
50#683—111no—
51#683D1111yescharacteristic
52C4×Dic5—111no—
53C5×C11C4⋊Q811yescharacteristic, complemented, Hall
54C22×C11C22×D511yescharacteristic
55C4×C11—21no—
56C4×C11—52no—
57C4×C11—101no—
58Dic11—21no—
59Dic11—52no—
60Dic11—101no—
61Dic11C22⋊D512yes—
62C5×Q8—222no—
63C2×C4×C5—111no—
64C2×C4×C5—111no—
65C2×C4×C5C2×D1111yescharacteristic
66C2×Dic5—111no—
67C2×Dic5—111no—
68C2×Dic5C2×D1111yescharacteristic
69C2×Dic5C2×D1111yescharacteristic
70Dic10—222no—
71C4⋊Q8—551noSylow
72C2×C11Q8×D511yescharacteristic
73C2×C11Q8×D511yescharacteristic
74C2×C11C2×C22⋊D511yescharacteristic
75C22×C5C22×D1111yescharacteristic
76C4×C5—21no—
77C4×C5—112no—
78C4×C5—221no—
79Dic5—21no—
80Dic5—112no—
81Dic5—221no—
82Dic5Dic2212yescomplemented
83C2×Q8—111no—
84C2×Q8—551no—
85C4⋊C4—51no—
86C4⋊C4—551no—
87C4⋊C4—551no—
88C4⋊C4—551no—
89C42—551no—
90C11#409011yescharacteristic, complemented, Sylow
91C2×C5C2×Dic2211yescharacteristic
92C2×C5D4×D1111yescharacteristic
93C2×C5Q8×D1111yescharacteristic
94Q8—222no—
95Q8—1102no—
96C2×C4—51no—
97C2×C4—51no—
98C2×C4—111no—
99C2×C4—111no—
100C2×C4—551no—
101C2×C4—551no—
102C2×C4D5×D1111yescharacteristic
103C5#6694111yescharacteristic, complemented, Sylow
104C22C2×D5×D1111yescharacteristic
105C4—21no—
106C4—52no—
107C4—101no—
108C4—112no—
109C4—221no—
110C4—552no—
111C4—1101no—
112C2D5×Dic2211yescharacteristic
113C2D55⋊Q811yescharacteristic
114C2D11×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, prime radical, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
hypercenterC2×C4D5×D11
hypocenterC5×C11C4⋊Q8
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
21. Dic55Q8semidirect
25. C11×Dic5Q8semidirect
53. C5×C11C4⋊Q8semidirect
82. Dic5Dic22semidirect
90. C11#4090semidirect
103. C5#66941semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Dic222
C2×#891702
#117249302
C11×#6832
#117248892
#117248882
Dic5×Dic112
#669415
#409011