Finite Group Databasebeta

← #13182823

Subgroups — #13182823

Order 1760.

148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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×#89170C211yesmaximal, characteristic, complemented
2C2×#89166C211yesmaximal, characteristic
3#11724932C211yesmaximal, characteristic
4C11×#683C211yesmaximal, characteristic, complemented
5C5×C4⋊Dic11C211yesmaximal, characteristic, complemented
6#11724889C211yesmaximal, characteristic, complemented
7#11724886C211yesmaximal, characteristic
8C22×D55C2211yescharacteristic
9C2×C4×C5×C11C2211yescharacteristic
10C2×Dic55C2211yescharacteristic
11C2×C11×Dic5C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C5×Dic11C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15#89170—22no—
16#89166—22no—
17#66950—51nomaximal, Hall
18C22×C5×C11C2311yescharacteristic
19C2×D55—21no—
20C2×D55—21no—
21C2×D55Q812yescomplemented
22C4×C5×C11—21no—
23Dic55—21no—
24C5×Dic11—21no—
25C5×Dic11—21no—
26C11×Dic5—21no—
27C11×Dic5D412yes—
28C2×C4×D11—51no—
29C2×Dic22—51no—
30C11×C4⋊C4—51no—
31(C2×D11)⋊C4—51no—
32(C2×D11)⋊C4—51no—
33C4⋊Dic11—51no—
34C4⋊Dic11D511yescharacteristic, complemented
35#4042—111nomaximal, Hall
36C2×C5×C11C2×D411yescharacteristic
37C2×C5×C11C2×Q811yescharacteristic
38C2×C5×C11#4111yescharacteristic
39D55—22no—
40C22×D11—51no—
41C2×C4×C11—51no—
42C2×C4×C11—51no—
43C2×C4×C11C2×D511yescharacteristic
44C2×Dic11—51no—
45C2×Dic11C2×D511yescharacteristic
46C2×Dic11C2×D511yescharacteristic
47C4×D11—102no—
48Dic22—102no—
49C2×C4×D5—111no—
50C2×Dic10—111no—
51C5×C4⋊C4—111no—
52#685—111no—
53#685—111no—
54#683—111no—
55#683D1111yescharacteristic, complemented
56C5×C11C22⋊Q811yescharacteristic, complemented, Hall
57C22×C11C22×D511yescharacteristic
58C2×D11—52no—
59C2×D11—101no—
60C2×D11—101no—
61C4×C11—21no—
62C4×C11—52no—
63C4×C11—101no—
64Dic11—21no—
65Dic11—21no—
66Dic11—101no—
67C22×D5—111no—
68C2×C4×C5—111no—
69C2×C4×C5—111no—
70C2×C4×C5C2×D1111yescharacteristic
71C2×Dic5—111no—
72C2×Dic5C2×D1111yescharacteristic
73C2×Dic5C2×D1111yescharacteristic
74C4×D5—222no—
75Dic10—222no—
76C22⋊Q8—551noSylow
77C2×C11#70911yescharacteristic
78C2×C11D4×D511yescharacteristic
79C2×C11Q8×D511yescharacteristic
80D11—102no—
81C22×C5C22×D1111yescharacteristic
82C2×D5—112no—
83C2×D5—221no—
84C2×D5—221no—
85C4×C5—21no—
86C4×C5—221no—
87C4×C5—221no—
88Dic5—21no—
89Dic5—221no—
90Dic5D4412yes—
91C2×Q8—551no—
92C22×C4—551no—
93C4⋊C4—51no—
94C4⋊C4—111no—
95C4⋊C4—551no—
96C22⋊C4—551no—
97C22⋊C4—551no—
98C11#404211yescharacteristic, complemented, Sylow
99C2×C5C2×D4411yescharacteristic
100C2×C5#434111yescharacteristic
101C2×C5Q8×D1111yescharacteristic
102D5—222no—
103C23—551no—
104Q8—1102no—
105C2×C4—51no—
106C2×C4—51no—
107C2×C4—111no—
108C2×C4—111no—
109C2×C4—551no—
110C2×C4—1102no—
111C2×C4D5×D1111yescharacteristic
112C5#6695011yescharacteristic, complemented, Sylow
113C22—552no—
114C22—1101no—
115C22—1101no—
116C22C2×D5×D1111yescharacteristic
117C4—21no—
118C4—52no—
119C4—101no—
120C4—221no—
121C4—221no—
122C4—1101no—
123C2—1102no—
124C2D55⋊Q811yescharacteristic
125C2D5×D4411yescharacteristic
126C2#1172499911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
prime radicalC22×D55C22
hypercenterC2×C4D5×D11
hypocenterC5×C11C22⋊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
1. C2×#89170C2semidirect
4. C11×#683C2semidirect
5. C5×C4⋊Dic11C2semidirect
6. #11724889C2semidirect
21. C2×D55Q8semidirect
34. C4⋊Dic11D5semidirect
55. #683D11semidirect
56. C5×C11C22⋊Q8semidirect
98. C11#4042semidirect
112. C5#66950semidirect

Maximal subgroups

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

subgroupindex
C2×#891702
C2×#891662
#117249322
C11×#6832
C5×C4⋊Dic112
#117248892
#117248862
#669505
#404211