Finite Group Databasebeta

← #13182842

Subgroups — #13182842

Order 1760.

188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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×#89169C211yesmaximal, characteristic
2C2×#89166C211yesmaximal, characteristic, complemented
3C2×D5×Dic11C211yesmaximal, characteristic, complemented
4#11724932C211yesmaximal, characteristic, complemented
5C11×#685C211yesmaximal, characteristic, complemented
6C4×C5×Dic11C211yesmaximal, characteristic, complemented
7Dic11⋊Dic5C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C22×D5×C11C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×Dic55C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C5×Dic11C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15#89169C414yescomplemented
16#89166—22no—
17D5×Dic11—22no—
18(C22⋊D11)⋊C4—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55—21no—
21C2×D55—21no—
22C2×D55C2×C412yescomplemented
23C2×D5×C11—21no—
24C2×D5×C11—21no—
25C2×D5×C11C2×C412yescomplemented
26C4×C5×C11—21no—
27Dic55—21no—
28C5×Dic11C2×C412yescomplemented
29C5×Dic11D412yescomplemented
30C11×Dic5—21no—
31C2×C22⋊D11—51no—
32C22×Dic11—51no—
33C2×C4×D11—51no—
34C11×C22⋊C4—51no—
35(C2×D11)⋊C4—51no—
36Dic11⋊C4—51no—
37C4×Dic11D511yescharacteristic, complemented
38C4×D20—111nomaximal, Hall
39C2×C5×C11C22×C411yescharacteristic
40C2×C5×C11C2×D411yescharacteristic
41C2×C5×C11#4111yescharacteristic
42D55—22no—
43D5×C11—22no—
44C23×C11—51no—
45C22×D11—51no—
46C2×C4×C11—51no—
47C2×C4×C11C2×D511yescharacteristic
48C22⋊D11—54no—
49C2×Dic11—51no—
50C2×Dic11—102no—
51C2×Dic11C2×D511yescharacteristic
52C2×Dic11C2×D511yescharacteristic
53C4×D11—102no—
54C2×D20—111no—
55C2×C4×D5—111no—
56C2×C4×D5—111no—
57C42×C5—111no—
58#685—111no—
59#685D1111yescharacteristic, complemented
60C4⋊Dic5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—52no—
63C22×C11—101no—
64C22×C11—101no—
65C22×C11C22×D511yescharacteristic
66C2×D11—52no—
67C2×D11—101no—
68C2×D11—101no—
69C4×C11—21no—
70C4×C11—101no—
71Dic11—101no—
72Dic11C4×D512yescomplemented
73Dic11D2012yescomplemented
74C22×D5—111no—
75C22×D5C2×D1111yescharacteristic
76C2×C4×C5—111no—
77C2×C4×C5—111no—
78C2×C4×C5C2×D1111yescharacteristic
79C2×Dic5—111no—
80C2×Dic5C2×D1111yescharacteristic
81D20—114no—
82C4×D5—222no—
83C4×D5—222no—
84C4×D4—551noSylow
85C2×C11—102no—
86C2×C11C2×C4×D511yescharacteristic
87C2×C11C2×D2011yescharacteristic
88C2×C11#70911yescharacteristic
89D11—102no—
90C22×C5C22×D1111yescharacteristic
91C2×D5—21no—
92C2×D5—21no—
93C2×D5—112no—
94C2×D5—221no—
95C2×D5—221no—
96C2×D5C4×D1112yescomplemented
97C4×C5—21no—
98C4×C5—112no—
99C4×C5—112no—
100Dic5—21no—
101Dic5—221no—
102C2×D4—551no—
103C22×C4—551no—
104C22×C4—551no—
105C4⋊C4—551no—
106C22⋊C4—51no—
107C22⋊C4—551no—
108C42—111no—
109C11C4×D2011yescharacteristic, complemented, Sylow
110C2×C5C2×C4×D1111yescharacteristic
111C2×C5D4×D1111yescharacteristic
112C2×C5#434111yescharacteristic
113D5—22no—
114D5—222no—
115C23—51no—
116C23—551no—
117D4—554no—
118C2×C4—51no—
119C2×C4—111no—
120C2×C4—111no—
121C2×C4—551no—
122C2×C4—1102no—
123C2×C4—1102no—
124C2×C4D5×D1111yescharacteristic
125C5(C22⋊D11)⋊C411yescharacteristic, complemented, Sylow
126C22—52no—
127C22—101no—
128C22—101no—
129C22—552no—
130C22—1101no—
131C22—1101no—
132C22C2×D5×D1111yescharacteristic
133C4—21no—
134C4—101no—
135C4—112no—
136C4—112no—
137C4—1101no—
138C2—102no—
139C2—1102no—
140C2C4×D5×D1111yescharacteristic
141C2D11×D2011yescharacteristic
142C2#1172499911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutatorC2×C5×C11C22×C4
FittingC2×C4×C5×C11C22
socle, cosocleC22×C5×C11C23
prime radicalC2×#89169C2
hypercenterC2×C4D5×D11
hypocenterC5×C11C4×D4
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×#89166C2semidirect
3. C2×D5×Dic11C2semidirect
4. #11724932C2semidirect
5. C11×#685C2semidirect
6. C4×C5×Dic11C2semidirect
7. Dic11⋊Dic5C2semidirect
15. #89169C4semidirect
22. C2×D55C2×C4semidirect
25. C2×D5×C11C2×C4semidirect
28. C5×Dic11C2×C4semidirect
29. C5×Dic11D4semidirect
37. C4×Dic11D5semidirect
59. #685D11semidirect
61. C5×C11C4×D4semidirect
72. Dic11C4×D5semidirect
73. Dic11D20semidirect
96. C2×D5C4×D11semidirect
109. C11C4×D20semidirect
125. C5(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#891692
C2×#891662
C2×D5×Dic112
#117249322
C11×#6852
C4×C5×Dic112
Dic11⋊Dic52
(C22⋊D11)⋊C45
C4×D2011