Finite Group Databasebeta

← #13182309

Subgroups — #13182309

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11725031C211yesmaximal, characteristic
2C11×#681C211yesmaximal, characteristic, complemented
3C4×C5×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C5×C11C2211yescharacteristic
5C22⋊D55—21no—
6D220C411yescharacteristic, complemented
7C4×D55—21no—
8Dic110C411yescharacteristic, complemented
9C2×C5×Dic11—21no—
10C11×#168—21no—
11#66889—51nomaximal, Hall
12C22×C5×C11D411yescharacteristic
13C2×D55—21no—
14C4×C5×C11C2×C411yescharacteristic
15C4×C5×C11D411yescharacteristic
16Dic55—21no—
17C5×Dic11—22no—
18#4339—51no—
19C11×M16—51no—
20C4×Dic11D511yescharacteristic, complemented
21#3937—111nomaximal, Hall
22C2×C5×C11—21no—
23C2×C5×C11C22⋊C411yescharacteristic
24D55—41no—
25C2×C4×C11C2×D511yescharacteristic
26C22⋊D11—101no—
27C2×Dic11—21no—
28D44—51no—
29C4×D11—101no—
30Dic22—51no—
31C8×C11—101no—
32#709—111no—
33C42×C5—111no—
34#681D1111yescharacteristic, complemented
35C5×C11#10411yescharacteristic, complemented, Hall
36C22×C11C22⋊D511yescharacteristic
37C2×D11—101no—
38C4×C11C4×D511yescharacteristic
39C4×C11D2011yescharacteristic
40Dic11—22no—
41Dic11—101no—
42C2×C4×C5—221no—
43C2×C4×C5C2×D1111yescharacteristic
44C22⋊D5—221no—
45D20—111no—
46C4×D5—221no—
47Dic10—111no—
48#168—21no—
49#104—551noSylow
50C2×C11—21no—
51C2×C11#68511yescharacteristic
52D11—201no—
53C22×C5D4411yescharacteristic
54C2×D5—221no—
55C4×C5—222no—
56C4×C5C4×D1111yescharacteristic
57C4×C5C22⋊D1111yescharacteristic
58Dic5—221no—
59#41—551no—
60M16—51no—
61C42—111no—
62C11#393711yescharacteristic, complemented, Sylow
63C2×C5—21no—
64C2×C5(C2×D11)⋊C411yescharacteristic
65D5—441no—
66Q8—551no—
67D4—551no—
68D4—1101no—
69C2×C4—221no—
70C2×C4—1101no—
71C2×C4D5×D1111yescharacteristic
72C8—101no—
73C5#6688911yescharacteristic, complemented, Sylow
74C22—1101no—
75C22#8916811yescharacteristic
76C4—222no—
77C4—1101no—
78C4#8916611yescharacteristic
79C4#8916911yescharacteristic
80C2—21no—
81C2—2201no—
82C2#1172488611yescharacteristic
subgroupG/H
centerC4#89169
commutatorC4×C5×C11C2×C4
Frattini, hypercenterC2×C4D5×D11
Fitting, cosocleC2×C4×C5×C11C22
socleC2×C5×C11C22⋊C4
prime radical#11725031C2
hypocenterC5×C11#104
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C11×#681C2semidirect
3. C4×C5×Dic11C2semidirect
6. D220C4semidirect
8. Dic110C4semidirect
20. C4×Dic11D5semidirect
34. #681D11semidirect
35. C5×C11#104semidirect
62. C11#3937semidirect
73. C5#66889semidirect

Maximal subgroups

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

subgroupindex
#117250312
C11×#6812
C4×C5×Dic112
#668895
#393711