Finite Group Databasebeta

← #13182307

Subgroups — #13182307

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#709C211yesmaximal, characteristic
2#11724928C211yesmaximal, characteristic, complemented
3C4×C5×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C5×C11C2211yescharacteristic
5C11×C22⋊D5—21no—
6C11×D20C411yescharacteristic, complemented
7C4×D5×C11—21no—
8C11×Dic10C411yescharacteristic, complemented
9C2×C5×Dic11—21no—
10C11⋊#168—21no—
11#66901—51nomaximal, Hall
12C22×C5×C11D411yescharacteristic
13C2×D5×C11—21no—
14C4×C5×C11C2×C411yescharacteristic
15C4×C5×C11D411yescharacteristic
16C5×Dic11—22no—
17C11×Dic5—21no—
18C11×#41—51no—
19C4×Dic11D511yescharacteristic, complemented
20#4318—51no—
21#3937—111nomaximal, Hall
22C2×C5×C11—21no—
23C2×C5×C11C22⋊C411yescharacteristic
24D5×C11—41no—
25Q8×C11—51no—
26D4×C11—51no—
27D4×C11—101no—
28C2×C4×C11—101no—
29C2×C4×C11C2×D511yescharacteristic
30C2×Dic11—21no—
31C11⋊C8—101no—
32#709D1111yescharacteristic
33C42×C5—111no—
34#681—111no—
35C5×C11#10411yescharacteristic, complemented, Hall
36C22×C11—101no—
37C22×C11C22⋊D511yescharacteristic
38C4×C11—101no—
39C4×C11C4×D511yescharacteristic
40C4×C11D2011yescharacteristic
41Dic11—22no—
42C2×C4×C5—221no—
43C2×C4×C5C2×D1111yescharacteristic
44C22⋊D5—21no—
45D20Dic1111yescharacteristic, complemented
46C4×D5—21no—
47Dic10Dic1111yescharacteristic, complemented
48#168—221no—
49#104—551noSylow
50C2×C11—21no—
51C2×C11—201no—
52C2×C11#68511yescharacteristic
53C22×C5C22⋊D1111yescharacteristic
54C2×D5—21no—
55C4×C5—222no—
56C4×C5C2×Dic1111yescharacteristic
57C4×C5C22⋊D1111yescharacteristic
58Dic5—21no—
59#41—51no—
60M16—551no—
61C42—111no—
62C11#393711yescharacteristic, complemented, Sylow
63C2×C5—21no—
64C2×C5C22⋊Dic1111yescharacteristic
65D5—41no—
66Q8—51no—
67D4—51no—
68D4—101no—
69C2×C4—101no—
70C2×C4—221no—
71C2×C4D5×D1111yescharacteristic
72C8—1101no—
73C5#6690111yescharacteristic, complemented, Sylow
74C22—101no—
75C22#8916711yescharacteristic
76C4—101no—
77C4—222no—
78C4D5×Dic1111yescharacteristic
79C4#8916911yescharacteristic
80C2—21no—
81C2—201no—
82C2#1172488511yescharacteristic
subgroupG/H
centerC4#89169
commutatorC4×C5×C11C2×C4
Frattini, hypercenterC2×C4D5×D11
Fitting, cosocleC2×C4×C5×C11C22
socleC2×C5×C11C22⋊C4
prime radicalC11×#709C2
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. #11724928C2semidirect
3. C4×C5×Dic11C2semidirect
6. C11×D20C4semidirect
8. C11×Dic10C4semidirect
19. C4×Dic11D5semidirect
35. C5×C11#104semidirect
45. D20Dic11semidirect
47. Dic10Dic11semidirect
62. C11#3937semidirect
73. C5#66901semidirect

Maximal subgroups

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

subgroupindex
C11×#7092
#117249282
C4×C5×Dic112
#669015
#393711