Finite Group Databasebeta

← #13182653

Subgroups — #13182653

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#711C211yesmaximal, characteristic
2C4×C11⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3#11724975C211yesmaximal, characteristic, complemented
4C2×C11⋊AGL(1,𝔽5)—21no—
5C5×D4×C11C411yescharacteristic, complemented
6C11×C22⋊D5—21no—
7C2×C11×Dic5—21no—
8C4×D5×C11C2211yescharacteristic
9C11×Dic10C411yescharacteristic, complemented
10C11⋊#170—21no—
11#66901—51nomaximal, Hall
12C22×C5×C11—21no—
13C2×D5×C11D411yescharacteristic
14C11⋊AGL(1,𝔽5)—22no—
15C4×C5×C11C2×C411yescharacteristic
16C11×Dic5—21no—
17C11×Dic5D411yescharacteristic
18C11×#41—51no—
19C4×Dic11—51no—
20#4318—51no—
21#4008—111nomaximal, Hall
22C2×C5×C11—41no—
23C2×C5×C11C22⋊C411yescharacteristic
24D5×C11—21no—
25Q8×C11—51no—
26D4×C11—101no—
27D4×C11AGL(1,𝔽5)11yescharacteristic, complemented
28C2×C4×C11—51no—
29C2×C4×C11—101no—
30C2×Dic11—101no—
31C11⋊C8—101no—
32#711D1111yescharacteristic
33C4×AGL(1,𝔽5)—111no—
34#700—111no—
35C5×C11#10411yescharacteristic, complemented, Hall
36C22×C11—21no—
37C22×C11—51no—
38C4×C11—51no—
39C4×C11—101no—
40C4×C11C2×AGL(1,𝔽5)11yescharacteristic
41Dic11—102no—
42C2×AGL(1,𝔽5)—221no—
43C5×D4Dic1111yescharacteristic, complemented
44C22⋊D5—21no—
45C2×Dic5—21no—
46C4×D5C2×D1111yescharacteristic
47Dic10Dic1111yescharacteristic, complemented
48#170—221no—
49#104—551noSylow
50C2×C11—41no—
51C2×C11—101no—
52C2×C11C22⋊AGL(1,𝔽5)11yescharacteristic
53C22×C5—21no—
54C2×D5C22⋊D1111yescharacteristic
55AGL(1,𝔽5)—222no—
56C4×C5C2×Dic1111yescharacteristic
57Dic5—21no—
58Dic5C22⋊D1111yescharacteristic
59#41—51no—
60M16—551no—
61C42—551no—
62C11#400811yescharacteristic, complemented, Sylow
63C2×C5—41no—
64C2×C5C22⋊Dic1111yescharacteristic
65D5—21no—
66Q8—51no—
67D4—101no—
68D4C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
69C2×C4—51no—
70C2×C4—101no—
71C2×C4—1101no—
72C8—1101no—
73C5#6690111yescharacteristic, complemented, Sylow
74C22—21no—
75C22—51no—
76C4—51no—
77C4—101no—
78C4—1102no—
79C4C2×C11⋊AGL(1,𝔽5)11yescharacteristic
80C2—41no—
81C2—101no—
82C2C22⋊(C11⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C22⋊(C11⋊AGL(1,𝔽5))
commutatorC4×C5×C11C2×C4
FrattiniC4C2×C11⋊AGL(1,𝔽5)
FittingC5×D4×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC11×#711C2
cosocleC4×D5×C11C22
hypercenterD4C11⋊AGL(1,𝔽5)
hypocenterC5×C11#104
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. C4×C11⋊AGL(1,𝔽5)C2semidirect
3. #11724975C2semidirect
5. C5×D4×C11C4semidirect
9. C11×Dic10C4semidirect
27. D4×C11AGL(1,𝔽5)semidirect
35. C5×C11#104semidirect
43. C5×D4Dic11semidirect
47. Dic10Dic11semidirect
62. C11#4008semidirect
68. D4C11⋊AGL(1,𝔽5)semidirect
73. C5#66901semidirect

Maximal subgroups

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

subgroupindex
C11×#7112
C4×C11⋊AGL(1,𝔽5)2
#117249752
#669015
#400811