Finite Group Databasebeta

← C11×C11⋊C5×A5 #49137836

Subgroups — C11×C11⋊C5×A5 #49137836

Order 36300.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C112×A5C511yesmaximal, characteristic, complemented
2C11×A4×C11⋊C5—51nomaximal
3D5×C11×C11⋊C5—61nomaximal
4D3×C11×C11⋊C5—101nomaximal
5C11⋊C5×A5C1111yesmaximal, characteristic, direct product factor
6C5×C11×A5—111nomaximal
7C5×C11×C11⋊C5—61noHall
8C22×C11×C11⋊C5—51no—
9C3×C11×C11⋊C5—101no—
10C112×A4—51noHall
11D5×C112—61no—
12C2×C11×C11⋊C5—151no—
13D3×C112—101no—
14C5×C11×A4—551no—
15A4×C11⋊C5—51no—
16C11×A5—52no—
17C11×A5C11⋊C511yescharacteristic, direct product factor
18C11×A5C5×C1111yescharacteristic, complemented
19C5×C112—61no—
20C11×C11⋊C5—122no—
21C11×C11⋊C5A511yesmaximal normal, characteristic, direct product factor
22C5×D5×C11—661no—
23D5×C11⋊C5—61no—
24C22×C112—51noHall
25C3×C112—101noHall
26C5×D3×C11—1101no—
27D3×C11⋊C5—101no—
28C5×A5—111noHall
29C52×C11—661no—
30C5×C11⋊C5—61no—
31C2×C112—151no—
32C22×C5×C11—551no—
33C22×C11⋊C5—51no—
34C3×C5×C11—1101no—
35C3×C11⋊C5—101no—
36C11×A4—51no—
37C11×A4—51no—
38C11×A4—252no—
39C112C5×A511yescharacteristic, complemented, Sylow
40C2×C5×C11—1651no—
41D5×C11—61no—
42D5×C11—61no—
43D5×C11—302no—
44C2×C11⋊C5—151no—
45D3×C11—101no—
46D3×C11—101no—
47D3×C11—502no—
48C5×A4—551no—
49A5C11×C11⋊C511yescharacteristic, direct product factor
50C5×C11—61no—
51C5×C11—61no—
52C5×C11—111no—
53C5×C11—302no—
54C5×C11—1322no—
55C11⋊C5—122no—
56C11⋊C5C11×A511yescharacteristic, direct product factor
57C5×D5—661no—
58C22×C11—51no—
59C22×C11—51no—
60C22×C11—252no—
61C3×C11—101no—
62C3×C11—101no—
63C3×C11—502no—
64C5×D3—1101no—
65C52—661noSylow
66C2×C11—151no—
67C2×C11—151no—
68C2×C11—752no—
69C22×C5—551no—
70C3×C5—1101no—
71A4—51noHall
72C11—52no—
73C11C5×C11×A511yescharacteristic, complemented
74C11C11⋊C5×A511yescharacteristic, direct product factor
75C2×C5—1651no—
76D5—61no—
77D3—101no—
78C5—61no—
79C5—111no—
80C5—1322no—
81C22—51noSylow
82C3—101noSylow
83C2—151no—
subgroupG/H
center, hypercenterC11C11⋊C5×A5
commutator, hypocenterC11×A5C5×C11
FrattiniC1G
FittingC112C5×A5
socleC112×A5C5
cosocleC11C5×C11×A5
LCSG ▷ C11×A5
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C112×A5C5semidirect
5. C11⋊C5×A5C11direct (N × H)
17. C11×A5C11⋊C5direct (N × H)
18. C11×A5C5×C11semidirect
21. C11×C11⋊C5A5direct (N × H)
39. C112C5×A5semidirect
49. A5C11×C11⋊C5direct (N × H)
56. C11⋊C5C11×A5direct (N × H)
73. C11C5×C11×A5semidirect
74. C11C11⋊C5×A5direct (N × H)

Maximal subgroups

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

subgroupindex
C112×A55
C11×A4×C11⋊C55
D5×C11×C11⋊C56
D3×C11×C11⋊C510
C11⋊C5×A511
C5×C11×A511