Finite Group Databasebeta

← C5×C3⋊(C3⋊(C11⋊#261)) #38788260

Subgroups — C5×C3⋊(C3⋊(C11⋊#261)) #38788260

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D13C211yesmaximal, characteristic
2C5×C3⋊(C11⋊#261)—34nomaximal
3C32×C5×C11×C13C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C11⋊#261))C511yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C11×D13D314yes—
6C5×C11⋊#261—91noHall
7C32×C11×D13C2×C511yescharacteristic
8C5×C3⋊(C3⋊#261)—111nomaximal, Hall
9C3×C5×C11×C13Dic314yescomplemented
10C5×C3⋊Dic33—131nomaximal, Hall
11C3⋊(C11⋊#261)—34no—
12C5×C11×D13C3⋊D311yescharacteristic
13C32×C11×C13C4×C511yescharacteristic, complemented, Hall
14C32×C5×D13D1111yescharacteristic
15C2×C32×C5×C11—131no—
16C3×C11×D13C5×D314yes—
17C5×C3⋊#261—334no—
18C5×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
19C5×Dic33—394no—
20C32×C5×C13Dic1111yescharacteristic, complemented, Hall
21C11⋊#261—91noHall
22C32×C5×C11#26111yescharacteristic, complemented, Hall
23C3⋊(C3⋊#261)—111noHall
24C3×C11×C13C5×Dic314yescomplemented
25C3⋊Dic33—131noHall
26C3×C5×D13D3314yes—
27C2×C3×C5×C11—134no—
28C11×D13C5×C3⋊D311yescharacteristic
29C5×#261—991noHall
30C32×D13C5×D1111yescharacteristic
31C5×Dic11—1171noHall
32C2×C32×C11—131no—
33C3×C5×C13Dic3314yescomplemented
34C5×C3⋊Dic3—1431noHall
35C3×C5×C11C3⋊#26114yescomplemented
36C3⋊#261—334no—
37C11×C13C5×C3⋊Dic311yescharacteristic, complemented, Hall
38Dic33—394no—
39C5×D13C3⋊D3311yescharacteristic
40C32×C13C5×Dic1111yescharacteristic, complemented, Hall
41C2×C5×C11—131no—
42C32×C11C5×#26111yescharacteristic, complemented, Hall
43C2×C32×C5—131no—
44C3×D13C5×D3314yes—
45C2×C3×C11—134no—
46C5×C13C3⋊Dic3311yescharacteristic, complemented, Hall
47C5×Dic3—4294no—
48C5×C11C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
49#261—991noHall
50C32×C5C11⋊#26111yescharacteristic, complemented, Hall
51Dic11—1171noHall
52C3×C13C5×Dic3314yescomplemented
53C3⋊Dic3—1431noHall
54C3×C11C5×C3⋊#26114yescomplemented
55C2×C3×C5—134no—
56D13C5×C3⋊D3311yescharacteristic
57C2×C11—131no—
58C4×C5—12871noHall
59C2×C32—131no—
60C3×C5C3⋊(C11⋊#261)14yescomplemented
61C13C5×C3⋊Dic3311yescharacteristic, complemented, Sylow
62Dic3—4294no—
63C11C5×C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
64C2×C5—131no—
65C32C5×C11⋊#26111yescharacteristic, complemented, Sylow
66C2×C3—134no—
67C5C3⋊(C3⋊(C11⋊#261))11yescharacteristic, direct product factor, Sylow
68C4—12871noSylow
69C3C5×C3⋊(C11⋊#261)14yescomplemented
70C2—131no—
subgroupG/H
center, hypercenterC5C3⋊(C3⋊(C11⋊#261))
commutator, hypocenterC32×C11×C13C4×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC32×C11×D13C2×C5
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C13C4semidirect
4. C3⋊(C3⋊(C11⋊#261))C5direct (N × H)
9. C3×C5×C11×C13Dic3semidirect
13. C32×C11×C13C4×C5semidirect
18. C5×C11×C13C3⋊Dic3semidirect
20. C32×C5×C13Dic11semidirect
22. C32×C5×C11#261semidirect
24. C3×C11×C13C5×Dic3semidirect
33. C3×C5×C13Dic33semidirect
35. C3×C5×C11C3⋊#261semidirect
37. C11×C13C5×C3⋊Dic3semidirect
40. C32×C13C5×Dic11semidirect
42. C32×C11C5×#261semidirect
46. C5×C13C3⋊Dic33semidirect
48. C5×C11C3⋊(C3⋊#261)semidirect
50. C32×C5C11⋊#261semidirect
52. C3×C13C5×Dic33semidirect
54. C3×C11C5×C3⋊#261semidirect
60. C3×C5C3⋊(C11⋊#261)semidirect
61. C13C5×C3⋊Dic33semidirect
63. C11C5×C3⋊(C3⋊#261)semidirect
65. C32C5×C11⋊#261semidirect
67. C5C3⋊(C3⋊(C11⋊#261))direct (N × H)
69. C3C5×C3⋊(C11⋊#261)semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×D132
C5×C3⋊(C11⋊#261)3
C3⋊(C3⋊(C11⋊#261))5
C5×C3⋊(C3⋊#261)11
C5×C3⋊Dic3313