Finite Group Databasebeta

← C5×C11×C3⋊(C3⋊#261) #38788258

Subgroups — C5×C11×C3⋊(C3⋊#261) #38788258

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D13C211yesmaximal, characteristic
2C5×C11×C3⋊#261—34nomaximal
3C32×C5×C11×C13C411yescharacteristic, complemented, Hall
4C11×C3⋊(C3⋊#261)C511yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C11×D13D314yes—
6C5×C11×#261—91noHall
7C32×C11×D13C2×C511yescharacteristic
8C5×C3⋊(C3⋊#261)C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11×C13Dic314yescomplemented
10C5×C11×C3⋊Dic3—131nomaximal, Hall
11C11×C3⋊#261—34no—
12C5×C11×D13C3⋊D311yescharacteristic
13C32×C11×C13C4×C511yescharacteristic, complemented, Hall
14C32×C5×D13C2×C1111yescharacteristic
15C2×C32×C5×C11—131no—
16C3×C11×D13C5×D314yes—
17C5×C3⋊#261—34no—
18C5×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
19C5×C11×Dic3—394no—
20C32×C5×C13C4×C1111yescharacteristic, complemented, Hall
21C11×#261—91noHall
22C32×C5×C11#26111yescharacteristic, complemented, Hall
23C3⋊(C3⋊#261)C5×C1111yescharacteristic, direct product factor, Hall
24C3×C11×C13C5×Dic314yescomplemented
25C11×C3⋊Dic3—131noHall
26C3×C5×D13D3×C1114yes—
27C2×C3×C5×C11—134no—
28C11×D13C5×C3⋊D311yescharacteristic
29C5×#261—91noHall
30C32×D13C2×C5×C1111yescharacteristic
31C4×C5×C11—1171noHall
32C2×C32×C11—131no—
33C3×C5×C13C11×Dic314yescomplemented
34C5×C3⋊Dic3—131noHall
35C3×C5×C11C3⋊#26114yescomplemented
36C3⋊#261—34no—
37C11×C13C5×C3⋊Dic311yescharacteristic, complemented, Hall
38C11×Dic3—394no—
39C5×D13C11×C3⋊D311yescharacteristic
40C32×C13C4×C5×C1111yescharacteristic, complemented, Hall
41C2×C5×C11—131no—
42C32×C11C5×#26111yescharacteristic, complemented, Hall
43C2×C32×C5—131no—
44C3×D13C5×D3×C1114yes—
45C2×C3×C11—134no—
46C5×C13C11×C3⋊Dic311yescharacteristic, complemented, Hall
47C5×Dic3—394no—
48C5×C11C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Hall
49#261—91noHall
50C32×C5C11×#26111yescharacteristic, complemented, Hall
51C4×C11—1171noHall
52C3×C13C5×C11×Dic314yescomplemented
53C3⋊Dic3—131noHall
54C3×C11C5×C3⋊#26114yescomplemented
55C2×C3×C5—134no—
56D13C5×C11×C3⋊D311yescharacteristic
57C2×C11—131no—
58C4×C5—1171noHall
59C2×C32—131no—
60C3×C5C11×C3⋊#26114yescomplemented
61C13C5×C11×C3⋊Dic311yescharacteristic, complemented, Sylow
62Dic3—394no—
63C11C5×C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Sylow
64C2×C5—131no—
65C32C5×C11×#26111yescharacteristic, complemented, Sylow
66C2×C3—134no—
67C5C11×C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Sylow
68C4—1171noSylow
69C3C5×C11×C3⋊#26114yescomplemented
70C2—131no—
subgroupG/H
center, hypercenterC5×C11C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC32×D13C2×C5×C11
LCSG ▷ C32×C13
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C13C4semidirect
4. C11×C3⋊(C3⋊#261)C5direct (N × H)
8. C5×C3⋊(C3⋊#261)C11direct (N × H)
9. C3×C5×C11×C13Dic3semidirect
13. C32×C11×C13C4×C5semidirect
18. C5×C11×C13C3⋊Dic3semidirect
20. C32×C5×C13C4×C11semidirect
22. C32×C5×C11#261semidirect
23. C3⋊(C3⋊#261)C5×C11direct (N × H)
24. C3×C11×C13C5×Dic3semidirect
33. C3×C5×C13C11×Dic3semidirect
35. C3×C5×C11C3⋊#261semidirect
37. C11×C13C5×C3⋊Dic3semidirect
40. C32×C13C4×C5×C11semidirect
42. C32×C11C5×#261semidirect
46. C5×C13C11×C3⋊Dic3semidirect
48. C5×C11C3⋊(C3⋊#261)direct (N × H)
50. C32×C5C11×#261semidirect
52. C3×C13C5×C11×Dic3semidirect
54. C3×C11C5×C3⋊#261semidirect
60. C3×C5C11×C3⋊#261semidirect
61. C13C5×C11×C3⋊Dic3semidirect
63. C11C5×C3⋊(C3⋊#261)direct (N × H)
65. C32C5×C11×#261semidirect
67. C5C11×C3⋊(C3⋊#261)direct (N × H)
69. C3C5×C11×C3⋊#261semidirect

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×C11×C3⋊#2613
C11×C3⋊(C3⋊#261)5
C5×C3⋊(C3⋊#261)11
C5×C11×C3⋊Dic313