Finite Group Databasebeta

← C3⋊(C3⋊(C11⋊#63120)) #38788273

Subgroups — C3⋊(C3⋊(C11⋊#63120)) #38788273

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D5×C11×C13C211yesmaximal, characteristic
2C3⋊(C11⋊#63120)—34nomaximal
3C32×C5×C11×C13C411yescharacteristic, complemented, Hall
4C3⋊Dic429—51nomaximal, Hall
5C3×D5×C11×C13D314yes—
6C11⋊#63120—91noHall
7C2×C32×C11×C13—51no—
8C3⋊(C3⋊#63120)—111nomaximal, Hall
9C3×C5×C11×C13Dic314yescomplemented
10C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))—131nomaximal, Hall
11Dic429—154no—
12D5×C11×C13C3⋊D311yescharacteristic
13C32×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C32×D5×C13D1111yescharacteristic
15C32×D5×C11D1311yescharacteristic
16C2×C3×C11×C13—54no—
17C3⋊#63120—334no—
18C5×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
19C3⋊(C11⋊AGL(1,𝔽5))—394no—
20C32×C5×C13Dic1111yescharacteristic, complemented, Hall
21Dic143—451noHall
22C32×C5×C11Dic1311yescharacteristic, complemented, Hall
23C3⋊Dic39—551noHall
24C3×C11×C13ΓL(1,𝔽16)14yescomplemented
25C3⋊Dic33—651noHall
26C3×D5×C13D3314yes—
27C3×D5×C11D3914yes—
28C2×C11×C13—51no—
29#63120—991noHall
30C2×C32×C13—51no—
31C11⋊AGL(1,𝔽5)—1171noHall
32C2×C32×C11—51no—
33C3×C5×C13Dic3314yescomplemented
34C3⋊ΓL(1,𝔽16)—1431noHall
35C3×C5×C11Dic3914yescomplemented
36Dic39—1654no—
37C11×C13C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
38Dic33—1954no—
39D5×C13C3⋊D3311yescharacteristic
40C32×C13C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
41D5×C11C3⋊D3911yescharacteristic
42C32×C11#6312011yescharacteristic, complemented, Hall
43C32×D5D14311yescharacteristic
44C2×C3×C13—54no—
45C2×C3×C11—54no—
46C5×C13C3⋊Dic3311yescharacteristic, complemented, Hall
47ΓL(1,𝔽16)—4294no—
48C5×C11C3⋊Dic3911yescharacteristic, complemented, Hall
49Dic13—4951noHall
50C32×C5Dic14311yescharacteristic, complemented, Hall
51Dic11—5851noHall
52C3×C13C3⋊(C11⋊AGL(1,𝔽5))14yescomplemented
53C3⋊Dic3—7151noHall
54C3×C11C3⋊#6312014yescomplemented
55C3×D5D42914yes—
56C2×C13—51no—
57C2×C11—51no—
58AGL(1,𝔽5)—12871noHall
59C2×C32—51no—
60C3×C5Dic42914yescomplemented
61C13C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))11yescharacteristic, complemented, Sylow
62Dic3—21454no—
63C11C3⋊(C3⋊#63120)11yescharacteristic, complemented, Sylow
64D5C3⋊D42911yescharacteristic
65C32C11⋊#6312011yescharacteristic, complemented, Sylow
66C2×C3—54no—
67C5C3⋊Dic42911yescharacteristic, complemented, Sylow
68C4—64351noSylow
69C3C3⋊(C11⋊#63120)14yescomplemented
70C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C11×C13C4
prime radical, cosocleC32×D5×C11×C13C2
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C13C4semidirect
9. C3×C5×C11×C13Dic3semidirect
13. C32×C11×C13AGL(1,𝔽5)semidirect
18. C5×C11×C13C3⋊Dic3semidirect
20. C32×C5×C13Dic11semidirect
22. C32×C5×C11Dic13semidirect
24. C3×C11×C13ΓL(1,𝔽16)semidirect
33. C3×C5×C13Dic33semidirect
35. C3×C5×C11Dic39semidirect
37. C11×C13C3⋊ΓL(1,𝔽16)semidirect
40. C32×C13C11⋊AGL(1,𝔽5)semidirect
42. C32×C11#63120semidirect
46. C5×C13C3⋊Dic33semidirect
48. C5×C11C3⋊Dic39semidirect
50. C32×C5Dic143semidirect
52. C3×C13C3⋊(C11⋊AGL(1,𝔽5))semidirect
54. C3×C11C3⋊#63120semidirect
60. C3×C5Dic429semidirect
61. C13C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))semidirect
63. C11C3⋊(C3⋊#63120)semidirect
65. C32C11⋊#63120semidirect
67. C5C3⋊Dic429semidirect
69. C3C3⋊(C11⋊#63120)semidirect

Maximal subgroups

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

subgroupindex
C32×D5×C11×C132
C3⋊(C11⋊#63120)3
C3⋊Dic4295
C3⋊(C3⋊#63120)11
C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))13