Finite Group Databasebeta

← D65⋊(C3⋊D33) #38788289

Subgroups — D65⋊(C3⋊D33) #38788289

Order 25740.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×D65C211yesmaximal, characteristic, complemented
2C5×C3⋊D429C211yesmaximal, characteristic, complemented
3C13×C3⋊D165C211yesmaximal, characteristic, complemented
4D65⋊D33—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6D13×C3⋊D33—51nomaximal, Hall
7C13×D165—34no—
8C5×D429—34no—
9C3×C11×D65D314yescomplemented
10D55⋊D13—91noHall
11C3⋊D429D511yescharacteristic, complemented
12C13×C3⋊D33—51no—
13C32×C11×D13—51no—
14D65⋊(C3⋊D3)—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D5×C3⋊D33—131nomaximal, Hall
17D13×D33—154no—
18C13×D55—91no—
19C11×D65C3⋊D311yescharacteristic, complemented
20C5×D143—91no—
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C13×C3⋊D15—111no—
23C5×C3⋊D39—111no—
24C32×D65D1111yescharacteristic, complemented
25C3⋊D165D1311yescharacteristic, complemented
26C5×C3⋊D33—131no—
27C32×D5×C11—131no—
28D429—34no—
29C13×D33—154no—
30C3×C11×D13—54no—
31D15⋊D13—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D5×D33—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—451noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—551noHall
38C3×C11×C13D3×D514yescomplemented
39C2×C3⋊D33—651noHall
40C13×D15—334no—
41C5×D39—334no—
42C3×D65D3314yescomplemented
43D165—34no—
44C5×D33—394no—
45C3×D5×C11—134no—
46D143—91no—
47C11×D13—51no—
48C13×D11—451no—
49D5×D13—991noHall
50C3⋊D39—111no—
51C13×C3⋊D3—551no—
52C32×D13—51no—
53D5×D11—1171noHall
54C2×C32×C11—651no—
55C3⋊D33—51no—
56C3⋊D33—131no—
57C3×C5×C13C2×D3314yescomplemented
58D5×C3⋊D3—1431noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—1654no—
61C11×C13D5×C3⋊D311yescharacteristic, complemented, Hall
62C2×D33—1954no—
63D65C3⋊D3311yescharacteristic, complemented
64C5×D13—991no—
65D5×C13—991no—
66C32×C13D5×D1111yescharacteristic, complemented, Hall
67D55—91no—
68C5×D11—1171no—
69D5×C11—131no—
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C3⋊D15—111no—
72C5×C3⋊D3—1431no—
73C32×D5—131no—
74D39—334no—
75C3×D13—54no—
76D3×C13—1654no—
77C2×C3×C11—654no—
78D33—154no—
79D33—394no—
80C5×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
81D3×D5—4294no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—4951noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—5851noHall
86C3×C13D5×D3314yescomplemented
87C2×C3⋊D3—7151noHall
88C3×C11D15⋊D1314yescomplemented
89D15—334no—
90C3×D5—134no—
91C5×D3—4294no—
92C2×C13—4951no—
93D13—51no—
94D13—991no—
95C2×C11—651no—
96D11—451no—
97D11—1171no—
98C2×D5—12871noHall
99C2×C32—651no—
100C3⋊D3—551no—
101C3⋊D3—1431no—
102C3×C5D13×D3314yescomplemented
103C13D5×C3⋊D3311yescharacteristic, complemented, Sylow
104C2×D3—21454no—
105C11D65⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
106C2×C5—12871no—
107D5—131no—
108D5—991no—
109C32D55⋊D1311yescharacteristic, complemented, Sylow
110C2×C3—654no—
111D3—1654no—
112D3—4294no—
113C5D13×C3⋊D3311yescharacteristic, complemented, Sylow
114C22—64351noSylow
115C3D65⋊D3314yescomplemented
116C2—12871no—
117C2—651no—
118C2—4951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C13C22
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C11×D65C2semidirect
2. C5×C3⋊D429C2semidirect
3. C13×C3⋊D165C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×C11×D65D3semidirect
11. C3⋊D429D5semidirect
15. C3×C5×C11×C13C2×D3semidirect
19. C11×D65C3⋊D3semidirect
21. C32×C11×C13C2×D5semidirect
24. C32×D65D11semidirect
25. C3⋊D165D13semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13D3×D5semidirect
42. C3×D65D33semidirect
57. C3×C5×C13C2×D33semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13D5×C3⋊D3semidirect
63. D65C3⋊D33semidirect
66. C32×C13D5×D11semidirect
70. C32×C11D5×D13semidirect
80. C5×C13C2×C3⋊D33semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5D11×D13semidirect
86. C3×C13D5×D33semidirect
88. C3×C11D15⋊D13semidirect
102. C3×C5D13×D33semidirect
103. C13D5×C3⋊D33semidirect
105. C11D65⋊(C3⋊D3)semidirect
109. C32D55⋊D13semidirect
113. C5D13×C3⋊D33semidirect
115. C3D65⋊D33semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D652
C5×C3⋊D4292
C13×C3⋊D1652
D65⋊D333
D13×C3⋊D335
D65⋊(C3⋊D3)11
D5×C3⋊D3313