Finite Group Databasebeta

← D13×C3⋊D165 #38788277

Subgroups — D13×C3⋊D165 #38788277

Order 25740.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×C5×C11×D13C211yesmaximal, characteristic, complemented
2C13×C3⋊D165C211yesmaximal, characteristic, complemented
3C3⋊D2145C211yesmaximal, characteristic, complemented
4D13×D165—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6D13×C3⋊D33—51nomaximal, Hall
7D2145—34no—
8C13×D165—34no—
9C3×C5×C11×D13D314yescomplemented
10D13×D55—91noHall
11C3⋊D429—51no—
12C13×C3⋊D33—51no—
13C32×C11×D13D511yescharacteristic, complemented
14D13×C3⋊D15—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C2×C3⋊D165—131nomaximal, Hall
17D13×D33—154no—
18D715—91no—
19C13×D55—91no—
20C5×C11×D13C3⋊D311yescharacteristic, complemented
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C3⋊D195—111no—
23C13×C3⋊D15—111no—
24C32×C5×D13D1111yescharacteristic, complemented
25C2×C32×C5×C11—131no—
26C3⋊D165—131no—
27C3⋊D165D1311yescharacteristic, direct product factor
28D429—154no—
29C13×D33—154no—
30C3×C11×D13D1514yescomplemented
31D13×D15—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C2×D165—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—451noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—551noHall
38C3×C11×C13C2×D1514yescomplemented
39C2×C3⋊D33—651noHall
40D195—334no—
41C13×D15—334no—
42C3×C5×D13D3314yescomplemented
43C2×C3×C5×C11—134no—
44D165—34no—
45D165—394no—
46D143—451no—
47C11×D13C3⋊D1511yescharacteristic, complemented
48C13×D11—451no—
49D5×D13—991noHall
50C3⋊D39—551no—
51C13×C3⋊D3—551no—
52C32×D13D5511yescharacteristic, complemented
53C2×D55—1171noHall
54C2×C32×C11—131no—
55C3⋊D33—51no—
56C3⋊D33—651no—
57C3×C5×C13C2×D3314yescomplemented
58C2×C3⋊D15—1431noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—1654no—
61C11×C13C2×C3⋊D1511yescharacteristic, complemented, Hall
62C2×D33—1954no—
63D65—991no—
64C5×D13C3⋊D3311yescharacteristic, complemented
65D5×C13—991no—
66C32×C13C2×D5511yescharacteristic, complemented, Hall
67C2×C5×C11—131no—
68D55—91no—
69D55—1171no—
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—131no—
72C3⋊D15—111no—
73C3⋊D15—1431no—
74D39—1654no—
75C3×D13D16514yescomplemented
76D3×C13—1654no—
77C2×C3×C11—134no—
78D33—154no—
79D33—1954no—
80C5×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
81C2×D15—4294no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—4951noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—5851noHall
86C3×C13C2×D16514yescomplemented
87C2×C3⋊D3—7151noHall
88C3×C11D13×D1514yescomplemented
89C2×C3×C5—134no—
90D15—334no—
91D15—4294no—
92C2×C13—4951no—
93D13—4951no—
94D13C3⋊D16511yescharacteristic, direct product factor
95C2×C11—131no—
96D11—451no—
97D11—5851no—
98C2×D5—12871noHall
99C2×C32—131no—
100C3⋊D3—551no—
101C3⋊D3—7151no—
102C3×C5D13×D3314yescomplemented
103C13C2×C3⋊D16511yescharacteristic, complemented, Sylow
104C2×D3—21454no—
105C11D13×C3⋊D1511yescharacteristic, complemented, Sylow
106C2×C5—131no—
107D5—12871no—
108D5—991no—
109C32D13×D5511yescharacteristic, complemented, Sylow
110C2×C3—134no—
111D3—21454no—
112D3—1654no—
113C5D13×C3⋊D3311yescharacteristic, complemented, Sylow
114C22—64351noSylow
115C3D13×D16514yescomplemented
116C2—131no—
117C2—64351no—
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×C5×C11×D13C2semidirect
2. C13×C3⋊D165C2semidirect
3. C3⋊D2145C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×C5×C11×D13D3semidirect
13. C32×C11×D13D5semidirect
15. C3×C5×C11×C13C2×D3semidirect
20. C5×C11×D13C3⋊D3semidirect
21. C32×C11×C13C2×D5semidirect
24. C32×C5×D13D11semidirect
27. C3⋊D165D13direct (N × H)
30. C3×C11×D13D15semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13C2×D15semidirect
42. C3×C5×D13D33semidirect
47. C11×D13C3⋊D15semidirect
52. C32×D13D55semidirect
57. C3×C5×C13C2×D33semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13C2×C3⋊D15semidirect
64. C5×D13C3⋊D33semidirect
66. C32×C13C2×D55semidirect
70. C32×C11D5×D13semidirect
75. C3×D13D165semidirect
80. C5×C13C2×C3⋊D33semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5D11×D13semidirect
86. C3×C13C2×D165semidirect
88. C3×C11D13×D15semidirect
94. D13C3⋊D165direct (N × H)
102. C3×C5D13×D33semidirect
103. C13C2×C3⋊D165semidirect
105. C11D13×C3⋊D15semidirect
109. C32D13×D55semidirect
113. C5D13×C3⋊D33semidirect
115. C3D13×D165semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×D132
C13×C3⋊D1652
C3⋊D21452
D13×D1653
D13×C3⋊D335
D13×C3⋊D1511
C2×C3⋊D16513