Finite Group Databasebeta

← C3×D13×D165 #38788201

Subgroups — C3×D13×D165 #38788201

Order 25740.

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C3×C13×D165C211yesmaximal, characteristic, complemented
3C3×D2145C211yesmaximal, characteristic, complemented
4D13×D165C311yesmaximal, characteristic, direct product factor
5C3×D13×D55—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D13×D33—51nomaximal, Hall
8D2145C2×C311yescharacteristic, complemented
9C13×D165C2×C311yescharacteristic, complemented
10C3×D715—31no—
11C3×C13×D55—31no—
12C3×C5×C11×D13—21no—
13C3×C5×C11×D13D311yescharacteristic, complemented
14C3×C5×C11×D13C2×C311yescharacteristic, complemented
15D13×D55—31noHall
16C3×D429—51no—
17C3×C13×D33—51no—
18C32×C11×D13D511yescharacteristic, complemented
19C3×D13×D15—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C2×C3×D165—131nomaximal, Hall
24D13×D33—51no—
25C3×D11×D13—151no—
26D715—31no—
27C13×D55—31no—
28C5×C11×D13C3×D311yescharacteristic, complemented
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195—111no—
31C3×C13×D15—111no—
32C32×C5×D13D1111yescharacteristic, complemented
33C2×C32×C5×C11—131no—
34C3×D165—131no—
35C3×D165D1311yescharacteristic, direct product factor
36D429—51no—
37C13×D33—51no—
38C3×D143—151no—
39C3×C13×D11—151no—
40C3×C11×D13—21no—
41C3×C11×D13C3×D511yescharacteristic, complemented
42C3×C11×D13D1511yescharacteristic, complemented
43D13×D15—111no—
44C3×D5×D13—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×D165—131no—
47C2×C3×D55—391no—
48C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
49D11×D13—151noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51C3×D3×D13—551noHall
52C3×C11×C13—21no—
53C3×C11×C13C2×C3×D511yescharacteristic, complemented
54C3×C11×C13C2×D1511yescharacteristic, complemented
55C2×C3×D33—651noHall
56D195—111no—
57C13×D15—111no—
58C3×D65—331no—
59C3×D5×C13—331no—
60C3×C5×D13—21no—
61C3×C5×D13C3×D1111yescharacteristic, complemented
62C3×C5×D13D3311yescharacteristic, complemented
63C2×C3×C5×C11—131no—
64C2×C3×C5×C11—131no—
65C2×C3×C5×C11—261no—
66D165—131no—
67D165C3×D1311yescharacteristic, direct product factor
68C3×D55—31no—
69C3×D55—391no—
70D143—151no—
71C11×D13C3×D1511yescharacteristic, complemented
72C13×D11—151no—
73D5×D13—331noHall
74C3×D39—551no—
75C3×D3×C13—551no—
76C32×D13D5511yescharacteristic, complemented
77C2×D55—391noHall
78C2×C32×C11—131no—
79C3×D33—51no—
80C3×D33—651no—
81C3×C5×C13—21no—
82C3×C5×C13C2×C3×D1111yescharacteristic, complemented
83C3×C5×C13C2×D3311yescharacteristic, complemented
84C2×C3×D15—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11D3×D1311yescharacteristic, complemented
87C3×C5×C11C2×C3×D1311yescharacteristic, complemented
88C2×C3×D13—1651no—
89D3×D13—551no—
90C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
91C2×D33—651no—
92C2×C3×D11—1951no—
93D65—331no—
94C5×D13C3×D3311yescharacteristic, complemented
95D5×C13—331no—
96C32×C13C2×D5511yescharacteristic, complemented, Hall
97C2×C5×C11—131no—
98D55—31no—
99D55—391no—
100C32×C11D5×D1311yescharacteristic, complemented, Hall
101C2×C32×C5—131no—
102C3×D15—111no—
103C3×D15—1431no—
104C2×C3×C13—1651no—
105D39—551no—
106C3×D13—21no—
107C3×D13—1651no—
108C3×D13C3×D5511yescharacteristic, complemented
109C3×D13D16511yescharacteristic, direct product factor
110D3×C13—551no—
111C2×C3×C11—131no—
112C2×C3×C11—131no—
113C2×C3×C11—261no—
114D33—51no—
115D33—651no—
116C3×D11—151no—
117C3×D11—1951no—
118C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
119C2×D15—1431no—
120C2×C3×D5—4291no—
121C5×C11C3×D3×D1311yescharacteristic, complemented, Hall
122C2×D13—1651noHall
123C32×C5D11×D1311yescharacteristic, complemented, Hall
124C2×D11—1951noHall
125C3×C13—21no—
126C3×C13C2×C3×D5511yescharacteristic, complemented
127C3×C13C2×D16511yescharacteristic, complemented
128C2×C3×D3—7151noHall
129C3×C11—21no—
130C3×C11C3×D5×D1311yescharacteristic, complemented
131C3×C11D13×D1511yescharacteristic, complemented
132C2×C3×C5—131no—
133C2×C3×C5—131no—
134C2×C3×C5—261no—
135D15—111no—
136D15—1431no—
137C3×D5—331no—
138C3×D5—4291no—
139C2×C13—1651no—
140D13—1651no—
141D13C3×D16511yescharacteristic, direct product factor
142C2×C11—131no—
143D11—151no—
144D11—1951no—
145C2×D5—4291noHall
146C2×C32—131no—
147C3×D3—551no—
148C3×D3—7151no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D13×D3311yescharacteristic, complemented
152C13C2×C3×D16511yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C3×D13×D1511yescharacteristic, complemented, Sylow
156C2×C5—131no—
157D5—331no—
158D5—4291no—
159C32D13×D5511yescharacteristic, complemented, Sylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—261no—
163C2×C3—21451no—
164C2×C3—1651no—
165D3—551no—
166D3—7151no—
167C5C3×D13×D3311yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D13×D5511yescharacteristic, complemented
171C3D13×D16511yescharacteristic, direct product factor
172C2—131no—
173C2—21451no—
174C2—1651no—
subgroupG/H
center, hypercenterC3D13×D165
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D13C2semidirect
2. C3×C13×D165C2semidirect
3. C3×D2145C2semidirect
4. D13×D165C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. D2145C2×C3semidirect
9. C13×D165C2×C3semidirect
13. C3×C5×C11×D13D3semidirect
14. C3×C5×C11×D13C2×C3semidirect
18. C32×C11×D13D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
28. C5×C11×D13C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
32. C32×C5×D13D11semidirect
35. C3×D165D13direct (N × H)
41. C3×C11×D13C3×D5semidirect
42. C3×C11×D13D15semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13C2×C3×D5semidirect
54. C3×C11×C13C2×D15semidirect
61. C3×C5×D13C3×D11semidirect
62. C3×C5×D13D33semidirect
67. D165C3×D13direct (N × H)
71. C11×D13C3×D15semidirect
76. C32×D13D55semidirect
82. C3×C5×C13C2×C3×D11semidirect
83. C3×C5×C13C2×D33semidirect
86. C3×C5×C11D3×D13semidirect
87. C3×C5×C11C2×C3×D13semidirect
90. C11×C13C2×C3×D15semidirect
94. C5×D13C3×D33semidirect
96. C32×C13C2×D55semidirect
100. C32×C11D5×D13semidirect
108. C3×D13C3×D55semidirect
109. C3×D13D165direct (N × H)
118. C5×C13C2×C3×D33semidirect
121. C5×C11C3×D3×D13semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C2×C3×D55semidirect
127. C3×C13C2×D165semidirect
130. C3×C11C3×D5×D13semidirect
131. C3×C11D13×D15semidirect
141. D13C3×D165direct (N × H)
150. C3×C5C3×D11×D13semidirect
151. C3×C5D13×D33semidirect
152. C13C2×C3×D165semidirect
155. C11C3×D13×D15semidirect
159. C32D13×D55semidirect
167. C5C3×D13×D33semidirect
170. C3C3×D13×D55semidirect
171. C3D13×D165direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C11×D132
C3×C13×D1652
C3×D21452
D13×D1653
C3×D13×D553
C3×D13×D335
C3×D13×D1511
C2×C3×D16513