Finite Group Databasebeta

← C3×D33×D65 #38788212

Subgroups — C3×D33×D65 #38788212

Order 25740.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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
2C3×C5×C13×D33C211yesmaximal, characteristic, complemented
3C3×D2145C211yesmaximal, characteristic, complemented
4D33×D65C311yesmaximal, characteristic, direct product factor
5C3×D11×D65—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D13×D33—51nomaximal, Hall
8D2145C2×C311yescharacteristic, complemented
9C5×C13×D33C2×C311yescharacteristic, complemented
10C3×D715—31no—
11C3×C11×D65—21no—
12C3×C11×D65D311yescharacteristic, complemented
13C3×C11×D65C2×C311yescharacteristic, complemented
14C3×C5×C13×D11—31no—
15D11×D65—31noHall
16C3×D429—51no—
17C3×C13×D33D511yescharacteristic, complemented
18C32×C11×D13—51no—
19C3×D3×D65—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D5×D33—131nomaximal, Hall
24D13×D33—51no—
25C3×D11×D13—151no—
26D715—31no—
27C11×D65C3×D311yescharacteristic, complemented
28C5×C13×D11—31no—
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195—111no—
31C3×C5×D3×C13—111no—
32C32×D65D1111yescharacteristic, complemented
33C3×D165—131no—
34C3×C5×D33D1311yescharacteristic, complemented
35C32×D5×C11—131no—
36D429—51no—
37C13×D33C3×D511yescharacteristic, complemented
38C3×D143—151no—
39C3×C13×D11—31no—
40C3×C11×D13—51no—
41C3×C11×D13—51no—
42C3×C11×D13—101no—
43C2×C3×D65—331no—
44D3×D65—111no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46D5×D33—131no—
47C3×D5×D11—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×C13D3×D511yescharacteristic, complemented
54C3×C11×C13C2×C3×D511yescharacteristic, complemented
55C2×C3×D33—651noHall
56C2×C3×C5×C13—331no—
57D195—111no—
58C5×D3×C13—111no—
59C3×D65—21no—
60C3×D65—331no—
61C3×D65C3×D1111yescharacteristic, complemented
62C3×D65D3311yescharacteristic, direct product factor
63D165—131no—
64C5×D33C3×D1311yescharacteristic, complemented
65C3×D55—391no—
66C3×D5×C11—131no—
67C3×D5×C11—131no—
68C3×D5×C11—261no—
69C3×C5×D11—31no—
70D143—151no—
71C11×D13—51no—
72C13×D11—31no—
73C2×D65—331noHall
74C3×D39—551no—
75C3×D3×C13—111no—
76C32×D13—51no—
77D5×D11—391noHall
78C2×C32×C11—651no—
79C3×D33—651no—
80C3×D33D6511yescharacteristic, direct product factor
81C3×C5×C13—21no—
82C3×C5×C13C2×C3×D1111yescharacteristic, complemented
83C3×C5×C13C2×D3311yescharacteristic, complemented
84C3×D3×D5—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11D3×D1311yescharacteristic, complemented
87C3×C5×C11C2×C3×D1311yescharacteristic, complemented
88C2×C3×D13—1651no—
89D3×D13—551no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C2×D33—651no—
92C2×C3×D11—1951no—
93C2×C5×C13—331no—
94D65—331no—
95D65C3×D3311yescharacteristic, direct product factor
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55—391no—
98C5×D11—31no—
99D5×C11—131no—
100C32×C11C2×D6511yescharacteristic, complemented, Hall
101C3×D15—1431no—
102C3×C5×D3—111no—
103C32×D5—131no—
104C2×C3×C13—331no—
105D39—551no—
106C3×D13—51no—
107C3×D13—51no—
108C3×D13—101no—
109C3×D13—1651no—
110D3×C13—111no—
111C2×C3×C11—651no—
112C2×C3×C11—651no—
113C2×C3×C11—1301no—
114D33—651no—
115D33C3×D6511yescharacteristic, direct product factor
116C3×D11—31no—
117C3×D11—1951no—
118C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
119C2×C3×D5—4291no—
120D3×D5—1431no—
121C5×C11C3×D3×D1311yescharacteristic, complemented, Hall
122C2×D13—1651noHall
123C32×C5D11×D1311yescharacteristic, complemented, Hall
124C2×D11—1951noHall
125C3×C13—21no—
126C3×C13C3×D5×D1111yescharacteristic, complemented
127C3×C13D5×D3311yescharacteristic, complemented
128C2×C3×D3—7151noHall
129C3×C11—21no—
130C3×C11D3×D6511yescharacteristic, complemented
131C3×C11C2×C3×D6511yescharacteristic, complemented
132C2×C3×C5—331no—
133D15—1431no—
134C3×D5—131no—
135C3×D5—131no—
136C3×D5—261no—
137C3×D5—4291no—
138C5×D3—111no—
139C2×C13—331no—
140D13—51no—
141D13—1651no—
142C2×C11—651no—
143D11—31no—
144D11—1951no—
145C2×D5—4291noHall
146C2×C32—651no—
147C3×D3—111no—
148C3×D3—7151no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D13×D3311yescharacteristic, complemented
152C13C3×D5×D3311yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11C3×D3×D6511yescharacteristic, complemented, Sylow
156C2×C5—331no—
157D5—131no—
158D5—4291no—
159C32D11×D6511yescharacteristic, complemented, Sylow
160C2×C3—331no—
161C2×C3—651no—
162C2×C3—651no—
163C2×C3—21451no—
164C2×C3—1301no—
165D3—111no—
166D3—7151no—
167C5C3×D13×D3311yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—21no—
170C3C3×D11×D6511yescharacteristic, complemented
171C3D33×D6511yescharacteristic, direct product factor
172C2—331no—
173C2—651no—
174C2—21451no—
subgroupG/H
center, hypercenterC3D33×D65
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×C11×D65C2semidirect
2. C3×C5×C13×D33C2semidirect
3. C3×D2145C2semidirect
4. D33×D65C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. D2145C2×C3semidirect
9. C5×C13×D33C2×C3semidirect
12. C3×C11×D65D3semidirect
13. C3×C11×D65C2×C3semidirect
17. C3×C13×D33D5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
27. C11×D65C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
32. C32×D65D11semidirect
34. C3×C5×D33D13semidirect
37. C13×D33C3×D5semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13D3×D5semidirect
54. C3×C11×C13C2×C3×D5semidirect
61. C3×D65C3×D11semidirect
62. C3×D65D33direct (N × H)
64. C5×D33C3×D13semidirect
80. C3×D33D65direct (N × H)
82. C3×C5×C13C2×C3×D11semidirect
83. C3×C5×C13C2×D33semidirect
86. C3×C5×C11D3×D13semidirect
87. C3×C5×C11C2×C3×D13semidirect
90. C11×C13C3×D3×D5semidirect
95. D65C3×D33direct (N × H)
96. C32×C13D5×D11semidirect
100. C32×C11C2×D65semidirect
115. D33C3×D65direct (N × H)
118. C5×C13C2×C3×D33semidirect
121. C5×C11C3×D3×D13semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D5×D33semidirect
130. C3×C11D3×D65semidirect
131. C3×C11C2×C3×D65semidirect
150. C3×C5C3×D11×D13semidirect
151. C3×C5D13×D33semidirect
152. C13C3×D5×D33semidirect
155. C11C3×D3×D65semidirect
159. C32D11×D65semidirect
167. C5C3×D13×D33semidirect
170. C3C3×D11×D65semidirect
171. C3D33×D65direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D652
C3×C5×C13×D332
C3×D21452
D33×D653
C3×D11×D653
C3×D13×D335
C3×D3×D6511
C3×D5×D3313