Finite Group Databasebeta

← C3×D5×C13×D33 #38788210

Subgroups — C3×D5×C13×D33 #38788210

Order 25740.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×D5×C11×C13C211yesmaximal, characteristic, complemented
2C3×C5×C13×D33C211yesmaximal, characteristic, complemented
3C3×C13×D165C211yesmaximal, characteristic, complemented
4D5×C13×D33C311yesmaximal, characteristic, direct product factor
5C3×D5×C13×D11—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C2×C3×C13×D33—51nomaximal, Hall
8C13×D165C2×C311yescharacteristic, complemented
9C5×C13×D33C2×C311yescharacteristic, complemented
10C3×C13×D55—31no—
11C3×D5×C11×C13—21no—
12C3×D5×C11×C13D311yescharacteristic, complemented
13C3×D5×C11×C13C2×C311yescharacteristic, complemented
14C3×C5×C13×D11—31no—
15D5×C13×D11—31noHall
16C3×C13×D33—51no—
17C3×C13×D33D511yescharacteristic, direct product factor
18C2×C32×C11×C13—51no—
19C3×D3×D5×C13—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D5×D33C1311yesmaximal, characteristic, direct product factor, Hall
24C2×C13×D33—51no—
25C2×C3×C13×D11—151no—
26C13×D55—31no—
27D5×C11×C13C3×D311yescharacteristic, complemented
28C5×C13×D11—31no—
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×C13×D15—111no—
31C3×C5×D3×C13—111no—
32C32×D5×C13D1111yescharacteristic, complemented
33C3×D165C2×C1311yescharacteristic, complemented
34C3×C5×D33C2×C1311yescharacteristic, complemented
35C32×D5×C11C2×C1311yescharacteristic, complemented
36C2×C3×C11×C13—51no—
37C2×C3×C11×C13—51no—
38C2×C3×C11×C13—101no—
39C13×D33—51no—
40C13×D33C3×D511yescharacteristic, direct product factor
41C3×C13×D11—31no—
42C3×C13×D11—151no—
43C2×C3×D5×C13—331no—
44D3×D5×C13—111no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46D5×D33C3×C1311yescharacteristic, direct product factor
47C3×D5×D11—31no—
48C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
49C2×C13×D11—151noHall
50C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
51C2×C3×D3×C13—551noHall
52C3×C11×C13—21no—
53C3×C11×C13D3×D511yescharacteristic, complemented
54C3×C11×C13C2×C3×D511yescharacteristic, complemented
55C2×C3×D33—51noHall
56C2×C3×C5×C13—331no—
57C13×D15—111no—
58C5×D3×C13—111no—
59C3×D5×C13—21no—
60C3×D5×C13—331no—
61C3×D5×C13C3×D1111yescharacteristic, complemented
62C3×D5×C13D3311yescharacteristic, direct product factor
63D165C2×C3×C1311yescharacteristic, complemented
64C5×D33C2×C3×C1311yescharacteristic, complemented
65C3×D55—31no—
66C3×D5×C11—21no—
67C3×D5×C11D3×C1311yescharacteristic, complemented
68C3×D5×C11C2×C3×C1311yescharacteristic, complemented
69C3×C5×D11—31no—
70C2×C11×C13—51no—
71C13×D11—31no—
72C13×D11—151no—
73C2×D5×C13—331noHall
74C2×C32×C13—51no—
75C3×D3×C13—111no—
76C3×D3×C13—551no—
77D5×D11—31noHall
78C2×C32×C11—51no—
79C3×D33—51no—
80C3×D33D5×C1311yescharacteristic, direct product factor
81C3×C5×C13—21no—
82C3×C5×C13C2×C3×D1111yescharacteristic, complemented
83C3×C5×C13C2×D3311yescharacteristic, complemented
84C3×D3×D5—111noHall
85C3×C5×C11—21no—
86C3×C5×C11C2×D3×C1311yescharacteristic, complemented
87C3×C5×C11C22×C3×C1311yescharacteristic, complemented
88C22×C3×C13—1651no—
89C2×D3×C13—551no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C2×D33—51no—
92C2×C3×D11—151no—
93C2×C5×C13—331no—
94D5×C13—331no—
95D5×C13C3×D3311yescharacteristic, direct product factor
96C32×C13D5×D1111yescharacteristic, complemented, Hall
97D55—31no—
98C5×D11—31no—
99D5×C11C3×D3×C1311yescharacteristic, complemented
100C32×C11C2×D5×C1311yescharacteristic, complemented, Hall
101C3×D15—111no—
102C3×C5×D3—111no—
103C32×D5C13×D1111yescharacteristic, complemented
104C2×C3×C13—51no—
105C2×C3×C13—51no—
106C2×C3×C13—101no—
107C2×C3×C13—331no—
108C2×C3×C13—1651no—
109D3×C13—111no—
110D3×C13—551no—
111C2×C3×C11—51no—
112C2×C3×C11—51no—
113C2×C3×C11—101no—
114D33—51no—
115D33C3×D5×C1311yescharacteristic, direct product factor
116C3×D11—31no—
117C3×D11—151no—
118C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
119C2×C3×D5—331no—
120D3×D5—111no—
121C5×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
122C22×C13—1651noHall
123C32×C5C2×C13×D1111yescharacteristic, complemented, Hall
124C2×D11—151noHall
125C3×C13—21no—
126C3×C13C3×D5×D1111yescharacteristic, complemented
127C3×C13D5×D3311yescharacteristic, direct product factor
128C2×C3×D3—551noHall
129C3×C11—21no—
130C3×C11D3×D5×C1311yescharacteristic, complemented
131C3×C11C2×C3×D5×C1311yescharacteristic, complemented
132C2×C3×C5—331no—
133D15—111no—
134C3×D5—21no—
135C3×D5—331no—
136C3×D5C3×C13×D1111yescharacteristic, complemented
137C3×D5C13×D3311yescharacteristic, direct product factor
138C5×D3—111no—
139C2×C13—51no—
140C2×C13—331no—
141C2×C13—1651no—
142C2×C11—51no—
143D11—31no—
144D11—151no—
145C2×D5—331noHall
146C2×C32—51no—
147C3×D3—111no—
148C3×D3—551no—
149C3×C5—21no—
150C3×C5C2×C3×C13×D1111yescharacteristic, complemented
151C3×C5C2×C13×D3311yescharacteristic, complemented
152C13C3×D5×D3311yescharacteristic, direct product factor, Sylow
153C22×C3—1651no—
154C2×D3—551no—
155C11C3×D3×D5×C1311yescharacteristic, complemented, Sylow
156C2×C5—331no—
157D5—331no—
158D5C3×C13×D3311yescharacteristic, direct product factor
159C32D5×C13×D1111yescharacteristic, complemented, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—331no—
164C2×C3—1651no—
165D3—111no—
166D3—551no—
167C5C2×C3×C13×D3311yescharacteristic, complemented, Sylow
168C22—1651noSylow
169C3—21no—
170C3C3×D5×C13×D1111yescharacteristic, complemented
171C3D5×C13×D3311yescharacteristic, direct product factor
172C2—51no—
173C2—331no—
174C2—1651no—
subgroupG/H
center, hypercenterC3×C13D5×D33
commutator, cosocle, hypocenterC3×C5×C11C22×C3×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C3×C13

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C13C2semidirect
2. C3×C5×C13×D33C2semidirect
3. C3×C13×D165C2semidirect
4. D5×C13×D33C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. C13×D165C2×C3semidirect
9. C5×C13×D33C2×C3semidirect
12. C3×D5×C11×C13D3semidirect
13. C3×D5×C11×C13C2×C3semidirect
17. C3×C13×D33D5direct (N × H)
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
23. C3×D5×D33C13direct (N × H)
27. D5×C11×C13C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
32. C32×D5×C13D11semidirect
33. C3×D165C2×C13semidirect
34. C3×C5×D33C2×C13semidirect
35. C32×D5×C11C2×C13semidirect
40. C13×D33C3×D5direct (N × H)
45. C5×C11×C13C2×C3×D3semidirect
46. D5×D33C3×C13direct (N × H)
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C22×C13semidirect
53. C3×C11×C13D3×D5semidirect
54. C3×C11×C13C2×C3×D5semidirect
61. C3×D5×C13C3×D11semidirect
62. C3×D5×C13D33direct (N × H)
63. D165C2×C3×C13semidirect
64. C5×D33C2×C3×C13semidirect
67. C3×D5×C11D3×C13semidirect
68. C3×D5×C11C2×C3×C13semidirect
80. C3×D33D5×C13direct (N × H)
82. C3×C5×C13C2×C3×D11semidirect
83. C3×C5×C13C2×D33semidirect
86. C3×C5×C11C2×D3×C13semidirect
87. C3×C5×C11C22×C3×C13semidirect
90. C11×C13C3×D3×D5semidirect
95. D5×C13C3×D33direct (N × H)
96. C32×C13D5×D11semidirect
99. D5×C11C3×D3×C13semidirect
100. C32×C11C2×D5×C13semidirect
103. C32×D5C13×D11semidirect
115. D33C3×D5×C13direct (N × H)
118. C5×C13C2×C3×D33semidirect
121. C5×C11C2×C3×D3×C13semidirect
123. C32×C5C2×C13×D11semidirect
126. C3×C13C3×D5×D11semidirect
127. C3×C13D5×D33direct (N × H)
130. C3×C11D3×D5×C13semidirect
131. C3×C11C2×C3×D5×C13semidirect
136. C3×D5C3×C13×D11semidirect
137. C3×D5C13×D33direct (N × H)
150. C3×C5C2×C3×C13×D11semidirect
151. C3×C5C2×C13×D33semidirect
152. C13C3×D5×D33direct (N × H)
155. C11C3×D3×D5×C13semidirect
158. D5C3×C13×D33direct (N × H)
159. C32D5×C13×D11semidirect
167. C5C2×C3×C13×D33semidirect
170. C3C3×D5×C13×D11semidirect
171. C3D5×C13×D33direct (N × H)

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×C5×C13×D332
C3×C13×D1652
D5×C13×D333
C3×D5×C13×D113
C2×C3×C13×D335
C3×D3×D5×C1311
C3×D5×D3313