Finite Group Databasebeta

← C3×D3×D5×C11×C13 #38788206

Subgroups — C3×D3×D5×C11×C13 #38788206

Order 25740.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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×D3×C11×C13C211yesmaximal, characteristic, complemented
3C3×C11×C13×D15C211yesmaximal, characteristic, complemented
4C2×C3×D5×C11×C13—31nomaximal
5D3×D5×C11×C13C311yesmaximal, characteristic, direct product factor
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C2×C3×D3×C11×C13—51nomaximal, Hall
8C11×C13×D15C2×C311yescharacteristic, complemented
9C5×D3×C11×C13C2×C311yescharacteristic, complemented
10C3×D5×C11×C13—21no—
11C3×D5×C11×C13—31no—
12C3×D5×C11×C13D311yescharacteristic, direct product factor
13C3×D5×C11×C13C2×C311yescharacteristic, complemented
14C2×C3×C5×C11×C13—31no—
15C2×D5×C11×C13—31noHall
16C3×D3×C11×C13—51no—
17C3×D3×C11×C13D511yescharacteristic, direct product factor
18C2×C32×C11×C13—51no—
19C3×D3×D5×C13C1111yesmaximal, characteristic, direct product factor, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×D3×D5×C11C1311yesmaximal, characteristic, direct product factor, Hall
24C22×C3×C11×C13—151no—
25C2×D3×C11×C13—51no—
26C2×C5×C11×C13—31no—
27D5×C11×C13—31no—
28D5×C11×C13C3×D311yescharacteristic, direct product factor
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×C13×D15C2×C1111yescharacteristic, complemented
31C3×C5×D3×C13C2×C1111yescharacteristic, complemented
32C32×D5×C13C2×C1111yescharacteristic, complemented
33C3×C11×D15C2×C1311yescharacteristic, complemented
34C3×C5×D3×C11C2×C1311yescharacteristic, complemented
35C32×D5×C11C2×C1311yescharacteristic, complemented
36C2×C3×C11×C13—31no—
37C2×C3×C11×C13—51no—
38C2×C3×C11×C13—51no—
39C2×C3×C11×C13—101no—
40C2×C3×C11×C13—151no—
41D3×C11×C13—51no—
42D3×C11×C13C3×D511yescharacteristic, direct product factor
43C2×C3×D5×C13—31no—
44D3×D5×C13C3×C1111yescharacteristic, direct product factor
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×C3×D5×C11—31no—
47D3×D5×C11C3×C1311yescharacteristic, direct product factor
48C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
49C22×C11×C13—151noHall
50C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
51C2×C3×D3×C13—51noHall
52C3×C11×C13—21no—
53C3×C11×C13D3×D511yescharacteristic, direct product factor
54C3×C11×C13C2×C3×D511yescharacteristic, complemented
55C2×C3×D3×C11—51noHall
56C2×C3×C5×C13—31no—
57C13×D15C2×C3×C1111yescharacteristic, complemented
58C5×D3×C13C2×C3×C1111yescharacteristic, complemented
59C3×D5×C13—21no—
60C3×D5×C13—31no—
61C3×D5×C13D3×C1111yescharacteristic, direct product factor
62C3×D5×C13C2×C3×C1111yescharacteristic, complemented
63C2×C3×C5×C11—31no—
64C11×D15C2×C3×C1311yescharacteristic, complemented
65C5×D3×C11C2×C3×C1311yescharacteristic, complemented
66C3×D5×C11—21no—
67C3×D5×C11—31no—
68C3×D5×C11D3×C1311yescharacteristic, direct product factor
69C3×D5×C11C2×C3×C1311yescharacteristic, complemented
70C2×C11×C13—31no—
71C2×C11×C13—51no—
72C2×C11×C13—151no—
73C2×D5×C13—31noHall
74C2×C32×C13—51no—
75C3×D3×C13—51no—
76C3×D3×C13D5×C1111yescharacteristic, direct product factor
77C2×D5×C11—31noHall
78C2×C32×C11—51no—
79C3×D3×C11—51no—
80C3×D3×C11D5×C1311yescharacteristic, direct product factor
81C3×C5×C13—21no—
82C3×C5×C13C2×D3×C1111yescharacteristic, complemented
83C3×C5×C13C22×C3×C1111yescharacteristic, complemented
84C3×D3×D5C11×C1311yescharacteristic, direct product factor, Hall
85C3×C5×C11—21no—
86C3×C5×C11C2×D3×C1311yescharacteristic, complemented
87C3×C5×C11C22×C3×C1311yescharacteristic, complemented
88C22×C3×C13—151no—
89C2×D3×C13—51no—
90C11×C13C3×D3×D511yescharacteristic, direct product factor, Hall
91C22×C3×C11—151no—
92C2×D3×C11—51no—
93C2×C5×C13—31no—
94D5×C13—31no—
95D5×C13C3×D3×C1111yescharacteristic, direct product factor
96C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—31no—
98D5×C11—31no—
99D5×C11C3×D3×C1311yescharacteristic, direct product factor
100C32×C11C2×D5×C1311yescharacteristic, complemented, Hall
101C3×D15C2×C11×C1311yescharacteristic, complemented
102C3×C5×D3C2×C11×C1311yescharacteristic, complemented
103C32×D5C2×C11×C1311yescharacteristic, complemented
104C2×C3×C13—31no—
105C2×C3×C13—51no—
106C2×C3×C13—51no—
107C2×C3×C13—101no—
108C2×C3×C13—151no—
109D3×C13—51no—
110D3×C13C3×D5×C1111yescharacteristic, direct product factor
111C2×C3×C11—31no—
112C2×C3×C11—51no—
113C2×C3×C11—51no—
114C2×C3×C11—101no—
115C2×C3×C11—151no—
116D3×C11—51no—
117D3×C11C3×D5×C1311yescharacteristic, direct product factor
118C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
119C2×C3×D5—31no—
120D3×D5C3×C11×C1311yescharacteristic, direct product factor
121C5×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
122C22×C13—151noHall
123C32×C5C22×C11×C1311yescharacteristic, complemented, Hall
124C22×C11—151noHall
125C3×C13—21no—
126C3×C13D3×D5×C1111yescharacteristic, direct product factor
127C3×C13C2×C3×D5×C1111yescharacteristic, complemented
128C2×C3×D3—51noHall
129C3×C11—21no—
130C3×C11D3×D5×C1311yescharacteristic, direct product factor
131C3×C11C2×C3×D5×C1311yescharacteristic, complemented
132C2×C3×C5—31no—
133D15C2×C3×C11×C1311yescharacteristic, complemented
134C3×D5—21no—
135C3×D5—31no—
136C3×D5D3×C11×C1311yescharacteristic, direct product factor
137C3×D5C2×C3×C11×C1311yescharacteristic, complemented
138C5×D3C2×C3×C11×C1311yescharacteristic, complemented
139C2×C13—31no—
140C2×C13—51no—
141C2×C13—151no—
142C2×C11—31no—
143C2×C11—51no—
144C2×C11—151no—
145C2×D5—31noHall
146C2×C32—51no—
147C3×D3—51no—
148C3×D3D5×C11×C1311yescharacteristic, direct product factor
149C3×C5—21no—
150C3×C5C2×D3×C11×C1311yescharacteristic, complemented
151C3×C5C22×C3×C11×C1311yescharacteristic, complemented
152C13C3×D3×D5×C1111yescharacteristic, direct product factor, Sylow
153C22×C3—151no—
154C2×D3—51no—
155C11C3×D3×D5×C1311yescharacteristic, direct product factor, Sylow
156C2×C5—31no—
157D5—31no—
158D5C3×D3×C11×C1311yescharacteristic, direct product factor
159C32C2×D5×C11×C1311yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—51no—
162C2×C3—51no—
163C2×C3—101no—
164C2×C3—151no—
165D3—51no—
166D3C3×D5×C11×C1311yescharacteristic, direct product factor
167C5C2×C3×D3×C11×C1311yescharacteristic, complemented, Sylow
168C22—151noSylow
169C3—21no—
170C3D3×D5×C11×C1311yescharacteristic, direct product factor
171C3C2×C3×D5×C11×C1311yescharacteristic, complemented
172C2—31no—
173C2—51no—
174C2—151no—
subgroupG/H
center, hypercenterC3×C11×C13D3×D5
commutator, cosocle, hypocenterC3×C5C22×C3×C11×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5
UCSC1 ◁ C3×C11×C13

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C13C2semidirect
2. C3×C5×D3×C11×C13C2semidirect
3. C3×C11×C13×D15C2semidirect
5. D3×D5×C11×C13C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. C11×C13×D15C2×C3semidirect
9. C5×D3×C11×C13C2×C3semidirect
12. C3×D5×C11×C13D3direct (N × H)
13. C3×D5×C11×C13C2×C3semidirect
17. C3×D3×C11×C13D5direct (N × H)
19. C3×D3×D5×C13C11direct (N × H)
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
23. C3×D3×D5×C11C13direct (N × H)
28. D5×C11×C13C3×D3direct (N × H)
29. C32×C11×C13C2×D5semidirect
30. C3×C13×D15C2×C11semidirect
31. C3×C5×D3×C13C2×C11semidirect
32. C32×D5×C13C2×C11semidirect
33. C3×C11×D15C2×C13semidirect
34. C3×C5×D3×C11C2×C13semidirect
35. C32×D5×C11C2×C13semidirect
42. D3×C11×C13C3×D5direct (N × H)
44. D3×D5×C13C3×C11direct (N × H)
45. C5×C11×C13C2×C3×D3semidirect
47. D3×D5×C11C3×C13direct (N × H)
48. C32×C5×C13C22×C11semidirect
50. C32×C5×C11C22×C13semidirect
53. C3×C11×C13D3×D5direct (N × H)
54. C3×C11×C13C2×C3×D5semidirect
57. C13×D15C2×C3×C11semidirect
58. C5×D3×C13C2×C3×C11semidirect
61. C3×D5×C13D3×C11direct (N × H)
62. C3×D5×C13C2×C3×C11semidirect
64. C11×D15C2×C3×C13semidirect
65. C5×D3×C11C2×C3×C13semidirect
68. C3×D5×C11D3×C13direct (N × H)
69. C3×D5×C11C2×C3×C13semidirect
76. C3×D3×C13D5×C11direct (N × H)
80. C3×D3×C11D5×C13direct (N × H)
82. C3×C5×C13C2×D3×C11semidirect
83. C3×C5×C13C22×C3×C11semidirect
84. C3×D3×D5C11×C13direct (N × H)
86. C3×C5×C11C2×D3×C13semidirect
87. C3×C5×C11C22×C3×C13semidirect
90. C11×C13C3×D3×D5direct (N × H)
95. D5×C13C3×D3×C11direct (N × H)
96. C32×C13C2×D5×C11semidirect
99. D5×C11C3×D3×C13direct (N × H)
100. C32×C11C2×D5×C13semidirect
101. C3×D15C2×C11×C13semidirect
102. C3×C5×D3C2×C11×C13semidirect
103. C32×D5C2×C11×C13semidirect
110. D3×C13C3×D5×C11direct (N × H)
117. D3×C11C3×D5×C13direct (N × H)
118. C5×C13C2×C3×D3×C11semidirect
120. D3×D5C3×C11×C13direct (N × H)
121. C5×C11C2×C3×D3×C13semidirect
123. C32×C5C22×C11×C13semidirect
126. C3×C13D3×D5×C11direct (N × H)
127. C3×C13C2×C3×D5×C11semidirect
130. C3×C11D3×D5×C13direct (N × H)
131. C3×C11C2×C3×D5×C13semidirect
133. D15C2×C3×C11×C13semidirect
136. C3×D5D3×C11×C13direct (N × H)
137. C3×D5C2×C3×C11×C13semidirect
138. C5×D3C2×C3×C11×C13semidirect
148. C3×D3D5×C11×C13direct (N × H)
150. C3×C5C2×D3×C11×C13semidirect
151. C3×C5C22×C3×C11×C13semidirect
152. C13C3×D3×D5×C11direct (N × H)
155. C11C3×D3×D5×C13direct (N × H)
158. D5C3×D3×C11×C13direct (N × H)
159. C32C2×D5×C11×C13semidirect
166. D3C3×D5×C11×C13direct (N × H)
167. C5C2×C3×D3×C11×C13semidirect
170. C3D3×D5×C11×C13direct (N × H)
171. C3C2×C3×D5×C11×C13semidirect

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×D3×C11×C132
C3×C11×C13×D152
C2×C3×D5×C11×C133
D3×D5×C11×C133
C2×C3×D3×C11×C135
C3×D3×D5×C1311
C3×D3×D5×C1113