Finite Group Databasebeta

← C3×C5×D3×C11×D13 #38788183

Subgroups — C3×C5×D3×C11×D13 #38788183

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×C5×C11×D13C211yesmaximal, characteristic, complemented
2C3×C5×D3×C11×C13C211yesmaximal, characteristic, complemented
3C3×C5×C11×D39C211yesmaximal, characteristic, complemented
4C2×C3×C5×C11×D13—31nomaximal
5C5×D3×C11×D13C311yesmaximal, characteristic, direct product factor
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D3×C11×D13C511yesmaximal, characteristic, direct product factor, Hall
8C5×C11×D39C2×C311yescharacteristic, complemented
9C5×D3×C11×C13C2×C311yescharacteristic, complemented
10C3×C5×C11×D13—21no—
11C3×C5×C11×D13—31no—
12C3×C5×C11×D13D311yescharacteristic, direct product factor
13C3×C5×C11×D13C2×C311yescharacteristic, complemented
14C2×C3×C5×C11×C13—31no—
15C2×C5×C11×D13—31noHall
16C3×C11×D39C2×C511yescharacteristic, complemented
17C3×D3×C11×C13C2×C511yescharacteristic, complemented
18C32×C11×D13C2×C511yescharacteristic, complemented
19C3×C5×D3×D13C1111yesmaximal, characteristic, direct product factor, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C2×C3×C5×D3×C11—131nomaximal, Hall
24C2×C3×C11×D13—31no—
25D3×C11×D13C3×C511yescharacteristic, direct product factor
26C2×C5×C11×C13—31no—
27C5×C11×D13—31no—
28C5×C11×D13C3×D311yescharacteristic, direct product factor
29C32×C11×C13C22×C511yescharacteristic, complemented, Hall
30C3×C5×D39C2×C1111yescharacteristic, complemented
31C3×C5×D3×C13C2×C1111yescharacteristic, complemented
32C32×C5×D13C2×C1111yescharacteristic, complemented
33C2×C32×C5×C11—131no—
34C3×C5×D3×C11—131no—
35C3×C5×D3×C11D1311yescharacteristic, direct product factor
36C2×C3×C11×C13—31no—
37C11×D39C2×C3×C511yescharacteristic, complemented
38D3×C11×C13C2×C3×C511yescharacteristic, complemented
39C3×C11×D13—21no—
40C3×C11×D13—31no—
41C3×C11×D13C5×D311yescharacteristic, direct product factor
42C3×C11×D13C2×C3×C511yescharacteristic, complemented
43C2×C3×C5×D13—31no—
44C5×D3×D13C3×C1111yescharacteristic, direct product factor
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C22×C3×C5×C11—391no—
47C2×C5×D3×C11—131no—
48C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
49C2×C11×D13—31noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51C3×D3×D13C5×C1111yescharacteristic, direct product factor, Hall
52C3×C11×C13—21no—
53C3×C11×C13C2×C5×D311yescharacteristic, complemented
54C3×C11×C13C22×C3×C511yescharacteristic, complemented
55C2×C3×D3×C11—131noHall
56C2×C3×C5×C13—31no—
57C5×D39C2×C3×C1111yescharacteristic, complemented
58C5×D3×C13C2×C3×C1111yescharacteristic, complemented
59C3×C5×D13—21no—
60C3×C5×D13—31no—
61C3×C5×D13D3×C1111yescharacteristic, direct product factor
62C3×C5×D13C2×C3×C1111yescharacteristic, complemented
63C2×C3×C5×C11—31no—
64C2×C3×C5×C11—131no—
65C2×C3×C5×C11—131no—
66C2×C3×C5×C11—261no—
67C2×C3×C5×C11—391no—
68C5×D3×C11—131no—
69C5×D3×C11C3×D1311yescharacteristic, direct product factor
70C2×C11×C13—31no—
71C11×D13—31no—
72C11×D13C3×C5×D311yescharacteristic, direct product factor
73C2×C5×D13—31noHall
74C3×D39C2×C5×C1111yescharacteristic, complemented
75C3×D3×C13C2×C5×C1111yescharacteristic, complemented
76C32×D13C2×C5×C1111yescharacteristic, complemented
77C22×C5×C11—391noHall
78C2×C32×C11—131no—
79C3×D3×C11—131no—
80C3×D3×C11C5×D1311yescharacteristic, direct product factor
81C3×C5×C13—21no—
82C3×C5×C13C2×D3×C1111yescharacteristic, complemented
83C3×C5×C13C22×C3×C1111yescharacteristic, complemented
84C2×C3×C5×D3—131noHall
85C3×C5×C11—21no—
86C3×C5×C11D3×D1311yescharacteristic, direct product factor
87C3×C5×C11C2×C3×D1311yescharacteristic, complemented
88C2×C3×D13—31no—
89D3×D13C3×C5×C1111yescharacteristic, direct product factor
90C11×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
91C22×C3×C11—391no—
92C2×D3×C11—131no—
93C2×C5×C13—31no—
94C5×D13—31no—
95C5×D13C3×D3×C1111yescharacteristic, direct product factor
96C32×C13C22×C5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—31no—
98C2×C5×C11—131no—
99C2×C5×C11—391no—
100C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
101C2×C32×C5—131no—
102C3×C5×D3—131no—
103C3×C5×D3C11×D1311yescharacteristic, direct product factor
104C2×C3×C13—31no—
105D39C2×C3×C5×C1111yescharacteristic, complemented
106C3×D13—21no—
107C3×D13—31no—
108C3×D13C5×D3×C1111yescharacteristic, direct product factor
109C3×D13C2×C3×C5×C1111yescharacteristic, complemented
110D3×C13C2×C3×C5×C1111yescharacteristic, complemented
111C2×C3×C11—31no—
112C2×C3×C11—131no—
113C2×C3×C11—131no—
114C2×C3×C11—261no—
115C2×C3×C11—391no—
116D3×C11—131no—
117D3×C11C3×C5×D1311yescharacteristic, direct product factor
118C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
119C22×C3×C5—391no—
120C2×C5×D3—131no—
121C5×C11C3×D3×D1311yescharacteristic, direct product factor, Hall
122C2×D13—31noHall
123C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
124C22×C11—391noHall
125C3×C13—21no—
126C3×C13C2×C5×D3×C1111yescharacteristic, complemented
127C3×C13C22×C3×C5×C1111yescharacteristic, complemented
128C2×C3×D3—131noHall
129C3×C11—21no—
130C3×C11C5×D3×D1311yescharacteristic, direct product factor
131C3×C11C2×C3×C5×D1311yescharacteristic, complemented
132C2×C3×C5—31no—
133C2×C3×C5—131no—
134C2×C3×C5—131no—
135C2×C3×C5—261no—
136C2×C3×C5—391no—
137C5×D3—131no—
138C5×D3C3×C11×D1311yescharacteristic, direct product factor
139C2×C13—31no—
140D13—31no—
141D13C3×C5×D3×C1111yescharacteristic, direct product factor
142C2×C11—31no—
143C2×C11—131no—
144C2×C11—391no—
145C22×C5—391noHall
146C2×C32—131no—
147C3×D3—131no—
148C3×D3C5×C11×D1311yescharacteristic, direct product factor
149C3×C5—21no—
150C3×C5D3×C11×D1311yescharacteristic, direct product factor
151C3×C5C2×C3×C11×D1311yescharacteristic, complemented
152C13C2×C3×C5×D3×C1111yescharacteristic, complemented, Sylow
153C22×C3—391no—
154C2×D3—131no—
155C11C3×C5×D3×D1311yescharacteristic, direct product factor, Sylow
156C2×C5—31no—
157C2×C5—131no—
158C2×C5—391no—
159C32C2×C5×C11×D1311yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—131no—
162C2×C3—131no—
163C2×C3—261no—
164C2×C3—391no—
165D3—131no—
166D3C3×C5×C11×D1311yescharacteristic, direct product factor
167C5C3×D3×C11×D1311yescharacteristic, direct product factor, Sylow
168C22—391noSylow
169C3—21no—
170C3C5×D3×C11×D1311yescharacteristic, direct product factor
171C3C2×C3×C5×C11×D1311yescharacteristic, complemented
172C2—31no—
173C2—131no—
174C2—391no—
subgroupG/H
center, hypercenterC3×C5×C11D3×D13
commutator, cosocle, hypocenterC3×C13C22×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C13
UCSC1 ◁ C3×C5×C11

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D13C2semidirect
2. C3×C5×D3×C11×C13C2semidirect
3. C3×C5×C11×D39C2semidirect
5. C5×D3×C11×D13C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
7. C3×D3×C11×D13C5direct (N × H)
8. C5×C11×D39C2×C3semidirect
9. C5×D3×C11×C13C2×C3semidirect
12. C3×C5×C11×D13D3direct (N × H)
13. C3×C5×C11×D13C2×C3semidirect
16. C3×C11×D39C2×C5semidirect
17. C3×D3×C11×C13C2×C5semidirect
18. C32×C11×D13C2×C5semidirect
19. C3×C5×D3×D13C11direct (N × H)
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
25. D3×C11×D13C3×C5direct (N × H)
28. C5×C11×D13C3×D3direct (N × H)
29. C32×C11×C13C22×C5semidirect
30. C3×C5×D39C2×C11semidirect
31. C3×C5×D3×C13C2×C11semidirect
32. C32×C5×D13C2×C11semidirect
35. C3×C5×D3×C11D13direct (N × H)
37. C11×D39C2×C3×C5semidirect
38. D3×C11×C13C2×C3×C5semidirect
41. C3×C11×D13C5×D3direct (N × H)
42. C3×C11×D13C2×C3×C5semidirect
44. C5×D3×D13C3×C11direct (N × H)
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C22×C11semidirect
50. C32×C5×C11C2×D13semidirect
51. C3×D3×D13C5×C11direct (N × H)
53. C3×C11×C13C2×C5×D3semidirect
54. C3×C11×C13C22×C3×C5semidirect
57. C5×D39C2×C3×C11semidirect
58. C5×D3×C13C2×C3×C11semidirect
61. C3×C5×D13D3×C11direct (N × H)
62. C3×C5×D13C2×C3×C11semidirect
69. C5×D3×C11C3×D13direct (N × H)
72. C11×D13C3×C5×D3direct (N × H)
74. C3×D39C2×C5×C11semidirect
75. C3×D3×C13C2×C5×C11semidirect
76. C32×D13C2×C5×C11semidirect
80. C3×D3×C11C5×D13direct (N × H)
82. C3×C5×C13C2×D3×C11semidirect
83. C3×C5×C13C22×C3×C11semidirect
86. C3×C5×C11D3×D13direct (N × H)
87. C3×C5×C11C2×C3×D13semidirect
89. D3×D13C3×C5×C11direct (N × H)
90. C11×C13C2×C3×C5×D3semidirect
95. C5×D13C3×D3×C11direct (N × H)
96. C32×C13C22×C5×C11semidirect
100. C32×C11C2×C5×D13semidirect
103. C3×C5×D3C11×D13direct (N × H)
105. D39C2×C3×C5×C11semidirect
108. C3×D13C5×D3×C11direct (N × H)
109. C3×D13C2×C3×C5×C11semidirect
110. D3×C13C2×C3×C5×C11semidirect
117. D3×C11C3×C5×D13direct (N × H)
118. C5×C13C2×C3×D3×C11semidirect
121. C5×C11C3×D3×D13direct (N × H)
123. C32×C5C2×C11×D13semidirect
126. C3×C13C2×C5×D3×C11semidirect
127. C3×C13C22×C3×C5×C11semidirect
130. C3×C11C5×D3×D13direct (N × H)
131. C3×C11C2×C3×C5×D13semidirect
138. C5×D3C3×C11×D13direct (N × H)
141. D13C3×C5×D3×C11direct (N × H)
148. C3×D3C5×C11×D13direct (N × H)
150. C3×C5D3×C11×D13direct (N × H)
151. C3×C5C2×C3×C11×D13semidirect
152. C13C2×C3×C5×D3×C11semidirect
155. C11C3×C5×D3×D13direct (N × H)
159. C32C2×C5×C11×D13semidirect
166. D3C3×C5×C11×D13direct (N × H)
167. C5C3×D3×C11×D13direct (N × H)
170. C3C5×D3×C11×D13direct (N × H)
171. C3C2×C3×C5×C11×D13semidirect

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×C5×D3×C11×C132
C3×C5×C11×D392
C2×C3×C5×C11×D133
C5×D3×C11×D133
C3×D3×C11×D135
C3×C5×D3×D1311
C2×C3×C5×D3×C1113