Finite Group Databasebeta

← C3×D5×C11×D39 #38788207

Subgroups — C3×D5×C11×D39 #38788207

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×C11×D39C211yesmaximal, characteristic, complemented
3C3×C11×D195C211yesmaximal, characteristic, complemented
4D5×C11×D39C311yesmaximal, characteristic, direct product factor
5C3×D5×C11×D13—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C2×C3×C11×D39—51nomaximal, Hall
8C11×D195C2×C311yescharacteristic, complemented
9C5×C11×D39C2×C311yescharacteristic, complemented
10C3×C11×D65—31no—
11C3×D5×C11×C13—21no—
12C3×D5×C11×C13D311yescharacteristic, complemented
13C3×D5×C11×C13C2×C311yescharacteristic, complemented
14C3×C5×C11×D13—31no—
15D5×C11×D13—31noHall
16C3×C11×D39—51no—
17C3×C11×D39D511yescharacteristic, direct product factor
18C2×C32×C11×C13—51no—
19C3×D5×D39C1111yesmaximal, 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×C11—131nomaximal, Hall
24C2×C11×D39—51no—
25C2×C3×C11×D13—151no—
26C11×D65—31no—
27D5×C11×C13C3×D311yescharacteristic, complemented
28C5×C11×D13—31no—
29C32×C11×C13C2×D511yescharacteristic, complemented, Hall
30C3×D195C2×C1111yescharacteristic, complemented
31C3×C5×D39C2×C1111yescharacteristic, complemented
32C32×D5×C13C2×C1111yescharacteristic, complemented
33C3×C11×D15—131no—
34C3×C5×D3×C11—131no—
35C32×D5×C11D1311yescharacteristic, complemented
36C2×C3×C11×C13—51no—
37C2×C3×C11×C13—51no—
38C2×C3×C11×C13—101no—
39C11×D39—51no—
40C11×D39C3×D511yescharacteristic, direct product factor
41C3×C11×D13—31no—
42C3×C11×D13—151no—
43D5×D39C3×C1111yescharacteristic, direct product factor
44C3×D5×D13—31no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×C3×D5×C11—391no—
47D3×D5×C11—131no—
48C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
49C2×C11×D13—151noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51C2×C3×D39—51noHall
52C3×C11×C13—21no—
53C3×C11×C13D3×D511yescharacteristic, complemented
54C3×C11×C13C2×C3×D511yescharacteristic, complemented
55C2×C3×D3×C11—651noHall
56D195C2×C3×C1111yescharacteristic, complemented
57C5×D39C2×C3×C1111yescharacteristic, complemented
58C3×D65—31no—
59C3×D5×C13—21no—
60C3×D5×C13D3×C1111yescharacteristic, complemented
61C3×D5×C13C2×C3×C1111yescharacteristic, complemented
62C3×C5×D13—31no—
63C2×C3×C5×C11—391no—
64C11×D15—131no—
65C5×D3×C11—131no—
66C3×D5×C11—21no—
67C3×D5×C11—391no—
68C3×D5×C11C3×D1311yescharacteristic, complemented
69C3×D5×C11D3911yescharacteristic, direct product factor
70C2×C11×C13—51no—
71C11×D13—31no—
72C11×D13—151no—
73D5×D13—31noHall
74C2×C32×C13—51no—
75C3×D39—51no—
76C3×D39D5×C1111yescharacteristic, direct product factor
77C2×D5×C11—391noHall
78C2×C32×C11—51no—
79C3×D3×C11—131no—
80C3×D3×C11—651no—
81C3×C5×C13—21no—
82C3×C5×C13C2×D3×C1111yescharacteristic, complemented
83C3×C5×C13C22×C3×C1111yescharacteristic, complemented
84C3×D3×D5—131noHall
85C3×C5×C11—21no—
86C3×C5×C11C2×C3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—51no—
89C2×C3×D13—151no—
90C11×C13C3×D3×D511yescharacteristic, complemented, Hall
91C22×C3×C11—1951no—
92C2×D3×C11—651no—
93D65—31no—
94C5×D13—31no—
95D5×C13C3×D3×C1111yescharacteristic, complemented
96C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
97C2×C5×C11—391no—
98D5×C11—391no—
99D5×C11C3×D3911yescharacteristic, direct product factor
100C32×C11D5×D1311yescharacteristic, complemented, Hall
101C3×D15—131no—
102C3×C5×D3—131no—
103C32×D5C11×D1311yescharacteristic, complemented
104C2×C3×C13—51no—
105C2×C3×C13—51no—
106C2×C3×C13—101no—
107D39—51no—
108D39C3×D5×C1111yescharacteristic, direct product factor
109C3×D13—31no—
110C3×D13—151no—
111C2×C3×C11—51no—
112C2×C3×C11—51no—
113C2×C3×C11—101no—
114C2×C3×C11—391no—
115C2×C3×C11—1951no—
116D3×C11—131no—
117D3×C11—651no—
118C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
119C2×C3×D5—391no—
120D3×D5—131no—
121C5×C11C2×C3×D3911yescharacteristic, complemented, Hall
122C2×D13—151noHall
123C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
124C22×C11—1951noHall
125C3×C13—21no—
126C3×C13D3×D5×C1111yescharacteristic, complemented
127C3×C13C2×C3×D5×C1111yescharacteristic, complemented
128C2×C3×D3—651noHall
129C3×C11—21no—
130C3×C11C3×D5×D1311yescharacteristic, complemented
131C3×C11D5×D3911yescharacteristic, direct product factor
132C2×C3×C5—391no—
133D15—131no—
134C3×D5—21no—
135C3×D5—391no—
136C3×D5C3×C11×D1311yescharacteristic, complemented
137C3×D5C11×D3911yescharacteristic, direct product factor
138C5×D3—131no—
139C2×C13—51no—
140D13—31no—
141D13—151no—
142C2×C11—51no—
143C2×C11—391no—
144C2×C11—1951no—
145C2×D5—391noHall
146C2×C32—51no—
147C3×D3—131no—
148C3×D3—651no—
149C3×C5—21no—
150C3×C5C2×C3×C11×D1311yescharacteristic, complemented
151C3×C5C2×C11×D3911yescharacteristic, complemented
152C13C3×D3×D5×C1111yescharacteristic, complemented, Sylow
153C22×C3—1951no—
154C2×D3—651no—
155C11C3×D5×D3911yescharacteristic, direct product factor, Sylow
156C2×C5—391no—
157D5—391no—
158D5C3×C11×D3911yescharacteristic, direct product factor
159C32D5×C11×D1311yescharacteristic, complemented, Sylow
160C2×C3—51no—
161C2×C3—51no—
162C2×C3—101no—
163C2×C3—391no—
164C2×C3—1951no—
165D3—131no—
166D3—651no—
167C5C2×C3×C11×D3911yescharacteristic, complemented, Sylow
168C22—1951noSylow
169C3—21no—
170C3C3×D5×C11×D1311yescharacteristic, complemented
171C3D5×C11×D3911yescharacteristic, direct product factor
172C2—51no—
173C2—391no—
174C2—1951no—
subgroupG/H
center, hypercenterC3×C11D5×D39
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C13C2semidirect
2. C3×C5×C11×D39C2semidirect
3. C3×C11×D195C2semidirect
4. D5×C11×D39C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
8. C11×D195C2×C3semidirect
9. C5×C11×D39C2×C3semidirect
12. C3×D5×C11×C13D3semidirect
13. C3×D5×C11×C13C2×C3semidirect
17. C3×C11×D39D5direct (N × H)
19. C3×D5×D39C11direct (N × H)
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
27. D5×C11×C13C3×D3semidirect
29. C32×C11×C13C2×D5semidirect
30. C3×D195C2×C11semidirect
31. C3×C5×D39C2×C11semidirect
32. C32×D5×C13C2×C11semidirect
35. C32×D5×C11D13semidirect
40. C11×D39C3×D5direct (N × H)
43. D5×D39C3×C11direct (N × H)
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C22×C11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13D3×D5semidirect
54. C3×C11×C13C2×C3×D5semidirect
56. D195C2×C3×C11semidirect
57. C5×D39C2×C3×C11semidirect
60. C3×D5×C13D3×C11semidirect
61. C3×D5×C13C2×C3×C11semidirect
68. C3×D5×C11C3×D13semidirect
69. C3×D5×C11D39direct (N × H)
76. C3×D39D5×C11direct (N × H)
82. C3×C5×C13C2×D3×C11semidirect
83. C3×C5×C13C22×C3×C11semidirect
86. C3×C5×C11C2×C3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13C3×D3×D5semidirect
95. D5×C13C3×D3×C11semidirect
96. C32×C13C2×D5×C11semidirect
99. D5×C11C3×D39direct (N × H)
100. C32×C11D5×D13semidirect
103. C32×D5C11×D13semidirect
108. D39C3×D5×C11direct (N × H)
118. C5×C13C2×C3×D3×C11semidirect
121. C5×C11C2×C3×D39semidirect
123. C32×C5C2×C11×D13semidirect
126. C3×C13D3×D5×C11semidirect
127. C3×C13C2×C3×D5×C11semidirect
130. C3×C11C3×D5×D13semidirect
131. C3×C11D5×D39direct (N × H)
136. C3×D5C3×C11×D13semidirect
137. C3×D5C11×D39direct (N × H)
150. C3×C5C2×C3×C11×D13semidirect
151. C3×C5C2×C11×D39semidirect
152. C13C3×D3×D5×C11semidirect
155. C11C3×D5×D39direct (N × H)
158. D5C3×C11×D39direct (N × H)
159. C32D5×C11×D13semidirect
167. C5C2×C3×C11×D39semidirect
170. C3C3×D5×C11×D13semidirect
171. C3D5×C11×D39direct (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×C11×D392
C3×C11×D1952
D5×C11×D393
C3×D5×C11×D133
C2×C3×C11×D395
C3×D5×D3911
C3×D3×D5×C1113