Finite Group Databasebeta

← C3×C5×D11×D39 #38788187

Subgroups — C3×C5×D11×D39 #38788187

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×C5×C13×D11C211yesmaximal, characteristic, complemented
2C3×C5×C11×D39C211yesmaximal, characteristic, complemented
3C3×C5×D429C211yesmaximal, characteristic, complemented
4C5×D11×D39C311yesmaximal, characteristic, direct product factor
5C3×C5×D11×D13—31nomaximal
6C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
7C3×D11×D39C511yesmaximal, characteristic, direct product factor, Hall
8C5×D429C2×C311yescharacteristic, complemented
9C5×C11×D39C2×C311yescharacteristic, complemented
10C3×C5×D143—31no—
11C3×C5×C13×D11—21no—
12C3×C5×C13×D11D311yescharacteristic, complemented
13C3×C5×C13×D11C2×C311yescharacteristic, complemented
14C3×C5×C11×D13—31no—
15C5×D11×D13—31noHall
16C3×D429C2×C511yescharacteristic, complemented
17C3×C11×D39C2×C511yescharacteristic, complemented
18C32×C13×D11C2×C511yescharacteristic, complemented
19C2×C3×C5×D39—111nomaximal, Hall
20C3×C5×C11×C13—21no—
21C3×C5×C11×C13C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C3×C5×D3×D11—131nomaximal, Hall
24D11×D39C3×C511yescharacteristic, direct product factor
25C3×D11×D13—31no—
26C5×D143—31no—
27C5×C13×D11C3×D311yescharacteristic, complemented
28C5×C11×D13—31no—
29C32×C11×C13C22×C511yescharacteristic, complemented, Hall
30C2×C32×C5×C13—111no—
31C3×C5×D39—111no—
32C3×C5×D39D1111yescharacteristic, direct product factor
33C3×C5×D33—131no—
34C3×C5×D3×C11—131no—
35C32×C5×D11D1311yescharacteristic, complemented
36D429C2×C3×C511yescharacteristic, complemented
37C11×D39C2×C3×C511yescharacteristic, complemented
38C3×D143—31no—
39C3×C13×D11—21no—
40C3×C13×D11C5×D311yescharacteristic, complemented
41C3×C13×D11C2×C3×C511yescharacteristic, complemented
42C3×C11×D13—31no—
43C2×C5×D39—111no—
44C2×C3×C5×D13—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×C3×C5×D11—391no—
47C5×D3×D11—131no—
48C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
49D11×D13—31noHall
50C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
51C2×C3×D39—111noHall
52C3×C11×C13—21no—
53C3×C11×C13C2×C5×D311yescharacteristic, complemented
54C3×C11×C13C22×C3×C511yescharacteristic, complemented
55C3×D3×D11—131noHall
56C2×C3×C5×C13—111no—
57C2×C3×C5×C13—111no—
58C2×C3×C5×C13—221no—
59C5×D39—111no—
60C5×D39C3×D1111yescharacteristic, direct product factor
61C3×C5×D13—31no—
62C3×C5×D13—331no—
63C2×C3×C5×C11—391no—
64C5×D33—131no—
65C5×D3×C11—131no—
66C3×C5×D11—21no—
67C3×C5×D11—391no—
68C3×C5×D11C3×D1311yescharacteristic, complemented
69C3×C5×D11D3911yescharacteristic, direct product factor
70D143—31no—
71C11×D13—31no—
72C13×D11C3×C5×D311yescharacteristic, complemented
73C2×C5×D13—331noHall
74C2×C32×C13—111no—
75C3×D39—111no—
76C3×D39C5×D1111yescharacteristic, direct product factor
77C2×C5×D11—391noHall
78C3×D33—131no—
79C3×D3×C11—131no—
80C32×D11C5×D1311yescharacteristic, complemented
81C3×C5×C13—21no—
82C3×C5×C13D3×D1111yescharacteristic, complemented
83C3×C5×C13C2×C3×D1111yescharacteristic, complemented
84C2×C3×C5×D3—1431noHall
85C3×C5×C11—21no—
86C3×C5×C11C2×C3×D1311yescharacteristic, complemented
87C3×C5×C11C2×D3911yescharacteristic, complemented
88C2×D39—111no—
89C2×C3×D13—331no—
90C11×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
91C2×C3×D11—391no—
92D3×D11—131no—
93C2×C5×C13—111no—
94C5×D13—31no—
95C5×D13—331no—
96C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
97C2×C5×C11—391no—
98C5×D11—391no—
99C5×D11C3×D3911yescharacteristic, direct product factor
100C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
101C2×C32×C5—111no—
102C3×C5×D3—131no—
103C3×C5×D3—1431no—
104C2×C3×C13—111no—
105C2×C3×C13—111no—
106C2×C3×C13—221no—
107D39—111no—
108D39C3×C5×D1111yescharacteristic, direct product factor
109C3×D13—31no—
110C3×D13—331no—
111C2×C3×C11—391no—
112D33—131no—
113C3×D11—21no—
114C3×D11—391no—
115C3×D11C3×C5×D1311yescharacteristic, complemented
116C3×D11C5×D3911yescharacteristic, direct product factor
117D3×C11—131no—
118C5×C13C3×D3×D1111yescharacteristic, complemented, Hall
119C22×C3×C5—4291no—
120C2×C5×D3—1431no—
121C5×C11C2×C3×D3911yescharacteristic, complemented, Hall
122C2×D13—331noHall
123C32×C5D11×D1311yescharacteristic, complemented, Hall
124C2×D11—391noHall
125C3×C13—21no—
126C3×C13C5×D3×D1111yescharacteristic, complemented
127C3×C13C2×C3×C5×D1111yescharacteristic, complemented
128C2×C3×D3—1431noHall
129C3×C11—21no—
130C3×C11C2×C3×C5×D1311yescharacteristic, complemented
131C3×C11C2×C5×D3911yescharacteristic, complemented
132C2×C3×C5—111no—
133C2×C3×C5—111no—
134C2×C3×C5—221no—
135C2×C3×C5—391no—
136C2×C3×C5—4291no—
137C5×D3—131no—
138C5×D3—1431no—
139C2×C13—111no—
140D13—31no—
141D13—331no—
142C2×C11—391no—
143D11—391no—
144D11C3×C5×D3911yescharacteristic, direct product factor
145C22×C5—4291noHall
146C2×C32—111no—
147C3×D3—131no—
148C3×D3—1431no—
149C3×C5—21no—
150C3×C5C3×D11×D1311yescharacteristic, complemented
151C3×C5D11×D3911yescharacteristic, direct product factor
152C13C3×C5×D3×D1111yescharacteristic, complemented, Sylow
153C22×C3—4291no—
154C2×D3—1431no—
155C11C2×C3×C5×D3911yescharacteristic, complemented, Sylow
156C2×C5—111no—
157C2×C5—391no—
158C2×C5—4291no—
159C32C5×D11×D1311yescharacteristic, complemented, Sylow
160C2×C3—111no—
161C2×C3—111no—
162C2×C3—221no—
163C2×C3—391no—
164C2×C3—4291no—
165D3—131no—
166D3—1431no—
167C5C3×D11×D3911yescharacteristic, direct product factor, Sylow
168C22—4291noSylow
169C3—21no—
170C3C3×C5×D11×D1311yescharacteristic, complemented
171C3C5×D11×D3911yescharacteristic, direct product factor
172C2—111no—
173C2—391no—
174C2—4291no—
subgroupG/H
center, hypercenterC3×C5D11×D39
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D11C2semidirect
2. C3×C5×C11×D39C2semidirect
3. C3×C5×D429C2semidirect
4. C5×D11×D39C3direct (N × H)
6. C32×C5×C11×C13C22semidirect
7. C3×D11×D39C5direct (N × H)
8. C5×D429C2×C3semidirect
9. C5×C11×D39C2×C3semidirect
12. C3×C5×C13×D11D3semidirect
13. C3×C5×C13×D11C2×C3semidirect
16. C3×D429C2×C5semidirect
17. C3×C11×D39C2×C5semidirect
18. C32×C13×D11C2×C5semidirect
21. C3×C5×C11×C13C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
24. D11×D39C3×C5direct (N × H)
27. C5×C13×D11C3×D3semidirect
29. C32×C11×C13C22×C5semidirect
32. C3×C5×D39D11direct (N × H)
35. C32×C5×D11D13semidirect
36. D429C2×C3×C5semidirect
37. C11×D39C2×C3×C5semidirect
40. C3×C13×D11C5×D3semidirect
41. C3×C13×D11C2×C3×C5semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C32×C5×C13C2×D11semidirect
50. C32×C5×C11C2×D13semidirect
53. C3×C11×C13C2×C5×D3semidirect
54. C3×C11×C13C22×C3×C5semidirect
60. C5×D39C3×D11direct (N × H)
68. C3×C5×D11C3×D13semidirect
69. C3×C5×D11D39direct (N × H)
72. C13×D11C3×C5×D3semidirect
76. C3×D39C5×D11direct (N × H)
80. C32×D11C5×D13semidirect
82. C3×C5×C13D3×D11semidirect
83. C3×C5×C13C2×C3×D11semidirect
86. C3×C5×C11C2×C3×D13semidirect
87. C3×C5×C11C2×D39semidirect
90. C11×C13C2×C3×C5×D3semidirect
96. C32×C13C2×C5×D11semidirect
99. C5×D11C3×D39direct (N × H)
100. C32×C11C2×C5×D13semidirect
108. D39C3×C5×D11direct (N × H)
115. C3×D11C3×C5×D13semidirect
116. C3×D11C5×D39direct (N × H)
118. C5×C13C3×D3×D11semidirect
121. C5×C11C2×C3×D39semidirect
123. C32×C5D11×D13semidirect
126. C3×C13C5×D3×D11semidirect
127. C3×C13C2×C3×C5×D11semidirect
130. C3×C11C2×C3×C5×D13semidirect
131. C3×C11C2×C5×D39semidirect
144. D11C3×C5×D39direct (N × H)
150. C3×C5C3×D11×D13semidirect
151. C3×C5D11×D39direct (N × H)
152. C13C3×C5×D3×D11semidirect
155. C11C2×C3×C5×D39semidirect
159. C32C5×D11×D13semidirect
167. C5C3×D11×D39direct (N × H)
170. C3C3×C5×D11×D13semidirect
171. C3C5×D11×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13×D112
C3×C5×C11×D392
C3×C5×D4292
C5×D11×D393
C3×C5×D11×D133
C3×D11×D395
C2×C3×C5×D3911
C3×C5×D3×D1113