Finite Group Databasebeta

← C2×C3×C5×C11×D39 #38788309

Subgroups — C2×C3×C5×C11×D39 #38788309

Order 25740.

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×C5×C11×D39C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×C5×C11×D13—31nomaximal
4C2×C5×C11×D39C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C3×C11×D39C511yesmaximal, characteristic, direct product factor, Hall
7C5×C11×D39C2×C312yesdirect product factor
8C3×C5×C11×D13—32no—
9C2×C3×C5×C11×C13—21no—
10C2×C3×C5×C11×C13D311yescharacteristic, complemented
11C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
12C2×C5×C11×D13—31noHall
13C3×C11×D39C2×C512yesdirect product factor
14C2×C32×C11×C13C2×C511yescharacteristic, complemented
15C2×C3×C5×D39C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C11×C13—21no—
17C3×C5×C11×C13C2×D311yescharacteristic, complemented
18C3×C5×C11×C13C22×C311yescharacteristic, complemented
19C2×C3×C5×D3×C11—131nomaximal, Hall
20C2×C11×D39C3×C511yescharacteristic, direct product factor
21C2×C3×C11×D13—31no—
22C2×C5×C11×C13C3×D311yescharacteristic, complemented
23C5×C11×D13—32no—
24C32×C11×C13C22×C511yescharacteristic, complemented, Hall
25C2×C32×C5×C13C2×C1111yescharacteristic, complemented
26C3×C5×D39C2×C1112yesdirect product factor
27C2×C32×C5×C11D1311yescharacteristic, complemented
28C3×C5×D3×C11—132no—
29C2×C3×C11×C13—21no—
30C2×C3×C11×C13C5×D311yescharacteristic, complemented
31C2×C3×C11×C13C2×C3×C511yescharacteristic, complemented
32C11×D39C2×C3×C512yesdirect product factor
33C3×C11×D13—32no—
34C2×C5×D39C3×C1111yescharacteristic, direct product factor
35C2×C3×C5×D13—31no—
36C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
37C22×C3×C5×C11—391no—
38C2×C5×D3×C11—131no—
39C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
40C2×C11×D13—31noHall
41C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
42C2×C3×D39C5×C1111yescharacteristic, direct product factor, Hall
43C3×C11×C13—21no—
44C3×C11×C13C2×C5×D311yescharacteristic, complemented
45C3×C11×C13C22×C3×C511yescharacteristic, complemented
46C2×C3×D3×C11—131noHall
47C2×C3×C5×C13—21no—
48C2×C3×C5×C13D3×C1111yescharacteristic, complemented
49C2×C3×C5×C13C2×C3×C1111yescharacteristic, complemented
50C5×D39C2×C3×C1112yesdirect product factor
51C3×C5×D13—32no—
52C2×C3×C5×C11—21no—
53C2×C3×C5×C11—392no—
54C2×C3×C5×C11C3×D1311yescharacteristic, complemented
55C2×C3×C5×C11D3911yescharacteristic, direct product factor
56C5×D3×C11—132no—
57C2×C11×C13C3×C5×D311yescharacteristic, complemented
58C11×D13—32no—
59C2×C5×D13—31noHall
60C2×C32×C13C2×C5×C1111yescharacteristic, complemented
61C3×D39C2×C5×C1112yesdirect product factor
62C22×C5×C11—391noHall
63C2×C32×C11C5×D1311yescharacteristic, complemented
64C3×D3×C11—132no—
65C3×C5×C13—21no—
66C3×C5×C13C2×D3×C1111yescharacteristic, complemented
67C3×C5×C13C22×C3×C1111yescharacteristic, complemented
68C2×C3×C5×D3—131noHall
69C3×C5×C11—21no—
70C3×C5×C11C2×C3×D1311yescharacteristic, complemented
71C3×C5×C11C2×D3911yescharacteristic, direct product factor
72C2×D39C3×C5×C1111yescharacteristic, direct product factor
73C2×C3×D13—31no—
74C11×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
75C22×C3×C11—391no—
76C2×D3×C11—131no—
77C2×C5×C13C3×D3×C1111yescharacteristic, complemented
78C5×D13—32no—
79C32×C13C22×C5×C1111yescharacteristic, complemented, Hall
80C2×C5×C11—392no—
81C2×C5×C11C3×D3911yescharacteristic, direct product factor
82C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
83C2×C32×C5C11×D1311yescharacteristic, complemented
84C3×C5×D3—132no—
85C2×C3×C13—21no—
86C2×C3×C13C5×D3×C1111yescharacteristic, complemented
87C2×C3×C13C2×C3×C5×C1111yescharacteristic, complemented
88D39C2×C3×C5×C1112yesdirect product factor
89C3×D13—32no—
90C2×C3×C11—21no—
91C2×C3×C11—392no—
92C2×C3×C11C3×C5×D1311yescharacteristic, complemented
93C2×C3×C11C5×D3911yescharacteristic, direct product factor
94D3×C11—132no—
95C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
96C22×C3×C5—391no—
97C2×C5×D3—131no—
98C5×C11C2×C3×D3911yescharacteristic, direct product factor, Hall
99C2×D13—31noHall
100C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
101C22×C11—391noHall
102C3×C13—21no—
103C3×C13C2×C5×D3×C1111yescharacteristic, complemented
104C3×C13C22×C3×C5×C1111yescharacteristic, complemented
105C2×C3×D3—131noHall
106C3×C11—21no—
107C3×C11C2×C3×C5×D1311yescharacteristic, complemented
108C3×C11C2×C5×D3911yescharacteristic, direct product factor
109C2×C3×C5—21no—
110C2×C3×C5—392no—
111C2×C3×C5C3×C11×D1311yescharacteristic, complemented
112C2×C3×C5C11×D3911yescharacteristic, direct product factor
113C5×D3—132no—
114C2×C13C3×C5×D3×C1111yescharacteristic, complemented
115D13—32no—
116C2×C11—392no—
117C2×C11C3×C5×D3911yescharacteristic, direct product factor
118C22×C5—391noHall
119C2×C32C5×C11×D1311yescharacteristic, complemented
120C3×D3—132no—
121C3×C5—21no—
122C3×C5C2×C3×C11×D1311yescharacteristic, complemented
123C3×C5C2×C11×D3911yescharacteristic, direct product factor
124C13C2×C3×C5×D3×C1111yescharacteristic, complemented, Sylow
125C22×C3—391no—
126C2×D3—131no—
127C11C2×C3×C5×D3911yescharacteristic, direct product factor, Sylow
128C2×C5—392no—
129C2×C5C3×C11×D3911yescharacteristic, direct product factor
130C32C2×C5×C11×D1311yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—392no—
133C2×C3C3×C5×C11×D1311yescharacteristic, complemented
134C2×C3C5×C11×D3911yescharacteristic, direct product factor
135D3—132no—
136C5C2×C3×C11×D3911yescharacteristic, direct product factor, Sylow
137C22—391noSylow
138C3—21no—
139C3C2×C5×C11×D3911yescharacteristic, direct product factor
140C3C2×C3×C5×C11×D1311yescharacteristic, complemented
141C2—392no—
142C2C3×C5×C11×D3911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C11D39
commutator, cosocle, hypocenterC3×C13C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3×C5×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×D39C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C2×C5×C11×D39C3direct (N × H)
5. C32×C5×C11×C13C22semidirect
6. C2×C3×C11×D39C5direct (N × H)
7. C5×C11×D39C2×C3direct (N × H)
10. C2×C3×C5×C11×C13D3semidirect
11. C2×C3×C5×C11×C13C2×C3semidirect
13. C3×C11×D39C2×C5direct (N × H)
14. C2×C32×C11×C13C2×C5semidirect
15. C2×C3×C5×D39C11direct (N × H)
17. C3×C5×C11×C13C2×D3semidirect
18. C3×C5×C11×C13C22×C3semidirect
20. C2×C11×D39C3×C5direct (N × H)
22. C2×C5×C11×C13C3×D3semidirect
24. C32×C11×C13C22×C5semidirect
25. C2×C32×C5×C13C2×C11semidirect
26. C3×C5×D39C2×C11direct (N × H)
27. C2×C32×C5×C11D13semidirect
30. C2×C3×C11×C13C5×D3semidirect
31. C2×C3×C11×C13C2×C3×C5semidirect
32. C11×D39C2×C3×C5direct (N × H)
34. C2×C5×D39C3×C11direct (N × H)
36. C5×C11×C13C2×C3×D3semidirect
39. C32×C5×C13C22×C11semidirect
41. C32×C5×C11C2×D13semidirect
42. C2×C3×D39C5×C11direct (N × H)
44. C3×C11×C13C2×C5×D3semidirect
45. C3×C11×C13C22×C3×C5semidirect
48. C2×C3×C5×C13D3×C11semidirect
49. C2×C3×C5×C13C2×C3×C11semidirect
50. C5×D39C2×C3×C11direct (N × H)
54. C2×C3×C5×C11C3×D13semidirect
55. C2×C3×C5×C11D39direct (N × H)
57. C2×C11×C13C3×C5×D3semidirect
60. C2×C32×C13C2×C5×C11semidirect
61. C3×D39C2×C5×C11direct (N × H)
63. C2×C32×C11C5×D13semidirect
66. C3×C5×C13C2×D3×C11semidirect
67. C3×C5×C13C22×C3×C11semidirect
70. C3×C5×C11C2×C3×D13semidirect
71. C3×C5×C11C2×D39direct (N × H)
72. C2×D39C3×C5×C11direct (N × H)
74. C11×C13C2×C3×C5×D3semidirect
77. C2×C5×C13C3×D3×C11semidirect
79. C32×C13C22×C5×C11semidirect
81. C2×C5×C11C3×D39direct (N × H)
82. C32×C11C2×C5×D13semidirect
83. C2×C32×C5C11×D13semidirect
86. C2×C3×C13C5×D3×C11semidirect
87. C2×C3×C13C2×C3×C5×C11semidirect
88. D39C2×C3×C5×C11direct (N × H)
92. C2×C3×C11C3×C5×D13semidirect
93. C2×C3×C11C5×D39direct (N × H)
95. C5×C13C2×C3×D3×C11semidirect
98. C5×C11C2×C3×D39direct (N × H)
100. C32×C5C2×C11×D13semidirect
103. C3×C13C2×C5×D3×C11semidirect
104. C3×C13C22×C3×C5×C11semidirect
107. C3×C11C2×C3×C5×D13semidirect
108. C3×C11C2×C5×D39direct (N × H)
111. C2×C3×C5C3×C11×D13semidirect
112. C2×C3×C5C11×D39direct (N × H)
114. C2×C13C3×C5×D3×C11semidirect
117. C2×C11C3×C5×D39direct (N × H)
119. C2×C32C5×C11×D13semidirect
122. C3×C5C2×C3×C11×D13semidirect
123. C3×C5C2×C11×D39direct (N × H)
124. C13C2×C3×C5×D3×C11semidirect
127. C11C2×C3×C5×D39direct (N × H)
129. C2×C5C3×C11×D39direct (N × H)
130. C32C2×C5×C11×D13semidirect
133. C2×C3C3×C5×C11×D13semidirect
134. C2×C3C5×C11×D39direct (N × H)
136. C5C2×C3×C11×D39direct (N × H)
139. C3C2×C5×C11×D39direct (N × H)
140. C3C2×C3×C5×C11×D13semidirect
142. C2C3×C5×C11×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C11×D392
C2×C32×C5×C11×C132
C2×C3×C5×C11×D133
C2×C5×C11×D393
C2×C3×C11×D395
C2×C3×C5×D3911
C2×C3×C5×D3×C1113