Finite Group Databasebeta

← C2×C3×C11×C13×D15 #38788312

Subgroups — C2×C3×C11×C13×D15 #38788312

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×C11×C13×D15C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×D5×C11×C13—31nomaximal
4C2×C11×C13×D15C311yesmaximal, characteristic, direct product factor
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C3×D3×C11×C13—51nomaximal, Hall
7C11×C13×D15C2×C312yesdirect product factor
8C3×D5×C11×C13—32no—
9C2×C3×C5×C11×C13—21no—
10C2×C3×C5×C11×C13D311yescharacteristic, complemented
11C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
12C2×D5×C11×C13—31noHall
13C3×D3×C11×C13—52no—
14C2×C32×C11×C13D511yescharacteristic, complemented
15C2×C3×C13×D15C1111yesmaximal, characteristic, direct product factor, Hall
16C3×C5×C11×C13—21no—
17C3×C5×C11×C13C2×D311yescharacteristic, complemented
18C3×C5×C11×C13C22×C311yescharacteristic, complemented
19C2×C3×C11×D15C1311yesmaximal, characteristic, direct product factor, Hall
20C22×C3×C11×C13—151no—
21C2×D3×C11×C13—51no—
22C2×C5×C11×C13C3×D311yescharacteristic, complemented
23D5×C11×C13—32no—
24C32×C11×C13C2×D511yescharacteristic, complemented, Hall
25C2×C32×C5×C13C2×C1111yescharacteristic, complemented
26C3×C13×D15C2×C1112yesdirect product factor
27C2×C32×C5×C11C2×C1311yescharacteristic, complemented
28C3×C11×D15C2×C1312yesdirect product factor
29C2×C3×C11×C13—21no—
30C2×C3×C11×C13—152no—
31C2×C3×C11×C13C3×D511yescharacteristic, complemented
32C2×C3×C11×C13D1511yescharacteristic, direct product factor
33D3×C11×C13—52no—
34C2×C13×D15C3×C1111yescharacteristic, direct product factor
35C2×C3×D5×C13—31no—
36C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
37C2×C11×D15C3×C1311yescharacteristic, direct product factor
38C2×C3×D5×C11—31no—
39C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
40C22×C11×C13—151noHall
41C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
42C2×C3×D3×C13—51noHall
43C3×C11×C13—21no—
44C3×C11×C13C2×C3×D511yescharacteristic, complemented
45C3×C11×C13C2×D1511yescharacteristic, direct product factor
46C2×C3×D3×C11—51noHall
47C2×C3×C5×C13—21no—
48C2×C3×C5×C13D3×C1111yescharacteristic, complemented
49C2×C3×C5×C13C2×C3×C1111yescharacteristic, complemented
50C13×D15C2×C3×C1112yesdirect product factor
51C3×D5×C13—32no—
52C2×C3×C5×C11—21no—
53C2×C3×C5×C11D3×C1311yescharacteristic, complemented
54C2×C3×C5×C11C2×C3×C1311yescharacteristic, complemented
55C11×D15C2×C3×C1312yesdirect product factor
56C3×D5×C11—32no—
57C2×C11×C13—152no—
58C2×C11×C13C3×D1511yescharacteristic, direct product factor
59C2×D5×C13—31noHall
60C2×C32×C13D5×C1111yescharacteristic, complemented
61C3×D3×C13—52no—
62C2×D5×C11—31noHall
63C2×C32×C11D5×C1311yescharacteristic, complemented
64C3×D3×C11—52no—
65C3×C5×C13—21no—
66C3×C5×C13C2×D3×C1111yescharacteristic, complemented
67C3×C5×C13C22×C3×C1111yescharacteristic, complemented
68C2×C3×D15C11×C1311yescharacteristic, direct product factor, Hall
69C3×C5×C11—21no—
70C3×C5×C11C2×D3×C1311yescharacteristic, complemented
71C3×C5×C11C22×C3×C1311yescharacteristic, complemented
72C22×C3×C13—151no—
73C2×D3×C13—51no—
74C11×C13C2×C3×D1511yescharacteristic, direct product factor, Hall
75C22×C3×C11—151no—
76C2×D3×C11—51no—
77C2×C5×C13C3×D3×C1111yescharacteristic, complemented
78D5×C13—32no—
79C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
80C2×C5×C11C3×D3×C1311yescharacteristic, complemented
81D5×C11—32no—
82C32×C11C2×D5×C1311yescharacteristic, complemented, Hall
83C2×C32×C5C2×C11×C1311yescharacteristic, complemented
84C3×D15C2×C11×C1312yesdirect product factor
85C2×C3×C13—21no—
86C2×C3×C13—152no—
87C2×C3×C13C3×D5×C1111yescharacteristic, complemented
88C2×C3×C13C11×D1511yescharacteristic, direct product factor
89D3×C13—52no—
90C2×C3×C11—21no—
91C2×C3×C11—152no—
92C2×C3×C11C3×D5×C1311yescharacteristic, complemented
93C2×C3×C11C13×D1511yescharacteristic, direct product factor
94D3×C11—52no—
95C5×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
96C2×D15C3×C11×C1311yescharacteristic, direct product factor
97C2×C3×D5—31no—
98C5×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
99C22×C13—151noHall
100C32×C5C22×C11×C1311yescharacteristic, complemented, Hall
101C22×C11—151noHall
102C3×C13—21no—
103C3×C13C2×C3×D5×C1111yescharacteristic, complemented
104C3×C13C2×C11×D1511yescharacteristic, direct product factor
105C2×C3×D3—51noHall
106C3×C11—21no—
107C3×C11C2×C3×D5×C1311yescharacteristic, complemented
108C3×C11C2×C13×D1511yescharacteristic, direct product factor
109C2×C3×C5—21no—
110C2×C3×C5D3×C11×C1311yescharacteristic, complemented
111C2×C3×C5C2×C3×C11×C1311yescharacteristic, complemented
112D15C2×C3×C11×C1312yesdirect product factor
113C3×D5—32no—
114C2×C13—152no—
115C2×C13C3×C11×D1511yescharacteristic, direct product factor
116C2×C11—152no—
117C2×C11C3×C13×D1511yescharacteristic, direct product factor
118C2×D5—31noHall
119C2×C32D5×C11×C1311yescharacteristic, complemented
120C3×D3—52no—
121C3×C5—21no—
122C3×C5C2×D3×C11×C1311yescharacteristic, complemented
123C3×C5C22×C3×C11×C1311yescharacteristic, complemented
124C13C2×C3×C11×D1511yescharacteristic, direct product factor, Sylow
125C22×C3—151no—
126C2×D3—51no—
127C11C2×C3×C13×D1511yescharacteristic, direct product factor, Sylow
128C2×C5C3×D3×C11×C1311yescharacteristic, complemented
129D5—32no—
130C32C2×D5×C11×C1311yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—152no—
133C2×C3C3×D5×C11×C1311yescharacteristic, complemented
134C2×C3C11×C13×D1511yescharacteristic, direct product factor
135D3—52no—
136C5C2×C3×D3×C11×C1311yescharacteristic, complemented, Sylow
137C22—151noSylow
138C3—21no—
139C3C2×C11×C13×D1511yescharacteristic, direct product factor
140C3C2×C3×D5×C11×C1311yescharacteristic, complemented
141C2—152no—
142C2C3×C11×C13×D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11×C13D15
commutator, cosocle, hypocenterC3×C5C22×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C11×C13

Complements

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

NH ≅ G/Ntype
1. C3×C11×C13×D15C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C2×C11×C13×D15C3direct (N × H)
5. C32×C5×C11×C13C22semidirect
7. C11×C13×D15C2×C3direct (N × H)
10. C2×C3×C5×C11×C13D3semidirect
11. C2×C3×C5×C11×C13C2×C3semidirect
14. C2×C32×C11×C13D5semidirect
15. C2×C3×C13×D15C11direct (N × H)
17. C3×C5×C11×C13C2×D3semidirect
18. C3×C5×C11×C13C22×C3semidirect
19. C2×C3×C11×D15C13direct (N × H)
22. C2×C5×C11×C13C3×D3semidirect
24. C32×C11×C13C2×D5semidirect
25. C2×C32×C5×C13C2×C11semidirect
26. C3×C13×D15C2×C11direct (N × H)
27. C2×C32×C5×C11C2×C13semidirect
28. C3×C11×D15C2×C13direct (N × H)
31. C2×C3×C11×C13C3×D5semidirect
32. C2×C3×C11×C13D15direct (N × H)
34. C2×C13×D15C3×C11direct (N × H)
36. C5×C11×C13C2×C3×D3semidirect
37. C2×C11×D15C3×C13direct (N × H)
39. C32×C5×C13C22×C11semidirect
41. C32×C5×C11C22×C13semidirect
44. C3×C11×C13C2×C3×D5semidirect
45. C3×C11×C13C2×D15direct (N × H)
48. C2×C3×C5×C13D3×C11semidirect
49. C2×C3×C5×C13C2×C3×C11semidirect
50. C13×D15C2×C3×C11direct (N × H)
53. C2×C3×C5×C11D3×C13semidirect
54. C2×C3×C5×C11C2×C3×C13semidirect
55. C11×D15C2×C3×C13direct (N × H)
58. C2×C11×C13C3×D15direct (N × H)
60. C2×C32×C13D5×C11semidirect
63. C2×C32×C11D5×C13semidirect
66. C3×C5×C13C2×D3×C11semidirect
67. C3×C5×C13C22×C3×C11semidirect
68. C2×C3×D15C11×C13direct (N × H)
70. C3×C5×C11C2×D3×C13semidirect
71. C3×C5×C11C22×C3×C13semidirect
74. C11×C13C2×C3×D15direct (N × H)
77. C2×C5×C13C3×D3×C11semidirect
79. C32×C13C2×D5×C11semidirect
80. C2×C5×C11C3×D3×C13semidirect
82. C32×C11C2×D5×C13semidirect
83. C2×C32×C5C2×C11×C13semidirect
84. C3×D15C2×C11×C13direct (N × H)
87. C2×C3×C13C3×D5×C11semidirect
88. C2×C3×C13C11×D15direct (N × H)
92. C2×C3×C11C3×D5×C13semidirect
93. C2×C3×C11C13×D15direct (N × H)
95. C5×C13C2×C3×D3×C11semidirect
96. C2×D15C3×C11×C13direct (N × H)
98. C5×C11C2×C3×D3×C13semidirect
100. C32×C5C22×C11×C13semidirect
103. C3×C13C2×C3×D5×C11semidirect
104. C3×C13C2×C11×D15direct (N × H)
107. C3×C11C2×C3×D5×C13semidirect
108. C3×C11C2×C13×D15direct (N × H)
110. C2×C3×C5D3×C11×C13semidirect
111. C2×C3×C5C2×C3×C11×C13semidirect
112. D15C2×C3×C11×C13direct (N × H)
115. C2×C13C3×C11×D15direct (N × H)
117. C2×C11C3×C13×D15direct (N × H)
119. C2×C32D5×C11×C13semidirect
122. C3×C5C2×D3×C11×C13semidirect
123. C3×C5C22×C3×C11×C13semidirect
124. C13C2×C3×C11×D15direct (N × H)
127. C11C2×C3×C13×D15direct (N × H)
128. C2×C5C3×D3×C11×C13semidirect
130. C32C2×D5×C11×C13semidirect
133. C2×C3C3×D5×C11×C13semidirect
134. C2×C3C11×C13×D15direct (N × H)
136. C5C2×C3×D3×C11×C13semidirect
139. C3C2×C11×C13×D15direct (N × H)
140. C3C2×C3×D5×C11×C13semidirect
142. C2C3×C11×C13×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×C13×D152
C2×C32×C5×C11×C132
C2×C3×D5×C11×C133
C2×C11×C13×D153
C2×C3×D3×C11×C135
C2×C3×C13×D1511
C2×C3×C11×D1513