Finite Group Databasebeta

← C2×D4×D5×C11 #13183429

Subgroups — C2×D4×D5×C11 #13183429

Order 1760.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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
1C23×D5×C11C212yesmaximal, complemented
2C2×C5×D4×C11C211yesmaximal, characteristic, complemented
3C2×C11×C22⋊D5C212yesmaximal, complemented
4D4×D5×C11C218yesmaximal, direct product factor
5C2×C11×D20C211yesmaximal, characteristic, complemented
6C2×C4×D5×C11C211yesmaximal, characteristic, complemented
7C23×C5×C11C2212yescomplemented
8C22×D5×C11—28no—
9C22×D5×C11C2211yescharacteristic
10C22×D5×C11C2218yescomplemented
11C22×D5×C11C2212yescomplemented
12C5×D4×C11C2214yescomplemented
13C2×C4×C5×C11C2211yescharacteristic, complemented
14C11×C22⋊D5C2218yescomplemented
15C2×C11×Dic5C2211yescharacteristic, complemented
16C11×D20C2214yescomplemented
17C4×D5×C11C2214yescomplemented
18C22×D4×C11—51nomaximal, Hall
19C22×C5×C11—24no—
20C22×C5×C11C2311yescharacteristic
21C22×C5×C11C2314yescomplemented
22C2×D5×C11—24no—
23C2×D5×C11—216no—
24C2×D5×C11D414yesdirect product factor
25C2×D5×C11C2312yes—
26C2×D5×C11C2314yescomplemented
27C4×C5×C11C2312yescomplemented
28C11×Dic5C2312yescomplemented
29C24×C11—52no—
30C2×D4×C11—52no—
31C2×D4×C11—58no—
32C2×D4×C11—51no—
33C2×D4×C11D511yescharacteristic, direct product factor
34C22×C4×C11—51no—
35C2×D4×D5C1111yesmaximal, characteristic, direct product factor, Hall
36C2×C5×C11—24no—
37C2×C5×C11C2×D412yescomplemented
38C2×C5×C11C2411yescharacteristic
39D5×C11—24no—
40D5×C11C2×D414yesdirect product factor
41C23×C11—51no—
42C23×C11—52no—
43C23×C11—58no—
44C23×C11—108no—
45C23×C11C2×D512yescomplemented
46D4×C11—58no—
47D4×C11—54no—
48D4×C11C2×D514yesdirect product factor
49C2×C4×C11—51no—
50C2×C4×C11—54no—
51C2×C4×C11C2×D511yescharacteristic, complemented
52C23×D5C2×C1112yescomplemented
53C2×C5×D4C2×C1111yescharacteristic, complemented
54C2×C22⋊D5C2×C1112yescomplemented
55D4×D5C2×C1118yesdirect product factor
56C2×D20C2×C1111yescharacteristic, complemented
57C2×C4×D5C2×C1111yescharacteristic, complemented
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—24no—
60C22×C11—54no—
61C22×C11—52no—
62C22×C11—54no—
63C22×C11—1016no—
64C22×C11—104no—
65C22×C11C22×D511yescharacteristic
66C22×C11C22×D514yescomplemented
67C4×C11—52no—
68C4×C11C22×D512yescomplemented
69C23×C5C22×C1112yescomplemented
70C22×D5—28no—
71C22×D5C22×C1111yescharacteristic
72C22×D5C22×C1118yescomplemented
73C22×D5C22×C1112yescomplemented
74C5×D4C22×C1114yescomplemented
75C2×C4×C5C22×C1111yescharacteristic, complemented
76C22⋊D5C22×C1118yescomplemented
77C2×Dic5C22×C1111yescharacteristic, complemented
78D20C22×C1114yescomplemented
79C4×D5C22×C1114yescomplemented
80C22×D4—51noSylow
81C2×C11—24no—
82C2×C11—54no—
83C2×C11—104no—
84C2×C11D4×D512yesdirect product factor
85C2×C11C23×D511yescharacteristic
86C22×C5—24no—
87C22×C5C23×C1111yescharacteristic
88C22×C5C23×C1114yescomplemented
89C2×D5—24no—
90C2×D5—216no—
91C2×D5D4×C1114yesdirect product factor
92C2×D5C23×C1112yes—
93C2×D5C23×C1114yescomplemented
94C4×C5C23×C1112yescomplemented
95Dic5C23×C1112yescomplemented
96C24—52no—
97C2×D4—52no—
98C2×D4—58no—
99C2×D4—51no—
100C2×D4D5×C1111yescharacteristic, direct product factor
101C22×C4—51no—
102C11C2×D4×D511yescharacteristic, direct product factor, Sylow
103C2×C5—24no—
104C2×C5C2×D4×C1112yescomplemented
105C2×C5C24×C1111yescharacteristic
106D5—24no—
107D5C2×D4×C1114yesdirect product factor
108C23—51no—
109C23—52no—
110C23—58no—
111C23—108no—
112C23C2×D5×C1112yescomplemented
113D4—58no—
114D4—54no—
115D4C2×D5×C1114yesdirect product factor
116C2×C4—51no—
117C2×C4—54no—
118C2×C4C2×D5×C1111yescharacteristic, complemented
119C5C22×D4×C1111yescharacteristic, complemented, Sylow
120C22—24no—
121C22—54no—
122C22—52no—
123C22—54no—
124C22—1016no—
125C22—104no—
126C22C22×D5×C1111yescharacteristic
127C22C22×D5×C1114yescomplemented
128C4—52no—
129C4C22×D5×C1112yescomplemented
130C2—24no—
131C2—54no—
132C2—104no—
133C2D4×D5×C1112yesdirect product factor
134C2C23×D5×C1111yescharacteristic
subgroupG/H
centerC22×C11C22×D5
commutator, cosocleC2×C5C24×C11
FrattiniC2C23×D5×C11
FittingC2×C5×D4×C11C2
socleC22×C5×C11C23
hypercenterC2×D4×C11D5
hypocenterC5C22×D4×C11
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C2×D4×C11

Complements

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

NH ≅ G/Ntype
1. C23×D5×C11C2semidirect
2. C2×C5×D4×C11C2semidirect
3. C2×C11×C22⋊D5C2semidirect
4. D4×D5×C11C2direct (N × H)
5. C2×C11×D20C2semidirect
6. C2×C4×D5×C11C2semidirect
7. C23×C5×C11C22semidirect
10. C22×D5×C11C22semidirect
11. C22×D5×C11C22semidirect
12. C5×D4×C11C22semidirect
13. C2×C4×C5×C11C22semidirect
14. C11×C22⋊D5C22semidirect
15. C2×C11×Dic5C22semidirect
16. C11×D20C22semidirect
17. C4×D5×C11C22semidirect
21. C22×C5×C11C23semidirect
24. C2×D5×C11D4direct (N × H)
26. C2×D5×C11C23semidirect
27. C4×C5×C11C23semidirect
28. C11×Dic5C23semidirect
33. C2×D4×C11D5direct (N × H)
35. C2×D4×D5C11direct (N × H)
37. C2×C5×C11C2×D4semidirect
40. D5×C11C2×D4direct (N × H)
45. C23×C11C2×D5semidirect
48. D4×C11C2×D5direct (N × H)
51. C2×C4×C11C2×D5semidirect
52. C23×D5C2×C11semidirect
53. C2×C5×D4C2×C11semidirect
54. C2×C22⋊D5C2×C11semidirect
55. D4×D5C2×C11direct (N × H)
56. C2×D20C2×C11semidirect
57. C2×C4×D5C2×C11semidirect
58. C5×C11C22×D4semidirect
66. C22×C11C22×D5semidirect
68. C4×C11C22×D5semidirect
69. C23×C5C22×C11semidirect
72. C22×D5C22×C11semidirect
73. C22×D5C22×C11semidirect
74. C5×D4C22×C11semidirect
75. C2×C4×C5C22×C11semidirect
76. C22⋊D5C22×C11semidirect
77. C2×Dic5C22×C11semidirect
78. D20C22×C11semidirect
79. C4×D5C22×C11semidirect
84. C2×C11D4×D5direct (N × H)
88. C22×C5C23×C11semidirect
91. C2×D5D4×C11direct (N × H)
93. C2×D5C23×C11semidirect
94. C4×C5C23×C11semidirect
95. Dic5C23×C11semidirect
100. C2×D4D5×C11direct (N × H)
102. C11C2×D4×D5direct (N × H)
104. C2×C5C2×D4×C11semidirect
107. D5C2×D4×C11direct (N × H)
112. C23C2×D5×C11semidirect
115. D4C2×D5×C11direct (N × H)
118. C2×C4C2×D5×C11semidirect
119. C5C22×D4×C11semidirect
127. C22C22×D5×C11semidirect
129. C4C22×D5×C11semidirect
133. C2D4×D5×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5×C112
C2×C5×D4×C112
C2×C11×C22⋊D52
D4×D5×C112
C2×C11×D202
C2×C4×D5×C112
C22×D4×C115
C2×D4×D511