Finite Group Databasebeta

← C2×D11×D20 #13183371

Subgroups — C2×D11×D20 #13183371

Order 1760.

472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C22×D5×D11C212yesmaximal, complemented
2C2×D220C211yesmaximal, characteristic, complemented
3C2×C11×D20C211yesmaximal, characteristic, complemented
4C2×C4×C5×D11C211yesmaximal, characteristic, complemented
5C2×#89169C212yesmaximal, complemented
6D11×D20C218yesmaximal, direct product factor
7C22×D55C2212yescomplemented
8C22×D5×C11C2212yescomplemented
9C22×C5×D11C2211yescharacteristic
10C2×D5×D11—28no—
11C2×D5×D11C2218yescomplemented
12C2×C4×C5×C11C2211yescharacteristic, complemented
13D220C2214yescomplemented
14C11×D20C2214yescomplemented
15C2×C5×Dic11C2211yescharacteristic, complemented
16C4×C5×D11C2214yescomplemented
17#89169C2218yescomplemented
18C2×D4×D11—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55—24no—
21C2×D55C2314yescomplemented
22C2×D5×C11—24no—
23C2×D5×C11C2314yescomplemented
24C2×C5×D11D414yescomplemented
25C2×C5×D11C2312yes—
26D5×D11—216no—
27C4×C5×C11C2312yescomplemented
28C5×Dic11C2312yescomplemented
29C23×D11—52no—
30C2×D4×C11—51no—
31C2×C22⋊D11—52no—
32D4×D11—58no—
33C2×D44—51no—
34C2×C4×D11D511yescharacteristic, complemented
35C22×D20—111nomaximal, Hall
36C2×C5×C11C2×D412yescomplemented
37C2×C5×C11C2411yescharacteristic
38D55—24no—
39C5×D11C2×D414yescomplemented
40D5×C11—24no—
41C23×C11—52no—
42C22×D11—52no—
43C22×D11—58no—
44C22×D11—108no—
45C22×D11C2×D511yescharacteristic
46D4×C11—54no—
47C2×C4×C11C2×D511yescharacteristic, complemented
48C22⋊D11—58no—
49C2×Dic11C2×D511yescharacteristic, complemented
50D44—54no—
51C4×D11C2×D514yescomplemented
52C23×D5—112no—
53C22×C4×C5—111no—
54C2×D20—112no—
55C2×D20—111no—
56C2×D20—118no—
57C2×D20D1111yescharacteristic, direct product factor
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—54no—
60C22×C11—104no—
61C22×C11C22×D511yescharacteristic
62C2×D11—54no—
63C2×D11—104no—
64C2×D11—1016no—
65C2×D11D2014yesdirect product factor
66C2×D11C22×D512yes—
67C4×C11C22×D512yescomplemented
68Dic11C22×D512yescomplemented
69C23×C5—111no—
70C22×D5—112no—
71C22×D5—118no—
72C22×D5—228no—
73C22×D5C2×D1112yescomplemented
74C2×C4×C5—111no—
75C2×C4×C5—114no—
76C2×C4×C5C2×D1111yescharacteristic, complemented
77D20—118no—
78D20—114no—
79D20C2×D1114yesdirect product factor
80C22×D4—551noSylow
81C2×C11—104no—
82C2×C11C2×D2012yescomplemented
83C2×C11C23×D511yescharacteristic
84D11—104no—
85D11C2×D2014yesdirect product factor
86C22×C5—114no—
87C22×C5—112no—
88C22×C5C22×D1111yescharacteristic
89C2×D5—24no—
90C2×D5—114no—
91C2×D5—2216no—
92C2×D5—224no—
93C2×D5C22×D1114yescomplemented
94C4×C5—112no—
95C4×C5C22×D1112yescomplemented
96C24—552no—
97C2×D4—51no—
98C2×D4—558no—
99C2×D4—552no—
100C2×D4—551no—
101C22×C4—111no—
102C11C22×D2011yescharacteristic, complemented, Sylow
103C2×C5—114no—
104C2×C5D4×D1112yescomplemented
105C2×C5C23×D1111yescharacteristic
106D5—24no—
107D5—224no—
108C23—52no—
109C23—111no—
110C23—558no—
111C23—552no—
112C23—1108no—
113D4—54no—
114D4—558no—
115D4—554no—
116C2×C4—111no—
117C2×C4—114no—
118C2×C4D5×D1111yescharacteristic, complemented
119C5C2×D4×D1111yescharacteristic, complemented, Sylow
120C22—54no—
121C22—104no—
122C22—114no—
123C22—112no—
124C22—554no—
125C22—11016no—
126C22—1104no—
127C22C2×D5×D1111yescharacteristic
128C4—112no—
129C4C2×D5×D1112yescomplemented
130C2—104no—
131C2—114no—
132C2—1104no—
133C2D11×D2012yesdirect product factor
134C2C22×D5×D1111yescharacteristic
subgroupG/H
centerC22C2×D5×D11
commutator, cosocleC2×C5×C11C24
FrattiniC2C22×D5×D11
FittingC2×C4×C5×C11C22
socleC22×C5×C11C23
hypercenterC2×C4D5×D11
hypocenterC5×C11C22×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×D11C2semidirect
2. C2×D220C2semidirect
3. C2×C11×D20C2semidirect
4. C2×C4×C5×D11C2semidirect
5. C2×#89169C2semidirect
6. D11×D20C2direct (N × H)
7. C22×D55C22semidirect
8. C22×D5×C11C22semidirect
11. C2×D5×D11C22semidirect
12. C2×C4×C5×C11C22semidirect
13. D220C22semidirect
14. C11×D20C22semidirect
15. C2×C5×Dic11C22semidirect
16. C4×C5×D11C22semidirect
17. #89169C22semidirect
21. C2×D55C23semidirect
23. C2×D5×C11C23semidirect
24. C2×C5×D11D4semidirect
27. C4×C5×C11C23semidirect
28. C5×Dic11C23semidirect
34. C2×C4×D11D5semidirect
36. C2×C5×C11C2×D4semidirect
39. C5×D11C2×D4semidirect
47. C2×C4×C11C2×D5semidirect
49. C2×Dic11C2×D5semidirect
51. C4×D11C2×D5semidirect
57. C2×D20D11direct (N × H)
58. C5×C11C22×D4semidirect
65. C2×D11D20direct (N × H)
67. C4×C11C22×D5semidirect
68. Dic11C22×D5semidirect
73. C22×D5C2×D11semidirect
76. C2×C4×C5C2×D11semidirect
79. D20C2×D11direct (N × H)
82. C2×C11C2×D20semidirect
85. D11C2×D20direct (N × H)
93. C2×D5C22×D11semidirect
95. C4×C5C22×D11semidirect
102. C11C22×D20semidirect
104. C2×C5D4×D11semidirect
118. C2×C4D5×D11semidirect
119. C5C2×D4×D11semidirect
129. C4C2×D5×D11semidirect
133. C2D11×D20direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D112
C2×D2202
C2×C11×D202
C2×C4×C5×D112
C2×#891692
D11×D202
C2×D4×D115
C22×D2011