Finite Group Databasebeta

← C2×#11724994 #13183373

Subgroups — C2×#11724994 #13183373

Order 1760.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4×D55C211yesmaximal, characteristic, complemented
3C2×C11×D20C211yesmaximal, characteristic, complemented
4C2×C5×D44C211yesmaximal, characteristic, complemented
5C2×#89167C212yesmaximal, complemented
6#11724994C218yesmaximal, direct product factor
7C22×D55C2211yescharacteristic
8C22×D5×C11C2212yescomplemented
9C22×C5×D11C2212yescomplemented
10C2×D5×D11—28no—
11C2×D5×D11C2218yescomplemented
12C2×C4×C5×C11C2211yescharacteristic, complemented
13C2×Dic55C2211yescharacteristic, complemented
14C4×D55C2214yescomplemented
15C11×D20C2214yescomplemented
16C5×D44C2214yescomplemented
17#89167C2218yescomplemented
18C2×D4×D11—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55D414yescomplemented
21C2×D55C2312yes—
22C2×D5×C11—24no—
23C2×D5×C11C2314yescomplemented
24C2×C5×D11—24no—
25C2×C5×D11C2314yescomplemented
26D5×D11—216no—
27C4×C5×C11C2312yescomplemented
28Dic55C2312yescomplemented
29C23×D11—52no—
30C2×D4×C11—51no—
31C2×C22⋊D11—52no—
32D4×D11—58no—
33C2×D44D511yescharacteristic, complemented
34C2×C4×D11—51no—
35C2×D4×D5—111nomaximal, Hall
36C2×C5×C11C2×D412yescomplemented
37C2×C5×C11C2411yescharacteristic
38D55C2×D414yescomplemented
39C5×D11—24no—
40D5×C11—24no—
41C23×C11—52no—
42C22×D11—51no—
43C22×D11—58no—
44C22×D11—108no—
45C22×D11C2×D512yescomplemented
46D4×C11—54no—
47C2×C4×C11C2×D511yescharacteristic, complemented
48C22⋊D11—58no—
49C2×Dic11—51no—
50D44C2×D514yescomplemented
51C4×D11—54no—
52C23×D5—112no—
53C2×C5×D4—111no—
54C2×C22⋊D5—112no—
55D4×D5—118no—
56C2×D20D1111yescharacteristic, complemented
57C2×C4×D5—111no—
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—54no—
60C22×C11—104no—
61C22×C11C22×D511yescharacteristic
62C2×D11—24no—
63C2×D11—54no—
64C2×D11—52no—
65C2×D11—1016no—
66C2×D11C22×D514yescomplemented
67C4×C11C22×D512yescomplemented
68Dic11—52no—
69C23×C5—112no—
70C22×D5—111no—
71C22×D5—118no—
72C22×D5—228no—
73C22×D5C2×D1112yescomplemented
74C5×D4—114no—
75C2×C4×C5C2×D1111yescharacteristic, complemented
76C22⋊D5—118no—
77C2×Dic5—111no—
78D20C2×D1114yescomplemented
79C4×D5—114no—
80C22×D4—551noSylow
81C2×C11—104no—
82C2×C11D4×D512yescomplemented
83C2×C11C23×D511yescharacteristic
84D11—24no—
85D11—54no—
86C22×C5—114no—
87C22×C5—224no—
88C22×C5C22×D1111yescharacteristic
89C2×D5—24no—
90C2×D5—114no—
91C2×D5—112no—
92C2×D5—2216no—
93C2×D5C22×D1114yescomplemented
94C4×C5C22×D1112yescomplemented
95Dic5—112no—
96C24—552no—
97C2×D4—51no—
98C2×D4—111no—
99C2×D4—558no—
100C2×D4—552no—
101C22×C4—551no—
102C11C2×D4×D511yescharacteristic, complemented, Sylow
103C2×C5—224no—
104C2×C5D4×D1112yescomplemented
105C2×C5C23×D1111yescharacteristic
106D5—24no—
107D5—114no—
108C23—52no—
109C23—112no—
110C23—558no—
111C23—551no—
112C23—1108no—
113D4—54no—
114D4—114no—
115D4—558no—
116C2×C4—551no—
117C2×C4—554no—
118C2×C4D5×D1111yescharacteristic, complemented
119C5C2×D4×D1111yescharacteristic, complemented, Sylow
120C22—54no—
121C22—104no—
122C22—114no—
123C22—224no—
124C22—554no—
125C22—552no—
126C22—11016no—
127C22C2×D5×D1111yescharacteristic
128C4—552no—
129C4C2×D5×D1112yescomplemented
130C2—104no—
131C2—224no—
132C2—554no—
133C2#1172499412yesdirect 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×C4×D55C2semidirect
3. C2×C11×D20C2semidirect
4. C2×C5×D44C2semidirect
5. C2×#89167C2semidirect
6. #11724994C2direct (N × H)
8. C22×D5×C11C22semidirect
9. C22×C5×D11C22semidirect
11. C2×D5×D11C22semidirect
12. C2×C4×C5×C11C22semidirect
13. C2×Dic55C22semidirect
14. C4×D55C22semidirect
15. C11×D20C22semidirect
16. C5×D44C22semidirect
17. #89167C22semidirect
20. C2×D55D4semidirect
23. C2×D5×C11C23semidirect
25. C2×C5×D11C23semidirect
27. C4×C5×C11C23semidirect
28. Dic55C23semidirect
33. C2×D44D5semidirect
36. C2×C5×C11C2×D4semidirect
38. D55C2×D4semidirect
45. C22×D11C2×D5semidirect
47. C2×C4×C11C2×D5semidirect
50. D44C2×D5semidirect
56. C2×D20D11semidirect
58. C5×C11C22×D4semidirect
66. C2×D11C22×D5semidirect
67. C4×C11C22×D5semidirect
73. C22×D5C2×D11semidirect
75. C2×C4×C5C2×D11semidirect
78. D20C2×D11semidirect
82. C2×C11D4×D5semidirect
93. C2×D5C22×D11semidirect
94. C4×C5C22×D11semidirect
102. C11C2×D4×D5semidirect
104. C2×C5D4×D11semidirect
118. C2×C4D5×D11semidirect
119. C5C2×D4×D11semidirect
129. C4C2×D5×D11semidirect
133. C2#11724994direct (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×C4×D552
C2×C11×D202
C2×C5×D442
C2×#891672
#117249942
C2×D4×D115
C2×D4×D511