Finite Group Databasebeta

← C2×D5×D44 #13183372

Subgroups — C2×D5×D44 #13183372

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×C4×D5×C11C211yesmaximal, characteristic, complemented
4C2×C5×D44C211yesmaximal, characteristic, complemented
5C2×#89168C212yesmaximal, complemented
6D5×D44C218yesmaximal, direct product factor
7C22×D55C2212yescomplemented
8C22×D5×C11C2211yescharacteristic
9C22×C5×D11C2212yescomplemented
10C2×D5×D11—28no—
11C2×D5×D11C2218yescomplemented
12C2×C4×C5×C11C2211yescharacteristic, complemented
13D220C2214yescomplemented
14C2×C11×Dic5C2211yescharacteristic, complemented
15C4×D5×C11C2214yescomplemented
16C5×D44C2214yescomplemented
17#89168C2218yescomplemented
18C22×D44—51nomaximal, Hall
19C22×C5×C11C2311yescharacteristic
20C2×D55—24no—
21C2×D55C2314yescomplemented
22C2×D5×C11D414yescomplemented
23C2×D5×C11C2312yes—
24C2×C5×D11—24no—
25C2×C5×D11C2314yescomplemented
26D5×D11—216no—
27C4×C5×C11C2312yescomplemented
28C11×Dic5C2312yescomplemented
29C23×D11—52no—
30C22×C4×C11—51no—
31C2×D44—58no—
32C2×D44—52no—
33C2×D44—51no—
34C2×D44D511yescharacteristic, direct product factor
35C2×D4×D5—111nomaximal, Hall
36C2×C5×C11C2×D412yescomplemented
37C2×C5×C11C2411yescharacteristic
38D55—24no—
39C5×D11—24no—
40D5×C11C2×D414yescomplemented
41C23×C11—51no—
42C22×D11—52no—
43C22×D11—58no—
44C22×D11—108no—
45C22×D11C2×D512yescomplemented
46C2×C4×C11—51no—
47C2×C4×C11—54no—
48C2×C4×C11C2×D511yescharacteristic, complemented
49D44—58no—
50D44—54no—
51D44C2×D514yesdirect product factor
52C23×D5—112no—
53C2×C5×D4—111no—
54C2×C22⋊D5—112no—
55D4×D5—118no—
56C2×D20—111no—
57C2×C4×D5D1111yescharacteristic, complemented
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—54no—
60C22×C11—52no—
61C22×C11C22×D511yescharacteristic
62C2×D11—24no—
63C2×D11—54no—
64C2×D11—1016no—
65C2×D11—104no—
66C2×D11C22×D514yescomplemented
67C4×C11—52no—
68C4×C11C22×D512yescomplemented
69C23×C5—112no—
70C22×D5—112no—
71C22×D5—118no—
72C22×D5—228no—
73C22×D5C2×D1111yescharacteristic
74C5×D4—114no—
75C2×C4×C5C2×D1111yescharacteristic, complemented
76C22⋊D5—118no—
77C2×Dic5C2×D1111yescharacteristic, complemented
78D20—114no—
79C4×D5C2×D1114yescomplemented
80C22×D4—551noSylow
81C2×C11—54no—
82C2×C11D4×D512yescomplemented
83C2×C11C23×D511yescharacteristic
84D11—24no—
85D11—104no—
86C22×C5—114no—
87C22×C5—224no—
88C22×C5C22×D1111yescharacteristic
89C2×D5—114no—
90C2×D5—224no—
91C2×D5—2216no—
92C2×D5D4414yesdirect product factor
93C2×D5C22×D1112yes—
94C4×C5C22×D1112yescomplemented
95Dic5C22×D1112yescomplemented
96C24—552no—
97C2×D4—111no—
98C2×D4—558no—
99C2×D4—552no—
100C2×D4—551no—
101C22×C4—51no—
102C11C2×D4×D511yescharacteristic, complemented, Sylow
103C2×C5—224no—
104C2×C5C2×D4412yescomplemented
105C2×C5C23×D1111yescharacteristic
106D5—224no—
107D5C2×D4414yesdirect product factor
108C23—51no—
109C23—112no—
110C23—558no—
111C23—552no—
112C23—1108no—
113D4—114no—
114D4—558no—
115D4—554no—
116C2×C4—51no—
117C2×C4—54no—
118C2×C4D5×D1111yescharacteristic, complemented
119C5C22×D4411yescharacteristic, complemented, Sylow
120C22—54no—
121C22—52no—
122C22—114no—
123C22—224no—
124C22—554no—
125C22—11016no—
126C22—1104no—
127C22C2×D5×D1111yescharacteristic
128C4—52no—
129C4C2×D5×D1112yescomplemented
130C2—54no—
131C2—224no—
132C2—1104no—
133C2D5×D4412yesdirect 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×C4×D5×C11C2semidirect
4. C2×C5×D44C2semidirect
5. C2×#89168C2semidirect
6. D5×D44C2direct (N × H)
7. C22×D55C22semidirect
9. C22×C5×D11C22semidirect
11. C2×D5×D11C22semidirect
12. C2×C4×C5×C11C22semidirect
13. D220C22semidirect
14. C2×C11×Dic5C22semidirect
15. C4×D5×C11C22semidirect
16. C5×D44C22semidirect
17. #89168C22semidirect
21. C2×D55C23semidirect
22. C2×D5×C11D4semidirect
25. C2×C5×D11C23semidirect
27. C4×C5×C11C23semidirect
28. C11×Dic5C23semidirect
34. C2×D44D5direct (N × H)
36. C2×C5×C11C2×D4semidirect
40. D5×C11C2×D4semidirect
45. C22×D11C2×D5semidirect
48. C2×C4×C11C2×D5semidirect
51. D44C2×D5direct (N × H)
57. C2×C4×D5D11semidirect
58. C5×C11C22×D4semidirect
66. C2×D11C22×D5semidirect
68. C4×C11C22×D5semidirect
75. C2×C4×C5C2×D11semidirect
77. C2×Dic5C2×D11semidirect
79. C4×D5C2×D11semidirect
82. C2×C11D4×D5semidirect
92. C2×D5D44direct (N × H)
94. C4×C5C22×D11semidirect
95. Dic5C22×D11semidirect
102. C11C2×D4×D5semidirect
104. C2×C5C2×D44semidirect
107. D5C2×D44direct (N × H)
118. C2×C4D5×D11semidirect
119. C5C22×D44semidirect
129. C4C2×D5×D11semidirect
133. C2D5×D44direct (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×C4×D5×C112
C2×C5×D442
C2×#891682
D5×D442
C22×D445
C2×D4×D511