Finite Group Databasebeta

← C2×D4×D55 #13183444

Subgroups — C2×D4×D55 #13183444

Order 1760.

472 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 135 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×D55C212yesmaximal, complemented
2C2×C5×D4×C11C211yesmaximal, characteristic, complemented
3C2×C22⋊D55C212yesmaximal, complemented
4D4×D55C218yesmaximal, direct product factor
5C2×D220C211yesmaximal, characteristic, complemented
6C2×C4×D55C211yesmaximal, characteristic, complemented
7C23×C5×C11C2212yescomplemented
8C22×D55—28no—
9C22×D55C2211yescharacteristic
10C22×D55C2218yescomplemented
11C22×D55C2212yescomplemented
12C5×D4×C11C2214yescomplemented
13C2×C4×C5×C11C2211yescharacteristic, complemented
14C22⋊D55C2218yescomplemented
15C2×Dic55C2211yescharacteristic, complemented
16D220C2214yescomplemented
17C4×D55C2214yescomplemented
18C2×D4×D11—51nomaximal, Hall
19C22×C5×C11—24no—
20C22×C5×C11C2311yescharacteristic
21C22×C5×C11C2314yescomplemented
22C2×D55—24no—
23C2×D55—216no—
24C2×D55D414yesdirect product factor
25C2×D55C2312yes—
26C2×D55C2314yescomplemented
27C4×C5×C11C2312yescomplemented
28Dic55C2312yescomplemented
29C23×D11—52no—
30C2×D4×C11D511yescharacteristic, complemented
31C2×C22⋊D11—52no—
32D4×D11—58no—
33C2×D44—51no—
34C2×C4×D11—51no—
35C2×D4×D5—111nomaximal, Hall
36C2×C5×C11—24no—
37C2×C5×C11C2×D412yescomplemented
38C2×C5×C11C2411yescharacteristic
39D55—24no—
40D55C2×D414yesdirect product factor
41C23×C11C2×D512yescomplemented
42C22×D11—51no—
43C22×D11—52no—
44C22×D11—58no—
45C22×D11—108no—
46D4×C11C2×D514yescomplemented
47C2×C4×C11C2×D511yescharacteristic, complemented
48C22⋊D11—58no—
49C2×Dic11—51no—
50D44—54no—
51C4×D11—54no—
52C23×D5—112no—
53C2×C5×D4D1111yescharacteristic, complemented
54C2×C22⋊D5—112no—
55D4×D5—118no—
56C2×D20—111no—
57C2×C4×D5—111no—
58C5×C11C22×D411yescharacteristic, complemented, Hall
59C22×C11—24no—
60C22×C11C22×D511yescharacteristic
61C22×C11C22×D514yescomplemented
62C2×D11—54no—
63C2×D11—52no—
64C2×D11—54no—
65C2×D11—1016no—
66C2×D11—104no—
67C4×C11C22×D512yescomplemented
68Dic11—52no—
69C23×C5C2×D1112yescomplemented
70C22×D5—111no—
71C22×D5—112no—
72C22×D5—118no—
73C22×D5—228no—
74C5×D4C2×D1114yescomplemented
75C2×C4×C5C2×D1111yescharacteristic, complemented
76C22⋊D5—118no—
77C2×Dic5—111no—
78D20—114no—
79C4×D5—114no—
80C22×D4—551noSylow
81C2×C11—24no—
82C2×C11D4×D512yescomplemented
83C2×C11C23×D511yescharacteristic
84D11—54no—
85D11—104no—
86C22×C5—24no—
87C22×C5C22×D1111yescharacteristic
88C22×C5C22×D1114yescomplemented
89C2×D5—114no—
90C2×D5—112no—
91C2×D5—114no—
92C2×D5—2216no—
93C2×D5—224no—
94C4×C5C22×D1112yescomplemented
95Dic5—112no—
96C24—552no—
97C2×D4—552no—
98C2×D4—558no—
99C2×D4—551no—
100C2×D4D5511yescharacteristic, direct product factor
101C22×C4—551no—
102C11C2×D4×D511yescharacteristic, complemented, Sylow
103C2×C5—24no—
104C2×C5D4×D1112yescomplemented
105C2×C5C23×D1111yescharacteristic
106D5—114no—
107D5—224no—
108C23—551no—
109C23—552no—
110C23—558no—
111C23—1108no—
112C23C2×D5512yescomplemented
113D4—558no—
114D4—554no—
115D4C2×D5514yesdirect product factor
116C2×C4—551no—
117C2×C4—554no—
118C2×C4C2×D5511yescharacteristic, complemented
119C5C2×D4×D1111yescharacteristic, complemented, Sylow
120C22—24no—
121C22—554no—
122C22—552no—
123C22—554no—
124C22—11016no—
125C22—1104no—
126C22C22×D5511yescharacteristic
127C22C22×D5514yescomplemented
128C4—552no—
129C4C22×D5512yescomplemented
130C2—24no—
131C2—554no—
132C2—1104no—
133C2D4×D5512yesdirect product factor
134C2C23×D5511yescharacteristic
subgroupG/H
centerC22C22×D55
commutator, cosocleC2×C5×C11C24
FrattiniC2C23×D55
FittingC2×C5×D4×C11C2
socleC22×C5×C11C23
hypercenterC2×D4D55
hypocenterC5×C11C22×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×D55C2semidirect
2. C2×C5×D4×C11C2semidirect
3. C2×C22⋊D55C2semidirect
4. D4×D55C2direct (N × H)
5. C2×D220C2semidirect
6. C2×C4×D55C2semidirect
7. C23×C5×C11C22semidirect
10. C22×D55C22semidirect
11. C22×D55C22semidirect
12. C5×D4×C11C22semidirect
13. C2×C4×C5×C11C22semidirect
14. C22⋊D55C22semidirect
15. C2×Dic55C22semidirect
16. D220C22semidirect
17. C4×D55C22semidirect
21. C22×C5×C11C23semidirect
24. C2×D55D4direct (N × H)
26. C2×D55C23semidirect
27. C4×C5×C11C23semidirect
28. Dic55C23semidirect
30. C2×D4×C11D5semidirect
37. C2×C5×C11C2×D4semidirect
40. D55C2×D4direct (N × H)
41. C23×C11C2×D5semidirect
46. D4×C11C2×D5semidirect
47. C2×C4×C11C2×D5semidirect
53. C2×C5×D4D11semidirect
58. C5×C11C22×D4semidirect
61. C22×C11C22×D5semidirect
67. C4×C11C22×D5semidirect
69. C23×C5C2×D11semidirect
74. C5×D4C2×D11semidirect
75. C2×C4×C5C2×D11semidirect
82. C2×C11D4×D5semidirect
88. C22×C5C22×D11semidirect
94. C4×C5C22×D11semidirect
100. C2×D4D55direct (N × H)
102. C11C2×D4×D5semidirect
104. C2×C5D4×D11semidirect
112. C23C2×D55semidirect
115. D4C2×D55direct (N × H)
118. C2×C4C2×D55semidirect
119. C5C2×D4×D11semidirect
127. C22C22×D55semidirect
129. C4C22×D55semidirect
133. C2D4×D55direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D552
C2×C5×D4×C112
C2×C22⋊D552
D4×D552
C2×D2202
C2×C4×D552
C2×D4×D115
C2×D4×D511