Finite Group Databasebeta

← C2×C4×D5×D11 #13183370

Subgroups — C2×C4×D5×D11 #13183370

Order 1760.

472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 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×D11C211yesmaximal, characteristic
2C2×C4×D55C211yesmaximal, characteristic, complemented
3C2×C4×D5×C11C211yesmaximal, characteristic, complemented
4C2×C4×C5×D11C211yesmaximal, characteristic, complemented
5C2×#89166C211yesmaximal, characteristic, complemented
6C2×D5×Dic11C211yesmaximal, characteristic, complemented
7C2×Dic5×D11C211yesmaximal, characteristic, complemented
8C4×D5×D11C218yesmaximal, direct product factor
9C22×D55C2211yescharacteristic
10C22×D5×C11C2211yescharacteristic
11C22×C5×D11C2211yescharacteristic
12C2×D5×D11C418yesdirect product factor
13C2×D5×D11C2214yes—
14C2×C4×C5×C11C2211yescharacteristic, complemented
15C2×Dic55C2211yescharacteristic, complemented
16C4×D55C2214yescomplemented
17C2×C11×Dic5C2211yescharacteristic, complemented
18C4×D5×C11C2214yescomplemented
19C2×C5×Dic11C2211yescharacteristic, complemented
20C4×C5×D11C2214yescomplemented
21#89166C2214yescomplemented
22D5×Dic11C2214yescomplemented
23Dic5×D11C2214yescomplemented
24C22×C4×D11—51nomaximal, Hall
25C22×C5×C11C2311yescharacteristic
26C2×D55C2×C414yescomplemented
27C2×D55C2312yes—
28C2×D5×C11C2×C414yescomplemented
29C2×D5×C11C2312yes—
30C2×C5×D11C2×C414yescomplemented
31C2×C5×D11C2312yes—
32D5×D11C2×C4116yesdirect product factor
33C4×C5×C11C2312yescomplemented
34Dic55C2312yescomplemented
35C5×Dic11C2312yescomplemented
36C11×Dic5C2312yescomplemented
37C23×D11—51no—
38C22×C4×C11—51no—
39C22×Dic11—51no—
40C2×C4×D11—51no—
41C2×C4×D11—58no—
42C2×C4×D11—51no—
43C2×C4×D11—51no—
44C2×C4×D11D511yescharacteristic, direct product factor
45C22×C4×D5—111nomaximal, Hall
46C2×C5×C11C22×C412yescomplemented
47C2×C5×C11C2411yescharacteristic
48D55C22×C414yescomplemented
49C5×D11C22×C414yescomplemented
50D5×C11C22×C414yescomplemented
51C23×C11—51no—
52C22×D11—51no—
53C22×D11—58no—
54C22×D11—54no—
55C22×D11C2×D511yescharacteristic
56C2×C4×C11—51no—
57C2×C4×C11—54no—
58C2×C4×C11C2×D511yescharacteristic, complemented
59C2×Dic11—51no—
60C2×Dic11—54no—
61C2×Dic11C2×D511yescharacteristic, complemented
62C4×D11—54no—
63C4×D11—54no—
64C4×D11—54no—
65C4×D11C2×D514yesdirect product factor
66C23×D5—111no—
67C22×C4×C5—111no—
68C22×Dic5—111no—
69C2×C4×D5—111no—
70C2×C4×D5—111no—
71C2×C4×D5—111no—
72C2×C4×D5—118no—
73C2×C4×D5D1111yescharacteristic, direct product factor
74C5×C11C23×C411yescharacteristic, complemented, Hall
75C22×C11—54no—
76C22×C11—52no—
77C22×C11C22×D511yescharacteristic
78C2×D11—54no—
79C2×D11—52no—
80C2×D11—516no—
81C2×D11C4×D514yesdirect product factor
82C2×D11C22×D512yes—
83C4×C11—52no—
84C4×C11C22×D512yescomplemented
85Dic11—52no—
86Dic11C22×D512yescomplemented
87C23×C5—111no—
88C22×D5—111no—
89C22×D5—114no—
90C22×D5—118no—
91C22×D5C2×D1111yescharacteristic
92C2×C4×C5—111no—
93C2×C4×C5—114no—
94C2×C4×C5C2×D1111yescharacteristic, complemented
95C2×Dic5—111no—
96C2×Dic5—114no—
97C2×Dic5C2×D1111yescharacteristic, complemented
98C4×D5—114no—
99C4×D5—114no—
100C4×D5—114no—
101C4×D5C2×D1114yesdirect product factor
102C23×C4—551noSylow
103C2×C11—54no—
104C2×C11C2×C4×D512yescomplemented
105C2×C11C23×D511yescharacteristic
106D11—54no—
107D11C2×C4×D514yesdirect product factor
108C22×C5—114no—
109C22×C5—112no—
110C22×C5C22×D1111yescharacteristic
111C2×D5—114no—
112C2×D5—112no—
113C2×D5—1116no—
114C2×D5C4×D1114yesdirect product factor
115C2×D5C22×D1112yes—
116C4×C5—112no—
117C4×C5C22×D1112yescomplemented
118Dic5—112no—
119Dic5C22×D1112yescomplemented
120C24—551no—
121C22×C4—51no—
122C22×C4—111no—
123C22×C4—551no—
124C22×C4—558no—
125C22×C4—551no—
126C22×C4—551no—
127C22×C4—551no—
128C11C22×C4×D511yescharacteristic, complemented, Sylow
129C2×C5—114no—
130C2×C5C2×C4×D1112yescomplemented
131C2×C5C23×D1111yescharacteristic
132D5—114no—
133D5C2×C4×D1114yesdirect product factor
134C23—51no—
135C23—111no—
136C23—554no—
137C23—558no—
138C23—551no—
139C2×C4—51no—
140C2×C4—54no—
141C2×C4—111no—
142C2×C4—114no—
143C2×C4—554no—
144C2×C4—554no—
145C2×C4—554no—
146C2×C4—551no—
147C2×C4—554no—
148C2×C4D5×D1111yescharacteristic, direct product factor
149C5C22×C4×D1111yescharacteristic, complemented, Sylow
150C22—54no—
151C22—52no—
152C22—114no—
153C22—112no—
154C22—5516no—
155C22—554no—
156C22—552no—
157C22C2×D5×D1111yescharacteristic
158C4—52no—
159C4—112no—
160C4—552no—
161C4C2×D5×D1112yesdirect product factor
162C2—54no—
163C2—114no—
164C2—554no—
165C2C4×D5×D1112yesdirect product factor
166C2C22×D5×D1111yescharacteristic
subgroupG/H
center, hypercenterC2×C4D5×D11
commutator, hypocenterC5×C11C23×C4
FrattiniC2C22×D5×D11
FittingC2×C4×C5×C11C22
socleC22×C5×C11C23
prime radicalC22×D5×D11C2
cosocleC2×C5×C11C24
LCSG ▷ C5×C11
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D55C2semidirect
3. C2×C4×D5×C11C2semidirect
4. C2×C4×C5×D11C2semidirect
5. C2×#89166C2semidirect
6. C2×D5×Dic11C2semidirect
7. C2×Dic5×D11C2semidirect
8. C4×D5×D11C2direct (N × H)
12. C2×D5×D11C4direct (N × H)
14. C2×C4×C5×C11C22semidirect
15. C2×Dic55C22semidirect
16. C4×D55C22semidirect
17. C2×C11×Dic5C22semidirect
18. C4×D5×C11C22semidirect
19. C2×C5×Dic11C22semidirect
20. C4×C5×D11C22semidirect
21. #89166C22semidirect
22. D5×Dic11C22semidirect
23. Dic5×D11C22semidirect
26. C2×D55C2×C4semidirect
28. C2×D5×C11C2×C4semidirect
30. C2×C5×D11C2×C4semidirect
32. D5×D11C2×C4direct (N × H)
33. C4×C5×C11C23semidirect
34. Dic55C23semidirect
35. C5×Dic11C23semidirect
36. C11×Dic5C23semidirect
44. C2×C4×D11D5direct (N × H)
46. C2×C5×C11C22×C4semidirect
48. D55C22×C4semidirect
49. C5×D11C22×C4semidirect
50. D5×C11C22×C4semidirect
58. C2×C4×C11C2×D5semidirect
61. C2×Dic11C2×D5semidirect
65. C4×D11C2×D5direct (N × H)
73. C2×C4×D5D11direct (N × H)
74. C5×C11C23×C4semidirect
81. C2×D11C4×D5direct (N × H)
84. C4×C11C22×D5semidirect
86. Dic11C22×D5semidirect
94. C2×C4×C5C2×D11semidirect
97. C2×Dic5C2×D11semidirect
101. C4×D5C2×D11direct (N × H)
104. C2×C11C2×C4×D5semidirect
107. D11C2×C4×D5direct (N × H)
114. C2×D5C4×D11direct (N × H)
117. C4×C5C22×D11semidirect
119. Dic5C22×D11semidirect
128. C11C22×C4×D5semidirect
130. C2×C5C2×C4×D11semidirect
133. D5C2×C4×D11direct (N × H)
148. C2×C4D5×D11direct (N × H)
149. C5C22×C4×D11semidirect
161. C4C2×D5×D11direct (N × H)
165. C2C4×D5×D11direct (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×C4×D5×C112
C2×C4×C5×D112
C2×#891662
C2×D5×Dic112
C2×Dic5×D112
C4×D5×D112
C22×C4×D115
C22×C4×D511