Finite Group Databasebeta

← C11⋊C5×#534 #72248887

Subgroups — C11⋊C5×#534 #72248887

Order 3520.

692 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 243 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×D4×C11⋊C5C212yesmaximal, complemented
2#123×C11⋊C5C214yesmaximal, complemented
3#121×C11⋊C5C214yesmaximal, complemented
4#120×C11⋊C5C214yesmaximal, complemented
5C2×C22⋊C4×C11⋊C5C211yesmaximal, characteristic, complemented
6C24×C11⋊C5C2211yescharacteristic
7C24×C11⋊C5C2212yescomplemented
8C2×D4×C11⋊C5—28no—
9C2×D4×C11⋊C5C2214yes—
10C2×D4×C11⋊C5C2214yescomplemented
11C2×D4×C11⋊C5C2214yescomplemented
12C22×C4×C11⋊C5C2212yescomplemented
13C22×C4×C11⋊C5C2212yescomplemented
14C4⋊C4×C11⋊C5C2214yescomplemented
15C22⋊C4×C11⋊C5C2214yescomplemented
16C22⋊C4×C11⋊C5C2218yescomplemented
17C11×#534C511yesmaximal, characteristic, complemented, Hall
18C23×C11⋊C5—24no—
19C23×C11⋊C5—42no—
20C23×C11⋊C5—44no—
21C23×C11⋊C5D414yescomplemented
22C23×C11⋊C5C2314yes—
23C23×C11⋊C5C2312yes—
24C23×C11⋊C5C2311yescharacteristic
25D4×C11⋊C5—28no—
26D4×C11⋊C5—28no—
27D4×C11⋊C5—44no—
28C2×C4×C11⋊C5—24no—
29C2×C4×C11⋊C5—42no—
30C2×C4×C11⋊C5C2314yes—
31C2×C4×C11⋊C5C2314yes—
32C22×D4×C11C2×C512yescomplemented
33C11×#123C2×C514yescomplemented
34C11×#121C2×C514yescomplemented
35C11×#120C2×C514yescomplemented
36C2×C11×C22⋊C4C2×C511yescharacteristic, complemented
37C5×#534—111nomaximal, Hall
38C22×C11⋊C5—22no—
39C22×C11⋊C5—24no—
40C22×C11⋊C5—24no—
41C22×C11⋊C5—28no—
42C22×C11⋊C5—44no—
43C22×C11⋊C5—48no—
44C22×C11⋊C5C2×D414yes—
45C22×C11⋊C5C2×D412yes—
46C22×C11⋊C5C2411yescharacteristic
47C4×C11⋊C5—24no—
48C4×C11⋊C5—24no—
49C24×C11C22×C511yescharacteristic
50C24×C11C22×C512yescomplemented
51C2×D4×C11—28no—
52C2×D4×C11C22×C514yes—
53C2×D4×C11C22×C514yescomplemented
54C2×D4×C11C22×C514yescomplemented
55C22×C4×C11C22×C512yescomplemented
56C22×C4×C11C22×C512yescomplemented
57C11×C4⋊C4C22×C514yescomplemented
58C11×C22⋊C4C22×C514yescomplemented
59C11×C22⋊C4C22×C518yescomplemented
60C22×C5×D4—112no—
61C5×#123—114no—
62C5×#121—114no—
63C5×#120—114no—
64C2×C5×C22⋊C4—111no—
65C2×C11⋊C5—24no—
66C2×C11⋊C5—22no—
67C2×C11⋊C5—44no—
68C2×C11⋊C5C22×D411yescharacteristic
69C2×C11⋊C5H(5,𝔽2)12yes—
70C23×C11—24no—
71C23×C11—42no—
72C23×C11—44no—
73C23×C11C5×D414yescomplemented
74C23×C11C23×C514yes—
75C23×C11C23×C512yes—
76C23×C11C23×C511yescharacteristic
77D4×C11—28no—
78D4×C11—28no—
79D4×C11—44no—
80C2×C4×C11—24no—
81C2×C4×C11—42no—
82C2×C4×C11C23×C514yes—
83C2×C4×C11C23×C514yes—
84C24×C5—111no—
85C24×C5—112no—
86C2×C5×D4—114no—
87C2×C5×D4—114no—
88C2×C5×D4—114no—
89C2×C5×D4—228no—
90C22×C4×C5—112no—
91C22×C4×C5—112no—
92C5×C4⋊C4—114no—
93C5×C22⋊C4—114no—
94C5×C22⋊C4—118no—
95#534C11⋊C511yescharacteristic, direct product factor, Sylow
96C11⋊C5#53411yescharacteristic, direct product factor, Hall
97C22×C11—22no—
98C22×C11—24no—
99C22×C11—24no—
100C22×C11—28no—
101C22×C11—44no—
102C22×C11—48no—
103C22×C11C2×C5×D414yes—
104C22×C11C2×C5×D412yes—
105C22×C11C24×C511yescharacteristic
106C4×C11—24no—
107C4×C11—24no—
108C23×C5—114no—
109C23×C5—112no—
110C23×C5—111no—
111C23×C5—114no—
112C23×C5—224no—
113C23×C5—442no—
114C23×C5—444no—
115C5×D4—228no—
116C5×D4—228no—
117C5×D4—444no—
118C2×C4×C5—114no—
119C2×C4×C5—114no—
120C2×C4×C5—224no—
121C2×C4×C5—442no—
122C22×D4C2×C11⋊C512yescomplemented
123#123C2×C11⋊C514yescomplemented
124#121C2×C11⋊C514yescomplemented
125#120C2×C11⋊C514yescomplemented
126C2×C22⋊C4C2×C11⋊C511yescharacteristic, complemented
127C2×C11—24no—
128C2×C11—22no—
129C2×C11—44no—
130C2×C11C22×C5×D411yescharacteristic
131C2×C11C5×H(5,𝔽2)12yes—
132C22×C5—114no—
133C22×C5—112no—
134C22×C5—111no—
135C22×C5—222no—
136C22×C5—224no—
137C22×C5—224no—
138C22×C5—228no—
139C22×C5—444no—
140C22×C5—448no—
141C4×C5—224no—
142C4×C5—224no—
143C24C22×C11⋊C511yescharacteristic
144C24C22×C11⋊C512yescomplemented
145C2×D4—28no—
146C2×D4C22×C11⋊C514yes—
147C2×D4C22×C11⋊C514yescomplemented
148C2×D4C22×C11⋊C514yescomplemented
149C22×C4C22×C11⋊C512yescomplemented
150C22×C4C22×C11⋊C512yescomplemented
151C4⋊C4C22×C11⋊C514yescomplemented
152C22⋊C4C22×C11⋊C514yescomplemented
153C22⋊C4C22×C11⋊C518yescomplemented
154C11C5×#53411yescharacteristic, complemented, Sylow
155C2×C5—111no—
156C2×C5—112no—
157C2×C5—224no—
158C2×C5—222no—
159C2×C5—444no—
160C23—24no—
161C23—42no—
162C23—44no—
163C23D4×C11⋊C514yescomplemented
164C23C23×C11⋊C514yes—
165C23C23×C11⋊C512yes—
166C23C23×C11⋊C511yescharacteristic
167D4—28no—
168D4—28no—
169D4—44no—
170C2×C4—24no—
171C2×C4—42no—
172C2×C4C23×C11⋊C514yes—
173C2×C4C23×C11⋊C514yes—
174C5—111noSylow
175C22—22no—
176C22—24no—
177C22—24no—
178C22—28no—
179C22—44no—
180C22—48no—
181C22C2×D4×C11⋊C514yes—
182C22C2×D4×C11⋊C512yes—
183C22C24×C11⋊C511yescharacteristic
184C4—24no—
185C4—24no—
186C2—24no—
187C2—22no—
188C2—44no—
189C2C22×D4×C11⋊C511yescharacteristic
190C2H(5,𝔽2)×C11⋊C512yes—
subgroupG/H
center, FrattiniC22C24×C11⋊C5
commutator, socle, cosocleC22×C11C24×C5
FittingC11×#534C5
hypercenter#534C11⋊C5
hypocenterC11C5×#534
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C22×D4×C11⋊C5C2semidirect
2. #123×C11⋊C5C2semidirect
3. #121×C11⋊C5C2semidirect
4. #120×C11⋊C5C2semidirect
5. C2×C22⋊C4×C11⋊C5C2semidirect
7. C24×C11⋊C5C22semidirect
10. C2×D4×C11⋊C5C22semidirect
11. C2×D4×C11⋊C5C22semidirect
12. C22×C4×C11⋊C5C22semidirect
13. C22×C4×C11⋊C5C22semidirect
14. C4⋊C4×C11⋊C5C22semidirect
15. C22⋊C4×C11⋊C5C22semidirect
16. C22⋊C4×C11⋊C5C22semidirect
17. C11×#534C5semidirect
21. C23×C11⋊C5D4semidirect
32. C22×D4×C11C2×C5semidirect
33. C11×#123C2×C5semidirect
34. C11×#121C2×C5semidirect
35. C11×#120C2×C5semidirect
36. C2×C11×C22⋊C4C2×C5semidirect
50. C24×C11C22×C5semidirect
53. C2×D4×C11C22×C5semidirect
54. C2×D4×C11C22×C5semidirect
55. C22×C4×C11C22×C5semidirect
56. C22×C4×C11C22×C5semidirect
57. C11×C4⋊C4C22×C5semidirect
58. C11×C22⋊C4C22×C5semidirect
59. C11×C22⋊C4C22×C5semidirect
73. C23×C11C5×D4semidirect
95. #534C11⋊C5direct (N × H)
96. C11⋊C5#534direct (N × H)
122. C22×D4C2×C11⋊C5semidirect
123. #123C2×C11⋊C5semidirect
124. #121C2×C11⋊C5semidirect
125. #120C2×C11⋊C5semidirect
126. C2×C22⋊C4C2×C11⋊C5semidirect
144. C24C22×C11⋊C5semidirect
147. C2×D4C22×C11⋊C5semidirect
148. C2×D4C22×C11⋊C5semidirect
149. C22×C4C22×C11⋊C5semidirect
150. C22×C4C22×C11⋊C5semidirect
151. C4⋊C4C22×C11⋊C5semidirect
152. C22⋊C4C22×C11⋊C5semidirect
153. C22⋊C4C22×C11⋊C5semidirect
154. C11C5×#534semidirect
163. C23D4×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C11⋊C52
#123×C11⋊C52
#121×C11⋊C52
#120×C11⋊C52
C2×C22⋊C4×C11⋊C52
C11×#5345
C5×#53411