Finite Group Databasebeta

← C2×#11717039 #13106145

Subgroups — C2×#11717039 #13106145

Order 1600.

1584 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 264 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×D52C211yesmaximal, characteristic
2C22×C4×C5⋊D5C211yesmaximal, characteristic, complemented
3C22×#6036C211yesmaximal, characteristic, complemented
4C2×C5×#685C212yesmaximal, complemented
5C2×#87778C212yesmaximal, complemented
6#11717039C218yesmaximal, direct product factor
7C23×C5⋊D5C2211yescharacteristic
8C23×C5×D5C2212yes—
9C22×D52—24no—
10C22×D52—24no—
11C22×D52C418yescomplemented
12C22×D52C2214yes—
13C22×C4×C52C2211yescharacteristic, complemented
14C22×#1039C2211yescharacteristic, complemented
15C2×C4×C5⋊D5—24no—
16C2×C4×C5⋊D5C2214yescomplemented
17C22×C5×Dic5C2212yescomplemented
18C2×#6036—24no—
19C2×#6036C2214yescomplemented
20C5×#685C2218yescomplemented
21#87778C2218yescomplemented
22C2×D5×C22⋊C4—52nomaximal
23C23×C52C2311yescharacteristic
24C22×C5⋊D5C2×C414yes—
25C22×C5⋊D5D414yes—
26C22×C5⋊D5D414yes—
27C22×C5⋊D5C2312yes—
28C22×C5×D5—24no—
29C22×C5×D5—24no—
30C22×C5×D5C2×C418yescomplemented
31C22×C5×D5C2314yes—
32C2×D52—232no—
33C2×D52—28no—
34C2×D52—28no—
35C2×D52C2×C4116yescomplemented
36C2×C4×C52—22no—
37C2×C4×C52C2312yescomplemented
38C2×#1039—22no—
39C2×#1039C2312yescomplemented
40C4×C5⋊D5—28no—
41C2×C5×Dic5—24no—
42C2×C5×Dic5C2314yescomplemented
43#6036—28no—
44C24×D5—52no—
45C22×C4×D5—52no—
46C22×C4×D5—52no—
47C22×C4×D5—102no—
48C2×C5×C22⋊C4—52no—
49C2×C22⋊Dic5—52no—
50C2×#685—52no—
51C2×#685D512yescomplemented
52D5×C22⋊C4—516no—
53C22×C52C22×C412yes—
54C22×C52C2×D412yes—
55C22×C52C2×D412yes—
56C22×C52C2411yescharacteristic
57C2×C5⋊D5C22⋊C4116yescomplemented
58C2×C5⋊D5C22×C414yes—
59C2×C5⋊D5C2×D414yes—
60C2×C5⋊D5C2×D414yes—
61C2×C5×D5—216no—
62C2×C5×D5—24no—
63C2×C5×D5—24no—
64C2×C5×D5C22×C418yescomplemented
65D52—232no—
66C4×C52—22no—
67#1039—22no—
68C5×Dic5—24no—
69C24×C5—52no—
70C23×D5—52no—
71C23×D5—516no—
72C23×D5—58no—
73C23×D5—102no—
74C23×D5—108no—
75C23×D5—108no—
76C23×D5C2×D512yes—
77C22×C4×C5—22no—
78C22×C4×C5—52no—
79C22×C4×C5C2×D512yescomplemented
80C22×Dic5—52no—
81C22×Dic5—102no—
82C22×Dic5C2×D512yescomplemented
83C2×C4×D5—58no—
84C2×C4×D5—58no—
85C2×C4×D5—108no—
86C2×C4×D5—108no—
87C2×C4×D5—108no—
88C2×C4×D5—1016no—
89C5×C22⋊C4—58no—
90C22⋊Dic5—58no—
91#685—58no—
92#685C2×D518yescomplemented
93C22×C22⋊C4—251noSylow
94C2×C52C2×C22⋊C414yescomplemented
95C2×C52C23×C411yescharacteristic
96C2×C52C22×D411yescharacteristic
97C2×C52C22×D411yescharacteristic
98C5⋊D5C2×C22⋊C418yescomplemented
99C5×D5—28no—
100C23×C5—22no—
101C23×C5—58no—
102C23×C5—54no—
103C23×C5—104no—
104C23×C5—104no—
105C23×C5C22×D512yes—
106C22×D5—24no—
107C22×D5—24no—
108C22×D5—58no—
109C22×D5—58no—
110C22×D5—58no—
111C22×D5—54no—
112C22×D5—532no—
113C22×D5—108no—
114C22×D5—108no—
115C22×D5—108no—
116C22×D5—104no—
117C22×D5—1016no—
118C22×D5—1016no—
119C22×D5—1064no—
120C22×D5C4×D518yescomplemented
121C22×D5C22×D514yes—
122C2×C4×C5—28no—
123C2×C4×C5—24no—
124C2×C4×C5—24no—
125C2×C4×C5—54no—
126C2×C4×C5—104no—
127C2×C4×C5C22×D514yescomplemented
128C2×Dic5—24no—
129C2×Dic5—54no—
130C2×Dic5—104no—
131C2×Dic5—108no—
132C2×Dic5—104no—
133C2×Dic5C22×D514yescomplemented
134C4×D5—1016no—
135C4×D5—1016no—
136C4×D5—1032no—
137C25—251no—
138C23×C4—251no—
139C23×C4—251no—
140C2×C22⋊C4—52no—
141C2×C22⋊C4—258no—
142C2×C22⋊C4—252no—
143C52C22×C22⋊C411yescharacteristic, complemented, Sylow
144C22×C5—24no—
145C22×C5—24no—
146C22×C5—24no—
147C22×C5—22no—
148C22×C5—58no—
149C22×C5—104no—
150C22×C5—104no—
151C22×C5—1016no—
152C22×C5C2×C4×D514yes—
153C22×C5D4×D514yes—
154C22×C5D4×D514yes—
155C22×C5C23×D512yes—
156C2×D5—24no—
157C2×D5—24no—
158C2×D5—216no—
159C2×D5—58no—
160C2×D5—58no—
161C2×D5—58no—
162C2×D5—532no—
163C2×D5—1032no—
164C2×D5—108no—
165C2×D5—108no—
166C2×D5—108no—
167C2×D5—1064no—
168C2×D5C2×C4×D518yescomplemented
169C4×C5—28no—
170C4×C5—24no—
171C4×C5—104no—
172Dic5—24no—
173Dic5—108no—
174Dic5—104no—
175C24—52no—
176C24—254no—
177C24—258no—
178C24—251no—
179C24—504no—
180C24—504no—
181C22×C4—52no—
182C22×C4—254no—
183C22×C4—251no—
184C22×C4—254no—
185C22×C4—504no—
186C22×C4—504no—
187C22×C4D5211yescharacteristic, complemented
188C22⋊C4—58no—
189C22⋊C4—258no—
190C2×C5—22no—
191C2×C5—22no—
192C2×C5—22no—
193C2×C5—28no—
194C2×C5—108no—
195C2×C5D5×C22⋊C418yescomplemented
196C2×C5C22×C4×D512yes—
197C2×C5C2×D4×D512yes—
198C2×C5C2×D4×D512yes—
199D5—28no—
200D5—516no—
201D5—1016no—
202C23—58no—
203C23—54no—
204C23—104no—
205C23—104no—
206C23—2516no—
207C23—254no—
208C23—254no—
209C23—254no—
210C23—252no—
211C23—508no—
212C23—508no—
213C23—5032no—
214C23C2×D5211yescharacteristic
215C2×C4—22no—
216C2×C4—54no—
217C2×C4—104no—
218C2×C4—252no—
219C2×C4—508no—
220C2×C4—508no—
221C2×C4—502no—
222C2×C4C2×D5212yescomplemented
223C5—22no—
224C5C2×D5×C22⋊C412yescomplemented
225C22—58no—
226C22—104no—
227C22—104no—
228C22—1016no—
229C22—254no—
230C22—254no—
231C22—254no—
232C22—2516no—
233C22—5032no—
234C22C4×D5212yes—
235C22#8787712yes—
236C22#8788612yes—
237C22C22×D5211yescharacteristic
238C4—22no—
239C4—104no—
240C4—502no—
241C2—108no—
242C2—258no—
243C2#1171703914yesdirect product factor
244C2C2×C4×D5211yescharacteristic
245C2C2×#8787711yescharacteristic
246C2C2×#8788611yescharacteristic
subgroupG/H
centerC23C2×D52
commutatorC2×C52C23×C4
FrattiniC22C22×D52
FittingC22×C4×C52C22
socleC23×C52C23
prime radicalC23×D52C2
cosocleC22×C52C24
hypercenterC22×C4D52
hypocenterC52C22×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C5⋊D5C2semidirect
3. C22×#6036C2semidirect
4. C2×C5×#685C2semidirect
5. C2×#87778C2semidirect
6. #11717039C2direct (N × H)
11. C22×D52C4semidirect
13. C22×C4×C52C22semidirect
14. C22×#1039C22semidirect
16. C2×C4×C5⋊D5C22semidirect
17. C22×C5×Dic5C22semidirect
19. C2×#6036C22semidirect
20. C5×#685C22semidirect
21. #87778C22semidirect
30. C22×C5×D5C2×C4semidirect
35. C2×D52C2×C4semidirect
37. C2×C4×C52C23semidirect
39. C2×#1039C23semidirect
42. C2×C5×Dic5C23semidirect
51. C2×#685D5semidirect
57. C2×C5⋊D5C22⋊C4semidirect
64. C2×C5×D5C22×C4semidirect
79. C22×C4×C5C2×D5semidirect
82. C22×Dic5C2×D5semidirect
92. #685C2×D5semidirect
94. C2×C52C2×C22⋊C4semidirect
98. C5⋊D5C2×C22⋊C4semidirect
120. C22×D5C4×D5semidirect
127. C2×C4×C5C22×D5semidirect
133. C2×Dic5C22×D5semidirect
143. C52C22×C22⋊C4semidirect
168. C2×D5C2×C4×D5semidirect
187. C22×C4D52semidirect
195. C2×C5D5×C22⋊C4semidirect
222. C2×C4C2×D52semidirect
224. C5C2×D5×C22⋊C4semidirect
243. C2#11717039direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D522
C22×C4×C5⋊D52
C22×#60362
C2×C5×#6852
C2×#877782
#117170392
C2×D5×C22⋊C45