Finite Group Databasebeta

← #13098930

Subgroups — #13098930

Order 1600.

519 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 519 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×D4×D25C212yesmaximal, complemented
2C25×#121C211yesmaximal, characteristic, complemented
3#11716501C212yesmaximal, complemented
4#11716499C212yesmaximal, complemented
5#11716492C211yesmaximal, characteristic, complemented
6C2×#87720C211yesmaximal, characteristic, complemented
7#11716456C212yesmaximal, complemented
8#11716445C212yesmaximal, complemented
9#11716444C212yesmaximal, complemented
10C23×D25C2211yescharacteristic
11C23×D25C2212yescomplemented
12C2×D4×C25C2212yescomplemented
13C2×D4×C25C2211yescharacteristic, complemented
14C22×C4×C25C2211yescharacteristic, complemented
15C2×C22⋊D25C2212yes—
16C2×C22⋊D25C2212yescomplemented
17C2×C22⋊D25C2212yescomplemented
18C22×Dic25C2211yescharacteristic, complemented
19D4×D25—28no—
20C2×D100C2212yes—
21C2×D100C2211yescharacteristic, complemented
22C2×C4×D25C2212yescomplemented
23C4⋊C4×C25C2211yescharacteristic, complemented
24C22⋊C4×C25C2212yescomplemented
25C22⋊Dic25C2212yescomplemented
26#87720C2212yescomplemented
27#87720C2212yescomplemented
28#87720C2212yescomplemented
29#87720C2212yescomplemented
30C4⋊Dic25C2211yescharacteristic, complemented
31#87718C2212yescomplemented
32#65939—51nomaximal
33C23×C25C2312yes—
34C23×C25C2311yescharacteristic
35C22×D25—24no—
36C22×D25—41no—
37C22×D25—41no—
38C22×D25—42no—
39C22×D25—42no—
40C22×D25D414yescomplemented
41C22×D25C2312yes—
42C22×D25C2312yes—
43D4×C25—24no—
44D4×C25—41no—
45C2×C4×C25—41no—
46C2×C4×C25C2312yes—
47C2×C4×C25C2311yescharacteristic
48C2×C4×C25C2311yescharacteristic
49C22⋊D25—24no—
50C22⋊D25—24no—
51C22⋊D25—42no—
52C2×Dic25—41no—
53C2×Dic25C2312yes—
54C2×Dic25C2312yes—
55D100—24no—
56D100—41no—
57C4×D25—24no—
58C2×D4×D5—52no—
59C5×#121D511yescharacteristic
60#4085—52no—
61#4083—52no—
62#4076—51no—
63C2×#685—51no—
64#4040—52no—
65#4029—52no—
66#4028—52no—
67C22×C25—21no—
68C22×C25—21no—
69C22×C25—22no—
70C22×C25—22no—
71C22×C25—22no—
72C22×C25C2×D412yes—
73C22×C25C2411yescharacteristic
74C2×D25—22no—
75C2×D25—22no—
76C2×D25—22no—
77C2×D25—22no—
78C2×D25—22no—
79C2×D25—44no—
80C2×D25—48no—
81C2×D25C2×D414yes—
82C4×C25—22no—
83C4×C25—21no—
84C4×C25—21no—
85Dic25—22no—
86Dic25—22no—
87C23×D5—51no—
88C23×D5—52no—
89C2×C5×D4C2×D512yes—
90C2×C5×D4C2×D511yescharacteristic
91C22×C4×C5C2×D511yescharacteristic
92C2×C22⋊D5—52no—
93C2×C22⋊D5—52no—
94C2×C22⋊D5—52no—
95C22×Dic5—51no—
96D4×D5—108no—
97C2×D20—52no—
98C2×D20—51no—
99C2×C4×D5—52no—
100C5×C4⋊C4C2×D511yescharacteristic
101C5×C22⋊C4C2×D512yes—
102C22⋊Dic5—52no—
103#685—52no—
104#685—52no—
105#685—52no—
106#685—52no—
107C4⋊Dic5—51no—
108#683—52no—
109#534—251noSylow
110C2×C25—22no—
111C2×C25—42no—
112C2×C25C22×D411yescharacteristic
113C2×C25H(5,𝔽2)11yescharacteristic
114C2×C25H(5,𝔽2)11yescharacteristic
115D25—24no—
116D25—42no—
117C23×C5C22×D512yes—
118C23×C5C22×D511yescharacteristic
119C22×D5—52no—
120C22×D5—54no—
121C22×D5—52no—
122C22×D5—104no—
123C22×D5—201no—
124C22×D5—202no—
125C22×D5—201no—
126C22×D5—202no—
127C5×D4—24no—
128C5×D4—41no—
129C2×C4×C5—41no—
130C2×C4×C5C22×D512yes—
131C2×C4×C5C22×D511yescharacteristic
132C2×C4×C5C22×D511yescharacteristic
133C22⋊D5—104no—
134C22⋊D5—104no—
135C22⋊D5—202no—
136C2×Dic5—52no—
137C2×Dic5—52no—
138C2×Dic5—201no—
139D20—104no—
140D20—201no—
141C4×D5—104no—
142C22×D4—252no—
143#123—252no—
144#123—252no—
145#121—252no—
146#121—251no—
147#121D2511yescharacteristic, complemented
148#120—252no—
149#120—252no—
150C2×C22⋊C4—251no—
151C25#53411yescharacteristic, complemented, Sylow
152C22×C5—21no—
153C22×C5—21no—
154C22×C5—22no—
155C22×C5—22no—
156C22×C5—22no—
157C22×C5D4×D512yes—
158C22×C5C23×D511yescharacteristic
159C2×D5—54no—
160C2×D5—102no—
161C2×D5—102no—
162C2×D5—102no—
163C2×D5—102no—
164C2×D5—102no—
165C2×D5—204no—
166C2×D5—208no—
167C4×C5—22no—
168C4×C5—21no—
169C4×C5—21no—
170Dic5—102no—
171Dic5—102no—
172C24—251no—
173C24—252no—
174C2×D4—252no—
175C2×D4—252no—
176C2×D4—252no—
177C2×D4—252no—
178C2×D4—251no—
179C2×D4—508no—
180C2×D4C2×D2512yescomplemented
181C2×D4C2×D2511yescharacteristic, complemented
182C22×C4—251no—
183C22×C4—252no—
184C22×C4C2×D2511yescharacteristic, complemented
185C4⋊C4—252no—
186C4⋊C4—251no—
187C4⋊C4C2×D2511yescharacteristic, complemented
188C22⋊C4—252no—
189C22⋊C4—252no—
190C22⋊C4—252no—
191C22⋊C4—252no—
192C22⋊C4—252no—
193C22⋊C4C2×D2512yescomplemented
194C2×C5—22no—
195C2×C5—42no—
196C2×C5C2×D4×D511yescharacteristic
197C2×C5#414411yescharacteristic
198C2×C5#414911yescharacteristic
199D5—104no—
200D5—202no—
201C23—252no—
202C23—254no—
203C23—252no—
204C23—504no—
205C23—1001no—
206C23—1001no—
207C23—1002no—
208C23—1002no—
209C23C22×D2512yes—
210C23C22×D2511yescharacteristic
211D4—24no—
212D4—41no—
213D4—504no—
214D4—504no—
215D4—504no—
216D4—1001no—
217D4—1002no—
218C2×C4—41no—
219C2×C4—252no—
220C2×C4—252no—
221C2×C4—504no—
222C2×C4—1001no—
223C2×C4C22×D2511yescharacteristic
224C2×C4C22×D2511yescharacteristic
225C2×C4C22×D2512yes—
226C5#6593911yescharacteristic
227C22—21no—
228C22—21no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—254no—
233C22—502no—
234C22—502no—
235C22—502no—
236C22—502no—
237C22—502no—
238C22—1004no—
239C22—1008no—
240C22D4×D2512yes—
241C22C23×D2511yescharacteristic
242C4—22no—
243C4—21no—
244C4—21no—
245C4—502no—
246C4—502no—
247C2—22no—
248C2—42no—
249C2—504no—
250C2—1002no—
251C2C2×D4×D2511yescharacteristic
252C2#1171656311yescharacteristic
253C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#534
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D25C2semidirect
2. C25×#121C2semidirect
3. #11716501C2semidirect
4. #11716499C2semidirect
5. #11716492C2semidirect
6. C2×#87720C2semidirect
7. #11716456C2semidirect
8. #11716445C2semidirect
9. #11716444C2semidirect
11. C23×D25C22semidirect
12. C2×D4×C25C22semidirect
13. C2×D4×C25C22semidirect
14. C22×C4×C25C22semidirect
16. C2×C22⋊D25C22semidirect
17. C2×C22⋊D25C22semidirect
18. C22×Dic25C22semidirect
21. C2×D100C22semidirect
22. C2×C4×D25C22semidirect
23. C4⋊C4×C25C22semidirect
24. C22⋊C4×C25C22semidirect
25. C22⋊Dic25C22semidirect
26. #87720C22semidirect
27. #87720C22semidirect
28. #87720C22semidirect
29. #87720C22semidirect
30. C4⋊Dic25C22semidirect
31. #87718C22semidirect
40. C22×D25D4semidirect
147. #121D25semidirect
151. C25#534semidirect
180. C2×D4C2×D25semidirect
181. C2×D4C2×D25semidirect
184. C22×C4C2×D25semidirect
187. C4⋊C4C2×D25semidirect
193. C22⋊C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D252
C25×#1212
#117165012
#117164992
#117164922
C2×#877202
#117164562
#117164452
#117164442
#659395