Finite Group Databasebeta

← #13098980

Subgroups — #13098980

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×D25C211yesmaximal, characteristic, complemented
2C22×D100C211yesmaximal, characteristic, complemented
3C25×#123C211yesmaximal, characteristic, complemented
4#11716499C211yesmaximal, characteristic, complemented
5#11716491C211yesmaximal, characteristic, complemented
6#11716457C212yesmaximal, complemented
7#11716456C212yesmaximal, complemented
8#11716446C212yesmaximal, complemented
9#11716444C212yesmaximal, complemented
10#11716444C211yesmaximal, characteristic, complemented
11C22⋊C4×D25C211yesmaximal, characteristic, complemented
12C23×D25C2211yescharacteristic
13C23×D25C2211yescharacteristic, complemented
14C23×D25C2211yescharacteristic, complemented
15C2×D4×C25C2211yescharacteristic
16C22×C4×C25C2211yescharacteristic, complemented
17C2×C22⋊D25C2211yescharacteristic
18C2×C22⋊D25C2211yescharacteristic, complemented
19C2×C22⋊D25C2212yescomplemented
20D4×D25—24no—
21C2×D100—24no—
22C2×D100C2212yes—
23C2×D100C2212yescomplemented
24C2×D100C2211yescharacteristic, complemented
25C2×D100C2212yescomplemented
26C2×C4×D25C2211yescharacteristic, complemented
27C2×C4×D25C2212yescomplemented
28C4⋊C4×C25C2212yescomplemented
29C22⋊C4×C25C2211yescharacteristic, complemented
30C22⋊C4×C25C2212yescomplemented
31C22⋊Dic25C2211yescharacteristic, complemented
32#87720C2212yescomplemented
33#87720C2212yescomplemented
34#87720C2212yescomplemented
35#87720C2212yescomplemented
36#87718C2212yescomplemented
37#65987—51nomaximal
38C23×C25C2311yescharacteristic
39C23×C25C2311yescharacteristic
40C22×D25—22no—
41C22×D25—22no—
42C22×D25—42no—
43C22×D25—42no—
44C22×D25—42no—
45C22×D25D414yescomplemented
46C22×D25C2312yes—
47C22×D25C2311yescharacteristic
48C22×D25C2311yescharacteristic
49C22×D25C2311yescharacteristic
50D4×C25—22no—
51C2×C4×C25—22no—
52C2×C4×C25C2312yes—
53C2×C4×C25C2312yes—
54C2×C4×C25C2311yescharacteristic
55C22⋊D25—22no—
56C22⋊D25—22no—
57C22⋊D25—42no—
58C2×Dic25C2311yescharacteristic
59C2×Dic25C2312yes—
60D100—24no—
61D100—24no—
62D100—22no—
63D100—42no—
64C4×D25—22no—
65C4×D25—42no—
66C2×D4×D5—51no—
67C22×D20—51no—
68C5×#123D511yescharacteristic
69#4083—51no—
70#4075—51no—
71#4041—52no—
72#4040—52no—
73#4030—52no—
74#4028—52no—
75#4028—51no—
76D5×C22⋊C4—51no—
77C22×C25—22no—
78C22×C25—21no—
79C22×C25—22no—
80C22×C25C2×D412yes—
81C22×C25C2411yescharacteristic
82C2×D25—22no—
83C2×D25—22no—
84C2×D25—22no—
85C2×D25—21no—
86C2×D25—22no—
87C2×D25—22no—
88C2×D25—22no—
89C2×D25—44no—
90C2×D25—44no—
91C2×D25—44no—
92C2×D25C2×D412yes—
93C2×D25C2×D412yes—
94C4×C25—21no—
95C4×C25—22no—
96C4×C25—22no—
97Dic25—21no—
98Dic25—22no—
99C23×D5—51no—
100C23×D5—51no—
101C23×D5—51no—
102C2×C5×D4C2×D511yescharacteristic
103C22×C4×C5C2×D511yescharacteristic
104C2×C22⋊D5—51no—
105C2×C22⋊D5—51no—
106C2×C22⋊D5—52no—
107D4×D5—104no—
108C2×D20—52no—
109C2×D20—52no—
110C2×D20—51no—
111C2×D20—52no—
112C2×D20—104no—
113C2×C4×D5—51no—
114C2×C4×D5—52no—
115C5×C4⋊C4C2×D512yes—
116C5×C22⋊C4C2×D511yescharacteristic
117C5×C22⋊C4C2×D512yes—
118C22⋊Dic5—51no—
119#685—52no—
120#685—52no—
121#685—52no—
122#685—52no—
123#683—52no—
124#534—251noSylow
125C2×C25—22no—
126C2×C25—41no—
127C2×C25C22×D411yescharacteristic
128C2×C25H(5,𝔽2)12yes—
129D25—22no—
130D25—22no—
131D25—42no—
132D25—41no—
133C23×C5C22×D511yescharacteristic
134C23×C5C22×D511yescharacteristic
135C22×D5—51no—
136C22×D5—51no—
137C22×D5—54no—
138C22×D5—52no—
139C22×D5—51no—
140C22×D5—102no—
141C22×D5—102no—
142C22×D5—202no—
143C22×D5—202no—
144C22×D5—202no—
145C5×D4—22no—
146C2×C4×C5—22no—
147C2×C4×C5C22×D512yes—
148C2×C4×C5C22×D512yes—
149C2×C4×C5C22×D511yescharacteristic
150C22⋊D5—102no—
151C22⋊D5—102no—
152C22⋊D5—202no—
153C2×Dic5—51no—
154C2×Dic5—52no—
155D20—104no—
156D20—104no—
157D20—102no—
158D20—202no—
159C4×D5—102no—
160C4×D5—202no—
161C22×D4—251no—
162C22×D4—251no—
163#123—251no—
164#123—252no—
165#123D2511yescharacteristic, complemented
166#121—252no—
167#121—252no—
168#120—251no—
169#120—252no—
170#120—251no—
171C2×C22⋊C4—251no—
172C25#53411yescharacteristic, complemented, Sylow
173C22×C5—22no—
174C22×C5—21no—
175C22×C5—22no—
176C22×C5D4×D512yes—
177C22×C5C23×D511yescharacteristic
178C2×D5—52no—
179C2×D5—52no—
180C2×D5—102no—
181C2×D5—102no—
182C2×D5—102no—
183C2×D5—101no—
184C2×D5—102no—
185C2×D5—102no—
186C2×D5—102no—
187C2×D5—204no—
188C2×D5—204no—
189C2×D5—204no—
190C4×C5—21no—
191C4×C5—22no—
192C4×C5—22no—
193Dic5—101no—
194Dic5—102no—
195C24—251no—
196C24—251no—
197C24—251no—
198C2×D4—251no—
199C2×D4—251no—
200C2×D4—252no—
201C2×D4—252no—
202C2×D4—251no—
203C2×D4—252no—
204C2×D4—252no—
205C2×D4—504no—
206C2×D4—504no—
207C2×D4C2×D2511yescharacteristic
208C22×C4—251no—
209C22×C4—252no—
210C22×C4C2×D2511yescharacteristic, complemented
211C4⋊C4—252no—
212C4⋊C4C2×D2512yescomplemented
213C22⋊C4—251no—
214C22⋊C4—252no—
215C22⋊C4—252no—
216C22⋊C4—252no—
217C22⋊C4—252no—
218C22⋊C4C2×D2511yescharacteristic, complemented
219C22⋊C4C2×D2512yescomplemented
220C2×C5—22no—
221C2×C5—41no—
222C2×C5C2×D4×D511yescharacteristic
223C2×C5#414912yes—
224D5—102no—
225D5—102no—
226D5—202no—
227D5—201no—
228C23—251no—
229C23—251no—
230C23—254no—
231C23—251no—
232C23—252no—
233C23—502no—
234C23—502no—
235C23—1002no—
236C23—1002no—
237C23—1002no—
238C23C22×D2511yescharacteristic
239C23C22×D2511yescharacteristic
240D4—22no—
241D4—504no—
242D4—504no—
243D4—502no—
244D4—502no—
245D4—502no—
246D4—1002no—
247D4—1002no—
248C2×C4—22no—
249C2×C4—252no—
250C2×C4—251no—
251C2×C4—502no—
252C2×C4—1002no—
253C2×C4C22×D2512yes—
254C2×C4C22×D2511yescharacteristic
255C2×C4C22×D2512yes—
256C5#6598711yescharacteristic
257C22—22no—
258C22—21no—
259C22—22no—
260C22—252no—
261C22—252no—
262C22—502no—
263C22—502no—
264C22—502no—
265C22—501no—
266C22—502no—
267C22—502no—
268C22—502no—
269C22—1004no—
270C22—1004no—
271C22—1004no—
272C22D4×D2512yes—
273C22C23×D2511yescharacteristic
274C4—22no—
275C4—21no—
276C4—22no—
277C4—501no—
278C4—502no—
279C2—22no—
280C2—41no—
281C2—502no—
282C2—502no—
283C2—1002no—
284C2—1001no—
285C2C2×D4×D2511yescharacteristic
286C2#1171656812yes—
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#123C2
hypercenter#123D25
hypocenterC25#534
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×D4×D25C2semidirect
2. C22×D100C2semidirect
3. C25×#123C2semidirect
4. #11716499C2semidirect
5. #11716491C2semidirect
6. #11716457C2semidirect
7. #11716456C2semidirect
8. #11716446C2semidirect
9. #11716444C2semidirect
10. #11716444C2semidirect
11. C22⋊C4×D25C2semidirect
13. C23×D25C22semidirect
14. C23×D25C22semidirect
16. C22×C4×C25C22semidirect
18. C2×C22⋊D25C22semidirect
19. C2×C22⋊D25C22semidirect
23. C2×D100C22semidirect
24. C2×D100C22semidirect
25. C2×D100C22semidirect
26. C2×C4×D25C22semidirect
27. C2×C4×D25C22semidirect
28. C4⋊C4×C25C22semidirect
29. C22⋊C4×C25C22semidirect
30. C22⋊C4×C25C22semidirect
31. C22⋊Dic25C22semidirect
32. #87720C22semidirect
33. #87720C22semidirect
34. #87720C22semidirect
35. #87720C22semidirect
36. #87718C22semidirect
45. C22×D25D4semidirect
165. #123D25semidirect
172. C25#534semidirect
210. C22×C4C2×D25semidirect
212. C4⋊C4C2×D25semidirect
218. C22⋊C4C2×D25semidirect
219. 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
C22×D1002
C25×#1232
#117164992
#117164912
#117164572
#117164562
#117164462
#117164442
C22⋊C4×D252
#659875