Finite Group Databasebeta

← #13098934

Subgroups — #13098934

Order 1600.

642 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 139 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
2C2×D4×D25C212yesmaximal, complemented
3C22×D100C211yesmaximal, characteristic, complemented
4C25×#121C211yesmaximal, characteristic, complemented
5#11716502C211yesmaximal, characteristic, complemented
6#11716499C212yesmaximal, complemented
7C4×C22⋊D25C211yesmaximal, characteristic, complemented
8#11716457C211yesmaximal, characteristic, complemented
9#11716455C211yesmaximal, characteristic, complemented
10#11716446C212yesmaximal, complemented
11#11716444C212yesmaximal, complemented
12C23×D25C2212yescomplemented
13C23×D25C2212yescomplemented
14C2×D4×C25C2212yescomplemented
15C2×D4×C25C2211yescharacteristic, complemented
16C22×C4×C25C2211yescharacteristic, complemented
17C2×C22⋊D25C2211yescharacteristic
18C2×C22⋊D25C2212yescomplemented
19C2×C22⋊D25C2212yescomplemented
20C2×C22⋊D25C2212yescomplemented
21D4×D25—28no—
22D4×D25—24no—
23C2×D100—24no—
24C2×D100C2211yescharacteristic
25C2×D100C2212yescomplemented
26C2×D100C2212yescomplemented
27C2×D100C2211yescharacteristic, complemented
28C2×C4×D25C2212yescomplemented
29C2×C4×D25C2211yescharacteristic, complemented
30C4⋊C4×C25C2211yescharacteristic, complemented
31C22⋊C4×C25C2212yescomplemented
32C22⋊Dic25C2211yescharacteristic, complemented
33#87720C2211yescharacteristic, complemented
34#87720C2212yescomplemented
35#87720C2212yescomplemented
36#87718C2211yescharacteristic, complemented
37C4×Dic25C2211yescharacteristic, complemented
38#65943—51nomaximal
39C23×C25C2312yes—
40C23×C25C2311yescharacteristic
41C22×D25—24no—
42C22×D25—24no—
43C22×D25—24no—
44C22×D25—24no—
45C22×D25—42no—
46C22×D25—42no—
47C22×D25C2312yes—
48C22×D25C2312yes—
49C22×D25C2311yescharacteristic
50D4×C25—24no—
51D4×C25—22no—
52C2×C4×C25—22no—
53C2×C4×C25C2311yescharacteristic
54C2×C4×C25C2312yes—
55C2×C4×C25C2311yescharacteristic
56C22⋊D25—24no—
57C22⋊D25—24no—
58C22⋊D25—42no—
59C22⋊D25D414yescomplemented
60C2×Dic25C2311yescharacteristic
61C2×Dic25C2311yescharacteristic
62C2×Dic25C2311yescharacteristic
63D100—24no—
64D100—24no—
65D100—22no—
66D100D414yescomplemented
67C4×D25—22no—
68C4×D25—24no—
69C2×D4×D5—52no—
70C2×D4×D5—51no—
71C22×D20—51no—
72C5×#121D511yescharacteristic
73#4086—51no—
74#4083—52no—
75C4×C22⋊D5—51no—
76#4041—51no—
77#4039—51no—
78#4030—52no—
79#4028—52no—
80C22×C25—21no—
81C22×C25—21no—
82C22×C25—22no—
83C22×C25—22no—
84C22×C25—22no—
85C22×C25C2×D412yescomplemented
86C22×C25C2411yescharacteristic
87C2×D25—21no—
88C2×D25—22no—
89C2×D25—22no—
90C2×D25—21no—
91C2×D25—22no—
92C2×D25—22no—
93C2×D25—22no—
94C2×D25—48no—
95C2×D25—48no—
96C2×D25C2×D412yescomplemented
97C2×D25C2×D414yescomplemented
98C4×C25—22no—
99C4×C25—21no—
100C4×C25C2×D412yescomplemented
101Dic25—21no—
102Dic25—21no—
103Dic25C2×D412yescomplemented
104C23×D5—52no—
105C23×D5—52no—
106C2×C5×D4C2×D512yes—
107C2×C5×D4C2×D511yescharacteristic
108C22×C4×C5C2×D511yescharacteristic
109C2×C22⋊D5—51no—
110C2×C22⋊D5—52no—
111C2×C22⋊D5—52no—
112C2×C22⋊D5—52no—
113D4×D5—104no—
114D4×D5—108no—
115C2×D20—51no—
116C2×D20—52no—
117C2×D20—51no—
118C2×D20—52no—
119C2×D20—104no—
120C2×C4×D5—52no—
121C2×C4×D5—51no—
122C5×C4⋊C4C2×D511yescharacteristic
123C5×C22⋊C4C2×D512yes—
124C22⋊Dic5—51no—
125#685—51no—
126#685—52no—
127#685—52no—
128#683—51no—
129C4×Dic5—51no—
130D42—251noSylow
131C2×C25—22no—
132C2×C25—42no—
133C2×C25C22×D411yescharacteristic
134C2×C25C22×D411yescharacteristic
135C2×C25H(5,𝔽2)11yescharacteristic
136D25—22no—
137D25—24no—
138D25—42no—
139C23×C5C22×D512yes—
140C23×C5C22×D511yescharacteristic
141C22×D5—52no—
142C22×D5—51no—
143C22×D5—52no—
144C22×D5—104no—
145C22×D5—104no—
146C22×D5—104no—
147C22×D5—104no—
148C22×D5—202no—
149C22×D5—202no—
150C5×D4—24no—
151C5×D4—22no—
152C2×C4×C5—22no—
153C2×C4×C5C22×D511yescharacteristic
154C2×C4×C5C22×D512yes—
155C2×C4×C5C22×D511yescharacteristic
156C22⋊D5—54no—
157C22⋊D5—104no—
158C22⋊D5—104no—
159C22⋊D5—202no—
160C2×Dic5—51no—
161C2×Dic5—51no—
162C2×Dic5—51no—
163D20—54no—
164D20—104no—
165D20—104no—
166D20—102no—
167C4×D5—104no—
168C4×D5—102no—
169C22×D4—252no—
170C22×D4—251no—
171C22×D4—251no—
172#127—251no—
173#121—251no—
174#121—252no—
175#121D2511yescharacteristic, complemented
176#120—252no—
177#120—252no—
178C4×D4—251no—
179C4×D4—251no—
180C25D4211yescharacteristic, complemented, Sylow
181C22×C5—21no—
182C22×C5—21no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—22no—
186C22×C5D4×D512yes—
187C22×C5C23×D511yescharacteristic
188C2×D5—54no—
189C2×D5—52no—
190C2×D5—102no—
191C2×D5—101no—
192C2×D5—102no—
193C2×D5—101no—
194C2×D5—102no—
195C2×D5—102no—
196C2×D5—102no—
197C2×D5—208no—
198C2×D5—208no—
199C4×C5—22no—
200C4×C5—21no—
201C4×C5D4×D512yes—
202Dic5—52no—
203Dic5—101no—
204Dic5—101no—
205C24—252no—
206C24—252no—
207C2×D4—251no—
208C2×D4—252no—
209C2×D4—252no—
210C2×D4—252no—
211C2×D4—251no—
212C2×D4—252no—
213C2×D4—252no—
214C2×D4—251no—
215C2×D4—504no—
216C2×D4—508no—
217C2×D4—504no—
218C2×D4C2×D2512yescomplemented
219C2×D4C2×D2511yescharacteristic, complemented
220C22×C4—252no—
221C22×C4—251no—
222C22×C4C2×D2511yescharacteristic, complemented
223C4⋊C4—251no—
224C4⋊C4C2×D2511yescharacteristic, complemented
225C22⋊C4—251no—
226C22⋊C4—252no—
227C22⋊C4—251no—
228C22⋊C4—252no—
229C22⋊C4C2×D2512yescomplemented
230C42—251no—
231C2×C5—22no—
232C2×C5—42no—
233C2×C5C2×D4×D511yescharacteristic
234C2×C5C2×D4×D511yescharacteristic
235C2×C5#414911yescharacteristic
236D5—104no—
237D5—102no—
238D5—202no—
239C23—251no—
240C23—252no—
241C23—252no—
242C23—504no—
243C23—504no—
244C23—504no—
245C23—504no—
246C23—1002no—
247C23—1002no—
248C23C22×D2512yes—
249C23C22×D2511yescharacteristic
250D4—24no—
251D4—22no—
252D4—254no—
253D4—254no—
254D4—504no—
255D4—504no—
256D4—504no—
257D4—504no—
258D4—502no—
259D4—1002no—
260C2×C4—22no—
261C2×C4—251no—
262C2×C4—251no—
263C2×C4—251no—
264C2×C4—504no—
265C2×C4—502no—
266C2×C4C22×D2512yes—
267C2×C4C22×D2511yescharacteristic
268C2×C4C22×D2511yescharacteristic
269C5#6594311yescharacteristic
270C22—21no—
271C22—21no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—252no—
276C22—254no—
277C22—502no—
278C22—501no—
279C22—502no—
280C22—501no—
281C22—502no—
282C22—502no—
283C22—502no—
284C22—1008no—
285C22—1008no—
286C22D4×D2512yescomplemented
287C22C23×D2511yescharacteristic
288C4—21no—
289C4—22no—
290C4—252no—
291C4—501no—
292C4—501no—
293C4D4×D2512yescomplemented
294C2—22no—
295C2—42no—
296C2—504no—
297C2—502no—
298C2—1002no—
299C2C2×D4×D2511yescharacteristic
300C2C2×D4×D2511yescharacteristic
301C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25D42
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. C2×D4×D25C2semidirect
3. C22×D100C2semidirect
4. C25×#121C2semidirect
5. #11716502C2semidirect
6. #11716499C2semidirect
7. C4×C22⋊D25C2semidirect
8. #11716457C2semidirect
9. #11716455C2semidirect
10. #11716446C2semidirect
11. #11716444C2semidirect
12. C23×D25C22semidirect
13. C23×D25C22semidirect
14. C2×D4×C25C22semidirect
15. C2×D4×C25C22semidirect
16. C22×C4×C25C22semidirect
18. C2×C22⋊D25C22semidirect
19. C2×C22⋊D25C22semidirect
20. C2×C22⋊D25C22semidirect
25. C2×D100C22semidirect
26. C2×D100C22semidirect
27. C2×D100C22semidirect
28. C2×C4×D25C22semidirect
29. C2×C4×D25C22semidirect
30. C4⋊C4×C25C22semidirect
31. C22⋊C4×C25C22semidirect
32. C22⋊Dic25C22semidirect
33. #87720C22semidirect
34. #87720C22semidirect
35. #87720C22semidirect
36. #87718C22semidirect
37. C4×Dic25C22semidirect
59. C22⋊D25D4semidirect
66. D100D4semidirect
85. C22×C25C2×D4semidirect
96. C2×D25C2×D4semidirect
97. C2×D25C2×D4semidirect
100. C4×C25C2×D4semidirect
103. Dic25C2×D4semidirect
175. #121D25semidirect
180. C25D42semidirect
218. C2×D4C2×D25semidirect
219. C2×D4C2×D25semidirect
222. C22×C4C2×D25semidirect
224. C4⋊C4C2×D25semidirect
229. C22⋊C4C2×D25semidirect
286. C22D4×D25semidirect
293. C4D4×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×#1212
#117165022
#117164992
C4×C22⋊D252
#117164572
#117164552
#117164462
#117164442
#659435