Finite Group Databasebeta

← #121×D25 #13098929

Subgroups — #121×D25 #13098929

Order 1600.

639 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 639 conjugacy classes of subgroups — too many to draw. Only its 145 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
2C2×D4×D25C211yesmaximal, characteristic, complemented
3C22×C4×D25C211yesmaximal, characteristic, complemented
4C25×#121C211yesmaximal, characteristic, complemented
5#11716501C212yesmaximal, complemented
6#11716500C211yesmaximal, characteristic, complemented
7#11716492C211yesmaximal, characteristic, complemented
8#11716457C211yesmaximal, characteristic, complemented
9C4⋊C4×D25C211yesmaximal, characteristic, complemented
10#11716446C212yesmaximal, complemented
11C22⋊C4×D25C212yesmaximal, complemented
12C23×D25C2212yes—
13C23×D25C2211yescharacteristic
14C2×D4×C25C2211yescharacteristic, complemented
15C2×D4×C25C2212yescomplemented
16C22×C4×C25C2211yescharacteristic, complemented
17C2×C22⋊D25C2212yescomplemented
18C2×C22⋊D25C2212yescomplemented
19C2×C22⋊D25C2212yescomplemented
20C22×Dic25C2211yescharacteristic, complemented
21D4×D25—28no—
22D4×D25—24no—
23C2×D100C2212yescomplemented
24C2×D100C2211yescharacteristic, complemented
25C2×C4×D25—24no—
26C2×C4×D25C2211yescharacteristic
27C2×C4×D25C2212yes—
28C2×C4×D25C2211yescharacteristic
29C2×C4×D25C2211yescharacteristic, complemented
30C2×C4×D25C2211yescharacteristic, complemented
31C4⋊C4×C25C2211yescharacteristic, complemented
32C22⋊C4×C25C2212yescomplemented
33C22⋊Dic25C2212yescomplemented
34#87720C2212yescomplemented
35#87720C2212yescomplemented
36C4⋊Dic25C2211yescharacteristic, complemented
37#87718C2212yescomplemented
38D5×#121—51nomaximal
39C23×C25C2312yes—
40C23×C25C2311yescharacteristic
41C22×D25—22no—
42C22×D25—22no—
43C22×D25—24no—
44C22×D25—24no—
45C22×D25—24no—
46C22×D25D414yescomplemented
47C22×D25C2312yes—
48C22×D25C2311yescharacteristic
49C22×D25C2311yescharacteristic
50D4×C25—24no—
51D4×C25—22no—
52C2×C4×C25—22no—
53C2×C4×C25C2312yes—
54C2×C4×C25C2311yescharacteristic
55C2×C4×C25C2311yescharacteristic
56C22⋊D25—24no—
57C22⋊D25—24no—
58C22⋊D25—24no—
59C2×Dic25—22no—
60C2×Dic25C2312yes—
61C2×Dic25C2311yescharacteristic
62C2×Dic25C2311yescharacteristic
63D100—24no—
64D100—22no—
65C4×D25—22no—
66C4×D25—24no—
67C4×D25—22no—
68C4×D25—22no—
69C4×D25D414yescomplemented
70C2×D4×D5—51no—
71C2×D4×D5—52no—
72C22×C4×D5—51no—
73C5×#121D511yescharacteristic
74#4085—52no—
75#4084—51no—
76#4076—51no—
77#4041—51no—
78D5×C4⋊C4—51no—
79#4030—52no—
80D5×C22⋊C4—52no—
81C22×C25—21no—
82C22×C25—21no—
83C22×C25—22no—
84C22×C25—22no—
85C22×C25—22no—
86C22×C25C2×D412yescomplemented
87C22×C25C2411yescharacteristic
88C2×D25—21no—
89C2×D25—21no—
90C2×D25—28no—
91C2×D25—22no—
92C2×D25—22no—
93C2×D25—22no—
94C2×D25—48no—
95C2×D25C2×D412yes—
96C2×D25C2×D412yes—
97C2×D25C2×D412yescomplemented
98C2×D25#4112yes—
99C4×C25—21no—
100C4×C25—22no—
101C4×C25C2×D412yescomplemented
102Dic25—21no—
103Dic25—22no—
104Dic25C2×D412yescomplemented
105C23×D5—51no—
106C23×D5—52no—
107C2×C5×D4C2×D511yescharacteristic
108C2×C5×D4C2×D512yes—
109C22×C4×C5C2×D511yescharacteristic
110C2×C22⋊D5—52no—
111C2×C22⋊D5—52no—
112C2×C22⋊D5—52no—
113C22×Dic5—51no—
114D4×D5—104no—
115D4×D5—108no—
116C2×D20—52no—
117C2×D20—51no—
118C2×C4×D5—51no—
119C2×C4×D5—51no—
120C2×C4×D5—51no—
121C2×C4×D5—51no—
122C2×C4×D5—52no—
123C2×C4×D5—104no—
124C5×C4⋊C4C2×D511yescharacteristic
125C5×C22⋊C4C2×D512yes—
126C22⋊Dic5—52no—
127#685—52no—
128#685—52no—
129C4⋊Dic5—51no—
130#683—52no—
131C2×#121—251noSylow
132C2×C25—22no—
133C2×C25—42no—
134C2×C25C22×D411yescharacteristic
135C2×C25C22×D411yescharacteristic
136C2×C25C2×#4111yescharacteristic
137D25—22no—
138D25—42no—
139D25#12114yesdirect product factor
140C23×C5C22×D512yes—
141C23×C5C22×D511yescharacteristic
142C22×D5—51no—
143C22×D5—54no—
144C22×D5—51no—
145C22×D5—52no—
146C22×D5—102no—
147C22×D5—102no—
148C22×D5—104no—
149C22×D5—104no—
150C22×D5—104no—
151C5×D4—24no—
152C5×D4—22no—
153C2×C4×C5—22no—
154C2×C4×C5C22×D512yes—
155C2×C4×C5C22×D511yescharacteristic
156C2×C4×C5C22×D511yescharacteristic
157C22⋊D5—104no—
158C22⋊D5—104no—
159C22⋊D5—104no—
160C2×Dic5—51no—
161C2×Dic5—52no—
162C2×Dic5—51no—
163C2×Dic5—102no—
164D20—104no—
165D20—102no—
166C4×D5—54no—
167C4×D5—102no—
168C4×D5—102no—
169C4×D5—104no—
170C4×D5—102no—
171C22×D4—251no—
172C22×D4—252no—
173C23×C4—251no—
174#121—251no—
175#121—252no—
176#121—251no—
177#121—251no—
178#121—252no—
179#121D2511yescharacteristic, direct product factor
180C2×C4⋊C4—251no—
181C2×C22⋊C4—252no—
182C25C2×#12111yescharacteristic, complemented, Sylow
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—22no—
186C22×C5—22no—
187C22×C5—22no—
188C22×C5D4×D512yes—
189C22×C5C23×D511yescharacteristic
190C2×D5—52no—
191C2×D5—52no—
192C2×D5—52no—
193C2×D5—52no—
194C2×D5—108no—
195C2×D5—101no—
196C2×D5—101no—
197C2×D5—102no—
198C2×D5—102no—
199C2×D5—102no—
200C2×D5—208no—
201C4×C5—21no—
202C4×C5—22no—
203C4×C5D4×D512yes—
204Dic5—52no—
205Dic5—101no—
206Dic5—102no—
207C24—251no—
208C24—252no—
209C2×D4—252no—
210C2×D4—252no—
211C2×D4—252no—
212C2×D4—252no—
213C2×D4—251no—
214C2×D4—504no—
215C2×D4—508no—
216C2×D4C2×D2512yescomplemented
217C2×D4C2×D2511yescharacteristic, complemented
218C22×C4—251no—
219C22×C4—251no—
220C22×C4—251no—
221C22×C4—252no—
222C22×C4—251no—
223C22×C4—251no—
224C22×C4—504no—
225C22×C4C2×D2511yescharacteristic, complemented
226C4⋊C4—252no—
227C4⋊C4—251no—
228C4⋊C4C2×D2511yescharacteristic, complemented
229C22⋊C4—252no—
230C22⋊C4—252no—
231C22⋊C4—252no—
232C22⋊C4C2×D2512yescomplemented
233C2×C5—22no—
234C2×C5—42no—
235C2×C5C2×D4×D511yescharacteristic
236C2×C5C2×D4×D511yescharacteristic
237C2×C5D5×#4111yescharacteristic
238D5—54no—
239D5—102no—
240D5—202no—
241C23—251no—
242C23—254no—
243C23—251no—
244C23—252no—
245C23—502no—
246C23—502no—
247C23—504no—
248C23—504no—
249C23—504no—
250C23C22×D2512yes—
251C23C22×D2511yescharacteristic
252D4—24no—
253D4—22no—
254D4—504no—
255D4—504no—
256D4—504no—
257D4—504no—
258D4—502no—
259C2×C4—22no—
260C2×C4—251no—
261C2×C4—254no—
262C2×C4—251no—
263C2×C4—252no—
264C2×C4—502no—
265C2×C4—502no—
266C2×C4—504no—
267C2×C4—502no—
268C2×C4—502no—
269C2×C4C22×D2511yescharacteristic
270C2×C4C22×D2512yes—
271C2×C4C22×D2511yescharacteristic
272C5D5×#12111yescharacteristic
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—22no—
278C22—252no—
279C22—252no—
280C22—252no—
281C22—252no—
282C22—508no—
283C22—501no—
284C22—501no—
285C22—502no—
286C22—502no—
287C22—502no—
288C22—1008no—
289C22D4×D2512yescomplemented
290C22C23×D2511yescharacteristic
291C4—21no—
292C4—22no—
293C4—252no—
294C4—501no—
295C4—502no—
296C4D4×D2512yescomplemented
297C2—22no—
298C2—42no—
299C2—254no—
300C2—502no—
301C2—1002no—
302C2C2×D4×D2511yescharacteristic
303C2C2×D4×D2511yescharacteristic
304C2#41×D2511yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25C2×#121
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×C4×D25C2semidirect
4. C25×#121C2semidirect
5. #11716501C2semidirect
6. #11716500C2semidirect
7. #11716492C2semidirect
8. #11716457C2semidirect
9. C4⋊C4×D25C2semidirect
10. #11716446C2semidirect
11. C22⋊C4×D25C2semidirect
14. C2×D4×C25C22semidirect
15. C2×D4×C25C22semidirect
16. C22×C4×C25C22semidirect
17. C2×C22⋊D25C22semidirect
18. C2×C22⋊D25C22semidirect
19. C2×C22⋊D25C22semidirect
20. C22×Dic25C22semidirect
23. C2×D100C22semidirect
24. C2×D100C22semidirect
29. C2×C4×D25C22semidirect
30. C2×C4×D25C22semidirect
31. C4⋊C4×C25C22semidirect
32. C22⋊C4×C25C22semidirect
33. C22⋊Dic25C22semidirect
34. #87720C22semidirect
35. #87720C22semidirect
36. C4⋊Dic25C22semidirect
37. #87718C22semidirect
46. C22×D25D4semidirect
69. C4×D25D4semidirect
86. C22×C25C2×D4semidirect
97. C2×D25C2×D4semidirect
101. C4×C25C2×D4semidirect
104. Dic25C2×D4semidirect
139. D25#121direct (N × H)
179. #121D25direct (N × H)
182. C25C2×#121semidirect
216. C2×D4C2×D25semidirect
217. C2×D4C2×D25semidirect
225. C22×C4C2×D25semidirect
228. C4⋊C4C2×D25semidirect
232. C22⋊C4C2×D25semidirect
289. C22D4×D25semidirect
296. 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×C4×D252
C25×#1212
#117165012
#117165002
#117164922
#117164572
C4⋊C4×D252
#117164462
C22⋊C4×D252
D5×#1215