Finite Group Databasebeta

← #13098943

Subgroups — #13098943

Order 1600.

378 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×#121C211yesmaximal, characteristic, complemented
2#11716502C211yesmaximal, characteristic, complemented
3#11716501C211yesmaximal, characteristic, complemented
4#11716501C211yesmaximal, characteristic, complemented
5#11716500C211yesmaximal, characteristic, complemented
6#11716499C211yesmaximal, characteristic, complemented
7#11716499C211yesmaximal, characteristic, complemented
8#11716492C211yesmaximal, characteristic, complemented
9#11716491C211yesmaximal, characteristic, complemented
10#11716460C211yesmaximal, characteristic, complemented
11#11716456C211yesmaximal, characteristic, complemented
12#11716448C211yesmaximal, characteristic, complemented
13#11716446C211yesmaximal, characteristic, complemented
14#11716444C211yesmaximal, characteristic, complemented
15#11716441C211yesmaximal, characteristic, complemented
16C23×D25C2211yescharacteristic
17C2×D4×C25C2211yescharacteristic
18C2×D4×C25C2211yescharacteristic
19C2×D4×C25C2211yescharacteristic, complemented
20C22×C4×C25C2211yescharacteristic, complemented
21C2×C22⋊D25C2211yescharacteristic
22C2×C22⋊D25C2211yescharacteristic
23C2×C22⋊D25C2211yescharacteristic
24C2×C22⋊D25C2211yescharacteristic
25C2×C22⋊D25C2211yescharacteristic
26C2×C22⋊D25C2211yescharacteristic, complemented
27C2×C22⋊D25C2211yescharacteristic, complemented
28C22×Dic25C2211yescharacteristic, complemented
29C2×D100C2211yescharacteristic
30C2×D100C2211yescharacteristic
31C2×C4×D25C2211yescharacteristic, complemented
32C4⋊C4×C25C2211yescharacteristic, complemented
33C22⋊C4×C25C2211yescharacteristic
34C22⋊C4×C25C2211yescharacteristic, complemented
35C22⋊Dic25C2211yescharacteristic
36C22⋊Dic25C2211yescharacteristic
37C22⋊Dic25C2211yescharacteristic, complemented
38#87720C2211yescharacteristic
39#87720C2211yescharacteristic
40#87720C2211yescharacteristic
41#87720C2211yescharacteristic
42#87720C2211yescharacteristic
43#87720C2211yescharacteristic
44#87720C2211yescharacteristic, complemented
45C4⋊Dic25C2211yescharacteristic, complemented
46C4⋊Dic25C2211yescharacteristic, complemented
47#87718C2211yescharacteristic, complemented
48#87718C2211yescharacteristic, complemented
49#87718C2211yescharacteristic, complemented
50C4×Dic25C2211yescharacteristic, complemented
51#65954—51nomaximal
52C23×C25C2311yescharacteristic
53C23×C25C2311yescharacteristic
54C23×C25C2311yescharacteristic
55C22×D25—41no—
56C22×D25—41no—
57C22×D25—41no—
58C22×D25C2311yescharacteristic
59C22×D25C2311yescharacteristic
60C22×D25C2311yescharacteristic
61D4×C25—41no—
62D4×C25—41no—
63D4×C25—41no—
64C2×C4×C25—41no—
65C2×C4×C25C2311yescharacteristic
66C2×C4×C25C2311yescharacteristic
67C2×C4×C25C2311yescharacteristic
68C2×C4×C25C2311yescharacteristic
69C22⋊D25—41no—
70C22⋊D25—41no—
71C22⋊D25—41no—
72C22⋊D25—41no—
73C22⋊D25—41no—
74C22⋊D25—41no—
75C22⋊D25—41no—
76C2×Dic25—41no—
77C2×Dic25C2311yescharacteristic
78C2×Dic25C2311yescharacteristic
79C2×Dic25C2311yescharacteristic
80C2×Dic25C2311yescharacteristic
81C2×Dic25C2311yescharacteristic
82D100—41no—
83D100—41no—
84C4×D25—41no—
85C5×#121D511yescharacteristic
86#4086—51no—
87#4085—51no—
88#4085—51no—
89#4084—51no—
90#4083—51no—
91#4083—51no—
92#4076—51no—
93#4075—51no—
94#4044—51no—
95#4040—51no—
96#4032—51no—
97#4030—51no—
98#4028—51no—
99#4025—51no—
100C22×C25—21no—
101C22×C25—21no—
102C22×C25—21no—
103C22×C25—21no—
104C22×C25—21no—
105C22×C25—21no—
106C22×C25—21no—
107C22×C25—21no—
108C22×C25—21no—
109C22×C25C2411yescharacteristic
110C2×D25—21no—
111C2×D25—21no—
112C2×D25—21no—
113C2×D25—21no—
114C2×D25—21no—
115C2×D25—21no—
116C2×D25—21no—
117C2×D25—21no—
118C2×D25—21no—
119C2×D25—44no—
120C4×C25—21no—
121C4×C25—21no—
122C4×C25—21no—
123C4×C25—21no—
124Dic25—21no—
125Dic25—21no—
126Dic25—21no—
127Dic25—21no—
128Dic25—21no—
129C23×D5—51no—
130C2×C5×D4C2×D511yescharacteristic
131C2×C5×D4C2×D511yescharacteristic
132C2×C5×D4C2×D511yescharacteristic
133C22×C4×C5C2×D511yescharacteristic
134C2×C22⋊D5—51no—
135C2×C22⋊D5—51no—
136C2×C22⋊D5—51no—
137C2×C22⋊D5—51no—
138C2×C22⋊D5—51no—
139C2×C22⋊D5—51no—
140C2×C22⋊D5—51no—
141C22×Dic5—51no—
142C2×D20—51no—
143C2×D20—51no—
144C2×C4×D5—51no—
145C5×C4⋊C4C2×D511yescharacteristic
146C5×C22⋊C4C2×D511yescharacteristic
147C5×C22⋊C4C2×D511yescharacteristic
148C22⋊Dic5—51no—
149C22⋊Dic5—51no—
150C22⋊Dic5—51no—
151#685—51no—
152#685—51no—
153#685—51no—
154#685—51no—
155#685—51no—
156#685—51no—
157#685—51no—
158C4⋊Dic5—51no—
159C4⋊Dic5—51no—
160#683—51no—
161#683—51no—
162#683—51no—
163C4×Dic5—51no—
164#560—251noSylow
165C2×C25—41no—
166C2×C25—41no—
167C2×C25—41no—
168C2×C25H(5,𝔽2)11yescharacteristic
169C2×C25H(5,𝔽2)11yescharacteristic
170C2×C25H(5,𝔽2)11yescharacteristic
171D25—41no—
172D25—41no—
173D25—41no—
174C23×C5C22×D511yescharacteristic
175C23×C5C22×D511yescharacteristic
176C23×C5C22×D511yescharacteristic
177C22×D5—51no—
178C22×D5—51no—
179C22×D5—51no—
180C22×D5—201no—
181C22×D5—201no—
182C22×D5—201no—
183C5×D4—41no—
184C5×D4—41no—
185C5×D4—41no—
186C2×C4×C5—41no—
187C2×C4×C5C22×D511yescharacteristic
188C2×C4×C5C22×D511yescharacteristic
189C2×C4×C5C22×D511yescharacteristic
190C2×C4×C5C22×D511yescharacteristic
191C22⋊D5—201no—
192C22⋊D5—201no—
193C22⋊D5—201no—
194C22⋊D5—201no—
195C22⋊D5—201no—
196C22⋊D5—201no—
197C22⋊D5—201no—
198C2×Dic5—51no—
199C2×Dic5—51no—
200C2×Dic5—51no—
201C2×Dic5—51no—
202C2×Dic5—51no—
203C2×Dic5—201no—
204D20—201no—
205D20—201no—
206C4×D5—201no—
207#127—251no—
208#126—251no—
209#126—251no—
210#123—251no—
211#123—251no—
212#123—251no—
213#121—251no—
214#121—251no—
215#121—251no—
216#121—251no—
217#121—251no—
218#121D2511yescharacteristic, complemented
219#120—251no—
220#120—251no—
221#120—251no—
222C25#56011yescharacteristic, complemented, Sylow
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5C23×D511yescharacteristic
233C2×D5—101no—
234C2×D5—101no—
235C2×D5—101no—
236C2×D5—101no—
237C2×D5—101no—
238C2×D5—101no—
239C2×D5—101no—
240C2×D5—101no—
241C2×D5—101no—
242C2×D5—204no—
243C4×C5—21no—
244C4×C5—21no—
245C4×C5—21no—
246C4×C5—21no—
247Dic5—101no—
248Dic5—101no—
249Dic5—101no—
250Dic5—101no—
251Dic5—101no—
252C24—251no—
253C2×D4—251no—
254C2×D4—251no—
255C2×D4—251no—
256C2×D4—251no—
257C2×D4—251no—
258C2×D4—251no—
259C2×D4—251no—
260C2×D4—251no—
261C2×D4—251no—
262C2×D4C2×D2511yescharacteristic
263C2×D4C2×D2511yescharacteristic
264C2×D4C2×D2511yescharacteristic, complemented
265C22×C4—251no—
266C22×C4—251no—
267C22×C4C2×D2511yescharacteristic, complemented
268C4⋊C4—251no—
269C4⋊C4—251no—
270C4⋊C4—251no—
271C4⋊C4—251no—
272C4⋊C4—251no—
273C4⋊C4C2×D2511yescharacteristic, complemented
274C22⋊C4—251no—
275C22⋊C4—251no—
276C22⋊C4—251no—
277C22⋊C4—251no—
278C22⋊C4—251no—
279C22⋊C4—251no—
280C22⋊C4—251no—
281C22⋊C4—251no—
282C22⋊C4—251no—
283C22⋊C4—251no—
284C22⋊C4C2×D2511yescharacteristic
285C22⋊C4C2×D2511yescharacteristic, complemented
286C42—251no—
287C2×C5—41no—
288C2×C5—41no—
289C2×C5—41no—
290C2×C5#414411yescharacteristic
291C2×C5#414411yescharacteristic
292C2×C5#414911yescharacteristic
293D5—201no—
294D5—201no—
295D5—201no—
296C23—251no—
297C23—251no—
298C23—251no—
299C23—1001no—
300C23—1001no—
301C23—1001no—
302C23C22×D2511yescharacteristic
303C23C22×D2511yescharacteristic
304C23C22×D2511yescharacteristic
305D4—41no—
306D4—41no—
307D4—41no—
308D4—1001no—
309D4—1001no—
310D4—1001no—
311D4—1001no—
312D4—1001no—
313D4—1001no—
314D4—1001no—
315D4—1001no—
316D4—1001no—
317C2×C4—41no—
318C2×C4—251no—
319C2×C4—251no—
320C2×C4—251no—
321C2×C4—251no—
322C2×C4—251no—
323C2×C4—1001no—
324C2×C4—1001no—
325C2×C4C22×D2511yescharacteristic
326C2×C4C22×D2511yescharacteristic
327C2×C4C22×D2511yescharacteristic
328C2×C4C22×D2511yescharacteristic
329C5#6595411yescharacteristic
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—501no—
340C22—501no—
341C22—501no—
342C22—501no—
343C22—501no—
344C22—501no—
345C22—501no—
346C22—501no—
347C22—501no—
348C22—1004no—
349C22C23×D2511yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—501no—
355C4—501no—
356C4—501no—
357C4—501no—
358C4—501no—
359C2—41no—
360C2—41no—
361C2—41no—
362C2—1001no—
363C2—1001no—
364C2—1001no—
365C2#1171656311yescharacteristic
366C2#1171656311yescharacteristic
367C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#560
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C25×#121C2semidirect
2. #11716502C2semidirect
3. #11716501C2semidirect
4. #11716501C2semidirect
5. #11716500C2semidirect
6. #11716499C2semidirect
7. #11716499C2semidirect
8. #11716492C2semidirect
9. #11716491C2semidirect
10. #11716460C2semidirect
11. #11716456C2semidirect
12. #11716448C2semidirect
13. #11716446C2semidirect
14. #11716444C2semidirect
15. #11716441C2semidirect
19. C2×D4×C25C22semidirect
20. C22×C4×C25C22semidirect
26. C2×C22⋊D25C22semidirect
27. C2×C22⋊D25C22semidirect
28. C22×Dic25C22semidirect
31. C2×C4×D25C22semidirect
32. C4⋊C4×C25C22semidirect
34. C22⋊C4×C25C22semidirect
37. C22⋊Dic25C22semidirect
44. #87720C22semidirect
45. C4⋊Dic25C22semidirect
46. C4⋊Dic25C22semidirect
47. #87718C22semidirect
48. #87718C22semidirect
49. #87718C22semidirect
50. C4×Dic25C22semidirect
218. #121D25semidirect
222. C25#560semidirect
264. C2×D4C2×D25semidirect
267. C22×C4C2×D25semidirect
273. C4⋊C4C2×D25semidirect
285. C22⋊C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C25×#1212
#117165022
#117165012
#117165002
#117164992
#117164922
#117164912
#117164602
#117164562
#117164482
#117164462
#117164442
#117164412
#659545