Finite Group Databasebeta

← #13098924

Subgroups — #13098924

Order 1600.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 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#11716501C211yesmaximal, characteristic, complemented
6#11716500C211yesmaximal, characteristic, complemented
7#11716497C211yesmaximal, characteristic, complemented
8#11716491C211yesmaximal, characteristic, complemented
9C4×C22⋊D25C211yesmaximal, characteristic, complemented
10#11716456C211yesmaximal, characteristic, complemented
11#11716451C211yesmaximal, characteristic, complemented
12#11716446C211yesmaximal, characteristic, complemented
13#11716445C211yesmaximal, characteristic, complemented
14#11716443C211yesmaximal, characteristic, complemented
15#11716439C211yesmaximal, characteristic, complemented
16C2×D4×C25C2211yescharacteristic
17C2×D4×C25C2211yescharacteristic
18C2×D4×C25C2211yescharacteristic
19C22×C4×C25C2211yescharacteristic
20C2×C22⋊D25C2211yescharacteristic
21C2×C22⋊D25C2211yescharacteristic
22C2×C22⋊D25C2211yescharacteristic
23C2×C22⋊D25C2211yescharacteristic
24C2×C22⋊D25C2211yescharacteristic
25C2×C22⋊D25C2211yescharacteristic
26C22×Dic25C2211yescharacteristic
27C22×Dic25C2211yescharacteristic
28C2×D100C2211yescharacteristic
29C2×C4×D25C2211yescharacteristic
30C2×C4×D25C2211yescharacteristic
31C4⋊C4×C25C2211yescharacteristic
32C22⋊C4×C25C2211yescharacteristic
33C22⋊C4×C25C2211yescharacteristic
34C22⋊Dic25C2211yescharacteristic
35C22⋊Dic25C2211yescharacteristic
36C22⋊Dic25C2211yescharacteristic
37C22⋊Dic25C2211yescharacteristic
38#87720C2211yescharacteristic
39#87720C2211yescharacteristic
40#87720C2211yescharacteristic
41#87720C2211yescharacteristic
42C4⋊Dic25C2211yescharacteristic
43#87718C2211yescharacteristic
44#87718C2211yescharacteristic
45#87718C2211yescharacteristic
46#87718C2211yescharacteristic
47#87718C2211yescharacteristic
48#87718C2211yescharacteristic
49C4×Dic25C2211yescharacteristic
50C4×Dic25C2211yescharacteristic
51#65949—51nomaximal
52C23×C25C2311yescharacteristic
53C23×C25C2311yescharacteristic
54C23×C25C2311yescharacteristic
55C22×D25C2311yescharacteristic
56C22×D25C2311yescharacteristic
57D4×C25—41no—
58D4×C25—41no—
59D4×C25—41no—
60C2×C4×C25—41no—
61C2×C4×C25C2311yescharacteristic
62C2×C4×C25C2311yescharacteristic
63C2×C4×C25C2311yescharacteristic
64C2×C4×C25C2311yescharacteristic
65C22⋊D25—22no—
66C22⋊D25—22no—
67C22⋊D25—41no—
68C22⋊D25—41no—
69C22⋊D25—41no—
70C22⋊D25—41no—
71C2×Dic25—22no—
72C2×Dic25—41no—
73C2×Dic25C2311yescharacteristic
74C2×Dic25C2311yescharacteristic
75C2×Dic25C2311yescharacteristic
76C2×Dic25C2311yescharacteristic
77C2×Dic25C2311yescharacteristic
78C2×Dic25C2311yescharacteristic
79D100—41no—
80C4×D25—41no—
81C4×D25—41no—
82C5×#121D511yescharacteristic
83#4086—51no—
84#4085—51no—
85#4085—51no—
86#4085—51no—
87#4084—51no—
88#4081—51no—
89#4075—51no—
90C4×C22⋊D5—51no—
91#4040—51no—
92#4035—51no—
93#4030—51no—
94#4029—51no—
95#4027—51no—
96#4023—51no—
97C22×C25—21no—
98C22×C25—21no—
99C22×C25—21no—
100C22×C25—21no—
101C22×C25—21no—
102C22×C25—21no—
103C22×C25—21no—
104C22×C25—21no—
105C22×C25—21no—
106C22×C25C2411yescharacteristic
107C2×D25—21no—
108C2×D25—21no—
109C2×D25—21no—
110C2×D25—21no—
111C2×D25—21no—
112C2×D25—21no—
113C4×C25—21no—
114C4×C25—21no—
115C4×C25—21no—
116C4×C25—21no—
117Dic25—21no—
118Dic25—21no—
119Dic25—21no—
120Dic25—21no—
121Dic25—21no—
122Dic25#4112yes—
123C2×C5×D4C2×D511yescharacteristic
124C2×C5×D4C2×D511yescharacteristic
125C2×C5×D4C2×D511yescharacteristic
126C22×C4×C5C2×D511yescharacteristic
127C2×C22⋊D5—51no—
128C2×C22⋊D5—51no—
129C2×C22⋊D5—51no—
130C2×C22⋊D5—51no—
131C2×C22⋊D5—51no—
132C2×C22⋊D5—51no—
133C22×Dic5—51no—
134C22×Dic5—51no—
135C2×D20—51no—
136C2×C4×D5—51no—
137C2×C4×D5—51no—
138C5×C4⋊C4C2×D511yescharacteristic
139C5×C22⋊C4C2×D511yescharacteristic
140C5×C22⋊C4C2×D511yescharacteristic
141C22⋊Dic5—51no—
142C22⋊Dic5—51no—
143C22⋊Dic5—51no—
144C22⋊Dic5—51no—
145#685—51no—
146#685—51no—
147#685—51no—
148#685—51no—
149C4⋊Dic5—51no—
150#683—51no—
151#683—51no—
152#683—51no—
153#683—51no—
154#683—51no—
155#683—51no—
156C4×Dic5—51no—
157C4×Dic5—51no—
158#540—251noSylow
159C2×C25—41no—
160C2×C25—41no—
161C2×C25—41no—
162C2×C25C2×#4111yescharacteristic
163C2×C25H(5,𝔽2)11yescharacteristic
164C2×C25H(5,𝔽2)11yescharacteristic
165D25—41no—
166D25—41no—
167C23×C5C22×D511yescharacteristic
168C23×C5C22×D511yescharacteristic
169C23×C5C22×D511yescharacteristic
170C22×D5—51no—
171C22×D5—51no—
172C5×D4—41no—
173C5×D4—41no—
174C5×D4—41no—
175C2×C4×C5—41no—
176C2×C4×C5C22×D511yescharacteristic
177C2×C4×C5C22×D511yescharacteristic
178C2×C4×C5C22×D511yescharacteristic
179C2×C4×C5C22×D511yescharacteristic
180C22⋊D5—102no—
181C22⋊D5—102no—
182C22⋊D5—201no—
183C22⋊D5—201no—
184C22⋊D5—201no—
185C22⋊D5—201no—
186C2×Dic5—51no—
187C2×Dic5—51no—
188C2×Dic5—51no—
189C2×Dic5—51no—
190C2×Dic5—51no—
191C2×Dic5—51no—
192C2×Dic5—102no—
193C2×Dic5—201no—
194D20—201no—
195C4×D5—201no—
196C4×D5—201no—
197#127—251no—
198#125—251no—
199#123—251no—
200#123—251no—
201#123—251no—
202#123—251no—
203#121—251no—
204#121—251no—
205#121—251no—
206#121—251no—
207#121—251no—
208#121D2511yescharacteristic, complemented
209C4×D4—251no—
210C4×D4—251no—
211#117—251no—
212C25#54011yescharacteristic, complemented, Sylow
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5C23×D511yescharacteristic
223C2×D5—101no—
224C2×D5—101no—
225C2×D5—101no—
226C2×D5—101no—
227C2×D5—101no—
228C2×D5—101no—
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233Dic5—52no—
234Dic5—101no—
235Dic5—101no—
236Dic5—101no—
237Dic5—101no—
238Dic5—101no—
239C2×D4—251no—
240C2×D4—251no—
241C2×D4—251no—
242C2×D4—251no—
243C2×D4—251no—
244C2×D4—251no—
245C2×D4—251no—
246C2×D4C2×D2511yescharacteristic
247C2×D4C2×D2511yescharacteristic
248C2×D4C2×D2511yescharacteristic
249C22×C4—251no—
250C22×C4—251no—
251C22×C4—251no—
252C22×C4—251no—
253C22×C4C2×D2511yescharacteristic
254C4⋊C4—251no—
255C4⋊C4—251no—
256C4⋊C4—251no—
257C4⋊C4—251no—
258C4⋊C4—251no—
259C4⋊C4—251no—
260C4⋊C4—251no—
261C4⋊C4C2×D2511yescharacteristic
262C22⋊C4—251no—
263C22⋊C4—251no—
264C22⋊C4—251no—
265C22⋊C4—251no—
266C22⋊C4—251no—
267C22⋊C4—251no—
268C22⋊C4—251no—
269C22⋊C4—251no—
270C22⋊C4C2×D2511yescharacteristic
271C22⋊C4C2×D2511yescharacteristic
272C42—251no—
273C42—251no—
274C2×C5—41no—
275C2×C5—41no—
276C2×C5—41no—
277C2×C5#414411yescharacteristic
278C2×C5#414411yescharacteristic
279C2×C5D5×#4111yescharacteristic
280D5—201no—
281D5—201no—
282C23—251no—
283C23—251no—
284C23C22×D2511yescharacteristic
285C23C22×D2511yescharacteristic
286C23C22×D2511yescharacteristic
287D4—41no—
288D4—41no—
289D4—41no—
290D4—502no—
291D4—502no—
292D4—1001no—
293D4—1001no—
294D4—1001no—
295D4—1001no—
296D4—1001no—
297C2×C4—41no—
298C2×C4—251no—
299C2×C4—251no—
300C2×C4—251no—
301C2×C4—251no—
302C2×C4—251no—
303C2×C4—251no—
304C2×C4—502no—
305C2×C4—1001no—
306C2×C4—1001no—
307C2×C4—1001no—
308C2×C4C22×D2511yescharacteristic
309C2×C4C22×D2511yescharacteristic
310C2×C4C22×D2511yescharacteristic
311C2×C4C22×D2511yescharacteristic
312C5#6594911yescharacteristic
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—501no—
323C22—501no—
324C22—501no—
325C22—501no—
326C22—501no—
327C22—501no—
328C22C23×D2511yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—252no—
334C4—501no—
335C4—501no—
336C4—501no—
337C4—501no—
338C4—501no—
339C2—41no—
340C2—41no—
341C2—41no—
342C2—1001no—
343C2—1001no—
344C2#1171656311yescharacteristic
345C2#1171656311yescharacteristic
346C2#41×D2511yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#540
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. #11716501C2semidirect
6. #11716500C2semidirect
7. #11716497C2semidirect
8. #11716491C2semidirect
9. C4×C22⋊D25C2semidirect
10. #11716456C2semidirect
11. #11716451C2semidirect
12. #11716446C2semidirect
13. #11716445C2semidirect
14. #11716443C2semidirect
15. #11716439C2semidirect
208. #121D25semidirect
212. C25#540semidirect

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
#117164972
#117164912
C4×C22⋊D252
#117164562
#117164512
#117164462
#117164452
#117164432
#117164392
#659495