Finite Group Databasebeta

← #13098935

Subgroups — #13098935

Order 1600.

501 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#87746C211yesmaximal, characteristic, complemented
2C2×D4×D25C211yesmaximal, characteristic, complemented
3C25×#121C211yesmaximal, characteristic, complemented
4#11716501C211yesmaximal, characteristic, complemented
5#11716499C211yesmaximal, characteristic, complemented
6#11716499C211yesmaximal, characteristic, complemented
7#11716497C211yesmaximal, characteristic, complemented
8C4×C22⋊D25C211yesmaximal, characteristic, complemented
9C2×#87720C211yesmaximal, characteristic, complemented
10#11716458C211yesmaximal, characteristic, complemented
11#11716456C211yesmaximal, characteristic, complemented
12#11716447C211yesmaximal, characteristic, complemented
13#11716446C211yesmaximal, characteristic, complemented
14#11716443C211yesmaximal, characteristic, complemented
15C22⋊C4×D25C211yesmaximal, characteristic, complemented
16C23×D25C2211yescharacteristic
17C23×D25C2211yescharacteristic
18C2×D4×C25C2211yescharacteristic
19C2×D4×C25C2211yescharacteristic, complemented
20C2×D4×C25C2211yescharacteristic, complemented
21C22×C4×C25C2211yescharacteristic, complemented
22C2×C22⋊D25C2211yescharacteristic
23C2×C22⋊D25C2211yescharacteristic
24C2×C22⋊D25C2211yescharacteristic
25C2×C22⋊D25C2211yescharacteristic, complemented
26C2×C22⋊D25C2211yescharacteristic, complemented
27C22×Dic25C2211yescharacteristic, complemented
28C22×Dic25C2211yescharacteristic, complemented
29#87746—24no—
30D4×D25—24no—
31C2×D100C2211yescharacteristic
32C2×C4×D25C2211yescharacteristic
33C2×C4×D25C2211yescharacteristic, complemented
34C2×C4×D25C2211yescharacteristic, complemented
35C2×Dic50C2211yescharacteristic, complemented
36C4⋊C4×C25C2211yescharacteristic, complemented
37C22⋊C4×C25C2211yescharacteristic, complemented
38C22⋊C4×C25C2211yescharacteristic, complemented
39C22⋊Dic25C2211yescharacteristic, complemented
40C22⋊Dic25C2211yescharacteristic, complemented
41C22⋊Dic25C2211yescharacteristic, complemented
42#87720C2211yescharacteristic
43#87720C2211yescharacteristic
44#87720C2211yescharacteristic
45#87720C2211yescharacteristic, complemented
46#87720C2211yescharacteristic, complemented
47#87720C2211yescharacteristic, complemented
48#87720C2211yescharacteristic, complemented
49#87718C2211yescharacteristic, complemented
50#87718C2211yescharacteristic, complemented
51#87718C2211yescharacteristic, complemented
52C4×Dic25C2211yescharacteristic, complemented
53#65944—51nomaximal
54C23×C25C2311yescharacteristic
55C23×C25C2311yescharacteristic
56C23×C25C2311yescharacteristic
57C22×D25—22no—
58C22×D25—22no—
59C22×D25—22no—
60C22×D25—22no—
61C22×D25—41no—
62C22×D25—41no—
63C22×D25C2311yescharacteristic
64C22×D25C2311yescharacteristic
65C22×D25C2311yescharacteristic
66D4×C25—22no—
67D4×C25—22no—
68D4×C25—41no—
69C2×C4×C25—41no—
70C2×C4×C25C2311yescharacteristic
71C2×C4×C25C2311yescharacteristic
72C2×C4×C25C2311yescharacteristic
73C2×C4×C25C2311yescharacteristic
74C22⋊D25—22no—
75C22⋊D25—22no—
76C22⋊D25—22no—
77C22⋊D25—41no—
78C22⋊D25D414yescomplemented
79C2×Dic25—22no—
80C2×Dic25—22no—
81C2×Dic25C2311yescharacteristic
82C2×Dic25C2311yescharacteristic
83C2×Dic25C2311yescharacteristic
84C2×Dic25C2311yescharacteristic
85C2×Dic25C2311yescharacteristic
86D100—22no—
87C4×D25—22no—
88C4×D25—22no—
89C4×D25—41no—
90Dic50—22no—
91C2×#711—51no—
92C2×D4×D5—51no—
93C5×#121D511yescharacteristic
94#4085—51no—
95#4083—51no—
96#4083—51no—
97#4081—51no—
98C4×C22⋊D5—51no—
99C2×#685—51no—
100#4042—51no—
101#4040—51no—
102#4031—51no—
103#4030—51no—
104#4027—51no—
105D5×C22⋊C4—51no—
106C22×C25—21no—
107C22×C25—21no—
108C22×C25—21no—
109C22×C25—21no—
110C22×C25—21no—
111C22×C25—21no—
112C22×C25—21no—
113C22×C25—21no—
114C22×C25C2×D412yes—
115C22×C25C2411yescharacteristic
116C2×D25—21no—
117C2×D25—21no—
118C2×D25—21no—
119C2×D25—21no—
120C2×D25—21no—
121C2×D25—21no—
122C2×D25—21no—
123C2×D25—44no—
124C2×D25—44no—
125C2×D25C2×D412yes—
126C2×D25#4112yescomplemented
127C4×C25—21no—
128C4×C25—21no—
129C4×C25—21no—
130C4×C25—21no—
131Dic25—21no—
132Dic25—21no—
133Dic25—21no—
134Dic25—21no—
135Dic25C2×D412yes—
136C23×D5—51no—
137C23×D5—51no—
138C2×C5×D4C2×D511yescharacteristic
139C2×C5×D4C2×D511yescharacteristic
140C2×C5×D4C2×D511yescharacteristic
141C22×C4×C5C2×D511yescharacteristic
142C2×C22⋊D5—51no—
143C2×C22⋊D5—51no—
144C2×C22⋊D5—51no—
145C2×C22⋊D5—51no—
146C2×C22⋊D5—51no—
147C22×Dic5—51no—
148C22×Dic5—51no—
149#711—104no—
150D4×D5—104no—
151C2×D20—51no—
152C2×C4×D5—51no—
153C2×C4×D5—51no—
154C2×C4×D5—51no—
155C2×Dic10—51no—
156C5×C4⋊C4C2×D511yescharacteristic
157C5×C22⋊C4C2×D511yescharacteristic
158C5×C22⋊C4C2×D511yescharacteristic
159C22⋊Dic5—51no—
160C22⋊Dic5—51no—
161C22⋊Dic5—51no—
162#685—51no—
163#685—51no—
164#685—51no—
165#685—51no—
166#685—51no—
167#685—51no—
168#685—51no—
169#683—51no—
170#683—51no—
171#683—51no—
172C4×Dic5—51no—
173#546—251noSylow
174C2×C25—22no—
175C2×C25—41no—
176C2×C25—41no—
177C2×C25C22×D411yescharacteristic
178C2×C25C2×#4111yescharacteristic
179C2×C25H(5,𝔽2)11yescharacteristic
180D25—22no—
181D25—22no—
182D25—41no—
183C23×C5C22×D511yescharacteristic
184C23×C5C22×D511yescharacteristic
185C23×C5C22×D511yescharacteristic
186C22×D5—51no—
187C22×D5—51no—
188C22×D5—51no—
189C22×D5—102no—
190C22×D5—102no—
191C22×D5—102no—
192C22×D5—102no—
193C22×D5—201no—
194C22×D5—201no—
195C5×D4—22no—
196C5×D4—22no—
197C5×D4—41no—
198C2×C4×C5—41no—
199C2×C4×C5C22×D511yescharacteristic
200C2×C4×C5C22×D511yescharacteristic
201C2×C4×C5C22×D511yescharacteristic
202C2×C4×C5C22×D511yescharacteristic
203C22⋊D5—54no—
204C22⋊D5—102no—
205C22⋊D5—102no—
206C22⋊D5—102no—
207C22⋊D5—201no—
208C2×Dic5—51no—
209C2×Dic5—51no—
210C2×Dic5—51no—
211C2×Dic5—51no—
212C2×Dic5—51no—
213C2×Dic5—102no—
214C2×Dic5—102no—
215D20—102no—
216C4×D5—102no—
217C4×D5—102no—
218C4×D5—201no—
219Dic10—102no—
220C2×#41—251no—
221C22×D4—251no—
222#124—251no—
223#123—251no—
224#123—251no—
225C22⋊Q8—251no—
226#121—251no—
227#121—251no—
228#121D2511yescharacteristic, complemented
229#120—251no—
230#120—251no—
231C4×D4—251no—
232C4×D4—251no—
233C2×C22⋊C4—251no—
234C2×C22⋊C4—251no—
235C25#54611yescharacteristic, complemented, Sylow
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5D4×D512yes—
245C22×C5C23×D511yescharacteristic
246C2×D5—52no—
247C2×D5—52no—
248C2×D5—101no—
249C2×D5—101no—
250C2×D5—101no—
251C2×D5—101no—
252C2×D5—101no—
253C2×D5—101no—
254C2×D5—101no—
255C2×D5—204no—
256C2×D5—204no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261Dic5—52no—
262Dic5—101no—
263Dic5—101no—
264Dic5—101no—
265Dic5—101no—
266C24—251no—
267C24—251no—
268#41—504no—
269C2×Q8—251no—
270C2×D4—251no—
271C2×D4—251no—
272C2×D4—251no—
273C2×D4—251no—
274C2×D4—251no—
275C2×D4—251no—
276C2×D4—504no—
277C2×D4C2×D2511yescharacteristic
278C2×D4C2×D2511yescharacteristic, complemented
279C2×D4C2×D2511yescharacteristic, complemented
280C22×C4—251no—
281C22×C4—251no—
282C22×C4—251no—
283C22×C4—251no—
284C22×C4—251no—
285C22×C4C2×D2511yescharacteristic, complemented
286C4⋊C4—251no—
287C4⋊C4—251no—
288C4⋊C4—251no—
289C4⋊C4C2×D2511yescharacteristic, complemented
290C22⋊C4—251no—
291C22⋊C4—251no—
292C22⋊C4—251no—
293C22⋊C4—251no—
294C22⋊C4—251no—
295C22⋊C4—251no—
296C22⋊C4—251no—
297C22⋊C4—251no—
298C22⋊C4—251no—
299C22⋊C4—251no—
300C22⋊C4C2×D2511yescharacteristic, complemented
301C22⋊C4C2×D2511yescharacteristic, complemented
302C42—251no—
303C2×C5—22no—
304C2×C5—41no—
305C2×C5—41no—
306C2×C5C2×D4×D511yescharacteristic
307C2×C5#414411yescharacteristic
308C2×C5D5×#4111yescharacteristic
309D5—102no—
310D5—102no—
311D5—201no—
312C23—251no—
313C23—251no—
314C23—251no—
315C23—502no—
316C23—502no—
317C23—502no—
318C23—502no—
319C23—1001no—
320C23—1001no—
321C23C22×D2511yescharacteristic
322C23C22×D2511yescharacteristic
323C23C22×D2511yescharacteristic
324Q8—502no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—254no—
329D4—502no—
330D4—502no—
331D4—502no—
332D4—502no—
333D4—1001no—
334C2×C4—41no—
335C2×C4—251no—
336C2×C4—251no—
337C2×C4—251no—
338C2×C4—251no—
339C2×C4—251no—
340C2×C4—502no—
341C2×C4—502no—
342C2×C4—502no—
343C2×C4—502no—
344C2×C4—1001no—
345C2×C4C22×D2511yescharacteristic
346C2×C4C22×D2511yescharacteristic
347C2×C4C22×D2511yescharacteristic
348C2×C4C22×D2511yescharacteristic
349C5#6594411yescharacteristic
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—252no—
359C22—252no—
360C22—501no—
361C22—501no—
362C22—501no—
363C22—501no—
364C22—501no—
365C22—501no—
366C22—501no—
367C22—1004no—
368C22—1004no—
369C22D4×D2512yes—
370C22C23×D2511yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—252no—
376C4—501no—
377C4—501no—
378C4—501no—
379C4—501no—
380C2—22no—
381C2—41no—
382C2—41no—
383C2—502no—
384C2—502no—
385C2—1001no—
386C2C2×D4×D2511yescharacteristic
387C2#1171656311yescharacteristic
388C2#41×D2511yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#546
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#87746C2semidirect
2. C2×D4×D25C2semidirect
3. C25×#121C2semidirect
4. #11716501C2semidirect
5. #11716499C2semidirect
6. #11716499C2semidirect
7. #11716497C2semidirect
8. C4×C22⋊D25C2semidirect
9. C2×#87720C2semidirect
10. #11716458C2semidirect
11. #11716456C2semidirect
12. #11716447C2semidirect
13. #11716446C2semidirect
14. #11716443C2semidirect
15. C22⋊C4×D25C2semidirect
19. C2×D4×C25C22semidirect
20. C2×D4×C25C22semidirect
21. C22×C4×C25C22semidirect
25. C2×C22⋊D25C22semidirect
26. C2×C22⋊D25C22semidirect
27. C22×Dic25C22semidirect
28. C22×Dic25C22semidirect
33. C2×C4×D25C22semidirect
34. C2×C4×D25C22semidirect
35. C2×Dic50C22semidirect
36. C4⋊C4×C25C22semidirect
37. C22⋊C4×C25C22semidirect
38. C22⋊C4×C25C22semidirect
39. C22⋊Dic25C22semidirect
40. C22⋊Dic25C22semidirect
41. C22⋊Dic25C22semidirect
45. #87720C22semidirect
46. #87720C22semidirect
47. #87720C22semidirect
48. #87720C22semidirect
49. #87718C22semidirect
50. #87718C22semidirect
51. #87718C22semidirect
52. C4×Dic25C22semidirect
78. C22⋊D25D4semidirect
126. C2×D25#41semidirect
228. #121D25semidirect
235. C25#546semidirect
278. C2×D4C2×D25semidirect
279. C2×D4C2×D25semidirect
285. C22×C4C2×D25semidirect
289. C4⋊C4C2×D25semidirect
300. C22⋊C4C2×D25semidirect
301. C22⋊C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×#877462
C2×D4×D252
C25×#1212
#117165012
#117164992
#117164972
C4×C22⋊D252
C2×#877202
#117164582
#117164562
#117164472
#117164462
#117164432
C22⋊C4×D252
#659445