Finite Group Databasebeta

← #10609435

Subgroups — #10609435

Order 640.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#397C211yesmaximal, characteristic, complemented
2#65283C211yesmaximal, characteristic, complemented
3#65279C211yesmaximal, characteristic, complemented
4#65244C211yesmaximal, characteristic
5#65244C211yesmaximal, characteristic
6#65244C211yesmaximal, characteristic
7#65240C211yesmaximal, characteristic, complemented
8#65240C211yesmaximal, characteristic, complemented
9#65237C211yesmaximal, characteristic, complemented
10#64966C211yesmaximal, characteristic, complemented
11#64964C211yesmaximal, characteristic, complemented
12#64964C211yesmaximal, characteristic, complemented
13#64959C211yesmaximal, characteristic, complemented
14#64959C211yesmaximal, characteristic, complemented
15#64958C211yesmaximal, characteristic, complemented
16C24×D5C2211yescharacteristic
17C2×C5×C4⋊C4C2211yescharacteristic, complemented
18C2×C5×C22⋊C4C2211yescharacteristic
19C2×C5×C22⋊C4C2211yescharacteristic
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic5C2211yescharacteristic
22C2×C22⋊Dic5C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×#685C2211yescharacteristic
25C2×#685C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×#685C2211yescharacteristic
32C2×#685C2211yescharacteristic
33C2×#685C2211yescharacteristic
34C2×#685C2211yescharacteristic
35C2×#685C2211yescharacteristic
36C2×C4⋊Dic5C2211yescharacteristic, complemented
37C2×C4⋊Dic5C2211yescharacteristic, complemented
38C2×C4⋊Dic5C2211yescharacteristic, complemented
39C2×#683C2211yescharacteristic, complemented
40C2×#683C2211yescharacteristic, complemented
41C2×C4×Dic5C2211yescharacteristic, complemented
42C2×C4×Dic5C2211yescharacteristic, complemented
43C5×#95C2211yescharacteristic, complemented
44C5×#95C2211yescharacteristic, complemented
45C5×#95C2211yescharacteristic, complemented
46#3963C2211yescharacteristic, complemented
47#3963C2211yescharacteristic, complemented
48#3963C2211yescharacteristic, complemented
49#3963C2211yescharacteristic, complemented
50#3963C2211yescharacteristic, complemented
51#2735—51nomaximal, Sylow
52C24×C5C2311yescharacteristic
53C23×D5—22no—
54C23×D5—22no—
55C23×D5—22no—
56C23×D5—41no—
57C23×D5—41no—
58C23×D5—41no—
59C23×D5—41no—
60C23×D5C2311yescharacteristic
61C23×D5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×Dic5C2311yescharacteristic
69C22×Dic5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C5×C4⋊C4—41no—
75C5×C22⋊C4—22no—
76C5×C22⋊C4—22no—
77C5×C22⋊C4—41no—
78C22⋊Dic5—41no—
79C22⋊Dic5—41no—
80C22⋊Dic5—41no—
81#685—22no—
82#685—22no—
83#685—22no—
84#685—22no—
85#685—41no—
86#685—41no—
87#685—41no—
88#685—41no—
89#685—41no—
90#685—41no—
91#685—41no—
92#685—41no—
93C4⋊Dic5—41no—
94C4⋊Dic5—41no—
95C4⋊Dic5—41no—
96#683—41no—
97#683—41no—
98C4×Dic5—41no—
99C4×Dic5—41no—
100#399—51no—
101#397—51no—
102#397—51no—
103#397D511yescharacteristic, complemented
104#396—51no—
105#396—51no—
106#388—51no—
107#388—51no—
108#388—51no—
109#388—51no—
110#388—51no—
111#388—51no—
112#379—51no—
113#379—51no—
114#379—51no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5#4112yes—
122C23×C5C2411yescharacteristic
123C22×D5—21no—
124C22×D5—21no—
125C22×D5—21no—
126C22×D5—21no—
127C22×D5—21no—
128C22×D5—21no—
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—21no—
134C22×D5—21no—
135C22×D5—44no—
136C22×D5—44no—
137C22×D5—44no—
138C22×D5—44no—
139C22×D5—44no—
140C22×D5—44no—
141C22×D5—44no—
142C22×D5#4112yes—
143C22×D5#4112yes—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—21no—
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5—21no—
168C2×Dic5—21no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—21no—
172C2×Dic5—21no—
173C2×Dic5—21no—
174C2×Dic5—21no—
175C2×Dic5—21no—
176C2×Dic5—21no—
177C2×Dic5—21no—
178C2×Dic5—21no—
179C2×Dic5—21no—
180C25—51no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—51no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4C2×D511yescharacteristic, complemented
187C2×C22⋊C4—51no—
188C2×C22⋊C4—51no—
189C2×C22⋊C4—51no—
190C2×C22⋊C4—51no—
191C2×C22⋊C4—51no—
192C2×C22⋊C4—51no—
193C2×C22⋊C4—51no—
194C2×C22⋊C4—51no—
195C2×C22⋊C4—51no—
196C2×C22⋊C4—51no—
197C2×C22⋊C4—51no—
198C2×C22⋊C4—51no—
199C2×C22⋊C4—51no—
200C2×C22⋊C4—51no—
201C2×C22⋊C4—51no—
202C2×C22⋊C4C2×D511yescharacteristic
203C2×C22⋊C4C2×D511yescharacteristic
204C2×C22⋊C4C2×D511yescharacteristic
205C2×C42—51no—
206C2×C42—51no—
207#95—51no—
208#95—51no—
209#95—51no—
210#95—51no—
211#95—51no—
212#95C2×D511yescharacteristic, complemented
213#95C2×D511yescharacteristic, complemented
214#95C2×D511yescharacteristic, complemented
215C22×C5—22no—
216C22×C5—22no—
217C22×C5—22no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5C2×#4111yescharacteristic
223C22×C5C2×#4111yescharacteristic
224C22×C5C2×#4111yescharacteristic
225C22×C5H(5,𝔽2)11yescharacteristic
226C22×C5H(5,𝔽2)11yescharacteristic
227C22×C5H(5,𝔽2)11yescharacteristic
228C22×C5H(5,𝔽2)11yescharacteristic
229C2×D5—22no—
230C2×D5—22no—
231C2×D5—22no—
232C2×D5—22no—
233C2×D5—22no—
234C2×D5—22no—
235C2×D5—416no—
236C2×D5—41no—
237C2×D5—41no—
238C2×D5—41no—
239C2×D5—41no—
240C2×D5—41no—
241C2×D5—41no—
242C2×D5—41no—
243C2×D5—41no—
244C4×C5—41no—
245C4×C5—41no—
246C4×C5—41no—
247C4×C5—41no—
248C4×C5—41no—
249C4×C5—41no—
250Dic5—41no—
251Dic5—41no—
252Dic5—41no—
253Dic5—41no—
254Dic5—41no—
255Dic5—41no—
256C24—51no—
257C24—51no—
258C24—102no—
259C24—102no—
260C24—102no—
261C24—201no—
262C24—201no—
263C24—201no—
264C24—201no—
265C24C22×D511yescharacteristic
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4C22×D511yescharacteristic
273C22×C4C22×D511yescharacteristic
274C22×C4C22×D511yescharacteristic
275C22×C4C22×D511yescharacteristic
276C22×C4C22×D511yescharacteristic
277C22×C4C22×D511yescharacteristic
278C4⋊C4—41no—
279C4⋊C4—201no—
280C4⋊C4—201no—
281C4⋊C4—201no—
282C4⋊C4—201no—
283C4⋊C4—201no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C22⋊C4—102no—
291C22⋊C4—201no—
292C22⋊C4—201no—
293C22⋊C4—201no—
294C22⋊C4—201no—
295C22⋊C4—201no—
296C22⋊C4—201no—
297C22⋊C4—201no—
298C22⋊C4—201no—
299C22⋊C4—201no—
300C22⋊C4—201no—
301C22⋊C4—201no—
302C42—201no—
303C42—201no—
304C2×C5—42no—
305C2×C5#53811yescharacteristic
306C2×C5#53811yescharacteristic
307C2×C5#53811yescharacteristic
308C2×C5#55111yescharacteristic
309C2×C5#55111yescharacteristic
310C2×C5#55111yescharacteristic
311C2×C5#56011yescharacteristic
312D5—42no—
313D5—42no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—52no—
321C23—52no—
322C23—101no—
323C23—101no—
324C23—101no—
325C23—101no—
326C23—101no—
327C23—101no—
328C23—101no—
329C23—101no—
330C23—101no—
331C23—101no—
332C23—101no—
333C23—101no—
334C23—204no—
335C23—204no—
336C23—204no—
337C23—204no—
338C23—204no—
339C23—204no—
340C23—204no—
341C23#71112yes—
342C23C23×D511yescharacteristic
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—101no—
364C2×C4—101no—
365C2×C4—101no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—101no—
379C5#273511yescharacteristic, complemented, Sylow
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—102no—
388C22—102no—
389C22—102no—
390C22—102no—
391C22—102no—
392C22—102no—
393C22—2016no—
394C22—201no—
395C22—201no—
396C22—201no—
397C22—201no—
398C22—201no—
399C22—201no—
400C22—201no—
401C22—201no—
402C22C2×#71111yescharacteristic
403C22#414411yescharacteristic
404C22D5×#4111yescharacteristic
405C22D5×#4111yescharacteristic
406C22#414911yescharacteristic
407C22#414911yescharacteristic
408C22#414911yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—201no—
416C4—201no—
417C4—201no—
418C4—201no—
419C4—201no—
420C4—201no—
421C2—42no—
422C2—202no—
423C2—202no—
424C2#6595111yescharacteristic
425C2#6599111yescharacteristic
426C2#6599211yescharacteristic
427C2#6599211yescharacteristic
428C2#6601211yescharacteristic
429C2#6603911yescharacteristic
430C2#6604511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#397C2
prime radicalC24×D5C22
hypercenter#397D5
hypocenterC5#2735
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C5×#397C2semidirect
2. #65283C2semidirect
3. #65279C2semidirect
7. #65240C2semidirect
8. #65240C2semidirect
9. #65237C2semidirect
10. #64966C2semidirect
11. #64964C2semidirect
12. #64964C2semidirect
13. #64959C2semidirect
14. #64959C2semidirect
15. #64958C2semidirect
17. C2×C5×C4⋊C4C22semidirect
36. C2×C4⋊Dic5C22semidirect
37. C2×C4⋊Dic5C22semidirect
38. C2×C4⋊Dic5C22semidirect
39. C2×#683C22semidirect
40. C2×#683C22semidirect
41. C2×C4×Dic5C22semidirect
42. C2×C4×Dic5C22semidirect
43. C5×#95C22semidirect
44. C5×#95C22semidirect
45. C5×#95C22semidirect
46. #3963C22semidirect
47. #3963C22semidirect
48. #3963C22semidirect
49. #3963C22semidirect
50. #3963C22semidirect
103. #397D5semidirect
186. C2×C4⋊C4C2×D5semidirect
212. #95C2×D5semidirect
213. #95C2×D5semidirect
214. #95C2×D5semidirect
379. C5#2735semidirect

Maximal subgroups

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

subgroupindex
C5×#3972
#652832
#652792
#652442
#652402
#652372
#649662
#649642
#649592
#649582
#27355