Finite Group Databasebeta

← #10610625

Subgroups — #10610625

Order 640.

442 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
1#66163C211yesmaximal, characteristic, complemented
2#65841C211yesmaximal, characteristic, complemented
3C5×#417C211yesmaximal, characteristic, complemented
4#65527C211yesmaximal, characteristic, complemented
5#65424C211yesmaximal, characteristic, complemented
6#65416C211yesmaximal, characteristic, complemented
7#65257C211yesmaximal, characteristic, complemented
8#65108C211yesmaximal, characteristic, complemented
9#65096C211yesmaximal, characteristic, complemented
10#65094C211yesmaximal, characteristic, complemented
11#65084C211yesmaximal, characteristic, complemented
12#65074C211yesmaximal, characteristic, complemented
13#65062C211yesmaximal, characteristic, complemented
14D5×#102C211yesmaximal, characteristic, complemented
15#65050C211yesmaximal, characteristic, complemented
16C2×C5×#41C2211yescharacteristic
17C2×D4×D5C2211yescharacteristic
18C2×#709—21no—
19C2×C5×M16C2211yescharacteristic, complemented
20C2×C5×C4⋊C4C2211yescharacteristic, complemented
21#4093C2211yescharacteristic
22#4092C2211yescharacteristic
23C2×#688C2211yescharacteristic, complemented
24#4085—21no—
25#4083—21no—
26D4×Dic5C2211yescharacteristic
27C2×#686C2211yescharacteristic
28#4076C2211yescharacteristic
29#4076C2211yescharacteristic, complemented
30#4075—21no—
31#4075—21no—
32C4×C22⋊D5C2211yescharacteristic
33C2×#685—21no—
34C2×D40C2211yescharacteristic
35C2×C8×D5C2211yescharacteristic
36#4042—21no—
37#4041C2211yescharacteristic
38#4040—21no—
39#4039C2211yescharacteristic, complemented
40D5×C4⋊C4C2211yescharacteristic
41#4034C2211yescharacteristic, complemented
42C5×#103C2211yescharacteristic, complemented
43C5×#103C2211yescharacteristic, complemented
44C5×#102C2211yescharacteristic
45C5×#102C2211yescharacteristic
46#3967C2211yescharacteristic, complemented
47#3964C2211yescharacteristic
48C22⋊#168C2211yescharacteristic, complemented
49#3953C2211yescharacteristic
50#3953C2211yescharacteristic, complemented
51#3952C2211yescharacteristic
52#3949C2211yescharacteristic, complemented
53#3947C2211yescharacteristic, complemented
54#3946C2211yescharacteristic, complemented
55#3941C2211yescharacteristic
56#3941C2211yescharacteristic
57#3940C2211yescharacteristic, complemented
58#3940C2211yescharacteristic, complemented
59#3306—51nomaximal, Sylow
60C23×D5—21no—
61C5×#41—22no—
62C5×#41—41no—
63C2×C5×Q8C2311yescharacteristic
64C2×C5×D4—21no—
65C2×C5×D4C2311yescharacteristic
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C2311yescharacteristic
69C2×C22⋊D5—21no—
70C2×C22⋊D5—21no—
71C2×C22⋊D5—21no—
72C2×C22⋊D5D411yescharacteristic
73C22×Dic5—21no—
74D4×D5—22no—
75D4×D5—41no—
76#709—44no—
77C2×D20—21no—
78C2×D20C2311yescharacteristic
79C2×D20C2311yescharacteristic
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×C4×D5C2311yescharacteristic
83C2×Dic10—21no—
84C5×M16—41no—
85C2×C5×C8C2311yescharacteristic
86C2×C5×C8C2311yescharacteristic
87C5×C4⋊C4—21no—
88C5×C4⋊C4C2311yescharacteristic
89C5×C4⋊C4C2311yescharacteristic
90C22⋊Dic5—21no—
91C22⋊Dic5D411yescharacteristic
92#688—41no—
93#686—22no—
94#685—21no—
95#685—21no—
96#685—21no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685—21no—
101#685D411yescharacteristic
102C4⋊Dic5C2311yescharacteristic
103C4⋊Dic5C2311yescharacteristic
104#683—21no—
105#683—21no—
106#683—21no—
107#683D411yescharacteristic
108C4×Dic5C2311yescharacteristic
109C2×#168C2311yescharacteristic
110C2×#168C2311yescharacteristic
111D40—41no—
112C8×D5—41no—
113#547—51no—
114#546—51no—
115#489—51no—
116#483—51no—
117#481—51no—
118#476—51no—
119#469—51no—
120#465—51no—
121#463—51no—
122#449—51no—
123#447—51no—
124#442—51no—
125#435—51no—
126#417D511yescharacteristic, complemented
127C2×#102—51no—
128C23×C5—21no—
129C23×C5C2×D411yescharacteristic
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—42no—
133C22×D5—42no—
134C22×D5—81no—
135C22×D5C2×D411yescharacteristic
136C5×Q8—21no—
137C5×Q8—21no—
138C5×D4—21no—
139C5×D4—42no—
140C5×D4#4112yescomplemented
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5C2×D411yescharacteristic
149C2×C4×C5C2411yescharacteristic
150C22⋊D5—22no—
151C22⋊D5—42no—
152C22⋊D5—42no—
153C22⋊D5—81no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—81no—
157C2×Dic5C2×D411yescharacteristic
158C2×Dic5C2×D411yescharacteristic
159C2×Dic5C2×D411yescharacteristic
160D20—21no—
161D20—21no—
162D20—21no—
163D20—21no—
164D20—42no—
165C4×D5—21no—
166C4×D5—21no—
167C4×D5—42no—
168C4×D5—42no—
169Dic10—42no—
170C5×C8—21no—
171C5×C8—21no—
172#168—21no—
173#168—21no—
174C2×#41—101no—
175C2×#41C2×D511yescharacteristic
176C22×D4—51no—
177C2×SD16—51no—
178C2×D8—51no—
179C2×D8—51no—
180C2×M16C2×D511yescharacteristic, complemented
181C22×C8—51no—
182C4⋊Q8—51no—
183#124—51no—
184#123—101no—
185#123—101no—
186#123—101no—
187C22⋊Q8—51no—
188C22⋊Q8—101no—
189#121—51no—
190#121—51no—
191#121—51no—
192#121—101no—
193#120—101no—
194C4×D4—51no—
195C4×D4—51no—
196C4×D4—51no—
197C2×C4⋊C4—51no—
198C2×C4⋊C4C2×D511yescharacteristic, complemented
199C2×C22⋊C4—101no—
200#106—51no—
201#106—51no—
202#106—51no—
203C4⋊C8—51no—
204#103—51no—
205#103C2×D511yescharacteristic, complemented
206#103C2×D511yescharacteristic, complemented
207#102—51no—
208#102—51no—
209#102—51no—
210#102—51no—
211#102—51no—
212#102C2×D511yescharacteristic
213#102C2×D511yescharacteristic
214C22⋊C8—51no—
215C22⋊C8—51no—
216#97—51no—
217C22×C5—22no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5C22×D411yescharacteristic
224C2×D5—21no—
225C2×D5—21no—
226C2×D5—41no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5—84no—
233C2×D5AGL(1,ℤ/8)12yes—
234C4×C5—21no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238C4×C5C2×#4111yescharacteristic
239C4×C5H(5,𝔽2)11yescharacteristic
240Dic5—21no—
241Dic5—21no—
242Dic5—21no—
243Dic5—41no—
244Dic5—41no—
245C24—101no—
246#41—22no—
247#41—41no—
248#41—204no—
249C2×Q8—101no—
250C2×Q8C22×D511yescharacteristic
251C2×D4—21no—
252C2×D4—51no—
253C2×D4—51no—
254C2×D4—51no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4—102no—
258C2×D4—101no—
259C2×D4—101no—
260C2×D4—201no—
261C2×D4C22×D511yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—51no—
265C22×C4—101no—
266C22×C4—101no—
267C22×C4—101no—
268C22×C4C22×D511yescharacteristic
269SD16—201no—
270D8—102no—
271D8—201no—
272M16—41no—
273C2×C8—51no—
274C2×C8—51no—
275C2×C8—201no—
276C2×C8C22×D511yescharacteristic
277C2×C8C22×D511yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4—51no—
282C4⋊C4—101no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4C22×D511yescharacteristic
286C4⋊C4C22×D511yescharacteristic
287C22⋊C4—51no—
288C22⋊C4—51no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C22⋊C4—101no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C22⋊C4—101no—
296C22⋊C4—101no—
297C42—51no—
298C2×C5—42no—
299C2×C5—41no—
300C2×C5#54611yescharacteristic
301C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
302C2×C5#57711yescharacteristic
303D5—22no—
304D5—81no—
305D5—81no—
306C23—21no—
307C23—51no—
308C23—101no—
309C23—101no—
310C23—202no—
311C23—202no—
312C23—401no—
313C23D4×D511yescharacteristic
314Q8—21no—
315Q8—21no—
316Q8—202no—
317D4—21no—
318D4—42no—
319D4—102no—
320D4—101no—
321D4—101no—
322D4—101no—
323D4—101no—
324D4—202no—
325D4—202no—
326D4—202no—
327D4—401no—
328D4#70912yescomplemented
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—51no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—101no—
342C2×C4—101no—
343C2×C4—202no—
344C2×C4—202no—
345C2×C4—401no—
346C2×C4D4×D511yescharacteristic
347C2×C4C23×D511yescharacteristic
348C8—21no—
349C8—21no—
350C8—101no—
351C8—101no—
352C5#330611yescharacteristic, complemented, Sylow
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—52no—
360C22—101no—
361C22—101no—
362C22—201no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22—201no—
368C22—404no—
369C22C2×D4×D511yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—101no—
375C4—101no—
376C4—101no—
377C4—201no—
378C4—201no—
379C4C2×#70911yescharacteristic
380C4#414411yescharacteristic
381C2—41no—
382C2—42no—
383C2—102no—
384C2—401no—
385C2—401no—
386C2#6582411yescharacteristic
387C2D5×AGL(1,ℤ/8)11yescharacteristic
388C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#417C2
socleC22×C5C22×D4
hypercenter#417D5
hypocenterC5#3306
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #66163C2semidirect
2. #65841C2semidirect
3. C5×#417C2semidirect
4. #65527C2semidirect
5. #65424C2semidirect
6. #65416C2semidirect
7. #65257C2semidirect
8. #65108C2semidirect
9. #65096C2semidirect
10. #65094C2semidirect
11. #65084C2semidirect
12. #65074C2semidirect
13. #65062C2semidirect
14. D5×#102C2semidirect
15. #65050C2semidirect
19. C2×C5×M16C22semidirect
20. C2×C5×C4⋊C4C22semidirect
23. C2×#688C22semidirect
29. #4076C22semidirect
39. #4039C22semidirect
41. #4034C22semidirect
42. C5×#103C22semidirect
43. C5×#103C22semidirect
46. #3967C22semidirect
48. C22⋊#168C22semidirect
50. #3953C22semidirect
52. #3949C22semidirect
53. #3947C22semidirect
54. #3946C22semidirect
57. #3940C22semidirect
58. #3940C22semidirect
126. #417D5semidirect
140. C5×D4#41semidirect
180. C2×M16C2×D5semidirect
198. C2×C4⋊C4C2×D5semidirect
205. #103C2×D5semidirect
206. #103C2×D5semidirect
328. D4#709semidirect
352. C5#3306semidirect

Maximal subgroups

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

subgroupindex
#661632
#658412
C5×#4172
#655272
#654242
#654162
#652572
#651082
#650962
#650942
#650842
#650742
#650622
D5×#1022
#650502
#33065