Finite Group Databasebeta

← #10611230

Subgroups — #10611230

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#65889C211yesmaximal, characteristic, complemented
2#65884C211yesmaximal, characteristic, complemented
3C5×#435C211yesmaximal, characteristic, complemented
4#65424C211yesmaximal, characteristic, complemented
5#65422C211yesmaximal, characteristic, complemented
6#65403C211yesmaximal, characteristic, complemented
7C2×#3953C211yesmaximal, characteristic, complemented
8#65133C211yesmaximal, characteristic, complemented
9#65131C211yesmaximal, characteristic, complemented
10#65024C211yesmaximal, characteristic, complemented
11#65023C211yesmaximal, characteristic, complemented
12#65021C211yesmaximal, characteristic, complemented
13#65010C211yesmaximal, characteristic, complemented
14#65003C211yesmaximal, characteristic, complemented
15#65000C211yesmaximal, characteristic, complemented
16C2×#711—21no—
17C2×#709C2211yescharacteristic
18C22×D20C2211yescharacteristic
19C2×C5×M16C2211yescharacteristic, complemented
20C22×C5×C8C2211yescharacteristic
21C4×C5×D4C2211yescharacteristic
22#4083—21no—
23#4076C2211yescharacteristic
24#4076C2211yescharacteristic
25#4076C2211yescharacteristic, complemented
26C2×C4⋊Dic5C2211yescharacteristic
27C2×C4⋊Dic5C2211yescharacteristic, complemented
28#4070C2211yescharacteristic
29C2×D40C2211yescharacteristic
30C2×D40C2211yescharacteristic
31C2×#677C2211yescharacteristic, complemented
32#4043—21no—
33#4040—21no—
34#4032—21no—
35#4032—21no—
36#4030—21no—
37D5×C22⋊C4—21no—
38#4021C2211yescharacteristic
39C4×D20C2211yescharacteristic
40C4×D20C2211yescharacteristic, complemented
41#4015C2211yescharacteristic, complemented
42C5×C4⋊C8C2211yescharacteristic, complemented
43C5×C22⋊C8C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic, complemented
45C5×#97C2211yescharacteristic, complemented
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3953C2211yescharacteristic
49#3953C2211yescharacteristic
50#3953C2211yescharacteristic
51#3953C2211yescharacteristic
52#3953C2211yescharacteristic, complemented
53#3949C2211yescharacteristic, complemented
54#3949C2211yescharacteristic, complemented
55#3949C2211yescharacteristic, complemented
56#3948C2211yescharacteristic, complemented
57#3948C2211yescharacteristic, complemented
58#3948C2211yescharacteristic, complemented
59#3306—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×D4D411yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C2×C22⋊D5—21no—
67C2×C22⋊D5—21no—
68C22×Dic5—21no—
69C22×Dic5—21no—
70#711—44no—
71#709—22no—
72#709—41no—
73C2×D20—22no—
74C2×D20—21no—
75C2×D20—41no—
76C2×D20C2311yescharacteristic
77C2×D20C2311yescharacteristic
78C2×D20C2311yescharacteristic
79C2×C4×D5—21no—
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×Dic10—21no—
83C2×Dic10C2311yescharacteristic
84C5×M16—41no—
85C2×C5×C8—41no—
86C2×C5×C8C2311yescharacteristic
87C2×C5×C8C2311yescharacteristic
88C2×C5×C8C2311yescharacteristic
89C2×C5×C8C2311yescharacteristic
90C5×C4⋊C4D411yescharacteristic
91C5×C22⋊C4D411yescharacteristic
92C5×C22⋊C4D411yescharacteristic
93C42×C5C2311yescharacteristic
94C22⋊Dic5—21no—
95#685—21no—
96#685—21no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685—21no—
101#685—21no—
102C4⋊Dic5—21no—
103C4⋊Dic5—21no—
104C4⋊Dic5—21no—
105C4⋊Dic5C2311yescharacteristic
106C4⋊Dic5C2311yescharacteristic
107C4⋊Dic5C2311yescharacteristic
108C4⋊Dic5C2311yescharacteristic
109#683—21no—
110D40—22no—
111D40—41no—
112#677—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#435D511yescharacteristic, complemented
126#417—51no—
127C2×#102—51no—
128C23×C5C2×D411yescharacteristic
129C23×C5C2×D411yescharacteristic
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—42no—
134C22×D5—42no—
135C22×D5—81no—
136C5×D4—22no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5C2×D411yescharacteristic
142C2×C4×C5C2×D411yescharacteristic
143C2×C4×C5C2×D411yescharacteristic
144C2×C4×C5C2×D411yescharacteristic
145C2×C4×C5C2411yescharacteristic
146C22⋊D5—42no—
147C22⋊D5—42no—
148C22⋊D5—42no—
149C22⋊D5—81no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—42no—
156C2×Dic5—42no—
157D20—21no—
158D20—21no—
159D20—21no—
160D20—21no—
161D20—21no—
162D20—42no—
163D20#4112yescomplemented
164C4×D5—42no—
165C4×D5—42no—
166C4×D5—81no—
167Dic10—21no—
168Dic10—21no—
169Dic10—42no—
170C5×C8—21no—
171C5×C8—21no—
172C5×C8—21no—
173C5×C8—21no—
174C2×#41—51no—
175C2×#41—101no—
176C22×D4—51no—
177C2×SD16—51no—
178C2×D8—51no—
179C2×D8—51no—
180C2×M16C2×D511yescharacteristic, complemented
181C22×C8C2×D511yescharacteristic
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×D4C2×D511yescharacteristic
197C2×C4⋊C4—51no—
198C2×C4⋊C4—51no—
199C2×C22⋊C4—101no—
200#106—51no—
201#106—51no—
202#106—51no—
203C4⋊C8C2×D511yescharacteristic, complemented
204#103—51no—
205#103—51no—
206#103—51no—
207#102—51no—
208#102—51no—
209#102—51no—
210#102—51no—
211#102—51no—
212#102—51no—
213#102—51no—
214C22⋊C8C2×D511yescharacteristic
215C22⋊C8C2×D511yescharacteristic, complemented
216#97C2×D511yescharacteristic, complemented
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5AGL(1,ℤ/8)12yes—
223C22×C5C22×D411yescharacteristic
224C2×D5—22no—
225C2×D5—41no—
226C2×D5—41no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5—41no—
233C2×D5—84no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5C2×#4111yescharacteristic
239C4×C5H(5,𝔽2)11yescharacteristic
240Dic5—41no—
241Dic5—41no—
242Dic5—41no—
243Dic5—41no—
244Dic5—41no—
245C24—101no—
246#41—102no—
247#41—201no—
248#41—204no—
249C2×Q8—51no—
250C2×Q8—101no—
251C2×D4—51no—
252C2×D4—51no—
253C2×D4—51no—
254C2×D4—102no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4—101no—
258C2×D4—101no—
259C2×D4—101no—
260C2×D4—201no—
261C2×D4D2011yescharacteristic
262C22×C4—101no—
263C22×C4—101no—
264C22×C4—101no—
265C22×C4—101no—
266C22×C4—101no—
267C22×C4C22×D511yescharacteristic
268C22×C4C22×D511yescharacteristic
269SD16—201no—
270D8—102no—
271D8—201no—
272M16—41no—
273C2×C8—41no—
274C2×C8C22×D511yescharacteristic
275C2×C8C22×D511yescharacteristic
276C2×C8C22×D511yescharacteristic
277C2×C8C22×D511yescharacteristic
278C4⋊C4—51no—
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4—51no—
282C4⋊C4—101no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4D2011yescharacteristic
287C22⋊C4—101no—
288C22⋊C4—101no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C22⋊C4—101no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C22⋊C4D2011yescharacteristic
296C22⋊C4D2011yescharacteristic
297C42C22×D511yescharacteristic
298C2×C5—22no—
299C2×C5—41no—
300C2×C5#54611yescharacteristic
301C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
302C2×C5#57711yescharacteristic
303D5—42no—
304D5—81no—
305D5—81no—
306C23—101no—
307C23—101no—
308C23—101no—
309C23—202no—
310C23—202no—
311C23—401no—
312C23C2×D2011yescharacteristic
313C23C2×D2011yescharacteristic
314Q8—101no—
315Q8—101no—
316Q8—202no—
317D4—22no—
318D4—52no—
319D4—101no—
320D4—101no—
321D4—101no—
322D4—101no—
323D4—101no—
324D4—202no—
325D4—202no—
326D4—202no—
327D4—202no—
328D4—401no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—202no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4—401no—
343C2×C4C2×D2011yescharacteristic
344C2×C4C2×D2011yescharacteristic
345C2×C4C2×D2011yescharacteristic
346C2×C4C2×D2011yescharacteristic
347C2×C4C23×D511yescharacteristic
348C8—21no—
349C8—21no—
350C8—21no—
351C8—21no—
352C5#330611yescharacteristic, complemented, Sylow
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—102no—
359C22—201no—
360C22—201no—
361C22—201no—
362C22—201no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22—404no—
368C22#405412yes—
369C22C22×D2011yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—201no—
375C4—201no—
376C4—201no—
377C4—201no—
378C4—201no—
379C4#414411yescharacteristic
380C4D5×#4111yescharacteristic
381C2—22no—
382C2—41no—
383C2—202no—
384C2—401no—
385C2—401no—
386C2#6588811yescharacteristic
387C2C2×#405411yescharacteristic
388C2#6608511yescharacteristic
subgroupG/H
centerC22C22×D20
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#435C2
socleC22×C5C22×D4
hypercenter#435D5
hypocenterC5#3306
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #65889C2semidirect
2. #65884C2semidirect
3. C5×#435C2semidirect
4. #65424C2semidirect
5. #65422C2semidirect
6. #65403C2semidirect
7. C2×#3953C2semidirect
8. #65133C2semidirect
9. #65131C2semidirect
10. #65024C2semidirect
11. #65023C2semidirect
12. #65021C2semidirect
13. #65010C2semidirect
14. #65003C2semidirect
15. #65000C2semidirect
19. C2×C5×M16C22semidirect
25. #4076C22semidirect
27. C2×C4⋊Dic5C22semidirect
31. C2×#677C22semidirect
40. C4×D20C22semidirect
41. #4015C22semidirect
42. C5×C4⋊C8C22semidirect
44. C5×C22⋊C8C22semidirect
45. C5×#97C22semidirect
52. #3953C22semidirect
53. #3949C22semidirect
54. #3949C22semidirect
55. #3949C22semidirect
56. #3948C22semidirect
57. #3948C22semidirect
58. #3948C22semidirect
125. #435D5semidirect
163. D20#41semidirect
180. C2×M16C2×D5semidirect
203. C4⋊C8C2×D5semidirect
215. C22⋊C8C2×D5semidirect
216. #97C2×D5semidirect
352. C5#3306semidirect

Maximal subgroups

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

subgroupindex
#658892
#658842
C5×#4352
#654242
#654222
#654032
C2×#39532
#651332
#651312
#650242
#650232
#650212
#650102
#650032
#650002
#33065