Finite Group Databasebeta

← #10611981

Subgroups — #10611981

Order 640.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66163C211yesmaximal, characteristic
2#65975C211yesmaximal, characteristic, complemented
3C5×#452C211yesmaximal, characteristic, complemented
4#65522C211yesmaximal, characteristic, complemented
5#65478C211yesmaximal, characteristic, complemented
6#65474C211yesmaximal, characteristic, complemented
7#65458C211yesmaximal, characteristic, complemented
8#65453C211yesmaximal, characteristic, complemented
9#65337C211yesmaximal, characteristic, complemented
10#65103C211yesmaximal, characteristic, complemented
11#65084C211yesmaximal, characteristic, complemented
12#65059C211yesmaximal, characteristic, complemented
13#65050C211yesmaximal, characteristic, complemented
14#65026C211yesmaximal, characteristic, complemented
15#65019C211yesmaximal, characteristic, complemented
16C2×C5×#41C2211yescharacteristic
17C2×D4×D5C2211yescharacteristic
18C2×C5×Q16C2211yescharacteristic, complemented
19C2×C5×SD16C2211yescharacteristic
20C5×C22⋊Q8C2211yescharacteristic, complemented
21#4093C2211yescharacteristic
22#4092C2211yescharacteristic
23#4092C2211yescharacteristic
24Q8×Dic5C2211yescharacteristic, complemented
25C2×#688C2211yescharacteristic
26#4085—21no—
27#4083—21no—
28D4×Dic5C2211yescharacteristic
29#4076C2211yescharacteristic
30#4075—21no—
31C4×C22⋊D5C2211yescharacteristic
32C2×#685—21no—
33#4072C2211yescharacteristic, complemented
34C22×#168C2211yescharacteristic, complemented
35C2×#676C2211yescharacteristic
36#4044—21no—
37#4038C2211yescharacteristic
38#4034C2211yescharacteristic, complemented
39#4033—21no—
40#4031—21no—
41#4025—21no—
42C5×#103C2211yescharacteristic, complemented
43C5×#102C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic, complemented
45#3967C2211yescharacteristic, complemented
46#3967C2211yescharacteristic, complemented
47#3967C2211yescharacteristic, complemented
48#3964C2211yescharacteristic
49#3964C2211yescharacteristic
50#3953C2211yescharacteristic
51#3953C2211yescharacteristic
52#3952C2211yescharacteristic
53#3950C2211yescharacteristic, complemented
54#3949C2211yescharacteristic, complemented
55#3947C2211yescharacteristic, complemented
56#3946C2211yescharacteristic, complemented
57#3941C2211yescharacteristic
58#3940C2211yescharacteristic, complemented
59#3311—51nomaximal, Sylow
60C23×D5—21no—
61C5×#41—22no—
62C5×#41—41no—
63C2×C5×Q8C2311yescharacteristic
64C2×C5×Q8C2311yescharacteristic
65C2×C5×D4—21no—
66C2×C5×D4C2311yescharacteristic
67C22×C4×C5—21no—
68C22×C4×C5C2311yescharacteristic
69C2×C22⋊D5—21no—
70C2×C22⋊D5—21no—
71C2×C22⋊D5D411yescharacteristic
72C22×Dic5—21no—
73D4×D5—22no—
74D4×D5—41no—
75C2×D20C2311yescharacteristic
76C2×C4×D5C2311yescharacteristic
77C2×Dic10—21no—
78C5×Q16—41no—
79C5×SD16—22no—
80C2×C5×C8C2311yescharacteristic
81C2×C5×C8C2311yescharacteristic
82C5×C4⋊C4—21no—
83C5×C4⋊C4C2311yescharacteristic
84C5×C22⋊C4—21no—
85C22⋊Dic5—21no—
86C22⋊Dic5—21no—
87C22⋊Dic5D411yescharacteristic
88#688—41no—
89#685—21no—
90#685—21no—
91#685—21no—
92#685—21no—
93#685—21no—
94#685—21no—
95#685D411yescharacteristic
96C4⋊Dic5—21no—
97C4⋊Dic5C2311yescharacteristic
98C4⋊Dic5C2311yescharacteristic
99C4⋊Dic5C2311yescharacteristic
100#683—21no—
101#683—21no—
102#683—21no—
103#683D411yescharacteristic
104C4×Dic5—21no—
105C4×Dic5—21no—
106C4×Dic5—21no—
107C4×Dic5C2311yescharacteristic
108C2×#168—41no—
109C2×#168C2311yescharacteristic
110C2×#168C2311yescharacteristic
111#676—41no—
112#556—51no—
113#546—51no—
114#489—51no—
115#485—51no—
116#482—51no—
117#476—51no—
118#470—51no—
119#465—51no—
120#464—51no—
121#452D511yescharacteristic, complemented
122#450—51no—
123#440—51no—
124#435—51no—
125#418—51no—
126#416—51no—
127C23×C5—21no—
128C23×C5C2×D411yescharacteristic
129C22×D5—21no—
130C22×D5—42no—
131C22×D5—42no—
132C22×D5—81no—
133C22×D5C2×D411yescharacteristic
134C5×Q8—21no—
135C5×Q8—21no—
136C5×Q8—21no—
137C5×Q8—21no—
138C5×D4—21no—
139C5×D4—42no—
140C5×D4#4112yes—
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×C5C2×D411yescharacteristic
148C2×C4×C5C2411yescharacteristic
149C22⋊D5—41no—
150C22⋊D5—42no—
151C22⋊D5—81no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—81no—
156C2×Dic5C2×D411yescharacteristic
157C2×Dic5C2×D411yescharacteristic
158C2×Dic5C2×D411yescharacteristic
159D20—21no—
160D20—21no—
161C4×D5—21no—
162C4×D5—21no—
163Dic10—42no—
164C5×C8—21no—
165C5×C8—21no—
166#168—21no—
167#168—21no—
168C2×#41C2×D511yescharacteristic
169C22×D4—51no—
170C2×Q16C2×D511yescharacteristic, complemented
171C2×SD16—51no—
172C2×SD16C2×D511yescharacteristic
173C2×M16—51no—
174C22×C8—51no—
175C4⋊Q8—51no—
176#126—101no—
177#126—101no—
178#124—51no—
179#124—101no—
180#123—101no—
181C22⋊Q8—51no—
182C22⋊Q8—51no—
183C22⋊Q8C2×D511yescharacteristic, complemented
184#121—51no—
185#121—101no—
186#120—101no—
187C4×Q8—51no—
188C4×Q8—101no—
189C4×D4—51no—
190C4×D4—51no—
191#117—51no—
192#117—51no—
193C2×C22⋊C4—101no—
194#107—51no—
195#106—51no—
196#106—51no—
197C4⋊C8—51no—
198#103—51no—
199#103—51no—
200#103—51no—
201#103C2×D511yescharacteristic, complemented
202#102—51no—
203#102—51no—
204#102—51no—
205#102—51no—
206#102—51no—
207#102C2×D511yescharacteristic
208C22⋊C8—51no—
209C22⋊C8C2×D511yescharacteristic, complemented
210#97—51no—
211C22×C5—22no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5C22×D411yescharacteristic
218C2×D5—21no—
219C2×D5—21no—
220C2×D5—21no—
221C2×D5—41no—
222C2×D5—41no—
223C2×D5—41no—
224C2×D5—84no—
225C4×C5—21no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5C2×#4111yescharacteristic
230C4×C5H(5,𝔽2)11yescharacteristic
231Dic5—21no—
232Dic5—21no—
233Dic5—21no—
234Dic5—41no—
235Dic5—41no—
236Dic5—41no—
237C24—101no—
238#41—22no—
239#41—41no—
240C2×Q8—101no—
241C2×Q8C22×D511yescharacteristic
242C2×Q8C22×D511yescharacteristic
243C2×D4—21no—
244C2×D4—51no—
245C2×D4—51no—
246C2×D4—101no—
247C2×D4—102no—
248C2×D4—101no—
249C2×D4—201no—
250C2×D4C22×D511yescharacteristic
251C22×C4—21no—
252C22×C4—51no—
253C22×C4—101no—
254C22×C4C22×D511yescharacteristic
255Q16—41no—
256SD16—22no—
257SD16—201no—
258M16—201no—
259C2×C8—51no—
260C2×C8—51no—
261C2×C8—201no—
262C2×C8C22×D511yescharacteristic
263C2×C8C22×D511yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—51no—
266C4⋊C4—51no—
267C4⋊C4—51no—
268C4⋊C4—51no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4C22×D511yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—51no—
276C22⋊C4—51no—
277C22⋊C4—101no—
278C22⋊C4—101no—
279C22⋊C4—101no—
280C22⋊C4—101no—
281C22⋊C4—101no—
282C22⋊C4—101no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C42—51no—
286C42—101no—
287C42—101no—
288C42—101no—
289C2×C5—42no—
290C2×C5—41no—
291C2×C5#54611yescharacteristic
292C2×C5#57511yescharacteristic
293C2×C5#57711yescharacteristic
294D5—41no—
295D5—81no—
296C23—21no—
297C23—51no—
298C23—101no—
299C23—202no—
300C23—202no—
301C23—401no—
302C23D4×D511yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—202no—
308D4—21no—
309D4—42no—
310D4—101no—
311D4—101no—
312D4—201no—
313D4—202no—
314D4—401no—
315D4#71112yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—51no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—401no—
331C2×C4D4×D511yescharacteristic
332C2×C4C23×D511yescharacteristic
333C8—21no—
334C8—21no—
335C8—101no—
336C8—101no—
337C5#331111yescharacteristic, complemented, Sylow
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—101no—
345C22—101no—
346C22—101no—
347C22—201no—
348C22—201no—
349C22—201no—
350C22—404no—
351C22C2×D4×D511yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—101no—
357C4—101no—
358C4—101no—
359C4—201no—
360C4—201no—
361C4—201no—
362C4C2×#71111yescharacteristic
363C4#414411yescharacteristic
364C2—41no—
365C2—42no—
366C2—201no—
367C2—401no—
368C2#6592511yescharacteristic
369C2#6610211yescharacteristic
370C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#452C2
socleC22×C5C22×D4
prime radical#66163C2
hypercenter#452D5
hypocenterC5#3311
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #65975C2semidirect
3. C5×#452C2semidirect
4. #65522C2semidirect
5. #65478C2semidirect
6. #65474C2semidirect
7. #65458C2semidirect
8. #65453C2semidirect
9. #65337C2semidirect
10. #65103C2semidirect
11. #65084C2semidirect
12. #65059C2semidirect
13. #65050C2semidirect
14. #65026C2semidirect
15. #65019C2semidirect
18. C2×C5×Q16C22semidirect
20. C5×C22⋊Q8C22semidirect
24. Q8×Dic5C22semidirect
33. #4072C22semidirect
34. C22×#168C22semidirect
38. #4034C22semidirect
42. C5×#103C22semidirect
44. C5×C22⋊C8C22semidirect
45. #3967C22semidirect
46. #3967C22semidirect
47. #3967C22semidirect
53. #3950C22semidirect
54. #3949C22semidirect
55. #3947C22semidirect
56. #3946C22semidirect
58. #3940C22semidirect
121. #452D5semidirect
170. C2×Q16C2×D5semidirect
183. C22⋊Q8C2×D5semidirect
201. #103C2×D5semidirect
209. C22⋊C8C2×D5semidirect
337. C5#3311semidirect

Maximal subgroups

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

subgroupindex
#661632
#659752
C5×#4522
#655222
#654782
#654742
#654582
#654532
#653372
#651032
#650842
#650592
#650502
#650262
#650192
#33115