Finite Group Databasebeta

← #10611234

Subgroups — #10611234

Order 640.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65884C211yesmaximal, characteristic
2#65877C211yesmaximal, characteristic, complemented
3C5×#435C211yesmaximal, characteristic, complemented
4#65423C211yesmaximal, characteristic, complemented
5#65422C211yesmaximal, characteristic, complemented
6#65405C211yesmaximal, characteristic, complemented
7C2×#3953C211yesmaximal, characteristic, complemented
8#65135C211yesmaximal, characteristic, complemented
9#65134C211yesmaximal, characteristic, complemented
10#65025C211yesmaximal, characteristic, complemented
11#65022C211yesmaximal, characteristic, complemented
12#65020C211yesmaximal, characteristic, complemented
13#65011C211yesmaximal, characteristic, complemented
14#65003C211yesmaximal, characteristic, complemented
15#64999C211yesmaximal, characteristic, complemented
16C2×#709C2211yescharacteristic
17C22×D20C2211yescharacteristic
18C2×C5×M16C2211yescharacteristic, complemented
19C22×C5×C8C2211yescharacteristic
20C4×C5×D4C2211yescharacteristic
21#4083—21no—
22D4×Dic5—21no—
23#4076C2211yescharacteristic
24C2×C4⋊Dic5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic, complemented
26#4070C2211yescharacteristic
27#4070C2211yescharacteristic
28#4070C2211yescharacteristic, complemented
29C2×Dic20C2211yescharacteristic, complemented
30C2×#677C2211yescharacteristic
31C2×#677C2211yescharacteristic
32#4040—21no—
33#4036—21no—
34#4030—21no—
35D5×C22⋊C4—21no—
36#4024—21no—
37#4024—21no—
38#4021C2211yescharacteristic
39C4×D20C2211yescharacteristic
40#4015C2211yescharacteristic, complemented
41C4×Dic10C2211yescharacteristic, 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#3950C2211yescharacteristic, complemented
53#3950C2211yescharacteristic, complemented
54#3950C2211yescharacteristic, complemented
55#3948C2211yescharacteristic, complemented
56#3948C2211yescharacteristic, complemented
57#3948C2211yescharacteristic, complemented
58#3948C2211yescharacteristic, complemented
59#3314—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×D4D411yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C2×C22⋊D5—21no—
66C22×Dic5—21no—
67C22×Dic5—21no—
68#709—22no—
69#709—41no—
70C2×D20—22no—
71C2×D20—21no—
72C2×D20—41no—
73C2×D20C2311yescharacteristic
74C2×D20C2311yescharacteristic
75C2×C4×D5—21no—
76C2×C4×D5—21no—
77C2×Dic10—21no—
78C2×Dic10C2311yescharacteristic
79C2×Dic10C2311yescharacteristic
80C5×M16—41no—
81C2×C5×C8—41no—
82C2×C5×C8C2311yescharacteristic
83C2×C5×C8C2311yescharacteristic
84C2×C5×C8C2311yescharacteristic
85C2×C5×C8C2311yescharacteristic
86C5×C4⋊C4D411yescharacteristic
87C5×C22⋊C4D411yescharacteristic
88C5×C22⋊C4D411yescharacteristic
89C42×C5C2311yescharacteristic
90C22⋊Dic5—21no—
91C22⋊Dic5—21no—
92C22⋊Dic5—21no—
93#685—21no—
94#685—21no—
95#685—21no—
96#685—21no—
97C4⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—21no—
100C4⋊Dic5C2311yescharacteristic
101C4⋊Dic5C2311yescharacteristic
102C4⋊Dic5C2311yescharacteristic
103C4⋊Dic5C2311yescharacteristic
104#683—21no—
105#683—21no—
106#683—21no—
107#683—21no—
108C4×Dic5—21no—
109Dic20—41no—
110#677—22no—
111#677—41no—
112#554—51no—
113#546—51no—
114#489—51no—
115#484—51no—
116#480—51no—
117#474—51no—
118#468—51no—
119#467—51no—
120#464—51no—
121#452—51no—
122#450—51no—
123#440—51no—
124#435D511yescharacteristic, complemented
125#417—51no—
126C2×#102—51no—
127C23×C5C2×D411yescharacteristic
128C23×C5C2×D411yescharacteristic
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—42no—
132C22×D5—42no—
133C22×D5—81no—
134C5×D4—22no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5C2×D411yescharacteristic
140C2×C4×C5C2×D411yescharacteristic
141C2×C4×C5C2×D411yescharacteristic
142C2×C4×C5C2×D411yescharacteristic
143C2×C4×C5C2411yescharacteristic
144C22⋊D5—42no—
145C22⋊D5—81no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—81no—
153C2×Dic5—81no—
154D20—21no—
155D20—21no—
156D20—21no—
157D20—42no—
158D20#4112yes—
159C4×D5—42no—
160C4×D5—81no—
161Dic10—21no—
162Dic10—21no—
163Dic10—21no—
164Dic10—21no—
165Dic10—81no—
166C5×C8—21no—
167C5×C8—21no—
168C5×C8—21no—
169C5×C8—21no—
170C2×#41—51no—
171C22×D4—51no—
172C2×Q16—51no—
173C2×SD16—51no—
174C2×SD16—51no—
175C2×M16C2×D511yescharacteristic, complemented
176C22×C8C2×D511yescharacteristic
177C4⋊Q8—51no—
178#125—101no—
179#124—51no—
180#123—101no—
181C22⋊Q8—51no—
182C22⋊Q8—51no—
183C22⋊Q8—51no—
184C22⋊Q8—101no—
185C22⋊Q8—101no—
186#121—51no—
187#121—101no—
188#120—101no—
189C4×Q8—51no—
190C4×D4—51no—
191C4×D4—101no—
192C4×D4C2×D511yescharacteristic
193C2×C4⋊C4—51no—
194C2×C4⋊C4—51no—
195C2×C22⋊C4—101no—
196#107—51no—
197#107—51no—
198#107—51no—
199C4⋊C8C2×D511yescharacteristic, complemented
200#103—51no—
201#103—51no—
202#103—51no—
203#103—51no—
204#102—51no—
205#102—51no—
206#102—51no—
207#102—51no—
208#102—51no—
209#102—51no—
210C22⋊C8C2×D511yescharacteristic
211C22⋊C8C2×D511yescharacteristic, complemented
212#97C2×D511yescharacteristic, complemented
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5#13712yes—
219C22×C5C22×D411yescharacteristic
220C2×D5—22no—
221C2×D5—41no—
222C2×D5—41no—
223C2×D5—41no—
224C2×D5—41no—
225C2×D5—41no—
226C2×D5—84no—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—21no—
230C4×C5—21no—
231C4×C5C2×#4111yescharacteristic
232C4×C5H(5,𝔽2)11yescharacteristic
233Dic5—41no—
234Dic5—41no—
235Dic5—41no—
236Dic5—41no—
237Dic5—41no—
238Dic5—41no—
239C24—101no—
240#41—102no—
241#41—201no—
242C2×Q8—51no—
243C2×Q8—51no—
244C2×Q8—101no—
245C2×D4—51no—
246C2×D4—51no—
247C2×D4—102no—
248C2×D4—101no—
249C2×D4—101no—
250C2×D4—101no—
251C2×D4—201no—
252C2×D4D2011yescharacteristic
253C22×C4—101no—
254C22×C4—101no—
255C22×C4—101no—
256C22×C4—101no—
257C22×C4C22×D511yescharacteristic
258C22×C4C22×D511yescharacteristic
259Q16—201no—
260SD16—102no—
261SD16—201no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D511yescharacteristic
265C2×C8C22×D511yescharacteristic
266C2×C8C22×D511yescharacteristic
267C2×C8C22×D511yescharacteristic
268C4⋊C4—51no—
269C4⋊C4—51no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4D2011yescharacteristic
280C22⋊C4—101no—
281C22⋊C4—101no—
282C22⋊C4—101no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C22⋊C4—101no—
286C22⋊C4—101no—
287C22⋊C4D2011yescharacteristic
288C22⋊C4D2011yescharacteristic
289C42—101no—
290C42C22×D511yescharacteristic
291C2×C5—22no—
292C2×C5—41no—
293C2×C5#54611yescharacteristic
294C2×C5C2×#13711yescharacteristic
295C2×C5#57611yescharacteristic
296D5—42no—
297D5—81no—
298C23—101no—
299C23—101no—
300C23—202no—
301C23—202no—
302C23—401no—
303C23C2×D2011yescharacteristic
304C23C2×D2011yescharacteristic
305Q8—101no—
306Q8—101no—
307Q8—101no—
308Q8—101no—
309Q8—401no—
310D4—22no—
311D4—52no—
312D4—101no—
313D4—101no—
314D4—101no—
315D4—202no—
316D4—202no—
317D4—401no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—202no—
329C2×C4—401no—
330C2×C4—401no—
331C2×C4—401no—
332C2×C4C2×D2011yescharacteristic
333C2×C4C2×D2011yescharacteristic
334C2×C4C2×D2011yescharacteristic
335C2×C4C2×D2011yescharacteristic
336C2×C4C23×D511yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—21no—
341C5#331411yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—102no—
348C22—201no—
349C22—201no—
350C22—201no—
351C22—201no—
352C22—201no—
353C22—404no—
354C22#405512yes—
355C22C22×D2011yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—201no—
361C4—201no—
362C4—201no—
363C4—201no—
364C4—201no—
365C4—201no—
366C4#414411yescharacteristic
367C4D5×#4111yescharacteristic
368C2—22no—
369C2—41no—
370C2—202no—
371C2—401no—
372C2#6588811yescharacteristic
373C2C2×#405511yescharacteristic
374C2#6608611yescharacteristic
subgroupG/H
centerC22C22×D20
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#435C2
socleC22×C5C22×D4
prime radical#65884C2
hypercenter#435D5
hypocenterC5#3314
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
2. #65877C2semidirect
3. C5×#435C2semidirect
4. #65423C2semidirect
5. #65422C2semidirect
6. #65405C2semidirect
7. C2×#3953C2semidirect
8. #65135C2semidirect
9. #65134C2semidirect
10. #65025C2semidirect
11. #65022C2semidirect
12. #65020C2semidirect
13. #65011C2semidirect
14. #65003C2semidirect
15. #64999C2semidirect
18. C2×C5×M16C22semidirect
25. C2×C4⋊Dic5C22semidirect
28. #4070C22semidirect
29. C2×Dic20C22semidirect
40. #4015C22semidirect
41. C4×Dic10C22semidirect
42. C5×C4⋊C8C22semidirect
44. C5×C22⋊C8C22semidirect
45. C5×#97C22semidirect
52. #3950C22semidirect
53. #3950C22semidirect
54. #3950C22semidirect
55. #3948C22semidirect
56. #3948C22semidirect
57. #3948C22semidirect
58. #3948C22semidirect
124. #435D5semidirect
175. C2×M16C2×D5semidirect
199. C4⋊C8C2×D5semidirect
211. C22⋊C8C2×D5semidirect
212. #97C2×D5semidirect
341. C5#3314semidirect

Maximal subgroups

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

subgroupindex
#658842
#658772
C5×#4352
#654232
#654222
#654052
C2×#39532
#651352
#651342
#650252
#650222
#650202
#650112
#650032
#649992
#33145