Finite Group Databasebeta

← #10612495

Subgroups — #10612495

Order 640.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65961C211yesmaximal, characteristic
2D5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C5×#467C211yesmaximal, characteristic, complemented
4#65476C211yesmaximal, characteristic, complemented
5#65475C211yesmaximal, characteristic, complemented
6#65403C211yesmaximal, characteristic, complemented
7C2×#3952C211yesmaximal, characteristic, complemented
8#65340C211yesmaximal, characteristic, complemented
9#65337C211yesmaximal, characteristic, complemented
10#65177C211yesmaximal, characteristic, complemented
11#65171C211yesmaximal, characteristic, complemented
12#65104C211yesmaximal, characteristic, complemented
13#65099C211yesmaximal, characteristic, complemented
14#65095C211yesmaximal, characteristic, complemented
15#65094C211yesmaximal, characteristic, complemented
16C2×#713C2211yescharacteristic
17C2×Q8×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C2×C5×Q16C2211yescharacteristic, complemented
20C22×C5×C8C2211yescharacteristic
21C5×C22⋊Q8C2211yescharacteristic
22C5×C22⋊Q8C2211yescharacteristic
23#4092C2211yescharacteristic
24#4092C2211yescharacteristic
25C2×#689C2211yescharacteristic, complemented
26C2×#688C2211yescharacteristic, complemented
27#4076C2211yescharacteristic
28#4070C2211yescharacteristic
29C22×#168C2211yescharacteristic
30C2×#677C2211yescharacteristic, complemented
31#4043C2211yescharacteristic
32#4042—21no—
33#4041C2211yescharacteristic
34#4040—21no—
35#4039—21no—
36#4038C2211yescharacteristic
37D5×C4⋊C4—21no—
38D5×C4⋊C4C2211yescharacteristic
39#4028—21no—
40#4027—21no—
41D5×C22⋊C4—21no—
42#4024—21no—
43C5×#107C2211yescharacteristic, complemented
44C5×#103C2211yescharacteristic, complemented
45C5×#103C2211yescharacteristic, complemented
46#3967C2211yescharacteristic, complemented
47#3967C2211yescharacteristic, complemented
48#3953C2211yescharacteristic, complemented
49#3952C2211yescharacteristic
50#3952C2211yescharacteristic
51#3952C2211yescharacteristic
52#3952C2211yescharacteristic
53#3949C2211yescharacteristic, complemented
54#3948C2211yescharacteristic, complemented
55#3942C2211yescharacteristic, complemented
56#3941C2211yescharacteristic, complemented
57#3940C2211yescharacteristic, complemented
58#3939C2211yescharacteristic, complemented
59#3190—51nomaximal, Sylow
60C23×D5D411yescharacteristic
61C2×C5×Q8C2311yescharacteristic
62C2×C5×Q8C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C2×C22⋊D5—21no—
65C22×Dic5D411yescharacteristic
66#713—41no—
67#713—41no—
68Q8×D5—41no—
69Q8×D5—41no—
70C2×D20—21no—
71C2×D20—21no—
72C2×D20C2311yescharacteristic
73C2×C4×D5—21no—
74C2×C4×D5—21no—
75C2×C4×D5—21no—
76C2×C4×D5—41no—
77C2×C4×D5—41no—
78C2×C4×D5D411yescharacteristic
79C2×C4×D5D411yescharacteristic
80C2×C4×D5C2311yescharacteristic
81C2×C4×D5C2311yescharacteristic
82C2×Dic10—21no—
83C2×Dic10C2311yescharacteristic
84C5×Q16—41no—
85C2×C5×C8—41no—
86C2×C5×C8C2311yescharacteristic
87C2×C5×C8C2311yescharacteristic
88C5×C4⋊C4—21no—
89C5×C4⋊C4—21no—
90C5×C4⋊C4C2311yescharacteristic
91C5×C4⋊C4C2311yescharacteristic
92C5×C22⋊C4—21no—
93C5×C22⋊C4—21no—
94C22⋊Dic5—21no—
95#689—41no—
96#688—41no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685—21no—
101#685—21no—
102#685—21no—
103C4⋊Dic5—21no—
104C4⋊Dic5C2311yescharacteristic
105C4⋊Dic5C2311yescharacteristic
106#683—21no—
107#683—21no—
108#683—21no—
109#683—21no—
110C4×Dic5—21no—
111C2×#168—41no—
112C2×#168C2311yescharacteristic
113C2×#168C2311yescharacteristic
114#677—41no—
115#525—51no—
116C2×C22⋊Q8—51no—
117#485—51no—
118#485—51no—
119#483—51no—
120#480—51no—
121#467—51no—
122#467D511yescharacteristic, complemented
123#465—51no—
124#465—51no—
125#452—51no—
126#452—51no—
127#451—51no—
128#448—51no—
129C2×C22⋊C8—51no—
130C23×C5C2×D411yescharacteristic
131C22×D5—22no—
132C22×D5—22no—
133C22×D5—21no—
134C22×D5—41no—
135C22×D5C2×D411yescharacteristic
136C22×D5C2×D411yescharacteristic
137C5×Q8—21no—
138C5×Q8—21no—
139C5×Q8—21no—
140C5×Q8—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5C2×D411yescharacteristic
148C2×C4×C5C2411yescharacteristic
149C22⋊D5—42no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—41no—
154C2×Dic5C2×D411yescharacteristic
155C2×Dic5C2×D411yescharacteristic
156D20—21no—
157D20—21no—
158D20—42no—
159D20—42no—
160C4×D5—21no—
161C4×D5—21no—
162C4×D5—21no—
163C4×D5—21no—
164C4×D5—41no—
165C4×D5—41no—
166C4×D5—42no—
167C4×D5—42no—
168C4×D5—42no—
169Dic10—21no—
170Dic10—21no—
171Dic10—42no—
172C5×C8—21no—
173C5×C8—21no—
174#168—21no—
175#168—21no—
176C2×#41—51no—
177C22×Q8—51no—
178C23×C4—51no—
179C2×Q16—51no—
180C2×Q16C2×D511yescharacteristic, complemented
181C2×SD16—51no—
182C2×SD16—51no—
183C22×C8—51no—
184C22×C8C2×D511yescharacteristic
185#123—101no—
186C22⋊Q8—51no—
187C22⋊Q8—51no—
188C22⋊Q8—51no—
189C22⋊Q8—51no—
190C22⋊Q8—101no—
191C22⋊Q8—101no—
192C22⋊Q8C2×D511yescharacteristic
193C22⋊Q8C2×D511yescharacteristic
194#121—51no—
195#121—51no—
196#120—101no—
197C4×D4—101no—
198C4×D4—101no—
199#117—51no—
200C2×C4⋊C4—51no—
201C2×C4⋊C4—101no—
202C2×C22⋊C4—101no—
203#107—51no—
204#107C2×D511yescharacteristic, complemented
205#106—51no—
206#106—51no—
207#103—51no—
208#103—51no—
209#103—51no—
210#103—51no—
211#103C2×D511yescharacteristic, complemented
212#103C2×D511yescharacteristic, complemented
213#102—51no—
214#102—51no—
215C22⋊C8—51no—
216C22⋊C8—51no—
217C22⋊C8—51no—
218C22⋊C8—51no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5#13712yes—
222C22×C5C22×D411yescharacteristic
223C2×D5—21no—
224C2×D5—21no—
225C2×D5—21no—
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—44no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5#13512yes—
233C4×C5—21no—
234C4×C5—41no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238C4×C5H(5,𝔽2)11yescharacteristic
239C4×C5H(5,𝔽2)11yescharacteristic
240Dic5—21no—
241Dic5—21no—
242Dic5—41no—
243Dic5—41no—
244Dic5—41no—
245C24—51no—
246#41—201no—
247#41—201no—
248C2×Q8—51no—
249C2×Q8—101no—
250C2×Q8—201no—
251C2×Q8—201no—
252C2×Q8C22×D511yescharacteristic
253C2×Q8C22×D511yescharacteristic
254C2×D4—51no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4—101no—
258C22×C4—51no—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4—101no—
264C22×C4—101no—
265C22×C4—101no—
266C22×C4—201no—
267C22×C4—201no—
268C22×C4C22×D511yescharacteristic
269Q16—41no—
270Q16—201no—
271SD16—201no—
272SD16—201no—
273C2×C8—41no—
274C2×C8—51no—
275C2×C8—51no—
276C2×C8—201no—
277C2×C8C22×D511yescharacteristic
278C2×C8C22×D511yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—51no—
282C4⋊C4—51no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4C22×D511yescharacteristic
289C4⋊C4C22×D511yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C22⋊C4—101no—
296C22⋊C4—101no—
297C22⋊C4—101no—
298C22⋊C4—101no—
299C42—101no—
300C2×C5—22no—
301C2×C5#53411yescharacteristic
302C2×C5C2×#13511yescharacteristic
303C2×C5C2×#13711yescharacteristic
304D5—22no—
305D5—41no—
306D5—81no—
307C23—51no—
308C23—51no—
309C23—102no—
310C23—102no—
311C23—101no—
312C23—201no—
313C23D4×D511yescharacteristic
314Q8—21no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—101no—
319Q8—101no—
320Q8—202no—
321D4—101no—
322D4—101no—
323D4—202no—
324D4—202no—
325D4—202no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—51no—
333C2×C4—51no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—201no—
342C2×C4—201no—
343C2×C4—202no—
344C2×C4—202no—
345C2×C4—202no—
346C2×C4—201no—
347C2×C4D4×D511yescharacteristic
348C2×C4C23×D511yescharacteristic
349C8—21no—
350C8—21no—
351C8—101no—
352C8—101no—
353C5#319011yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—52no—
357C22—101no—
358C22—101no—
359C22—101no—
360C22—101no—
361C22—101no—
362C22—204no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22#406412yes—
367C22C2×D4×D511yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—101no—
374C4—101no—
375C4—201no—
376C4—201no—
377C4—201no—
378C4#414411yescharacteristic
379C4#414911yescharacteristic
380C2—22no—
381C2—102no—
382C2—201no—
383C2—401no—
384C2#6593911yescharacteristic
385C2C2×#406411yescharacteristic
386C2D5×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#467C2
socleC22×C5C22×D4
prime radical#65961C2
hypercenter#467D5
hypocenterC5#3190
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. D5×C22⋊Q8C2semidirect
3. C5×#467C2semidirect
4. #65476C2semidirect
5. #65475C2semidirect
6. #65403C2semidirect
7. C2×#3952C2semidirect
8. #65340C2semidirect
9. #65337C2semidirect
10. #65177C2semidirect
11. #65171C2semidirect
12. #65104C2semidirect
13. #65099C2semidirect
14. #65095C2semidirect
15. #65094C2semidirect
19. C2×C5×Q16C22semidirect
25. C2×#689C22semidirect
26. C2×#688C22semidirect
30. C2×#677C22semidirect
43. C5×#107C22semidirect
44. C5×#103C22semidirect
45. C5×#103C22semidirect
46. #3967C22semidirect
47. #3967C22semidirect
48. #3953C22semidirect
53. #3949C22semidirect
54. #3948C22semidirect
55. #3942C22semidirect
56. #3941C22semidirect
57. #3940C22semidirect
58. #3939C22semidirect
122. #467D5semidirect
180. C2×Q16C2×D5semidirect
204. #107C2×D5semidirect
211. #103C2×D5semidirect
212. #103C2×D5semidirect
353. C5#3190semidirect

Maximal subgroups

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

subgroupindex
#659612
D5×C22⋊Q82
C5×#4672
#654762
#654752
#654032
C2×#39522
#653402
#653372
#651772
#651712
#651042
#650992
#650952
#650942
#31905