Finite Group Databasebeta

← #10611966

Subgroups — #10611966

Order 640.

414 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#66162C211yesmaximal, characteristic
2D5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C5×#452C211yesmaximal, characteristic, complemented
4#65528C211yesmaximal, characteristic, complemented
5#65478C211yesmaximal, characteristic, complemented
6#65475C211yesmaximal, characteristic, complemented
7#65463C211yesmaximal, characteristic, complemented
8#65459C211yesmaximal, characteristic, complemented
9#65334C211yesmaximal, characteristic, complemented
10#65105C211yesmaximal, characteristic, complemented
11#65098C211yesmaximal, characteristic, complemented
12#65069C211yesmaximal, characteristic, complemented
13#65066C211yesmaximal, characteristic, complemented
14#65015C211yesmaximal, characteristic, complemented
15#65012C211yesmaximal, characteristic, complemented
16C2×C5×#41C2211yescharacteristic
17C2×Q8×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C2×C5×Q16C2211yescharacteristic, complemented
20C2×C5×SD16C2211yescharacteristic, complemented
21C5×C22⋊Q8C2211yescharacteristic
22#4092C2211yescharacteristic
23#4092C2211yescharacteristic
24#4092C2211yescharacteristic
25C2×#689C2211yescharacteristic, complemented
26#4084C2211yescharacteristic
27#4084C2211yescharacteristic
28#4083—21no—
29#4081—21no—
30C2×#687C2211yescharacteristic, complemented
31C4×C22⋊D5—21no—
32C4×C22⋊D5—21no—
33#4072C2211yescharacteristic
34#4070C2211yescharacteristic
35C2×#676C2211yescharacteristic
36C2×#676C2211yescharacteristic
37#4043C2211yescharacteristic
38#4042—21no—
39D5×C4⋊C4—21no—
40D5×C4⋊C4C2211yescharacteristic
41D5×C22⋊C4—21no—
42#4024—21no—
43C5×#103C2211yescharacteristic, complemented
44C5×#102C2211yescharacteristic, complemented
45C5×C22⋊C8C2211yescharacteristic
46#3967C2211yescharacteristic, complemented
47#3967C2211yescharacteristic, complemented
48#3967C2211yescharacteristic, complemented
49#3964C2211yescharacteristic, complemented
50C22⋊#168C2211yescharacteristic
51#3952C2211yescharacteristic
52#3952C2211yescharacteristic
53#3950C2211yescharacteristic, complemented
54#3949C2211yescharacteristic, complemented
55#3948C2211yescharacteristic, complemented
56#3948C2211yescharacteristic, complemented
57#3940C2211yescharacteristic, complemented
58#3939C2211yescharacteristic, complemented
59#3196—51nomaximal, Sylow
60C23×D5D411yescharacteristic
61C5×#41—41no—
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—
71C22×Dic5D411yescharacteristic
72Q8×D5—41no—
73Q8×D5—41no—
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—
85C5×SD16—41no—
86C2×C5×C8C2311yescharacteristic
87C2×C5×C8C2311yescharacteristic
88C5×C4⋊C4—21no—
89C5×C4⋊C4C2311yescharacteristic
90C5×C22⋊C4—21no—
91C22⋊Dic5—21no—
92C22⋊Dic5—21no—
93C22⋊Dic5—21no—
94C22⋊Dic5—21no—
95#689—41no—
96#687—41no—
97#685—21no—
98#685—21no—
99#685—21no—
100#685—21no—
101C4⋊Dic5—21no—
102C4⋊Dic5C2311yescharacteristic
103C4⋊Dic5C2311yescharacteristic
104C4⋊Dic5C2311yescharacteristic
105#683—21no—
106#683—21no—
107#683—21no—
108#683—21no—
109#683—21no—
110C4×Dic5—21no—
111C2×#168C2311yescharacteristic
112C2×#168C2311yescharacteristic
113#676—41no—
114#676—41no—
115#525—51no—
116C2×C22⋊Q8—51no—
117#485—51no—
118#485—51no—
119#484—51no—
120#481—51no—
121#470—51no—
122#470—51no—
123#468—51no—
124#468—51no—
125#452—51no—
126#452D511yescharacteristic, complemented
127#451—51no—
128#448—51no—
129#407—51no—
130C23×C5—21no—
131C23×C5C2×D411yescharacteristic
132C22×D5—22no—
133C22×D5—41no—
134C22×D5—41no—
135C22×D5C2×D411yescharacteristic
136C22×D5C2×D411yescharacteristic
137C5×Q8—21no—
138C5×Q8—21no—
139C5×Q8—21no—
140C5×Q8—21no—
141C5×D4—21no—
142C5×D4—21no—
143C5×D4—42no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—42no—
150C2×C4×C5C2×D411yescharacteristic
151C2×C4×C5C2411yescharacteristic
152C22⋊D5—42no—
153C22⋊D5—42no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—41no—
159C2×Dic5C2×D411yescharacteristic
160C2×Dic5C2×D411yescharacteristic
161C4×D5—21no—
162C4×D5—21no—
163C4×D5—21no—
164C4×D5—21no—
165C4×D5—41no—
166C4×D5—41no—
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×#41C2×D511yescharacteristic
177C22×Q8—51no—
178C23×C4—51no—
179C2×Q16—51no—
180C2×Q16C2×D511yescharacteristic, complemented
181C2×SD16—51no—
182C2×SD16C2×D511yescharacteristic, complemented
183C2×M16—51no—
184C2×M16—51no—
185#123—101no—
186C22⋊Q8—51no—
187C22⋊Q8—51no—
188C22⋊Q8—51no—
189C22⋊Q8—51no—
190C22⋊Q8—51no—
191C22⋊Q8—101no—
192C22⋊Q8—101no—
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#107—51no—
205#106—51no—
206#106—51no—
207#103—51no—
208#103—51no—
209#103—51no—
210#103—51no—
211#103—51no—
212#103C2×D511yescharacteristic, complemented
213#102—51no—
214#102C2×D511yescharacteristic, complemented
215C22⋊C8—51no—
216C22⋊C8—51no—
217C22⋊C8—51no—
218C22⋊C8C2×D511yescharacteristic
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5C22×D411yescharacteristic
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—21no—
229C2×D5—21no—
230C2×D5—21no—
231C2×D5—44no—
232C2×D5#13712yes—
233C4×C5—21no—
234C4×C5—41no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5H(5,𝔽2)11yescharacteristic
238C4×C5H(5,𝔽2)11yescharacteristic
239Dic5—21no—
240Dic5—21no—
241Dic5—41no—
242Dic5—41no—
243Dic5—41no—
244Dic5—41no—
245C24—51no—
246#41—41no—
247#41—41no—
248C2×Q8—51no—
249C2×Q8—101no—
250C2×Q8—201no—
251C2×Q8—201no—
252C2×Q8C22×D511yescharacteristic
253C2×Q8C22×D511yescharacteristic
254C2×D4—21no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4C22×D511yescharacteristic
258C22×C4—21no—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4—51no—
264C22×C4—101no—
265C22×C4—101no—
266C22×C4—201no—
267C22×C4—201no—
268C22×C4C22×D511yescharacteristic
269Q16—41no—
270Q16—201no—
271SD16—41no—
272SD16—201no—
273M16—201no—
274M16—201no—
275C2×C8—51no—
276C2×C8—51no—
277C2×C8C22×D511yescharacteristic
278C2×C8C22×D511yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—51no—
281C4⋊C4—51no—
282C4⋊C4—51no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4C22×D511yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—101no—
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—41no—
301C2×C5—81no—
302C2×C5#53411yescharacteristic
303C2×C5C2×#13711yescharacteristic
304C2×C5#57511yescharacteristic
305D5—22no—
306D5—41no—
307C23—21no—
308C23—51no—
309C23—51no—
310C23—102no—
311C23—201no—
312C23—201no—
313C23D4×D511yescharacteristic
314Q8—21no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—101no—
319Q8—101no—
320Q8—202no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—202no—
325D4—202no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
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—101no—
342C2×C4—201no—
343C2×C4—201no—
344C2×C4—202no—
345C2×C4—202no—
346C2×C4—201no—
347C2×C4D4×D511yescharacteristic
348C2×C4C23×D511yescharacteristic
349C8—21no—
350C8—21no—
351C8—101no—
352C8—101no—
353C5#319611yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—52no—
361C22—101no—
362C22—101no—
363C22—101no—
364C22—101no—
365C22—101no—
366C22—204no—
367C22C2×D4×D511yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—101no—
373C4—101no—
374C4—201no—
375C4—201no—
376C4—201no—
377C4—201no—
378C4#414411yescharacteristic
379C4#414411yescharacteristic
380C2—41no—
381C2—81no—
382C2—102no—
383C2—201no—
384C2#6592311yescharacteristic
385C2#6610211yescharacteristic
386C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#452C2
socleC22×C5C22×D4
prime radical#66162C2
hypercenter#452D5
hypocenterC5#3196
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. D5×C22⋊Q8C2semidirect
3. C5×#452C2semidirect
4. #65528C2semidirect
5. #65478C2semidirect
6. #65475C2semidirect
7. #65463C2semidirect
8. #65459C2semidirect
9. #65334C2semidirect
10. #65105C2semidirect
11. #65098C2semidirect
12. #65069C2semidirect
13. #65066C2semidirect
14. #65015C2semidirect
15. #65012C2semidirect
19. C2×C5×Q16C22semidirect
20. C2×C5×SD16C22semidirect
25. C2×#689C22semidirect
30. C2×#687C22semidirect
43. C5×#103C22semidirect
44. C5×#102C22semidirect
46. #3967C22semidirect
47. #3967C22semidirect
48. #3967C22semidirect
49. #3964C22semidirect
53. #3950C22semidirect
54. #3949C22semidirect
55. #3948C22semidirect
56. #3948C22semidirect
57. #3940C22semidirect
58. #3939C22semidirect
126. #452D5semidirect
180. C2×Q16C2×D5semidirect
182. C2×SD16C2×D5semidirect
212. #103C2×D5semidirect
214. #102C2×D5semidirect
353. C5#3196semidirect

Maximal subgroups

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

subgroupindex
#661622
D5×C22⋊Q82
C5×#4522
#655282
#654782
#654752
#654632
#654592
#653342
#651052
#650982
#650692
#650662
#650152
#650122
#31965