Finite Group Databasebeta

← #10612949

Subgroups — #10612949

Order 640.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66019C211yesmaximal, characteristic, complemented
2#65919C211yesmaximal, characteristic
3C5×#479C211yesmaximal, characteristic, complemented
4#65356C211yesmaximal, characteristic
5#65319C211yesmaximal, characteristic, complemented
6#65180C211yesmaximal, characteristic, complemented
7#65178C211yesmaximal, characteristic, complemented
8#65159C211yesmaximal, characteristic, complemented
9#65141C211yesmaximal, characteristic, complemented
10#65137C211yesmaximal, characteristic
11#65117C211yesmaximal, characteristic, complemented
12#65089C211yesmaximal, characteristic, complemented
13#65087C211yesmaximal, characteristic, complemented
14#65087C211yesmaximal, characteristic, complemented
15#65084C211yesmaximal, characteristic, complemented
16C5×#125C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18#4093C2211yescharacteristic
19#4093C2211yescharacteristic
20C2×#689C2211yescharacteristic
21C2×#677C2211yescharacteristic
22C2×#677C2211yescharacteristic
23#4040—21no—
24#4040—21no—
25#4039C2211yescharacteristic
26#4039C2211yescharacteristic
27#4036C2211yescharacteristic
28#4035—21no—
29#4035—21no—
30#4034—21no—
31#4034C2211yescharacteristic
32#4033—21no—
33#4033C2211yescharacteristic
34#4033C2211yescharacteristic
35#4021—21no—
36#4020C2211yescharacteristic
37C4×D20—21no—
38C4×Dic10C2211yescharacteristic
39C4×Dic10C2211yescharacteristic
40C5×#107C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×C4⋊C8C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×#103C2211yescharacteristic
45#3967C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3947C2211yescharacteristic
49#3946C2211yescharacteristic
50#3946C2211yescharacteristic
51C8×Dic5C2211yescharacteristic
52#3942C2211yescharacteristic
53#3941C2211yescharacteristic
54#3941C2211yescharacteristic
55#3941C2211yescharacteristic
56#3941C2211yescharacteristic
57#3940C2211yescharacteristic
58#3935C2211yescharacteristic
59#3371—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×D20—21no—
62C2×D20—21no—
63C2×D20C2311yescharacteristic
64C2×D20C2311yescharacteristic
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×Dic10—21no—
68C2×Dic10D411yescharacteristic
69C2×Dic10C2311yescharacteristic
70C2×C5×C8C2311yescharacteristic
71C2×C5×C8C2311yescharacteristic
72C5×C4⋊C4—21no—
73C5×C4⋊C4—21no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4C2311yescharacteristic
76C5×C4⋊C4C2311yescharacteristic
77C5×C4⋊C4C2311yescharacteristic
78C42×C5—21no—
79C42×C5C2311yescharacteristic
80#689—22no—
81#685—21no—
82#685—21no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5D411yescharacteristic
89C4⋊Dic5C2311yescharacteristic
90#683—21no—
91#683—21no—
92#683—21no—
93#683—21no—
94#683—21no—
95#683D411yescharacteristic
96#683D411yescharacteristic
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—21no—
100C4×Dic5C2311yescharacteristic
101C4×Dic5C2311yescharacteristic
102C2×#168C2311yescharacteristic
103C2×#168C2311yescharacteristic
104#677—22no—
105#677—22no—
106#559—51no—
107#557—51no—
108#490—51no—
109#489—51no—
110#488—51no—
111#479D511yescharacteristic, complemented
112#478—51no—
113#476—51no—
114#464—51no—
115#464—51no—
116#460—51no—
117#446—51no—
118#441—51no—
119#440—51no—
120C4×SD16—51no—
121C22×D5—21no—
122C22×D5—21no—
123C5×Q8—21no—
124C5×Q8—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5C2×D411yescharacteristic
130C2×C4×C5C2×D411yescharacteristic
131C2×C4×C5C2411yescharacteristic
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5C2×D411yescharacteristic
135C2×Dic5C2×D411yescharacteristic
136C2×Dic5C2×D411yescharacteristic
137C2×Dic5C2×D411yescharacteristic
138D20—21no—
139D20—21no—
140D20—21no—
141D20—21no—
142D20—42no—
143D20—81no—
144C4×D5—81no—
145C4×D5—81no—
146Dic10—21no—
147Dic10—41no—
148Dic10—42no—
149Dic10#4112yes—
150C5×C8—21no—
151C5×C8—21no—
152#168—21no—
153#168—21no—
154C2×Q16—51no—
155C2×SD16—51no—
156C2×SD16—51no—
157C4⋊Q8—51no—
158C4⋊Q8—101no—
159#127—51no—
160#125—51no—
161#125—101no—
162#125—101no—
163#125C2×D511yescharacteristic
164#124—51no—
165#124—51no—
166#124—101no—
167#123—101no—
168#123—101no—
169C4×Q8—51no—
170C4×Q8—51no—
171C4×Q8—51no—
172C4×Q8—51no—
173C4×Q8—101no—
174C4×Q8C2×D511yescharacteristic
175C4×D4—51no—
176C4×D4—51no—
177C4×D4—101no—
178#107C2×D511yescharacteristic
179#106—51no—
180#106C2×D511yescharacteristic
181C4⋊C8—51no—
182C4⋊C8—51no—
183C4⋊C8C2×D511yescharacteristic
184#103—51no—
185#103—51no—
186#103C2×D511yescharacteristic
187#103C2×D511yescharacteristic
188#102—51no—
189#102—51no—
190#102—51no—
191#102—51no—
192#102—51no—
193#102—51no—
194#97—51no—
195#97—51no—
196C4×C8—51no—
197C22×C5C22×D411yescharacteristic
198C2×D5—41no—
199C2×D5—41no—
200C2×D5—41no—
201C2×D5—41no—
202C2×D5—41no—
203C2×D5—41no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5C2×#4111yescharacteristic
211C4×C52−1+411yescharacteristic
212Dic5—22no—
213Dic5—21no—
214Dic5—21no—
215Dic5—21no—
216Dic5—21no—
217Dic5—41no—
218C2×Q8—51no—
219C2×Q8—51no—
220C2×Q8—101no—
221C2×Q8C22×D511yescharacteristic
222C2×D4—51no—
223C2×D4—51no—
224C2×D4—101no—
225C2×D4—101no—
226C22×C4—101no—
227C22×C4—101no—
228Q16—102no—
229SD16—102no—
230SD16—102no—
231C2×C8—51no—
232C2×C8—51no—
233C2×C8C22×D511yescharacteristic
234C2×C8C22×D511yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—51no—
239C4⋊C4—51no—
240C4⋊C4—51no—
241C4⋊C4—51no—
242C4⋊C4—101no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4C22×D511yescharacteristic
249C4⋊C4C22×D511yescharacteristic
250C4⋊C4C22×D511yescharacteristic
251C22⋊C4—101no—
252C22⋊C4—101no—
253C22⋊C4—101no—
254C22⋊C4—101no—
255C22⋊C4—101no—
256C22⋊C4—101no—
257C42—21no—
258C42—51no—
259C42—51no—
260C42—101no—
261C42—101no—
262C42—101no—
263C42C22×D511yescharacteristic
264C2×C5#54811yescharacteristic
265C2×C5#57511yescharacteristic
266C2×C5#57711yescharacteristic
267D5—81no—
268D5—81no—
269C23—101no—
270C23—101no—
271Q8—21no—
272Q8—21no—
273Q8—52no—
274Q8—101no—
275Q8—201no—
276Q8—202no—
277D4—101no—
278D4—101no—
279D4—101no—
280D4—101no—
281D4—202no—
282D4—401no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—51no—
288C2×C4—51no—
289C2×C4—51no—
290C2×C4—51no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4D4×D511yescharacteristic
296C2×C4D4×D511yescharacteristic
297C2×C4C23×D511yescharacteristic
298C8—21no—
299C8—21no—
300C8—101no—
301C8—101no—
302C5#337111yescharacteristic, complemented, Sylow
303C22—201no—
304C22—201no—
305C22—201no—
306C22—201no—
307C22—201no—
308C22—201no—
309C22C2×D4×D511yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—101no—
317C4—101no—
318C4—101no—
319C4—101no—
320C4—102no—
321C4—201no—
322C4#414711yescharacteristic
323C4D5×#4111yescharacteristic
324C2—401no—
325C2—401no—
326C2#6596711yescharacteristic
327C2#6610411yescharacteristic
328C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#479C2
socleC22×C5C22×D4
prime radical#4020C22
hypercenter#479D5
hypocenterC5#3371
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #66019C2semidirect
3. C5×#479C2semidirect
5. #65319C2semidirect
6. #65180C2semidirect
7. #65178C2semidirect
8. #65159C2semidirect
9. #65141C2semidirect
11. #65117C2semidirect
12. #65089C2semidirect
13. #65087C2semidirect
14. #65087C2semidirect
15. #65084C2semidirect
111. #479D5semidirect
302. C5#3371semidirect

Maximal subgroups

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

subgroupindex
#660192
#659192
C5×#4792
#653562
#653192
#651802
#651782
#651592
#651412
#651372
#651172
#650892
#650872
#650842
#33715