Finite Group Databasebeta

← #10612486

Subgroups — #10612486

Order 640.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65976C211yesmaximal, characteristic
2#65969C211yesmaximal, characteristic
3C5×#467C211yesmaximal, characteristic, complemented
4#65478C211yesmaximal, characteristic, complemented
5#65473C211yesmaximal, characteristic, complemented
6#65400C211yesmaximal, characteristic
7C2×#3949C211yesmaximal, characteristic, complemented
8#65333C211yesmaximal, characteristic, complemented
9#65332C211yesmaximal, characteristic, complemented
10#65170C211yesmaximal, characteristic, complemented
11#65165C211yesmaximal, characteristic, complemented
12#65104C211yesmaximal, characteristic, complemented
13#65094C211yesmaximal, characteristic, complemented
14#65088C211yesmaximal, characteristic, complemented
15#65080C211yesmaximal, characteristic, complemented
16C2×C5×Q16C2211yescharacteristic
17C22×C5×C8C2211yescharacteristic
18C5×C22⋊Q8C2211yescharacteristic
19C5×C22⋊Q8C2211yescharacteristic
20#4092C2211yescharacteristic
21#4092C2211yescharacteristic
22Q8×Dic5C2211yescharacteristic
23Q8×Dic5C2211yescharacteristic
24C4×C22⋊D5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C2×C4⋊Dic5C2211yescharacteristic
27C2×#676C2211yescharacteristic
28#4044—21no—
29#4043—21no—
30#4038C2211yescharacteristic
31D5×C4⋊C4C2211yescharacteristic
32#4036—21no—
33#4036C2211yescharacteristic
34#4035—21no—
35#4034C2211yescharacteristic
36#4032—21no—
37#4027—21no—
38#4024—21no—
39#4023—21no—
40C5×#107C2211yescharacteristic
41C5×#103C2211yescharacteristic
42C5×#103C2211yescharacteristic
43#3967C2211yescharacteristic
44#3967C2211yescharacteristic
45#3967C2211yescharacteristic
46#3967C2211yescharacteristic
47C22⋊#168C2211yescharacteristic
48#3952C2211yescharacteristic
49#3949C2211yescharacteristic
50#3949C2211yescharacteristic
51#3949C2211yescharacteristic
52#3949C2211yescharacteristic
53#3947C2211yescharacteristic
54#3946C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3344—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C5×Q8C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C2×C22⋊D5D411yescharacteristic
64C22×Dic5—21no—
65C22×Dic5—21no—
66C2×C4×D5—21no—
67C2×C4×D5C2311yescharacteristic
68C2×Dic10—21no—
69C5×Q16—22no—
70C2×C5×C8—22no—
71C2×C5×C8C2311yescharacteristic
72C2×C5×C8C2311yescharacteristic
73C5×C4⋊C4—21no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4C2311yescharacteristic
76C5×C4⋊C4C2311yescharacteristic
77C5×C22⋊C4—21no—
78C5×C22⋊C4—21no—
79C22⋊Dic5D411yescharacteristic
80#685—21no—
81#685—21no—
82#685—21no—
83#685D411yescharacteristic
84C4⋊Dic5—21no—
85C4⋊Dic5—21no—
86C4⋊Dic5—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5C2311yescharacteristic
90C4⋊Dic5C2311yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93#683—21no—
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683D411yescharacteristic
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5—21no—
102C4×Dic5C2311yescharacteristic
103C2×#168C2311yescharacteristic
104C2×#168C2311yescharacteristic
105#676—22no—
106#554—51no—
107#552—51no—
108#501—51no—
109#485—51no—
110#484—51no—
111#483—51no—
112#483—51no—
113#479—51no—
114#475—51no—
115#470—51no—
116#467D511yescharacteristic, complemented
117#441—51no—
118#435—51no—
119#428—51no—
120C2×#106—51no—
121C23×C5C2×D411yescharacteristic
122C22×D5C2×D411yescharacteristic
123C5×Q8—21no—
124C5×Q8—21no—
125C5×Q8—21no—
126C5×Q8—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5C2×D411yescharacteristic
134C2×C4×C5C2411yescharacteristic
135C22⋊D5—22no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—42no—
141C2×Dic5—81no—
142C2×Dic5C2×D411yescharacteristic
143C2×Dic5C2×D411yescharacteristic
144C2×Dic5C2×D411yescharacteristic
145C4×D5—21no—
146C4×D5—21no—
147C4×D5—81no—
148Dic10—81no—
149C5×C8—21no—
150C5×C8#4112yes—
151#168—21no—
152#168—21no—
153C2×Q16C2×D511yescharacteristic
154C2×M16—51no—
155C22×C8C2×D511yescharacteristic
156C4⋊Q8—51no—
157#126—101no—
158#125—51no—
159#125—101no—
160#125—101no—
161#123—101no—
162C22⋊Q8—51no—
163C22⋊Q8—51no—
164C22⋊Q8—101no—
165C22⋊Q8—101no—
166C22⋊Q8C2×D511yescharacteristic
167C22⋊Q8C2×D511yescharacteristic
168C4×Q8—51no—
169C4×Q8—51no—
170C4×D4—51no—
171C4×D4—101no—
172#117—51no—
173#117—101no—
174C2×C4⋊C4—51no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—51no—
177#107—51no—
178#107—51no—
179#107C2×D511yescharacteristic
180#106—51no—
181#106—51no—
182#106—51no—
183#106—51no—
184#106—51no—
185#106—51no—
186C4⋊C8—51no—
187#103—51no—
188#103—51no—
189#103—51no—
190#103—51no—
191#103C2×D511yescharacteristic
192#103C2×D511yescharacteristic
193C22⋊C8—51no—
194C22⋊C8—51no—
195#97—51no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5#13712yes—
199C22×C5C22×D411yescharacteristic
200C2×D5—21no—
201C2×D5—21no—
202C2×D5—21no—
203C4×C5—21no—
204C4×C5—41no—
205C4×C5—41no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5C2×#4111yescharacteristic
209C4×C52−1+411yescharacteristic
210Dic5—21no—
211Dic5—21no—
212Dic5—21no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216Dic5—41no—
217C2×Q8—101no—
218C2×Q8C22×D511yescharacteristic
219C2×Q8C22×D511yescharacteristic
220C2×D4—51no—
221C22×C4—51no—
222C22×C4—101no—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4C22×D511yescharacteristic
226Q16—22no—
227M16—102no—
228C2×C8—22no—
229C2×C8—51no—
230C2×C8—51no—
231C2×C8C22×D511yescharacteristic
232C2×C8C22×D511yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—51no—
236C4⋊C4—51no—
237C4⋊C4—51no—
238C4⋊C4—51no—
239C4⋊C4—51no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4—101no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4—101no—
250C4⋊C4C22×D511yescharacteristic
251C4⋊C4C22×D511yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—51no—
255C22⋊C4—51no—
256C22⋊C4—101no—
257C22⋊C4—101no—
258C22⋊C4—101no—
259C42—51no—
260C42—101no—
261C42—101no—
262C42—101no—
263C2×C5—22no—
264C2×C5#54711yescharacteristic
265C2×C5C2×#13711yescharacteristic
266C2×C5#57711yescharacteristic
267D5—41no—
268C23—51no—
269C23D4×D511yescharacteristic
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—401no—
275D4—102no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—51no—
283C2×C4—51no—
284C2×C4—51no—
285C2×C4—101no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—202no—
292C2×C4—401no—
293C2×C4—401no—
294C2×C4D4×D511yescharacteristic
295C2×C4C23×D511yescharacteristic
296C8—21no—
297C8—101no—
298C8—101no—
299C8#71112yes—
300C5#334411yescharacteristic, complemented, Sylow
301C22—21no—
302C22—21no—
303C22—101no—
304C22—101no—
305C22—101no—
306C22#406412yes—
307C22C2×D4×D511yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—101no—
314C4—101no—
315C4—101no—
316C4—201no—
317C4—201no—
318C4—201no—
319C4—201no—
320C4C2×#71111yescharacteristic
321C4#415011yescharacteristic
322C2—22no—
323C2—201no—
324C2#6594511yescharacteristic
325C2C2×#406411yescharacteristic
326C2#6610411yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#467C2
socleC22×C5C22×D4
prime radicalC2×C22⋊D5D4
hypercenter#467D5
hypocenterC5#3344
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
3. C5×#467C2semidirect
4. #65478C2semidirect
5. #65473C2semidirect
7. C2×#3949C2semidirect
8. #65333C2semidirect
9. #65332C2semidirect
10. #65170C2semidirect
11. #65165C2semidirect
12. #65104C2semidirect
13. #65094C2semidirect
14. #65088C2semidirect
15. #65080C2semidirect
116. #467D5semidirect
300. C5#3344semidirect

Maximal subgroups

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

subgroupindex
#659762
#659692
C5×#4672
#654782
#654732
#654002
C2×#39492
#653332
#653322
#651702
#651652
#651042
#650942
#650882
#650802
#33445