Finite Group Databasebeta

← #10612990

Subgroups — #10612990

Order 640.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66029C211yesmaximal, characteristic
2#65915C211yesmaximal, characteristic, complemented
3C5×#479C211yesmaximal, characteristic, complemented
4#65353C211yesmaximal, characteristic, complemented
5C4×#688C211yesmaximal, characteristic, complemented
6#65174C211yesmaximal, characteristic, complemented
7#65170C211yesmaximal, characteristic, complemented
8#65152C211yesmaximal, characteristic, complemented
9#65150C211yesmaximal, characteristic, complemented
10#65136C211yesmaximal, characteristic, complemented
11#65127C211yesmaximal, characteristic, complemented
12#65103C211yesmaximal, characteristic, complemented
13#65101C211yesmaximal, characteristic, complemented
14#65101C211yesmaximal, characteristic, complemented
15#65094C211yesmaximal, characteristic, complemented
16C5×#125C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18#4092C2211yescharacteristic
19#4092C2211yescharacteristic
20C2×#688C2211yescharacteristic
21C2×#676C2211yescharacteristic
22C2×#676C2211yescharacteristic
23#4044—21no—
24#4041—21no—
25#4041C2211yescharacteristic
26#4041C2211yescharacteristic
27#4040—21no—
28#4040—21no—
29#4039—21no—
30#4038C2211yescharacteristic
31#4038C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33D5×C4⋊C4C2211yescharacteristic
34#4035—21no—
35#4022—21no—
36C4×D20C2211yescharacteristic
37C4×D20C2211yescharacteristic
38#4018—21no—
39#4016C2211yescharacteristic
40C5×#107C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×C4⋊C8C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×#103C2211yescharacteristic
45#3967C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3952C2211yescharacteristic
50#3950C2211yescharacteristic
51#3949C2211yescharacteristic
52#3941C2211yescharacteristic
53#3940C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58C4×#168C2211yescharacteristic
59#3351—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×D20—21no—
62C2×D20—21no—
63C2×D20D411yescharacteristic
64C2×D20C2311yescharacteristic
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×C4×D5—21no—
68C2×C4×D5C2311yescharacteristic
69C2×C4×D5C2311yescharacteristic
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#688—22no—
81#685—21no—
82#685—21no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685—21no—
87#685—21no—
88#685D411yescharacteristic
89#685D411yescharacteristic
90C4⋊Dic5D411yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100C4×Dic5—21no—
101C4×Dic5—21no—
102C2×#168C2311yescharacteristic
103C2×#168C2311yescharacteristic
104#676—22no—
105#676—22no—
106#553—51no—
107#552—51no—
108#499—51no—
109#485—51no—
110#483—51no—
111#482—51no—
112#481—51no—
113#479D511yescharacteristic, complemented
114#478—51no—
115#468—51no—
116#468—51no—
117C4×SD16—51no—
118#436—51no—
119#428—51no—
120#428—51no—
121C22×D5—21no—
122C22×D5C2×D411yescharacteristic
123C22×D5C2×D411yescharacteristic
124C5×Q8—21no—
125C5×Q8—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5C2×D411yescharacteristic
131C2×C4×C5C2×D411yescharacteristic
132C2×C4×C5C2411yescharacteristic
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5C2×D411yescharacteristic
137C2×Dic5C2×D411yescharacteristic
138D20—21no—
139D20—21no—
140D20—41no—
141D20—42no—
142D20—81no—
143C4×D5—21no—
144C4×D5—21no—
145C4×D5—21no—
146C4×D5—21no—
147C4×D5—42no—
148C4×D5—81no—
149C4×D5—81no—
150C5×C8—21no—
151C5×C8—21no—
152#168—21no—
153#168#4112yes—
154C2×SD16—51no—
155C2×M16—51no—
156C2×M16—51no—
157#126—101no—
158#126—101no—
159#125—51no—
160#125—101no—
161#125C2×D511yescharacteristic
162#123—101no—
163#123—101no—
164C22⋊Q8—51no—
165C22⋊Q8—51no—
166#121—51no—
167#121—51no—
168#121—101no—
169C4×Q8C2×D511yescharacteristic
170C4×D4—51no—
171C4×D4—51no—
172C4×D4—101no—
173#117—51no—
174#117—51no—
175#117—101no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—51no—
178#107—51no—
179#107—51no—
180#107—51no—
181#107C2×D511yescharacteristic
182#106—51no—
183#106—51no—
184#106—51no—
185#106—51no—
186#106C2×D511yescharacteristic
187C4⋊C8C2×D511yescharacteristic
188#103—51no—
189#103C2×D511yescharacteristic
190#103C2×D511yescharacteristic
191#102—51no—
192#102—51no—
193#102—51no—
194C22⋊C8—51no—
195C22⋊C8—51no—
196C4×C8—51no—
197C22×C5C22×D411yescharacteristic
198C2×D5—21no—
199C2×D5—21no—
200C2×D5—21no—
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—41no—
205C2×D5—41no—
206C2×D5—41no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—41no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5C2×#4111yescharacteristic
214C4×C52−1+411yescharacteristic
215Dic5—21no—
216Dic5—21no—
217Dic5—41no—
218Dic5—41no—
219Dic5—41no—
220C2×Q8C22×D511yescharacteristic
221C2×D4—51no—
222C2×D4—51no—
223C2×D4—101no—
224C2×D4—101no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4—101no—
230SD16—102no—
231M16—102no—
232M16—102no—
233C2×C8—51no—
234C2×C8—51no—
235C2×C8C22×D511yescharacteristic
236C2×C8C22×D511yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—51no—
241C4⋊C4—51no—
242C4⋊C4—51no—
243C4⋊C4—51no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4—101no—
250C4⋊C4C22×D511yescharacteristic
251C4⋊C4C22×D511yescharacteristic
252C4⋊C4C22×D511yescharacteristic
253C22⋊C4—51no—
254C22⋊C4—51no—
255C22⋊C4—101no—
256C22⋊C4—101no—
257C22⋊C4—101no—
258C22⋊C4—101no—
259C22⋊C4—101no—
260C22⋊C4—101no—
261C22⋊C4—101no—
262C42—21no—
263C42—101no—
264C42—101no—
265C42C22×D511yescharacteristic
266C2×C5#54711yescharacteristic
267C2×C5#57511yescharacteristic
268C2×C5#57711yescharacteristic
269D5—41no—
270D5—41no—
271D5—81no—
272C23—51no—
273C23—51no—
274C23—101no—
275Q8—21no—
276Q8—21no—
277D4—101no—
278D4—101no—
279D4—201no—
280D4—202no—
281D4—401no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—202no—
296C2×C4—401no—
297C2×C4—401no—
298C2×C4D4×D511yescharacteristic
299C2×C4D4×D511yescharacteristic
300C2×C4C23×D511yescharacteristic
301C8—21no—
302C8—21no—
303C8—52no—
304C8—101no—
305C5#335111yescharacteristic, complemented, Sylow
306C22—101no—
307C22—101no—
308C22—101no—
309C22—101no—
310C22—101no—
311C22—101no—
312C22—201no—
313C22—201no—
314C22—201no—
315C22C2×D4×D511yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—101no—
323C4—101no—
324C4—201no—
325C4—201no—
326C4—201no—
327C4#414711yescharacteristic
328C4D5×#4111yescharacteristic
329C2—201no—
330C2—201no—
331C2—401no—
332C2#6596511yescharacteristic
333C2#6610211yescharacteristic
334C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#479C2
socleC22×C5C22×D4
prime radical#66029C2
hypercenter#479D5
hypocenterC5#3351
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
2. #65915C2semidirect
3. C5×#479C2semidirect
4. #65353C2semidirect
5. C4×#688C2semidirect
6. #65174C2semidirect
7. #65170C2semidirect
8. #65152C2semidirect
9. #65150C2semidirect
10. #65136C2semidirect
11. #65127C2semidirect
12. #65103C2semidirect
13. #65101C2semidirect
14. #65101C2semidirect
15. #65094C2semidirect
113. #479D5semidirect
305. C5#3351semidirect

Maximal subgroups

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

subgroupindex
#660292
#659152
C5×#4792
#653532
C4×#6882
#651742
#651702
#651522
#651502
#651362
#651272
#651032
#651012
#650942
#33515