Finite Group Databasebeta

← #10613241

Subgroups — #10613241

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#65976C211yesmaximal, characteristic, complemented
2#65864C211yesmaximal, characteristic
3C5×#485C211yesmaximal, characteristic, complemented
4#65338C211yesmaximal, characteristic, complemented
5#65284C211yesmaximal, characteristic, complemented
6#65180C211yesmaximal, characteristic, complemented
7#65170C211yesmaximal, characteristic, complemented
8#65155C211yesmaximal, characteristic, complemented
9#65147C211yesmaximal, characteristic, complemented
10#65101C211yesmaximal, characteristic, complemented
11#65094C211yesmaximal, characteristic, complemented
12#65088C211yesmaximal, characteristic, complemented
13#65077C211yesmaximal, characteristic, complemented
14#65024C211yesmaximal, characteristic, complemented
15#65018C211yesmaximal, characteristic, complemented
16C5×C22⋊Q8C2211yescharacteristic
17C5×#117C2211yescharacteristic
18#4092C2211yescharacteristic
19Q8×Dic5C2211yescharacteristic
20C2×#688C2211yescharacteristic
21#4076C2211yescharacteristic
22C4×C22⋊D5C2211yescharacteristic
23C2×C4⋊Dic5C2211yescharacteristic
24C2×#681C2211yescharacteristic
25C2×#676C2211yescharacteristic
26#4044—21no—
27#4041C2211yescharacteristic
28#4039C2211yescharacteristic
29#4038C2211yescharacteristic
30D5×C4⋊C4C2211yescharacteristic
31#4036—21no—
32#4036C2211yescharacteristic
33#4036C2211yescharacteristic
34#4032—21no—
35#4030—21no—
36#4029—21no—
37#4023—21no—
38#4022—21no—
39C4×D20—21no—
40C5×#107C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×#103C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic
45#3967C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3949C2211yescharacteristic
50#3949C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3941C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3351—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C2×C22⋊D5—21no—
63C2×C22⋊D5D411yescharacteristic
64C22×Dic5—21no—
65C2×D20—21no—
66C2×D20C2311yescharacteristic
67C2×C4×D5—21no—
68C2×C4×D5—21no—
69C2×C4×D5C2311yescharacteristic
70C2×C5×C8C2311yescharacteristic
71C2×C5×C8C2311yescharacteristic
72C5×C4⋊C4—21no—
73C5×C4⋊C4C2311yescharacteristic
74C5×C4⋊C4C2311yescharacteristic
75C5×C4⋊C4C2311yescharacteristic
76C5×C22⋊C4—21no—
77C5×C22⋊C4—21no—
78C42×C5—21no—
79C22⋊Dic5D411yescharacteristic
80#688—22no—
81#685—21no—
82#685—21no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685D411yescharacteristic
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5—21no—
90C4⋊Dic5—21no—
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94#683—21no—
95#683—21no—
96#683—21no—
97#683—21no—
98#683D411yescharacteristic
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5C2311yescharacteristic
102#681—22no—
103C2×#168C2311yescharacteristic
104C2×#168C2311yescharacteristic
105#676—22no—
106#553—51no—
107#552—51no—
108#499—51no—
109#485D511yescharacteristic, complemented
110#483—51no—
111#482—51no—
112#481—51no—
113#479—51no—
114#478—51no—
115#468—51no—
116#468—51no—
117C4×SD16—51no—
118#436—51no—
119#428—51no—
120#428—51no—
121C23×C5C2×D411yescharacteristic
122C22×D5—21no—
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×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5C2×D411yescharacteristic
133C2×C4×C5C2411yescharacteristic
134C22⋊D5—41no—
135C22⋊D5—81no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—42no—
140C2×Dic5C2×D411yescharacteristic
141C2×Dic5C2×D411yescharacteristic
142C2×Dic5C2×D411yescharacteristic
143D20—21no—
144D20—21no—
145D20—42no—
146C4×D5—21no—
147C4×D5—21no—
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—51no—
161#125—101no—
162#123—101no—
163#123—101no—
164C22⋊Q8—51no—
165C22⋊Q8C2×D511yescharacteristic
166#121—51no—
167#121—51no—
168#121—101no—
169C4×Q8—51no—
170C4×D4—51no—
171C4×D4—51no—
172C4×D4—101no—
173#117—51no—
174#117—101no—
175#117C2×D511yescharacteristic
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⋊C8—51no—
188#103—51no—
189#103C2×D511yescharacteristic
190#103C2×D511yescharacteristic
191#102—51no—
192#102—51no—
193#102—51no—
194C22⋊C8—51no—
195C22⋊C8C2×D511yescharacteristic
196C4×C8—51no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5C22×D411yescharacteristic
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—41no—
205C2×D5—41no—
206C2×D5—41no—
207C4×C5—21no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5C2×#4111yescharacteristic
213C4×C52−1+411yescharacteristic
214Dic5—21no—
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—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C22×D511yescharacteristic
230SD16—102no—
231M16—102no—
232M16—102no—
233C2×C8—51no—
234C2×C8—51no—
235C2×C8C22×D511yescharacteristic
236C2×C8C22×D511yescharacteristic
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⋊C4—101no—
249C4⋊C4—101no—
250C4⋊C4C22×D511yescharacteristic
251C4⋊C4C22×D511yescharacteristic
252C4⋊C4C22×D511yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—51no—
256C22⋊C4—51no—
257C22⋊C4—101no—
258C22⋊C4—101no—
259C22⋊C4—101no—
260C22⋊C4—101no—
261C22⋊C4—101no—
262C42—21no—
263C42—51no—
264C42—101no—
265C42—101no—
266C2×C5—41no—
267C2×C5#54711yescharacteristic
268C2×C5#57511yescharacteristic
269C2×C5#57711yescharacteristic
270D5—41no—
271D5—81no—
272C23—51no—
273C23—101no—
274C23D4×D511yescharacteristic
275Q8—21no—
276Q8—21no—
277D4—101no—
278D4—101no—
279D4—202no—
280D4—201no—
281D4—401no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—51no—
289C2×C4—51no—
290C2×C4—51no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—202no—
297C2×C4—401no—
298C2×C4—401no—
299C2×C4D4×D511yescharacteristic
300C2×C4C23×D511yescharacteristic
301C8—21no—
302C8—21no—
303C8—52no—
304C8—101no—
305C5#335111yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22—21no—
309C22—101no—
310C22—101no—
311C22—101no—
312C22—201no—
313C22—201no—
314C22—201no—
315C22C2×D4×D511yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—101no—
322C4—101no—
323C4—101no—
324C4—201no—
325C4—201no—
326C4—201no—
327C4D5×#4111yescharacteristic
328C4#415011yescharacteristic
329C2—41no—
330C2—201no—
331C2—401no—
332C2#6598911yescharacteristic
333C2#6610411yescharacteristic
334C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#485C2
socleC22×C5C22×D4
prime radical#65864C2
hypercenter#485D5
hypocenterC5#3351
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #65976C2semidirect
3. C5×#485C2semidirect
4. #65338C2semidirect
5. #65284C2semidirect
6. #65180C2semidirect
7. #65170C2semidirect
8. #65155C2semidirect
9. #65147C2semidirect
10. #65101C2semidirect
11. #65094C2semidirect
12. #65088C2semidirect
13. #65077C2semidirect
14. #65024C2semidirect
15. #65018C2semidirect
109. #485D5semidirect
305. C5#3351semidirect

Maximal subgroups

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

subgroupindex
#659762
#658642
C5×#4852
#653382
#652842
#651802
#651702
#651552
#651472
#651012
#650942
#650882
#650772
#650242
#650182
#33515