Finite Group Databasebeta

← #10613232

Subgroups — #10613232

Order 640.

332 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65958C211yesmaximal, characteristic
2#65851C211yesmaximal, characteristic, complemented
3C5×#485C211yesmaximal, characteristic, complemented
4#65334C211yesmaximal, characteristic, complemented
5#65292C211yesmaximal, characteristic
6#65179C211yesmaximal, characteristic, complemented
7#65167C211yesmaximal, characteristic, complemented
8#65159C211yesmaximal, characteristic, complemented
9#65147C211yesmaximal, characteristic, complemented
10#65089C211yesmaximal, characteristic, complemented
11#65089C211yesmaximal, characteristic, complemented
12#65083C211yesmaximal, characteristic, complemented
13#65080C211yesmaximal, characteristic, complemented
14#65026C211yesmaximal, characteristic
15#65007C211yesmaximal, characteristic, complemented
16C5×C22⋊Q8C2211yescharacteristic
17C5×#117C2211yescharacteristic
18#4093C2211yescharacteristic
19Q8×Dic5C2211yescharacteristic
20#4076C2211yescharacteristic
21#4072C2211yescharacteristic
22C2×C4×Dic5C2211yescharacteristic
23#4044—21no—
24#4039C2211yescharacteristic
25#4038—21no—
26#4036C2211yescharacteristic
27#4036C2211yescharacteristic
28#4036C2211yescharacteristic
29#4034C2211yescharacteristic
30#4034C2211yescharacteristic
31#4032—21no—
32#4027—21no—
33#4024—21no—
34#4024—21no—
35C4×Dic10—21no—
36C4×Dic10—21no—
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×#103C2211yescharacteristic
40C5×#103C2211yescharacteristic
41C5×C22⋊C8C2211yescharacteristic
42#3967C2211yescharacteristic
43#3967C2211yescharacteristic
44C22⋊#168C2211yescharacteristic
45#3953C2211yescharacteristic
46#3953C2211yescharacteristic
47#3950C2211yescharacteristic
48#3949C2211yescharacteristic
49#3946C2211yescharacteristic
50#3946C2211yescharacteristic
51C8×Dic5C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3941C2211yescharacteristic
54#3941C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3233—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C2×C22⋊D5—21no—
63C22×Dic5D411yescharacteristic
64C22×Dic5D411yescharacteristic
65C2×D20C2311yescharacteristic
66C2×C4×D5—21no—
67C2×Dic10—21no—
68C2×Dic10—21no—
69C2×C5×C8C2311yescharacteristic
70C2×C5×C8C2311yescharacteristic
71C5×C4⋊C4—21no—
72C5×C4⋊C4C2311yescharacteristic
73C5×C4⋊C4C2311yescharacteristic
74C5×C4⋊C4C2311yescharacteristic
75C5×C22⋊C4—21no—
76C5×C22⋊C4—21no—
77C42×C5—21no—
78C22⋊Dic5—21no—
79#685—21no—
80#685—21no—
81#685—21no—
82#685—21no—
83C4⋊Dic5—21no—
84C4⋊Dic5—21no—
85C4⋊Dic5—21no—
86C4⋊Dic5—21no—
87C4⋊Dic5C2311yescharacteristic
88C4⋊Dic5C2311yescharacteristic
89C4⋊Dic5C2311yescharacteristic
90#683—21no—
91#683—21no—
92#683—21no—
93#683—21no—
94#683—21no—
95C4×Dic5—21no—
96C4×Dic5—21no—
97C4×Dic5D411yescharacteristic
98C4×Dic5D411yescharacteristic
99C4×Dic5C2311yescharacteristic
100C4×Dic5C2311yescharacteristic
101C2×#168C2311yescharacteristic
102C2×#168C2311yescharacteristic
103#533—51no—
104#529—51no—
105#499—51no—
106#499—51no—
107#488—51no—
108#488—51no—
109#485—51no—
110#485D511yescharacteristic, complemented
111#482—51no—
112#482—51no—
113#477—51no—
114#476—51no—
115#475—51no—
116#474—51no—
117#431—51no—
118C23×C5C2×D411yescharacteristic
119C22×D5—21no—
120C5×Q8—21no—
121C5×Q8—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5C2×D411yescharacteristic
129C2×C4×C5C2411yescharacteristic
130C22⋊D5—42no—
131C2×Dic5—22no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—41no—
136C2×Dic5C2×D411yescharacteristic
137C2×Dic5C2×D411yescharacteristic
138C2×Dic5C2×D411yescharacteristic
139C2×Dic5C2×D411yescharacteristic
140D20—21no—
141D20—21no—
142C4×D5—42no—
143Dic10—42no—
144Dic10—42no—
145C5×C8—21no—
146C5×C8—21no—
147#168—21no—
148#168—21no—
149C4⋊Q8—51no—
150C4⋊Q8—51no—
151#126—101no—
152#125—51no—
153#125—51no—
154#125—51no—
155#124—51no—
156#123—101no—
157C22⋊Q8—101no—
158C22⋊Q8—101no—
159C22⋊Q8C2×D511yescharacteristic
160#121—51no—
161C4×Q8—51no—
162C4×Q8—101no—
163C4×Q8—101no—
164C4×D4—51no—
165C4×D4—101no—
166#117—51no—
167#117—101no—
168#117C2×D511yescharacteristic
169C2×C42—51no—
170#107—51no—
171#107—51no—
172#107—51no—
173#107C2×D511yescharacteristic
174#106—51no—
175#106—51no—
176#106—51no—
177#106C2×D511yescharacteristic
178C4⋊C8—51no—
179C4⋊C8—51no—
180#103—51no—
181#103—51no—
182#103C2×D511yescharacteristic
183#103C2×D511yescharacteristic
184#102—51no—
185#102—51no—
186#102—51no—
187#102—51no—
188C22⋊C8—51no—
189C22⋊C8C2×D511yescharacteristic
190C4×C8—51no—
191C4×C8—51no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5C22×D411yescharacteristic
196C2×D5—41no—
197C2×D5—41no—
198C2×D5—41no—
199C4×C5—21no—
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C52−1+411yescharacteristic
205C4×C52−1+411yescharacteristic
206Dic5—21no—
207Dic5—21no—
208Dic5—21no—
209Dic5—41no—
210Dic5—41no—
211Dic5—41no—
212Dic5#13512yes—
213C2×Q8—101no—
214C2×Q8—101no—
215C2×Q8C22×D511yescharacteristic
216C2×D4—51no—
217C2×D4—101no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—101no—
221C22×C4C22×D511yescharacteristic
222C2×C8—51no—
223C2×C8—51no—
224C2×C8C22×D511yescharacteristic
225C2×C8C22×D511yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—51no—
228C4⋊C4—51no—
229C4⋊C4—51no—
230C4⋊C4—101no—
231C4⋊C4—101no—
232C4⋊C4—101no—
233C4⋊C4—101no—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—101no—
237C4⋊C4—101no—
238C4⋊C4—101no—
239C4⋊C4C22×D511yescharacteristic
240C4⋊C4C22×D511yescharacteristic
241C4⋊C4C22×D511yescharacteristic
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—101no—
245C22⋊C4—101no—
246C22⋊C4—101no—
247C22⋊C4—101no—
248C22⋊C4—101no—
249C42—21no—
250C42—51no—
251C42—51no—
252C42—51no—
253C42—51no—
254C42—101no—
255C42—101no—
256C2×C5—41no—
257C2×C5#53611yescharacteristic
258C2×C5C2×#13511yescharacteristic
259C2×C5#57511yescharacteristic
260D5—81no—
261C23—101no—
262C23D4×D511yescharacteristic
263Q8—21no—
264Q8—21no—
265Q8—202no—
266Q8—202no—
267D4—101no—
268D4—101no—
269D4—202no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—51no—
277C2×C4—51no—
278C2×C4—51no—
279C2×C4—51no—
280C2×C4—102no—
281C2×C4—101no—
282C2×C4—101no—
283C2×C4—101no—
284C2×C4—202no—
285C2×C4—201no—
286C2×C4D4×D511yescharacteristic
287C2×C4C23×D511yescharacteristic
288C8—21no—
289C8—21no—
290C8—101no—
291C8—101no—
292C5#323311yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—21no—
296C22—201no—
297C22—201no—
298C22—201no—
299C22C2×D4×D511yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—52no—
306C4—101no—
307C4—101no—
308C4—101no—
309C4—201no—
310C4—201no—
311C4—201no—
312C4#415011yescharacteristic
313C4#415011yescharacteristic
314C2—41no—
315C2—401no—
316C2#6598211yescharacteristic
317C2D5×#13511yescharacteristic
318C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#485C2
socleC22×C5C22×D4
prime radical#4076C22
hypercenter#485D5
hypocenterC5#3233
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
2. #65851C2semidirect
3. C5×#485C2semidirect
4. #65334C2semidirect
6. #65179C2semidirect
7. #65167C2semidirect
8. #65159C2semidirect
9. #65147C2semidirect
10. #65089C2semidirect
11. #65089C2semidirect
12. #65083C2semidirect
13. #65080C2semidirect
15. #65007C2semidirect
110. #485D5semidirect
292. C5#3233semidirect

Maximal subgroups

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

subgroupindex
#659582
#658512
C5×#4852
#653342
#652922
#651792
#651672
#651592
#651472
#650892
#650832
#650802
#650262
#650072
#32335