Finite Group Databasebeta

← #10613090

Subgroups — #10613090

Order 640.

328 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#65934C211yesmaximal, characteristic
2#65851C211yesmaximal, characteristic, complemented
3C5×#482C211yesmaximal, characteristic
4#65324C211yesmaximal, characteristic
5#65285C211yesmaximal, characteristic, complemented
6#65166C211yesmaximal, characteristic, complemented
7#65165C211yesmaximal, characteristic, complemented
8#65146C211yesmaximal, characteristic, complemented
9#65145C211yesmaximal, characteristic, complemented
10#65055C211yesmaximal, characteristic, complemented
11#65054C211yesmaximal, characteristic, complemented
12#65054C211yesmaximal, characteristic, complemented
13#65052C211yesmaximal, characteristic, complemented
14#65012C211yesmaximal, characteristic, complemented
15#65008C211yesmaximal, characteristic, complemented
16C5×#121C2211yescharacteristic
17C5×#117C2211yescharacteristic
18#4082C2211yescharacteristic
19#4081—21no—
20D4×Dic5—21no—
21D4×Dic5C2211yescharacteristic
22#4072C2211yescharacteristic
23#4070C2211yescharacteristic
24C2×C4×Dic5C2211yescharacteristic
25#4036C2211yescharacteristic
26#4036C2211yescharacteristic
27#4036C2211yescharacteristic
28#4034C2211yescharacteristic
29#4034C2211yescharacteristic
30#4033C2211yescharacteristic
31#4025—21no—
32#4024—21no—
33#4024—21no—
34#4023—21no—
35C4×Dic10—21no—
36C4×Dic10—21no—
37C5×#107C2211yescharacteristic
38C5×#106C2211yescharacteristic
39C5×#102C2211yescharacteristic
40C5×#102C2211yescharacteristic
41C5×C22⋊C8C2211yescharacteristic
42#3964C2211yescharacteristic
43#3964C2211yescharacteristic
44C22⋊#168C2211yescharacteristic
45#3950C2211yescharacteristic
46#3949C2211yescharacteristic
47#3948C2211yescharacteristic
48#3948C2211yescharacteristic
49#3947C2211yescharacteristic
50#3947C2211yescharacteristic
51#3946C2211yescharacteristic
52#3946C2211yescharacteristic
53#3942C2211yescharacteristic
54#3942C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3939C2211yescharacteristic
58#3939C2211yescharacteristic
59#3240—51nomaximal, Sylow
60C2×C5×D4—21no—
61C2×C5×D4C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×Dic5—21no—
64C22×Dic5D411yescharacteristic
65C22×Dic5D411yescharacteristic
66C2×Dic10—21no—
67C2×Dic10—21no—
68C2×Dic10C2311yescharacteristic
69C2×C5×C8C2311yescharacteristic
70C2×C5×C8C2311yescharacteristic
71C5×C4⋊C4C2311yescharacteristic
72C5×C4⋊C4C2311yescharacteristic
73C5×C4⋊C4C2311yescharacteristic
74C5×C22⋊C4—21no—
75C5×C22⋊C4—21no—
76C42×C5—21no—
77C22⋊Dic5—21no—
78C22⋊Dic5—21no—
79C22⋊Dic5—21no—
80C22⋊Dic5—21no—
81C22⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5—21no—
84C4⋊Dic5—21no—
85C4⋊Dic5C2311yescharacteristic
86C4⋊Dic5C2311yescharacteristic
87C4⋊Dic5C2311yescharacteristic
88#683—21no—
89#683—21no—
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#501—51no—
106#501—51no—
107#489—51no—
108#489—51no—
109#485—51no—
110#485—51no—
111#482—51no—
112#482D511yescharacteristic
113#479—51no—
114#479—51no—
115#478—51no—
116#478—51no—
117#432—51no—
118C23×C5—21no—
119C23×C5C2×D411yescharacteristic
120C5×D4—21no—
121C5×D4—21no—
122C5×D4—42no—
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
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—41no—
135C2×Dic5—41no—
136C2×Dic5—42no—
137C2×Dic5C2×D411yescharacteristic
138C2×Dic5C2×D411yescharacteristic
139C2×Dic5C2×D411yescharacteristic
140C2×Dic5C2×D411yescharacteristic
141Dic10—21no—
142Dic10—21no—
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—51no—
158C22⋊Q8—101no—
159C22⋊Q8—101no—
160#121C2×D511yescharacteristic
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#103—51no—
183#103—51no—
184#102—51no—
185#102—51no—
186#102C2×D511yescharacteristic
187#102C2×D511yescharacteristic
188C22⋊C8—51no—
189C22⋊C8C2×D511yescharacteristic
190#97—51no—
191#97—51no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5—41no—
196C22×C5—41no—
197C22×C5—41no—
198C22×C5C22×D411yescharacteristic
199C4×C5—21no—
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C52−1+411yescharacteristic
204C4×C52−1+411yescharacteristic
205Dic5—21no—
206Dic5—21no—
207Dic5—21no—
208Dic5—21no—
209Dic5—41no—
210Dic5—41no—
211Dic5—41no—
212Dic5—41no—
213C2×Q8—51no—
214C2×Q8—101no—
215C2×Q8—101no—
216C2×D4—21no—
217C2×D4C22×D511yescharacteristic
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—51no—
227C4⋊C4—51no—
228C4⋊C4—51no—
229C4⋊C4—101no—
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—81no—
258C2×C5#53611yescharacteristic
259C2×C5#57511yescharacteristic
260C2×C5#57511yescharacteristic
261C23—21no—
262C23D4×D511yescharacteristic
263Q8—101no—
264Q8—101no—
265Q8—202no—
266Q8—202no—
267D4—21no—
268D4—21no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—51no—
278C2×C4—51no—
279C2×C4—101no—
280C2×C4—101no—
281C2×C4—101no—
282C2×C4—101no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4—202no—
286C2×C4D4×D511yescharacteristic
287C2×C4C23×D511yescharacteristic
288C8—21no—
289C8—21no—
290C8—101no—
291C8—101no—
292C5#324011yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C2×D4×D511yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—101no—
305C4—101no—
306C4—101no—
307C4—101no—
308C4—201no—
309C4—201no—
310C4—201no—
311C4—201no—
312C4#415011yescharacteristic
313C4#415011yescharacteristic
314C2—41no—
315C2—81no—
316C2#6598211yescharacteristic
317C2#6610211yescharacteristic
318C2#6610711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#482C2
socleC22×C5C22×D4
prime radicalC5×#121C22
hypercenter#482D5
hypocenterC5#3240
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #65851C2semidirect
5. #65285C2semidirect
6. #65166C2semidirect
7. #65165C2semidirect
8. #65146C2semidirect
9. #65145C2semidirect
10. #65055C2semidirect
11. #65054C2semidirect
12. #65054C2semidirect
13. #65052C2semidirect
14. #65012C2semidirect
15. #65008C2semidirect
292. C5#3240semidirect

Maximal subgroups

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

subgroupindex
#659342
#658512
C5×#4822
#653242
#652852
#651662
#651652
#651462
#651452
#650552
#650542
#650522
#650122
#650082
#32405