Finite Group Databasebeta

← #10611096

Subgroups — #10611096

Order 640.

320 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#65868C211yesmaximal, characteristic
2#65853C211yesmaximal, characteristic, complemented
3C5×#433C211yesmaximal, characteristic, complemented
4#65140C211yesmaximal, characteristic, complemented
5#65136C211yesmaximal, characteristic, complemented
6#65131C211yesmaximal, characteristic, complemented
7#65118C211yesmaximal, characteristic, complemented
8#65026C211yesmaximal, characteristic
9#65024C211yesmaximal, characteristic
10#65012C211yesmaximal, characteristic, complemented
11#65010C211yesmaximal, characteristic, complemented
12#65003C211yesmaximal, characteristic, complemented
13#64991C211yesmaximal, characteristic, complemented
14#64986C211yesmaximal, characteristic, complemented
15#64969C211yesmaximal, characteristic, complemented
16C5×#117C2211yescharacteristic
17#4076C2211yescharacteristic
18#4072C2211yescharacteristic
19C2×C4⋊Dic5C2211yescharacteristic
20#4070C2211yescharacteristic
21#4044—21no—
22#4042—21no—
23#4036—21no—
24#4034—21no—
25#4031—21no—
26#4029—21no—
27#4024—21no—
28#4024—21no—
29#4021C2211yescharacteristic
30C4×D20C2211yescharacteristic
31#4016C2211yescharacteristic
32#4016C2211yescharacteristic
33#4015C2211yescharacteristic
34#4015C2211yescharacteristic
35#4015C2211yescharacteristic
36C4×Dic10C2211yescharacteristic
37C5×C4⋊C8C2211yescharacteristic
38C5×C4⋊C8C2211yescharacteristic
39C5×C22⋊C8C2211yescharacteristic
40C5×C22⋊C8C2211yescharacteristic
41C5×#97C2211yescharacteristic
42C4×C5×C8C2211yescharacteristic
43#3953C2211yescharacteristic
44#3953C2211yescharacteristic
45#3953C2211yescharacteristic
46#3953C2211yescharacteristic
47#3950C2211yescharacteristic
48#3950C2211yescharacteristic
49#3949C2211yescharacteristic
50#3949C2211yescharacteristic
51#3949C2211yescharacteristic
52#3949C2211yescharacteristic
53#3949C2211yescharacteristic
54#3949C2211yescharacteristic
55#3948C2211yescharacteristic
56#3948C2211yescharacteristic
57#3948C2211yescharacteristic
58#3948C2211yescharacteristic
59#3244—51nomaximal, Sylow
60C22×C4×C5C2311yescharacteristic
61C2×C22⋊D5—21no—
62C22×Dic5—21no—
63C2×D20C2311yescharacteristic
64C2×C4×D5—21no—
65C2×Dic10—21no—
66C2×Dic10—21no—
67C2×Dic10—21no—
68C2×Dic10C2311yescharacteristic
69C2×C5×C8C2311yescharacteristic
70C2×C5×C8C2311yescharacteristic
71C2×C5×C8C2311yescharacteristic
72C2×C5×C8C2311yescharacteristic
73C5×C4⋊C4D411yescharacteristic
74C5×C4⋊C4D411yescharacteristic
75C5×C22⋊C4D411yescharacteristic
76C5×C22⋊C4D411yescharacteristic
77C42×C5C2311yescharacteristic
78C42×C5C2311yescharacteristic
79C22⋊Dic5—21no—
80C22⋊Dic5—21no—
81#685—21no—
82#685—21no—
83#685—21no—
84#685—21no—
85C4⋊Dic5—21no—
86C4⋊Dic5—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5C2311yescharacteristic
90C4⋊Dic5C2311yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100#683—21no—
101C4×Dic5—21no—
102C4×Dic5—21no—
103#544—51no—
104#542—51no—
105#501—51no—
106#498—51no—
107#489—51no—
108#488—51no—
109#485—51no—
110#483—51no—
111#482—51no—
112#481—51no—
113#479—51no—
114#478—51no—
115#476—51no—
116#475—51no—
117#433D511yescharacteristic, complemented
118C23×C5C2×D411yescharacteristic
119C22×D5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5C2×D411yescharacteristic
123C2×C4×C5C2×D411yescharacteristic
124C2×C4×C5C2×D411yescharacteristic
125C2×C4×C5C2×D411yescharacteristic
126C2×C4×C5C2×D411yescharacteristic
127C2×C4×C5C2411yescharacteristic
128C22⋊D5—81no—
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—81no—
137D20—21no—
138D20—21no—
139C4×D5—81no—
140Dic10—21no—
141Dic10—21no—
142Dic10—81no—
143Dic10—81no—
144Dic10—81no—
145C5×C8—21no—
146C5×C8—21no—
147C5×C8—21no—
148C5×C8—21no—
149C4⋊Q8—51no—
150C4⋊Q8—51no—
151C4⋊Q8—51no—
152C4⋊Q8—101no—
153#126—101no—
154#125—51no—
155#125—51no—
156#125—101no—
157#124—51no—
158#124—101no—
159#123—101no—
160C22⋊Q8—51no—
161C22⋊Q8—101no—
162C22⋊Q8—101no—
163C22⋊Q8—101no—
164#121—51no—
165C4×Q8—51no—
166C4×D4—51no—
167#117—51no—
168#117C2×D511yescharacteristic
169C2×C4⋊C4—51no—
170#107—51no—
171#107—51no—
172#106—51no—
173#106—51no—
174#106—51no—
175#106—51no—
176#106—51no—
177#106—51no—
178C4⋊C8C2×D511yescharacteristic
179C4⋊C8C2×D511yescharacteristic
180#103—51no—
181#103—51no—
182#103—51no—
183#103—51no—
184#102—51no—
185#102—51no—
186#102—51no—
187#102—51no—
188C22⋊C8C2×D511yescharacteristic
189C22⋊C8C2×D511yescharacteristic
190#97C2×D511yescharacteristic
191C4×C8C2×D511yescharacteristic
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—21no—
201C4×C5—21no—
202C4×C5—21no—
203C4×C5—21no—
204C4×C52−1+411yescharacteristic
205C4×C52−1+411yescharacteristic
206Dic5—41no—
207Dic5—41no—
208Dic5—41no—
209Dic5—41no—
210Dic5—41no—
211Dic5—41no—
212Dic5—41no—
213C2×Q8—51no—
214C2×Q8—101no—
215C2×Q8—101no—
216C2×Q8—101no—
217C2×D4—51no—
218C2×D4—101no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4C22×D511yescharacteristic
222C2×C8C22×D511yescharacteristic
223C2×C8C22×D511yescharacteristic
224C2×C8C22×D511yescharacteristic
225C2×C8C22×D511yescharacteristic
226C4⋊C4—51no—
227C4⋊C4—51no—
228C4⋊C4—51no—
229C4⋊C4—51no—
230C4⋊C4—51no—
231C4⋊C4—51no—
232C4⋊C4—101no—
233C4⋊C4—101no—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—101no—
237C4⋊C4—101no—
238C4⋊C4—101no—
239C4⋊C4—101no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4D2011yescharacteristic
243C4⋊C4D2011yescharacteristic
244C22⋊C4—101no—
245C22⋊C4—101no—
246C22⋊C4—101no—
247C22⋊C4—101no—
248C22⋊C4—101no—
249C22⋊C4—101no—
250C22⋊C4D2011yescharacteristic
251C22⋊C4D2011yescharacteristic
252C42—101no—
253C42—101no—
254C42C22×D511yescharacteristic
255C42C22×D511yescharacteristic
256C2×C5—41no—
257C2×C5#53611yescharacteristic
258C2×C5#57711yescharacteristic
259C2×C5#57711yescharacteristic
260D5—81no—
261C23—101no—
262C23C2×D2011yescharacteristic
263Q8—101no—
264Q8—101no—
265Q8—401no—
266Q8—401no—
267Q8—401no—
268D4—101no—
269D4—101no—
270D4—401no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—101no—
280C2×C4—401no—
281C2×C4—401no—
282C2×C4C2×D2011yescharacteristic
283C2×C4C2×D2011yescharacteristic
284C2×C4C2×D2011yescharacteristic
285C2×C4C2×D2011yescharacteristic
286C2×C4C2×D2011yescharacteristic
287C2×C4C23×D511yescharacteristic
288C8—21no—
289C8—21no—
290C8—21no—
291C8—21no—
292C5#324411yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—21no—
296C22—201no—
297C22—201no—
298C22—201no—
299C22C22×D2011yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—201no—
306C4—201no—
307C4—201no—
308C4—201no—
309C4—201no—
310C4—201no—
311C4—201no—
312C4#415011yescharacteristic
313C4#415011yescharacteristic
314C2—41no—
315C2—401no—
316C2#6586011yescharacteristic
317C2#6608511yescharacteristic
318C2#6608511yescharacteristic
subgroupG/H
centerC22C22×D20
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#433C2
socleC22×C5C22×D4
prime radical#4076C22
hypercenter#433D5
hypocenterC5#3244
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #65853C2semidirect
3. C5×#433C2semidirect
4. #65140C2semidirect
5. #65136C2semidirect
6. #65131C2semidirect
7. #65118C2semidirect
10. #65012C2semidirect
11. #65010C2semidirect
12. #65003C2semidirect
13. #64991C2semidirect
14. #64986C2semidirect
15. #64969C2semidirect
117. #433D5semidirect
292. C5#3244semidirect

Maximal subgroups

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

subgroupindex
#658682
#658532
C5×#4332
#651402
#651362
#651312
#651182
#650262
#650242
#650122
#650102
#650032
#649912
#649862
#649692
#32445