Finite Group Databasebeta

← #10611093

Subgroups — #10611093

Order 640.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65869C211yesmaximal, characteristic
2#65853C211yesmaximal, characteristic, complemented
3C5×#433C211yesmaximal, characteristic, complemented
4#65136C211yesmaximal, characteristic, complemented
5#65136C211yesmaximal, characteristic, complemented
6#65135C211yesmaximal, characteristic, complemented
7#65131C211yesmaximal, characteristic, complemented
8#65026C211yesmaximal, characteristic, complemented
9#65026C211yesmaximal, characteristic, complemented
10#65025C211yesmaximal, characteristic, complemented
11#65024C211yesmaximal, characteristic, complemented
12#65002C211yesmaximal, characteristic, complemented
13#64991C211yesmaximal, characteristic, complemented
14#64983C211yesmaximal, characteristic, complemented
15#64972C211yesmaximal, characteristic, complemented
16C5×#117C2211yescharacteristic
17#4076C2211yescharacteristic
18#4076C2211yescharacteristic
19#4072C2211yescharacteristic
20C2×C4⋊Dic5C2211yescharacteristic
21#4040—21no—
22#4040—21no—
23#4036—21no—
24#4034—21no—
25#4030—21no—
26#4030—21no—
27#4024—21no—
28#4024—21no—
29#4020C2211yescharacteristic
30C4×D20C2211yescharacteristic
31C4×D20C2211yescharacteristic
32#4016C2211yescharacteristic
33#4016C2211yescharacteristic
34#4016C2211yescharacteristic
35#4015C2211yescharacteristic
36#4015C2211yescharacteristic
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#3953C2211yescharacteristic
48#3953C2211yescharacteristic
49#3953C2211yescharacteristic
50#3953C2211yescharacteristic
51#3950C2211yescharacteristic
52#3950C2211yescharacteristic
53#3950C2211yescharacteristic
54#3950C2211yescharacteristic
55#3949C2211yescharacteristic
56#3949C2211yescharacteristic
57#3949C2211yescharacteristic
58#3949C2211yescharacteristic
59#3241—51nomaximal, Sylow
60C22×C4×C5C2311yescharacteristic
61C2×C22⋊D5—21no—
62C2×C22⋊D5—21no—
63C22×Dic5—21no—
64C2×D20—21no—
65C2×D20—21no—
66C2×D20C2311yescharacteristic
67C2×D20C2311yescharacteristic
68C2×C4×D5—21no—
69C2×C4×D5—21no—
70C2×Dic10—21no—
71C2×Dic10—21no—
72C2×C5×C8C2311yescharacteristic
73C2×C5×C8C2311yescharacteristic
74C2×C5×C8C2311yescharacteristic
75C2×C5×C8C2311yescharacteristic
76C5×C4⋊C4D411yescharacteristic
77C5×C4⋊C4D411yescharacteristic
78C5×C22⋊C4D411yescharacteristic
79C5×C22⋊C4D411yescharacteristic
80C42×C5C2311yescharacteristic
81C42×C5C2311yescharacteristic
82C22⋊Dic5—21no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685—21no—
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5—21no—
90C4⋊Dic5C2311yescharacteristic
91C4⋊Dic5C2311yescharacteristic
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95C4⋊Dic5C2311yescharacteristic
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100#683—21no—
101#683—21no—
102C4×Dic5—21no—
103#544—51no—
104#540—51no—
105#501—51no—
106#499—51no—
107#490—51no—
108#486—51no—
109#482—51no—
110#482—51no—
111#481—51no—
112#480—51no—
113#478—51no—
114#478—51no—
115#476—51no—
116#474—51no—
117#433D511yescharacteristic, complemented
118C23×C5C2×D411yescharacteristic
119C22×D5—21no—
120C22×D5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5C2×D411yescharacteristic
124C2×C4×C5C2×D411yescharacteristic
125C2×C4×C5C2×D411yescharacteristic
126C2×C4×C5C2×D411yescharacteristic
127C2×C4×C5C2×D411yescharacteristic
128C2×C4×C5C2411yescharacteristic
129C22⋊D5—81no—
130C22⋊D5—81no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—81no—
138D20—21no—
139D20—21no—
140D20—21no—
141D20—21no—
142D20—81no—
143D20—81no—
144C4×D5—81no—
145C4×D5—81no—
146Dic10—81no—
147Dic10—81no—
148C5×C8—21no—
149C5×C8—21no—
150C5×C8—21no—
151C5×C8—21no—
152C4⋊Q8—51no—
153C4⋊Q8—51no—
154C4⋊Q8—101no—
155#127—51no—
156#125—51no—
157#125—51no—
158#125—51no—
159#125—101no—
160#123—101no—
161#123—101no—
162C22⋊Q8—101no—
163C22⋊Q8—101no—
164#121—51no—
165#121—51no—
166#121—101no—
167#121—101no—
168C4×D4—51no—
169C4×D4—51no—
170#117—51no—
171#117C2×D511yescharacteristic
172C2×C4⋊C4—51no—
173#107—51no—
174#107—51no—
175#107—51no—
176#107—51no—
177#106—51no—
178#106—51no—
179#106—51no—
180#106—51no—
181C4⋊C8C2×D511yescharacteristic
182C4⋊C8C2×D511yescharacteristic
183#102—51no—
184#102—51no—
185#102—51no—
186#102—51no—
187#102—51no—
188#102—51no—
189#102—51no—
190#102—51no—
191C22⋊C8C2×D511yescharacteristic
192C22⋊C8C2×D511yescharacteristic
193#97C2×D511yescharacteristic
194C4×C8C2×D511yescharacteristic
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5C22×D411yescharacteristic
199C2×D5—41no—
200C2×D5—41no—
201C2×D5—41no—
202C2×D5—41no—
203C2×D5—41no—
204C2×D5—41no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C52−1+411yescharacteristic
211C4×C52−1+411yescharacteristic
212Dic5—41no—
213Dic5—41no—
214Dic5—41no—
215Dic5—41no—
216Dic5—41no—
217Dic5—41no—
218C2×Q8—101no—
219C2×Q8—101no—
220C2×D4—51no—
221C2×D4—51no—
222C2×D4—101no—
223C2×D4—101no—
224C2×D4—101no—
225C2×D4—101no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C22×D511yescharacteristic
230C2×C8C22×D511yescharacteristic
231C2×C8C22×D511yescharacteristic
232C2×C8C22×D511yescharacteristic
233C2×C8C22×D511yescharacteristic
234C4⋊C4—51no—
235C4⋊C4—51no—
236C4⋊C4—51no—
237C4⋊C4—51no—
238C4⋊C4—51no—
239C4⋊C4—51no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4—101no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4D2011yescharacteristic
250C4⋊C4D2011yescharacteristic
251C22⋊C4—101no—
252C22⋊C4—101no—
253C22⋊C4—101no—
254C22⋊C4—101no—
255C22⋊C4—101no—
256C22⋊C4D2011yescharacteristic
257C22⋊C4D2011yescharacteristic
258C42—101no—
259C42C22×D511yescharacteristic
260C42C22×D511yescharacteristic
261C2×C5—41no—
262C2×C5#53611yescharacteristic
263C2×C5#57611yescharacteristic
264C2×C5#57711yescharacteristic
265D5—81no—
266D5—81no—
267C23—101no—
268C23—101no—
269C23C2×D2011yescharacteristic
270Q8—401no—
271Q8—401no—
272D4—101no—
273D4—101no—
274D4—101no—
275D4—101no—
276D4—401no—
277D4—401no—
278D4—401no—
279D4—401no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—101no—
283C2×C4—101no—
284C2×C4—101no—
285C2×C4—101no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—401no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4C2×D2011yescharacteristic
292C2×C4C2×D2011yescharacteristic
293C2×C4C2×D2011yescharacteristic
294C2×C4C2×D2011yescharacteristic
295C2×C4C2×D2011yescharacteristic
296C2×C4C23×D511yescharacteristic
297C8—21no—
298C8—21no—
299C8—21no—
300C8—21no—
301C5#324111yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22—21no—
305C22—201no—
306C22—201no—
307C22—201no—
308C22—201no—
309C22—201no—
310C22—201no—
311C22C22×D2011yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—201no—
318C4—201no—
319C4—201no—
320C4—201no—
321C4—201no—
322C4—201no—
323C4#415011yescharacteristic
324C4#415011yescharacteristic
325C2—41no—
326C2—401no—
327C2—401no—
328C2#6586011yescharacteristic
329C2#6608511yescharacteristic
330C2#6608611yescharacteristic
subgroupG/H
centerC22C22×D20
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#433C2
socleC22×C5C22×D4
prime radical#65869C2
hypercenter#433D5
hypocenterC5#3241
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. #65136C2semidirect
5. #65136C2semidirect
6. #65135C2semidirect
7. #65131C2semidirect
8. #65026C2semidirect
9. #65026C2semidirect
10. #65025C2semidirect
11. #65024C2semidirect
12. #65002C2semidirect
13. #64991C2semidirect
14. #64983C2semidirect
15. #64972C2semidirect
117. #433D5semidirect
301. C5#3241semidirect

Maximal subgroups

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

subgroupindex
#658692
#658532
C5×#4332
#651362
#651352
#651312
#650262
#650252
#650242
#650022
#649912
#649832
#649722
#32415