Finite Group Databasebeta

← #10612987

Subgroups — #10612987

Order 640.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66029C211yesmaximal, characteristic
2#65913C211yesmaximal, characteristic, complemented
3C5×#479C211yesmaximal, characteristic, complemented
4#65354C211yesmaximal, characteristic, complemented
5#65315C211yesmaximal, characteristic, complemented
6#65171C211yesmaximal, characteristic, complemented
7D5×#107C211yesmaximal, characteristic, complemented
8#65152C211yesmaximal, characteristic, complemented
9#65150C211yesmaximal, characteristic, complemented
10#65135C211yesmaximal, characteristic, complemented
11#65125C211yesmaximal, characteristic, complemented
12#65103C211yesmaximal, characteristic, complemented
13#65101C211yesmaximal, characteristic, complemented
14#65098C211yesmaximal, characteristic, complemented
15#65096C211yesmaximal, characteristic, complemented
16C5×#125C2211yescharacteristic
17C4×C5×Q8C2211yescharacteristic
18#4092C2211yescharacteristic
19#4092C2211yescharacteristic
20C2×#688C2211yescharacteristic
21C2×#676C2211yescharacteristic
22C2×C8×D5C2211yescharacteristic
23#4044—21no—
24#4042—21no—
25#4042—21no—
26#4041—21no—
27#4041C2211yescharacteristic
28#4041C2211yescharacteristic
29#4040—21no—
30#4039—21no—
31#4038C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33D5×C4⋊C4C2211yescharacteristic
34D5×C4⋊C4C2211yescharacteristic
35C4×D20—21no—
36C4×D20C2211yescharacteristic
37C4×D20C2211yescharacteristic
38#4016—21no—
39#4015C2211yescharacteristic
40C5×#107C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×C4⋊C8C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×#103C2211yescharacteristic
45#3967C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3952C2211yescharacteristic
50#3950C2211yescharacteristic
51#3950C2211yescharacteristic
52#3941C2211yescharacteristic
53#3940C2211yescharacteristic
54#3940C2211yescharacteristic
55#3939C2211yescharacteristic
56#3939C2211yescharacteristic
57#3939C2211yescharacteristic
58#3935C2211yescharacteristic
59#3346—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×D20—21no—
62C2×D20—21no—
63C2×D20D411yescharacteristic
64C2×D20C2311yescharacteristic
65C2×C4×D5—21no—
66C2×C4×D5—21no—
67C2×C4×D5—21no—
68C2×C4×D5—21no—
69C2×C4×D5C2311yescharacteristic
70C2×C4×D5C2311yescharacteristic
71C2×Dic10—21no—
72C2×C5×C8C2311yescharacteristic
73C2×C5×C8C2311yescharacteristic
74C5×C4⋊C4—21no—
75C5×C4⋊C4—21no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4C2311yescharacteristic
78C5×C4⋊C4C2311yescharacteristic
79C5×C4⋊C4C2311yescharacteristic
80C42×C5—21no—
81C42×C5C2311yescharacteristic
82#688—22no—
83#685—21no—
84#685—21no—
85#685—21no—
86#685—21no—
87#685—21no—
88#685—21no—
89#685D411yescharacteristic
90#685D411yescharacteristic
91C4⋊Dic5—21no—
92C4⋊Dic5D411yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95C4⋊Dic5C2311yescharacteristic
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100#683—21no—
101C4×Dic5—21no—
102C2×#168C2311yescharacteristic
103C2×#168C2311yescharacteristic
104#676—22no—
105C8×D5—22no—
106#554—51no—
107#553—51no—
108#501—51no—
109#485—51no—
110#484—51no—
111#481—51no—
112#480—51no—
113#479D511yescharacteristic, complemented
114#474—51no—
115#468—51no—
116#465—51no—
117#440—51no—
118#435—51no—
119#428—51no—
120C2×#107—51no—
121C22×D5—21no—
122C22×D5C2×D411yescharacteristic
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×C5C2×D411yescharacteristic
131C2×C4×C5C2×D411yescharacteristic
132C2×C4×C5C2411yescharacteristic
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5C2×D411yescharacteristic
137C2×Dic5C2×D411yescharacteristic
138D20—22no—
139D20—21no—
140D20—21no—
141D20—42no—
142D20—81no—
143C4×D5—21no—
144C4×D5—21no—
145C4×D5—21no—
146C4×D5—21no—
147C4×D5—81no—
148C4×D5—81no—
149C4×D5—81no—
150C4×D5—81no—
151Dic10—81no—
152C5×C8—21no—
153C5×C8—21no—
154#168—21no—
155#168#4112yes—
156C2×SD16—51no—
157C2×M16—51no—
158C22×C8—51no—
159C4⋊Q8—51no—
160#126—101no—
161#125—101no—
162#125C2×D511yescharacteristic
163#123—101no—
164C22⋊Q8—51no—
165C22⋊Q8—51no—
166C22⋊Q8—101no—
167C22⋊Q8—101no—
168#121—51no—
169#121—51no—
170#121—101no—
171C4×Q8C2×D511yescharacteristic
172C4×D4—51no—
173C4×D4—51no—
174C4×D4—101no—
175C4×D4—101no—
176#117—51no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—51no—
180#107—51no—
181#107—51no—
182#107—51no—
183#107—51no—
184#107—51no—
185#107C2×D511yescharacteristic
186#106—51no—
187#106—51no—
188#106C2×D511yescharacteristic
189C4⋊C8C2×D511yescharacteristic
190#103—51no—
191#103C2×D511yescharacteristic
192#103C2×D511yescharacteristic
193#102—51no—
194#102—51no—
195#102—51no—
196C22⋊C8—51no—
197C22⋊C8—51no—
198#97—51no—
199C22×C5C22×D411yescharacteristic
200C2×D5—21no—
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—21no—
205C2×D5—41no—
206C2×D5—41no—
207C2×D5—41no—
208C2×D5#13712yes—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—41no—
214C4×C5—41no—
215C4×C5C2×#4111yescharacteristic
216C4×C52−1+411yescharacteristic
217Dic5—21no—
218Dic5—21no—
219Dic5—41no—
220Dic5—41no—
221Dic5—41no—
222C2×Q8—101no—
223C2×Q8C22×D511yescharacteristic
224C2×D4—51no—
225C2×D4—51no—
226C2×D4—101no—
227C2×D4—101no—
228C22×C4—51no—
229C22×C4—51no—
230C22×C4—101no—
231C22×C4—101no—
232C22×C4—101no—
233C22×C4—101no—
234SD16—102no—
235M16—102no—
236C2×C8—51no—
237C2×C8—51no—
238C2×C8—102no—
239C2×C8C22×D511yescharacteristic
240C2×C8C22×D511yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—51no—
245C4⋊C4—51no—
246C4⋊C4—51no—
247C4⋊C4—51no—
248C4⋊C4—101no—
249C4⋊C4—101no—
250C4⋊C4—101no—
251C4⋊C4—101no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C4⋊C4C22×D511yescharacteristic
255C4⋊C4C22×D511yescharacteristic
256C4⋊C4C22×D511yescharacteristic
257C22⋊C4—51no—
258C22⋊C4—51no—
259C22⋊C4—101no—
260C22⋊C4—101no—
261C22⋊C4—101no—
262C22⋊C4—101no—
263C22⋊C4—101no—
264C22⋊C4—101no—
265C42—21no—
266C42—101no—
267C42C22×D511yescharacteristic
268C2×C5#54711yescharacteristic
269C2×C5C2×#13711yescharacteristic
270C2×C5#57611yescharacteristic
271D5—22no—
272D5—41no—
273D5—81no—
274C23—51no—
275C23—51no—
276C23—101no—
277Q8—21no—
278Q8—21no—
279Q8—401no—
280D4—102no—
281D4—101no—
282D4—101no—
283D4—202no—
284D4—401no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—51no—
290C2×C4—51no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—401no—
299C2×C4—401no—
300C2×C4—401no—
301C2×C4—401no—
302C2×C4D4×D511yescharacteristic
303C2×C4D4×D511yescharacteristic
304C2×C4C23×D511yescharacteristic
305C8—21no—
306C8—21no—
307C8—52no—
308C8—101no—
309C5#334611yescharacteristic, complemented, Sylow
310C22—52no—
311C22—101no—
312C22—101no—
313C22—101no—
314C22—101no—
315C22—101no—
316C22—201no—
317C22—201no—
318C22—201no—
319C22C2×D4×D511yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—101no—
327C4—101no—
328C4—201no—
329C4—201no—
330C4—201no—
331C4#414711yescharacteristic
332C4D5×#4111yescharacteristic
333C2—102no—
334C2—201no—
335C2—401no—
336C2#6596511yescharacteristic
337C2#6610311yescharacteristic
338C2D5×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#479C2
socleC22×C5C22×D4
prime radical#66029C2
hypercenter#479D5
hypocenterC5#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #65913C2semidirect
3. C5×#479C2semidirect
4. #65354C2semidirect
5. #65315C2semidirect
6. #65171C2semidirect
7. D5×#107C2semidirect
8. #65152C2semidirect
9. #65150C2semidirect
10. #65135C2semidirect
11. #65125C2semidirect
12. #65103C2semidirect
13. #65101C2semidirect
14. #65098C2semidirect
15. #65096C2semidirect
113. #479D5semidirect
309. C5#3346semidirect

Maximal subgroups

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

subgroupindex
#660292
#659132
C5×#4792
#653542
#653152
#651712
D5×#1072
#651522
#651502
#651352
#651252
#651032
#651012
#650982
#650962
#33465