Finite Group Databasebeta

← #10613166

Subgroups — #10613166

Order 640.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65969C211yesmaximal, characteristic, complemented
2#65841C211yesmaximal, characteristic
3C5×#483C211yesmaximal, characteristic, complemented
4#65337C211yesmaximal, characteristic, complemented
5C2×#3940C211yesmaximal, characteristic, complemented
6#65159C211yesmaximal, characteristic, complemented
7#65152C211yesmaximal, characteristic, complemented
8D5×#106C211yesmaximal, characteristic, complemented
9#65144C211yesmaximal, characteristic, complemented
10#65096C211yesmaximal, characteristic, complemented
11#65094C211yesmaximal, characteristic, complemented
12#65080C211yesmaximal, characteristic, complemented
13#65077C211yesmaximal, characteristic, complemented
14#65024C211yesmaximal, characteristic, complemented
15#65014C211yesmaximal, characteristic, complemented
16C2×#709—21no—
17C5×C22⋊Q8C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19#4092C2211yescharacteristic
20Q8×Dic5C2211yescharacteristic
21C2×#688C2211yescharacteristic
22#4076C2211yescharacteristic
23#4075—21no—
24C4×C22⋊D5C2211yescharacteristic
25C2×C4⋊Dic5C2211yescharacteristic
26C22×#168C2211yescharacteristic
27C2×C8×D5C2211yescharacteristic
28#4043—21no—
29#4042—21no—
30#4041C2211yescharacteristic
31#4040—21no—
32#4039C2211yescharacteristic
33D5×C4⋊C4C2211yescharacteristic
34D5×C4⋊C4C2211yescharacteristic
35#4035—21no—
36#4034C2211yescharacteristic
37#4034C2211yescharacteristic
38#4027—21no—
39#4024—21no—
40C5×#106C2211yescharacteristic
41C5×#106C2211yescharacteristic
42C5×#103C2211yescharacteristic
43C5×#103C2211yescharacteristic
44C5×C22⋊C8C2211yescharacteristic
45#3967C2211yescharacteristic
46#3953C2211yescharacteristic
47#3953C2211yescharacteristic
48#3952C2211yescharacteristic
49#3949C2211yescharacteristic
50#3949C2211yescharacteristic
51#3946C2211yescharacteristic
52C8×Dic5C2211yescharacteristic
53#3941C2211yescharacteristic
54#3940C2211yescharacteristic
55#3940C2211yescharacteristic
56#3940C2211yescharacteristic
57#3940C2211yescharacteristic
58#3940C2211yescharacteristic
59#3335—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5C2311yescharacteristic
63C2×C22⋊D5—21no—
64C2×C22⋊D5D411yescharacteristic
65C22×Dic5—21no—
66#709—44no—
67C2×D20—21no—
68C2×D20C2311yescharacteristic
69C2×C4×D5—21no—
70C2×C4×D5—21no—
71C2×C4×D5—21no—
72C2×C4×D5C2311yescharacteristic
73C2×Dic10—21no—
74C2×Dic10—21no—
75C2×C5×C8C2311yescharacteristic
76C2×C5×C8C2311yescharacteristic
77C5×C4⋊C4—21no—
78C5×C4⋊C4—21no—
79C5×C4⋊C4C2311yescharacteristic
80C5×C4⋊C4C2311yescharacteristic
81C5×C4⋊C4C2311yescharacteristic
82C5×C22⋊C4—21no—
83C22⋊Dic5D411yescharacteristic
84#688—22no—
85#685—21no—
86#685—21no—
87#685—21no—
88#685—21no—
89#685D411yescharacteristic
90C4⋊Dic5—21no—
91C4⋊Dic5—21no—
92C4⋊Dic5C2311yescharacteristic
93C4⋊Dic5C2311yescharacteristic
94C4⋊Dic5C2311yescharacteristic
95#683—21no—
96#683—21no—
97#683—21no—
98#683—21no—
99#683—21no—
100#683D411yescharacteristic
101C4×Dic5—21no—
102C4×Dic5C2311yescharacteristic
103C2×#168—22no—
104C2×#168C2311yescharacteristic
105C2×#168C2311yescharacteristic
106C8×D5—22no—
107#554—51no—
108#547—51no—
109#498—51no—
110#483—51no—
111#483D511yescharacteristic, complemented
112#481—51no—
113#481—51no—
114#476—51no—
115#475—51no—
116#465—51no—
117#465—51no—
118C4×SD16—51no—
119C8×D4—51no—
120C2×#106—51no—
121C2×#106—51no—
122C23×C5C2×D411yescharacteristic
123C22×D5—21no—
124C22×D5C2×D411yescharacteristic
125C5×Q8—21no—
126C5×Q8—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—42no—
134C2×C4×C5C2×D411yescharacteristic
135C2×C4×C5C2411yescharacteristic
136C22⋊D5—42no—
137C22⋊D5SD1614yescomplemented
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5—81no—
142C2×Dic5C2×D411yescharacteristic
143C2×Dic5C2×D411yescharacteristic
144C2×Dic5C2×D411yescharacteristic
145D20—21no—
146D20—21no—
147D20—42no—
148C4×D5—21no—
149C4×D5—21no—
150C4×D5—42no—
151C4×D5—42no—
152C4×D5—81no—
153Dic10—42no—
154Dic10—81no—
155C5×C8—21no—
156C5×C8—21no—
157#168—21no—
158#168#4112yescomplemented
159C2×#41—101no—
160C2×SD16—51no—
161C22×C8—51no—
162C22×C8—51no—
163C4⋊Q8—51no—
164C4⋊Q8—51no—
165#125—101no—
166#123—101no—
167#123—101no—
168C22⋊Q8—51no—
169C22⋊Q8—101no—
170C22⋊Q8—101no—
171C22⋊Q8—101no—
172C22⋊Q8C2×D511yescharacteristic
173#121—51no—
174#121—51no—
175C4×Q8—51no—
176C4×D4—51no—
177C4×D4—51no—
178C4×D4—101no—
179C2×C4⋊C4—51no—
180C2×C4⋊C4—51no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4C2×D511yescharacteristic
183#106—51no—
184#106—51no—
185#106—51no—
186#106—51no—
187#106—51no—
188#106—51no—
189#106—51no—
190#106C2×D511yescharacteristic
191#106C2×D511yescharacteristic
192C4⋊C8—51no—
193#103—51no—
194#103C2×D511yescharacteristic
195#103C2×D511yescharacteristic
196#102—51no—
197#102—51no—
198#102—51no—
199C22⋊C8—51no—
200C22⋊C8C2×D511yescharacteristic
201C4×C8—51no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5C2×SD1612yes—
205C22×C5C22×D411yescharacteristic
206C2×D5—21no—
207C2×D5—21no—
208C2×D5—41no—
209C2×D5—41no—
210C2×D5—41no—
211C2×D5C2×SD1612yes—
212C4×C5—21no—
213C4×C5—41no—
214C4×C5—41no—
215C4×C5—41no—
216C4×C5—41no—
217C4×C5C2×#4111yescharacteristic
218C4×C52−1+411yescharacteristic
219Dic5—21no—
220Dic5—21no—
221Dic5—41no—
222Dic5—41no—
223Dic5—41no—
224Dic5C2×SD1612yes—
225#41—204no—
226C2×Q8—101no—
227C2×Q8—101no—
228C2×Q8C22×D511yescharacteristic
229C2×D4—51no—
230C2×D4—51no—
231C2×D4—101no—
232C2×D4—101no—
233C22×C4—21no—
234C22×C4—51no—
235C22×C4—101no—
236C22×C4—101no—
237C22×C4—101no—
238C22×C4—101no—
239C22×C4C22×D511yescharacteristic
240SD16—102no—
241C2×C8—51no—
242C2×C8—51no—
243C2×C8—102no—
244C2×C8—102no—
245C2×C8C22×D511yescharacteristic
246C2×C8C22×D511yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—51no—
250C4⋊C4—51no—
251C4⋊C4—51no—
252C4⋊C4—51no—
253C4⋊C4—101no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4—101no—
257C4⋊C4—101no—
258C4⋊C4—101no—
259C4⋊C4—101no—
260C4⋊C4C22×D511yescharacteristic
261C4⋊C4C22×D511yescharacteristic
262C4⋊C4C22×D511yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—51no—
265C22⋊C4—51no—
266C22⋊C4—101no—
267C22⋊C4—101no—
268C22⋊C4—101no—
269C22⋊C4—101no—
270C42—51no—
271C42—101no—
272C2×C5—22no—
273C2×C5#54711yescharacteristic
274C2×C5C22×SD1611yescharacteristic
275C2×C5#57711yescharacteristic
276D5—22no—
277D5—81no—
278C23—51no—
279C23—101no—
280C23D4×D511yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—202no—
284Q8—401no—
285D4—54no—
286D4—101no—
287D4—101no—
288D4—202no—
289D4—202no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—51no—
298C2×C4—51no—
299C2×C4—51no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—202no—
306C2×C4—202no—
307C2×C4—401no—
308C2×C4—401no—
309C2×C4D4×D511yescharacteristic
310C2×C4C23×D511yescharacteristic
311C8—21no—
312C8—21no—
313C8—52no—
314C8—101no—
315C5#333511yescharacteristic, complemented, Sylow
316C22—21no—
317C22—21no—
318C22—52no—
319C22—101no—
320C22—101no—
321C22—201no—
322C22—201no—
323C22—201no—
324C22D5×SD1612yes—
325C22C2×D4×D511yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—52no—
332C4—101no—
333C4—101no—
334C4—201no—
335C4—201no—
336C4—201no—
337C4D5×#4111yescharacteristic
338C4#415011yescharacteristic
339C2—22no—
340C2—102no—
341C2—401no—
342C2#6598911yescharacteristic
343C2C2×D5×SD1611yescharacteristic
344C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#483C2
socleC22×C5C22×D4
prime radical#65841C2
hypercenter#483D5
hypocenterC5#3335
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #65969C2semidirect
3. C5×#483C2semidirect
4. #65337C2semidirect
5. C2×#3940C2semidirect
6. #65159C2semidirect
7. #65152C2semidirect
8. D5×#106C2semidirect
9. #65144C2semidirect
10. #65096C2semidirect
11. #65094C2semidirect
12. #65080C2semidirect
13. #65077C2semidirect
14. #65024C2semidirect
15. #65014C2semidirect
111. #483D5semidirect
137. C22⋊D5SD16semidirect
158. #168#41semidirect
315. C5#3335semidirect

Maximal subgroups

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

subgroupindex
#659692
#658412
C5×#4832
#653372
C2×#39402
#651592
#651522
D5×#1062
#651442
#650962
#650942
#650802
#650772
#650242
#650142
#33355