Finite Group Databasebeta

← #10614865

Subgroups — #10614865

Order 640.

380 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
1C5×#529C211yesmaximal, characteristic, complemented
2#65813C211yesmaximal, characteristic, complemented
3#65357C211yesmaximal, characteristic, complemented
4#65353C211yesmaximal, characteristic, complemented
5#65348C211yesmaximal, characteristic, complemented
6#65345C211yesmaximal, characteristic, complemented
7#65340C211yesmaximal, characteristic, complemented
8#65337C211yesmaximal, characteristic, complemented
9#65330C211yesmaximal, characteristic, complemented
10#65327C211yesmaximal, characteristic
11C4×#689C211yesmaximal, characteristic, complemented
12C4×#688C211yesmaximal, characteristic, complemented
13C4×#687C211yesmaximal, characteristic, complemented
14C4×#686C211yesmaximal, characteristic, complemented
15C2×C4×#168C211yesmaximal, characteristic, complemented
16C5×#126—21no—
17C5×#125C2211yescharacteristic
18C5×#124C2211yescharacteristic
19C5×#123—21no—
20C5×C22⋊Q8C2211yescharacteristic
21C5×#121C2211yescharacteristic
22C4×C5×Q8C2211yescharacteristic
23C4×C5×D4—21no—
24C4×C5×D4C2211yescharacteristic
25C5×#117—21no—
26C2×C42×C5C2211yescharacteristic
27C2×#689C2211yescharacteristic
28C2×#688C2211yescharacteristic
29C2×#687C2211yescharacteristic
30C2×#686C2211yescharacteristic
31#4076C2211yescharacteristic
32#4075—21no—
33C4×C22⋊D5—21no—
34#4070C2211yescharacteristic
35C22×#168C2211yescharacteristic
36C22×#168C2211yescharacteristic
37#4022—21no—
38#4021C2211yescharacteristic
39C4×D20C2211yescharacteristic
40#4018—21no—
41#4016C2211yescharacteristic
42C4×Dic10C2211yescharacteristic
43#3967C2211yescharacteristic
44#3967C2211yescharacteristic
45#3964C2211yescharacteristic
46#3964C2211yescharacteristic
47#3942C2211yescharacteristic
48#3942C2211yescharacteristic
49#3941C2211yescharacteristic
50#3941C2211yescharacteristic
51#3940C2211yescharacteristic
52#3940C2211yescharacteristic
53#3939C2211yescharacteristic
54#3939C2211yescharacteristic
55C4×#168C2211yescharacteristic
56C4×#168C2211yescharacteristic
57C4×#168C2211yescharacteristic
58C4×#168C2211yescharacteristic
59#3168—51nomaximal, Sylow
60C2×C5×Q8C2311yescharacteristic
61C2×C5×D4—21no—
62C2×C5×D4C2311yescharacteristic
63C22×C4×C5—21no—
64C22×C4×C5D411yescharacteristic
65C22×C4×C5D411yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C2×C22⋊D5—21no—
68C2×D20C2311yescharacteristic
69C2×C4×D5—21no—
70C2×Dic10C2311yescharacteristic
71C5×C4⋊C4—21no—
72C5×C4⋊C4—21no—
73C5×C4⋊C4—21no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4C2311yescharacteristic
76C5×C4⋊C4C2311yescharacteristic
77C5×C22⋊C4—21no—
78C5×C22⋊C4—21no—
79C5×C22⋊C4—21no—
80C5×C22⋊C4—21no—
81C5×C22⋊C4—21no—
82C42×C5—21no—
83C42×C5D411yescharacteristic
84C42×C5D411yescharacteristic
85C42×C5C2311yescharacteristic
86C42×C5C2311yescharacteristic
87C22⋊Dic5—21no—
88#689—22no—
89#688—22no—
90#687—22no—
91#686—22no—
92#685—21no—
93#685—21no—
94#685—21no—
95#685—21no—
96C4⋊Dic5C2311yescharacteristic
97C4⋊Dic5C2311yescharacteristic
98#683—21no—
99#683—21no—
100#683—21no—
101#683—21no—
102C4×Dic5—21no—
103C2×#168—22no—
104C2×#168—22no—
105C2×#168C2311yescharacteristic
106C2×#168C2311yescharacteristic
107C2×#168C2311yescharacteristic
108C2×#168C2311yescharacteristic
109#529—51no—
110#529D511yescharacteristic, complemented
111#499—51no—
112#495—51no—
113#488—51no—
114#488—51no—
115#467—51no—
116#466—51no—
117#465—51no—
118#465—51no—
119C4×Q16—51no—
120C4×SD16—51no—
121C4×SD16—51no—
122C4×D8—51no—
123C2×C4×C8—51no—
124C23×C5—21no—
125C23×C5C2×D411yescharacteristic
126C22×D5—21no—
127C5×Q8—21no—
128C5×Q8—21no—
129C5×D4—21no—
130C5×D4—21no—
131C5×D4—42no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—42no—
140C2×C4×C5C2×D411yescharacteristic
141C2×C4×C5C2×D411yescharacteristic
142C2×C4×C5C2×D411yescharacteristic
143C2×C4×C5C2×D411yescharacteristic
144C2×C4×C5C2×D411yescharacteristic
145C2×C4×C5C2411yescharacteristic
146C22⋊D5—42no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150D20—21no—
151D20—21no—
152C4×D5—42no—
153Dic10—21no—
154Dic10—21no—
155#168—21no—
156#168—21no—
157#168#4112yes—
158#168#4112yes—
159C2×Q16—51no—
160C2×SD16—51no—
161C2×SD16—51no—
162C2×D8—51no—
163C22×C8—51no—
164C22×C8—51no—
165#126—21no—
166#126—101no—
167#125—51no—
168#125C2×D511yescharacteristic
169#124—51no—
170#124C2×D511yescharacteristic
171#123—21no—
172#123—101no—
173C22⋊Q8—51no—
174C22⋊Q8C2×D511yescharacteristic
175#121—51no—
176#121C2×D511yescharacteristic
177C4×Q8—51no—
178C4×Q8C2×D511yescharacteristic
179C4×D4—21no—
180C4×D4—51no—
181C4×D4—101no—
182C4×D4C2×D511yescharacteristic
183#117—21no—
184#117—101no—
185C2×C42C2×D511yescharacteristic
186#107—51no—
187#107—51no—
188#106—51no—
189#106—51no—
190#103—51no—
191#103—51no—
192#103—51no—
193#103—51no—
194#102—51no—
195#102—51no—
196#102—51no—
197#102—51no—
198C4×C8—51no—
199C4×C8—51no—
200C4×C8—51no—
201C4×C8—51no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—41no—
207C22×C5#13512yes—
208C22×C5C22×D411yescharacteristic
209C2×D5—41no—
210C2×D5—41no—
211C2×D5—41no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—41no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5#13512yes—
220C4×C5C2×#4111yescharacteristic
221C4×C5C2×#4111yescharacteristic
222Dic5—41no—
223Dic5—41no—
224Dic5—41no—
225C2×Q8—51no—
226C2×Q8C22×D511yescharacteristic
227C2×D4—21no—
228C2×D4—51no—
229C2×D4—101no—
230C2×D4C22×D511yescharacteristic
231C22×C4—21no—
232C22×C4—101no—
233C22×C4C22⋊D511yescharacteristic
234C22×C4C22⋊D511yescharacteristic
235C22×C4C22×D511yescharacteristic
236Q16—102no—
237SD16—102no—
238SD16—102no—
239D8—102no—
240C2×C8—51no—
241C2×C8—51no—
242C2×C8—51no—
243C2×C8—51no—
244C2×C8—102no—
245C2×C8—102no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—51no—
251C4⋊C4—51no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4C22×D511yescharacteristic
257C4⋊C4C22×D511yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—101no—
264C22⋊C4—101no—
265C22⋊C4—101no—
266C22⋊C4—101no—
267C22⋊C4—101no—
268C42—21no—
269C42—101no—
270C42C22⋊D511yescharacteristic
271C42C22⋊D511yescharacteristic
272C42C22×D511yescharacteristic
273C42C22×D511yescharacteristic
274C2×C5—22no—
275C2×C5—81no—
276C2×C5#53211yescharacteristic
277C2×C5C2×#13511yescharacteristic
278C2×C5C2×#13511yescharacteristic
279D5—81no—
280C23—21no—
281C23—101no—
282C23C2×C22⋊D511yescharacteristic
283Q8—21no—
284Q8—21no—
285Q8—101no—
286Q8—101no—
287D4—21no—
288D4—21no—
289D4—42no—
290D4—101no—
291D4—101no—
292D4—202no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—202no—
305C2×C4C2×C22⋊D511yescharacteristic
306C2×C4C2×C22⋊D511yescharacteristic
307C2×C4C2×C22⋊D511yescharacteristic
308C2×C4C2×C22⋊D511yescharacteristic
309C2×C4C2×C22⋊D511yescharacteristic
310C2×C4C23×D511yescharacteristic
311C8—52no—
312C8—52no—
313C8—101no—
314C8—101no—
315C5#316811yescharacteristic, complemented, Sylow
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—201no—
322C22—201no—
323C22—201no—
324C22#409612yes—
325C22C22×C22⋊D511yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—201no—
334C4—201no—
335C4—201no—
336C4#409612yes—
337C4D5×#4111yescharacteristic
338C4D5×#4111yescharacteristic
339C2—22no—
340C2—81no—
341C2—401no—
342C2C2×#409611yescharacteristic
343C2C2×#409611yescharacteristic
344C2#6616611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#529C2
socleC22×C5C22×D4
prime radical#65327C2
hypercenter#529D5
hypocenterC5#3168
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C5×#529C2semidirect
2. #65813C2semidirect
3. #65357C2semidirect
4. #65353C2semidirect
5. #65348C2semidirect
6. #65345C2semidirect
7. #65340C2semidirect
8. #65337C2semidirect
9. #65330C2semidirect
11. C4×#689C2semidirect
12. C4×#688C2semidirect
13. C4×#687C2semidirect
14. C4×#686C2semidirect
15. C2×C4×#168C2semidirect
110. #529D5semidirect
315. C5#3168semidirect

Maximal subgroups

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

subgroupindex
C5×#5292
#658132
#653572
#653532
#653482
#653452
#653402
#653372
#653302
#653272
C4×#6892
C4×#6882
C4×#6872
C4×#6862
C2×C4×#1682
#31685