Finite Group Databasebeta

← #10611513

Subgroups — #10611513

Order 640.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#65914C211yesmaximal, characteristic, complemented
2C4×D4×D5C211yesmaximal, characteristic, complemented
3C5×#440C211yesmaximal, characteristic, complemented
4#65458C211yesmaximal, characteristic, complemented
5#65454C211yesmaximal, characteristic, complemented
6#65315C211yesmaximal, characteristic, complemented
7#65303C211yesmaximal, characteristic, complemented
8#65180C211yesmaximal, characteristic, complemented
9#65171C211yesmaximal, characteristic, complemented
10#65108C211yesmaximal, characteristic, complemented
11#65094C211yesmaximal, characteristic, complemented
12#65062C211yesmaximal, characteristic
13#65052C211yesmaximal, characteristic, complemented
14#65000C211yesmaximal, characteristic, complemented
15#64994C211yesmaximal, characteristic, complemented
16C2×D4×D5C2211yescharacteristic
17C22×C4×D5—21no—
18C2×C5×SD16C2211yescharacteristic
19C4×C5×Q8C2211yescharacteristic, complemented
20C4×C5×D4C2211yescharacteristic
21#4093C2211yescharacteristic, complemented
22#4092C2211yescharacteristic
23C2×#688C2211yescharacteristic
24D4×Dic5C2211yescharacteristic
25C2×#686C2211yescharacteristic
26C4×C22⋊D5—21no—
27C2×D40C2211yescharacteristic
28#4044—21no—
29#4041C2211yescharacteristic
30#4040—21no—
31#4039C2211yescharacteristic
32D5×C4⋊C4C2211yescharacteristic
33#4036C2211yescharacteristic, complemented
34#4027—21no—
35D5×C22⋊C4—21no—
36C4×D20—21no—
37C4×D20C2211yescharacteristic
38C4×D20C2211yescharacteristic, complemented
39#4018—21no—
40C42×D5C2211yescharacteristic
41C5×#107C2211yescharacteristic, complemented
42C5×#103C2211yescharacteristic, complemented
43C5×#102C2211yescharacteristic
44C5×#97C2211yescharacteristic, complemented
45#3967C2211yescharacteristic, complemented
46#3964C2211yescharacteristic
47#3953C2211yescharacteristic
48#3953C2211yescharacteristic, complemented
49#3952C2211yescharacteristic
50#3952C2211yescharacteristic
51#3949C2211yescharacteristic, complemented
52#3946C2211yescharacteristic, complemented
53#3946C2211yescharacteristic, complemented
54#3941C2211yescharacteristic
55#3941C2211yescharacteristic, complemented
56#3940C2211yescharacteristic, complemented
57#3939C2211yescharacteristic, complemented
58#3935C2211yescharacteristic, complemented
59#3114—51nomaximal, Sylow
60C23×D5—21no—
61C2×C5×Q8C2311yescharacteristic
62C2×C5×D4C2311yescharacteristic
63C22×C4×C5—21no—
64C2×C22⋊D5—21no—
65C22×Dic5—21no—
66D4×D5—22no—
67D4×D5—22no—
68C2×D20—21no—
69C2×D20C2311yescharacteristic
70C2×D20C2311yescharacteristic
71C2×C4×D5—21no—
72C2×C4×D5—21no—
73C2×C4×D5—21no—
74C2×C4×D5—21no—
75C2×C4×D5—44no—
76C2×C4×D5D411yescharacteristic
77C2×C4×D5D411yescharacteristic
78C2×C4×D5C2311yescharacteristic
79C5×SD16—22no—
80C2×C5×C8C2311yescharacteristic
81C2×C5×C8C2311yescharacteristic
82C5×C4⋊C4—21no—
83C5×C4⋊C4C2311yescharacteristic
84C5×C4⋊C4C2311yescharacteristic
85C5×C22⋊C4—21no—
86C42×C5—21no—
87C42×C5C2311yescharacteristic
88C22⋊Dic5—21no—
89#688—22no—
90#686—22no—
91#685—21no—
92#685—21no—
93#685—21no—
94#685—21no—
95#685—21no—
96#685—21no—
97#685—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5C2311yescharacteristic
100C4⋊Dic5C2311yescharacteristic
101#683—21no—
102#683—21no—
103#683—21no—
104C4×Dic5D411yescharacteristic
105C4×Dic5D411yescharacteristic
106C4×Dic5C2311yescharacteristic
107C2×#168C2311yescharacteristic
108C2×#168C2311yescharacteristic
109D40—22no—
110#529—51no—
111C2×C4×D4—51no—
112#483—51no—
113#480—51no—
114#478—51no—
115#478—51no—
116#463—51no—
117#463—51no—
118#450—51no—
119#447—51no—
120#442—51no—
121#442—51no—
122#440—51no—
123#440D511yescharacteristic, complemented
124#432—51no—
125C23×C5—21no—
126C22×D5—24no—
127C22×D5—21no—
128C22×D5—21no—
129C22×D5—42no—
130C22×D5—42no—
131C22×D5C2×D411yescharacteristic
132C5×Q8—21no—
133C5×Q8—21no—
134C5×D4—21no—
135C5×D4#4112yes—
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×C5C2411yescharacteristic
143C22⋊D5—24no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—42no—
147C2×Dic5C2×D411yescharacteristic
148C2×Dic5C2×D411yescharacteristic
149C2×Dic5C2×D411yescharacteristic
150D20—21no—
151D20—21no—
152D20—21no—
153D20—42no—
154D20#4112yes—
155C4×D5—22no—
156C4×D5—21no—
157C4×D5—21no—
158C4×D5—41no—
159C4×D5—42no—
160C4×D5—42no—
161C4×D5—42no—
162C4×D5—42no—
163C5×C8—21no—
164C5×C8—21no—
165#168—21no—
166#168—21no—
167C22×D4—51no—
168C23×C4—101no—
169C2×SD16—51no—
170C2×SD16C2×D511yescharacteristic
171C2×D8—51no—
172C2×D8—51no—
173#126—101no—
174#125—51no—
175#124—51no—
176#123—101no—
177C22⋊Q8—51no—
178#121—51no—
179C4×Q8C2×D511yescharacteristic, complemented
180C4×D4—51no—
181C4×D4—51no—
182C4×D4—51no—
183C4×D4—51no—
184C4×D4—101no—
185C4×D4—101no—
186C4×D4—101no—
187C4×D4C2×D511yescharacteristic
188#117—101no—
189C2×C4⋊C4—51no—
190C2×C22⋊C4—101no—
191C2×C42—51no—
192#107—51no—
193#107C2×D511yescharacteristic, complemented
194#106—51no—
195#106—51no—
196C4⋊C8—51no—
197C4⋊C8—51no—
198#103—51no—
199#103C2×D511yescharacteristic, complemented
200#102—51no—
201#102—51no—
202#102—51no—
203#102—51no—
204#102—51no—
205#102C2×D511yescharacteristic
206C22⋊C8—51no—
207C22⋊C8—51no—
208#97—51no—
209#97C2×D511yescharacteristic, complemented
210C22×C5—22no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5C22×D411yescharacteristic
214C2×D5—21no—
215C2×D5—21no—
216C2×D5—22no—
217C2×D5—48no—
218C2×D5—41no—
219C2×D5—41no—
220C2×D5—41no—
221C2×D5—41no—
222C2×D5—41no—
223C2×D5AGL(1,ℤ/8)12yes—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5C2×#4111yescharacteristic
230C4×C5C2×#4111yescharacteristic
231Dic5—21no—
232Dic5—21no—
233Dic5—21no—
234Dic5—41no—
235Dic5—41no—
236C24—101no—
237C2×Q8C22×D511yescharacteristic
238C2×D4—51no—
239C2×D4—51no—
240C2×D4—101no—
241C2×D4—101no—
242C2×D4—102no—
243C2×D4—102no—
244C2×D4C22×D511yescharacteristic
245C22×C4—21no—
246C22×C4—51no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—101no—
250C22×C4—101no—
251C22×C4—101no—
252C22×C4—101no—
253C22×C4—101no—
254C22×C4—204no—
255SD16—22no—
256SD16—102no—
257D8—102no—
258D8—102no—
259C2×C8—51no—
260C2×C8—51no—
261C2×C8C22×D511yescharacteristic
262C2×C8C22×D511yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—51no—
265C4⋊C4—51no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4C22×D511yescharacteristic
271C4⋊C4C22×D511yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—101no—
274C22⋊C4—101no—
275C22⋊C4—101no—
276C22⋊C4—101no—
277C22⋊C4—101no—
278C22⋊C4—101no—
279C22⋊C4—101no—
280C22⋊C4—101no—
281C42—21no—
282C42—51no—
283C42—51no—
284C42—51no—
285C42C22×D511yescharacteristic
286C2×C5—42no—
287C2×C5#52511yescharacteristic
288C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
289C2×C5#57511yescharacteristic
290D5—22no—
291D5—42no—
292D5—81no—
293C23—21no—
294C23—51no—
295C23—104no—
296C23—101no—
297C23—101no—
298C23—202no—
299C23—202no—
300Q8—21no—
301Q8—21no—
302D4—21no—
303D4—52no—
304D4—104no—
305D4—101no—
306D4—101no—
307D4—101no—
308D4—202no—
309D4#70912yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—51no—
315C2×C4—51no—
316C2×C4—51no—
317C2×C4—102no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—201no—
323C2×C4—202no—
324C2×C4—202no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—202no—
328C2×C4D4×D511yescharacteristic
329C2×C4D4×D511yescharacteristic
330C2×C4C23×D511yescharacteristic
331C8—21no—
332C8—21no—
333C8—101no—
334C8—101no—
335C5#311411yescharacteristic, complemented, Sylow
336C22—22no—
337C22—41no—
338C22—41no—
339C22—52no—
340C22—101no—
341C22—101no—
342C22—102no—
343C22—208no—
344C22—201no—
345C22—201no—
346C22—201no—
347C22—201no—
348C22—201no—
349C22C2×D4×D511yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—201no—
359C4—201no—
360C4C2×#70911yescharacteristic
361C4D5×#4111yescharacteristic
362C2—42no—
363C2—102no—
364C2—202no—
365C2—401no—
366C2#6588111yescharacteristic
367C2D5×AGL(1,ℤ/8)11yescharacteristic
368C2#6611111yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#440C2
socleC22×C5C22×D4
prime radical#65062C2
hypercenter#440D5
hypocenterC5#3114
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #65914C2semidirect
2. C4×D4×D5C2semidirect
3. C5×#440C2semidirect
4. #65458C2semidirect
5. #65454C2semidirect
6. #65315C2semidirect
7. #65303C2semidirect
8. #65180C2semidirect
9. #65171C2semidirect
10. #65108C2semidirect
11. #65094C2semidirect
13. #65052C2semidirect
14. #65000C2semidirect
15. #64994C2semidirect
19. C4×C5×Q8C22semidirect
21. #4093C22semidirect
33. #4036C22semidirect
38. C4×D20C22semidirect
41. C5×#107C22semidirect
42. C5×#103C22semidirect
44. C5×#97C22semidirect
45. #3967C22semidirect
48. #3953C22semidirect
51. #3949C22semidirect
52. #3946C22semidirect
53. #3946C22semidirect
55. #3941C22semidirect
56. #3940C22semidirect
57. #3939C22semidirect
58. #3935C22semidirect
123. #440D5semidirect
179. C4×Q8C2×D5semidirect
193. #107C2×D5semidirect
199. #103C2×D5semidirect
209. #97C2×D5semidirect
335. C5#3114semidirect

Maximal subgroups

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

subgroupindex
#659142
C4×D4×D52
C5×#4402
#654582
#654542
#653152
#653032
#651802
#651712
#651082
#650942
#650622
#650522
#650002
#649942
#31145