Finite Group Databasebeta

← #10612161

Subgroups — #10612161

Order 640.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4060C211yesmaximal, characteristic
2C2×D5×SD16C211yesmaximal, characteristic, complemented
3#66058C211yesmaximal, characteristic, complemented
4#65879C211yesmaximal, characteristic, complemented
5C5×#461C211yesmaximal, characteristic, complemented
6#65454C211yesmaximal, characteristic, complemented
7#65451C211yesmaximal, characteristic, complemented
8#65372C211yesmaximal, characteristic, complemented
9#65305C211yesmaximal, characteristic, complemented
10#65133C211yesmaximal, characteristic, complemented
11#65128C211yesmaximal, characteristic, complemented
12#65108C211yesmaximal, characteristic, complemented
13#65107C211yesmaximal, characteristic, complemented
14#65093C211yesmaximal, characteristic, complemented
15#65091C211yesmaximal, characteristic, complemented
16C2×#713C2211yescharacteristic
17C2×Q8×D5C2211yescharacteristic
18C2×D4×D5C2211yescharacteristic
19C2×C5×SD16C2211yescharacteristic
20C2×C5×SD16C2211yescharacteristic
21C5×C4⋊Q8C2211yescharacteristic, complemented
22C4×C5×D4C2211yescharacteristic
23#4093C2211yescharacteristic, complemented
24#4090C2211yescharacteristic, complemented
25C2×#688C2211yescharacteristic
26C2×#688C2211yescharacteristic
27D4×Dic5C2211yescharacteristic
28C2×#687C2211yescharacteristic
29C2×#686C2211yescharacteristic
30C4×C22⋊D5—21no—
31C2×#685—21no—
32#4060—24no—
33D5×SD16—24no—
34C2×D40C2211yescharacteristic
35C2×#677C2211yescharacteristic
36C2×#676C2211yescharacteristic
37C2×C8×D5C2211yescharacteristic
38#4042—21no—
39#4042—21no—
40#4040—21no—
41#4040—21no—
42#4039C2211yescharacteristic
43#4038C2211yescharacteristic
44#4027—21no—
45D5×C22⋊C4—21no—
46#4021C2211yescharacteristic, complemented
47C4×D20C2211yescharacteristic
48#4018C2211yescharacteristic
49C5×C4⋊C8C2211yescharacteristic, complemented
50C5×#103C2211yescharacteristic, complemented
51C5×#103C2211yescharacteristic, complemented
52#3967C2211yescharacteristic, complemented
53#3967C2211yescharacteristic, complemented
54#3953C2211yescharacteristic, complemented
55#3948C2211yescharacteristic, complemented
56#3946C2211yescharacteristic, complemented
57#3946C2211yescharacteristic, complemented
58#3942C2211yescharacteristic, complemented
59#3941C2211yescharacteristic, complemented
60C4⋊#168C2211yescharacteristic, complemented
61#3042—51nomaximal, Sylow
62C23×D5—21no—
63C2×C5×Q8C2311yescharacteristic
64C2×C5×Q8C2311yescharacteristic
65C2×C5×D4C2311yescharacteristic
66C22×C4×C5—21no—
67C2×C22⋊D5—21no—
68C22×Dic5—21no—
69#713—22no—
70#713—22no—
71Q8×D5—22no—
72Q8×D5—22no—
73D4×D5—22no—
74D4×D5D414yes—
75C2×D20—21no—
76C2×D20C2311yescharacteristic
77C2×D20C2311yescharacteristic
78C2×C4×D5—21no—
79C2×C4×D5—21no—
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×C4×D5C2311yescharacteristic
83C2×Dic10—21no—
84C2×Dic10C2311yescharacteristic
85C5×SD16—22no—
86C5×SD16—22no—
87C2×C5×C8C2311yescharacteristic
88C2×C5×C8C2311yescharacteristic
89C5×C4⋊C4—21no—
90C5×C4⋊C4—21no—
91C5×C4⋊C4C2311yescharacteristic
92C5×C22⋊C4—21no—
93C42×C5C2311yescharacteristic
94C22⋊Dic5—21no—
95#688—22no—
96#688—22no—
97#687—22no—
98#686—22no—
99#685—21no—
100#685—21no—
101#685—21no—
102#685—21no—
103#685—21no—
104#685—21no—
105#685—21no—
106#685D411yescharacteristic
107#685D411yescharacteristic
108C4⋊Dic5C2311yescharacteristic
109#683—21no—
110#683—21no—
111#683D411yescharacteristic
112#683D411yescharacteristic
113C4×Dic5—21no—
114C4×Dic5C2311yescharacteristic
115C2×#168C2311yescharacteristic
116C2×#168C2311yescharacteristic
117D40—22no—
118#677—22no—
119#676—22no—
120C8×D5—22no—
121C2×AGL(1,ℤ/8)—51no—
122C22×SD16—51no—
123#536—51no—
124#518—51no—
125#463—51no—
126#463—51no—
127#463—51no—
128#463—51no—
129#461—51no—
130#461—51no—
131#461—51no—
132#461D511yescharacteristic, complemented
133#424—51no—
134#419—51no—
135#416—51no—
136C23×C5—21no—
137C22×D5—21no—
138C22×D5—24no—
139C22×D5—21no—
140C22×D5—81no—
141C22×D5—81no—
142C22×D5C2×D411yescharacteristic
143C5×Q8—21no—
144C5×Q8—21no—
145C5×Q8—21no—
146C5×Q8—21no—
147C5×D4—21no—
148C5×D4C2×D412yes—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—81no—
153C2×C4×C5C2×D411yescharacteristic
154C2×C4×C5C2×D411yescharacteristic
155C2×C4×C5C2411yescharacteristic
156C22⋊D5—24no—
157C2×Dic5—21no—
158C2×Dic5—21no—
159C2×Dic5—81no—
160C2×Dic5C2×D411yescharacteristic
161C2×Dic5C2×D411yescharacteristic
162C2×Dic5C2×D411yescharacteristic
163D20—21no—
164D20—21no—
165D20—21no—
166D20—42no—
167D20C2×D412yes—
168C4×D5—42no—
169C4×D5—42no—
170C4×D5—81no—
171C4×D5—81no—
172C4×D5C2×D412yes—
173C4×D5#4112yes—
174Dic10—21no—
175Dic10—21no—
176Dic10—42no—
177C5×C8—21no—
178C5×C8—21no—
179#168—21no—
180#168—21no—
181C2×#41—51no—
182C22×Q8—51no—
183C22×D4—51no—
184AGL(1,ℤ/8)—104no—
185C2×SD16—51no—
186C2×SD16—51no—
187C2×SD16—51no—
188C2×SD16—51no—
189C2×SD16—104no—
190C2×SD16C2×D511yescharacteristic
191C2×SD16C2×D511yescharacteristic
192C2×D8—51no—
193C2×D8—51no—
194C2×M16—51no—
195C22×C8—51no—
196C4⋊Q8—51no—
197C4⋊Q8C2×D511yescharacteristic, complemented
198#124—51no—
199#124—51no—
200#123—101no—
201#123—101no—
202C22⋊Q8—101no—
203C22⋊Q8—101no—
204C4×D4—51no—
205C4×D4—51no—
206C4×D4—51no—
207C4×D4—101no—
208C4×D4—101no—
209C4×D4C2×D511yescharacteristic
210#117—51no—
211#117—51no—
212C2×C22⋊C4—101no—
213C2×C22⋊C4—101no—
214C4⋊C8—51no—
215C4⋊C8—51no—
216C4⋊C8—51no—
217C4⋊C8C2×D511yescharacteristic, complemented
218#103—51no—
219#103—51no—
220#103—51no—
221#103—51no—
222#103C2×D511yescharacteristic, complemented
223#103C2×D511yescharacteristic, complemented
224#102—51no—
225#102—51no—
226C22×C5—22no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5C22×D411yescharacteristic
230C2×D5—21no—
231C2×D5—21no—
232C2×D5—22no—
233C2×D5—41no—
234C2×D5—41no—
235C2×D5—41no—
236C2×D5—41no—
237C2×D5—41no—
238C2×D5—84no—
239C2×D5#12112yes—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—41no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5C22×D411yescharacteristic
246C4×C5C2×#4111yescharacteristic
247Dic5—21no—
248Dic5—21no—
249Dic5—41no—
250Dic5—41no—
251Dic5#12112yes—
252C24—101no—
253#41—102no—
254#41—102no—
255C2×Q8—51no—
256C2×Q8—101no—
257C2×Q8—102no—
258C2×Q8—102no—
259C2×Q8C22×D511yescharacteristic
260C2×Q8C22×D511yescharacteristic
261C2×D4—54no—
262C2×D4—51no—
263C2×D4—51no—
264C2×D4—101no—
265C2×D4—102no—
266C2×D4—101no—
267C2×D4C22×D511yescharacteristic
268C22×C4—21no—
269C22×C4—51no—
270C22×C4—101no—
271C22×C4—101no—
272C22×C4—101no—
273C22×C4—101no—
274C22×C4—101no—
275SD16—22no—
276SD16—22no—
277SD16—102no—
278SD16—102no—
279SD16—102no—
280SD16—102no—
281D8—102no—
282D8—102no—
283M16—102no—
284C2×C8—51no—
285C2×C8—51no—
286C2×C8—102no—
287C2×C8C22×D511yescharacteristic
288C2×C8C22×D511yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—51no—
292C4⋊C4—51no—
293C4⋊C4—51no—
294C4⋊C4—101no—
295C4⋊C4—101no—
296C4⋊C4C22×D511yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—51no—
299C22⋊C4—51no—
300C22⋊C4—101no—
301C22⋊C4—101no—
302C22⋊C4—101no—
303C22⋊C4—101no—
304C22⋊C4—101no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C22⋊C4—101no—
308C42—51no—
309C42—101no—
310C42C22×D511yescharacteristic
311C2×C5—42no—
312C2×C5C2×#12111yescharacteristic
313C2×C5#57711yescharacteristic
314C2×C5#57711yescharacteristic
315D5—22no—
316D5—42no—
317D5—81no—
318C23—21no—
319C23—51no—
320C23—104no—
321C23—101no—
322C23—101no—
323C23—401no—
324C23—401no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—101no—
330Q8—101no—
331Q8—202no—
332D4—21no—
333D4—52no—
334D4—104no—
335D4—101no—
336D4—101no—
337D4—101no—
338D4—202no—
339D4D4×D512yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—51no—
344C2×C4—52no—
345C2×C4—52no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—81no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—202no—
352C2×C4—202no—
353C2×C4—401no—
354C2×C4—401no—
355C2×C4—401no—
356C2×C4D4×D511yescharacteristic
357C2×C4D4×D511yescharacteristic
358C2×C4C23×D511yescharacteristic
359C8—21no—
360C8—21no—
361C8—101no—
362C8—101no—
363C5#304211yescharacteristic, complemented, Sylow
364C22—22no—
365C22—41no—
366C22—41no—
367C22—52no—
368C22—101no—
369C22—101no—
370C22—102no—
371C22—201no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22—201no—
376C22—404no—
377C22C2×D4×D511yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—52no—
384C4—101no—
385C4—101no—
386C4—201no—
387C4—201no—
388C4C2×D4×D511yescharacteristic
389C4D5×#4111yescharacteristic
390C2—42no—
391C2—102no—
392C2—202no—
393C2—401no—
394C2D5×#12111yescharacteristic
395C2#6609611yescharacteristic
396C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#461C2
socleC22×C5C22×D4
prime radicalC2×#4060C2
hypercenter#461D5
hypocenterC5#3042
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×D5×SD16C2semidirect
3. #66058C2semidirect
4. #65879C2semidirect
5. C5×#461C2semidirect
6. #65454C2semidirect
7. #65451C2semidirect
8. #65372C2semidirect
9. #65305C2semidirect
10. #65133C2semidirect
11. #65128C2semidirect
12. #65108C2semidirect
13. #65107C2semidirect
14. #65093C2semidirect
15. #65091C2semidirect
21. C5×C4⋊Q8C22semidirect
23. #4093C22semidirect
24. #4090C22semidirect
46. #4021C22semidirect
49. C5×C4⋊C8C22semidirect
50. C5×#103C22semidirect
51. C5×#103C22semidirect
52. #3967C22semidirect
53. #3967C22semidirect
54. #3953C22semidirect
55. #3948C22semidirect
56. #3946C22semidirect
57. #3946C22semidirect
58. #3942C22semidirect
59. #3941C22semidirect
60. C4⋊#168C22semidirect
132. #461D5semidirect
197. C4⋊Q8C2×D5semidirect
217. C4⋊C8C2×D5semidirect
222. #103C2×D5semidirect
223. #103C2×D5semidirect
363. C5#3042semidirect

Maximal subgroups

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

subgroupindex
C2×#40602
C2×D5×SD162
#660582
#658792
C5×#4612
#654542
#654512
#653722
#653052
#651332
#651282
#651082
#651072
#650932
#650912
#30425