Finite Group Databasebeta

← #10612331

Subgroups — #10612331

Order 640.

490 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×#4064C211yesmaximal, characteristic, complemented
2C2×D5×SD16C211yesmaximal, characteristic, complemented
3#66008C211yesmaximal, characteristic
4#65906C211yesmaximal, characteristic, complemented
5C5×#464C211yesmaximal, characteristic, complemented
6#65474C211yesmaximal, characteristic, complemented
7#65452C211yesmaximal, characteristic, complemented
8#65343C211yesmaximal, characteristic, complemented
9#65316C211yesmaximal, characteristic, complemented
10#65137C211yesmaximal, characteristic, complemented
11#65128C211yesmaximal, characteristic, complemented
12#65093C211yesmaximal, characteristic, complemented
13#65087C211yesmaximal, characteristic, complemented
14#65059C211yesmaximal, characteristic, complemented
15#65051C211yesmaximal, characteristic, complemented
16C2×#713C2211yescharacteristic
17C2×Q8×D5C2211yescharacteristic
18C2×D4×D5C2211yescharacteristic
19C2×C5×Q16C2211yescharacteristic, complemented
20C2×C5×SD16C2211yescharacteristic
21C5×#124C2211yescharacteristic
22C4×C5×Q8C2211yescharacteristic, complemented
23#4093C2211yescharacteristic
24Q8×Dic5C2211yescharacteristic, complemented
25C2×#689C2211yescharacteristic, complemented
26C2×#688C2211yescharacteristic
27C2×#688C2211yescharacteristic, complemented
28#4086C2211yescharacteristic
29C2×#687C2211yescharacteristic
30#4064—24no—
31D5×SD16—24no—
32C2×#677C2211yescharacteristic
33C2×#677C2211yescharacteristic, complemented
34C2×#676C2211yescharacteristic
35C2×C8×D5C2211yescharacteristic
36#4038—21no—
37#4038C2211yescharacteristic
38#4033—21no—
39#4033C2211yescharacteristic, complemented
40#4030—21no—
41#4030—21no—
42#4028—21no—
43#4028—21no—
44#4020C2211yescharacteristic
45#4018—21no—
46#4018C2211yescharacteristic
47C4×Dic10—21no—
48C4×Dic10C2211yescharacteristic, complemented
49C5×C4⋊C8C2211yescharacteristic, complemented
50C5×#103C2211yescharacteristic, complemented
51C5×#102C2211yescharacteristic
52#3967C2211yescharacteristic, complemented
53#3964C2211yescharacteristic
54#3953C2211yescharacteristic
55#3953C2211yescharacteristic, complemented
56#3946C2211yescharacteristic, complemented
57#3946C2211yescharacteristic, complemented
58#3941C2211yescharacteristic
59#3941C2211yescharacteristic, complemented
60C4⋊#168C2211yescharacteristic, complemented
61#3043—51nomaximal, Sylow
62C23×D5—21no—
63C2×C5×Q8C2311yescharacteristic
64C2×C5×Q8C2311yescharacteristic
65C2×C5×D4C2311yescharacteristic
66C2×C22⋊D5—21no—
67C2×C22⋊D5—21no—
68C2×C22⋊D5—21no—
69#713—22no—
70#713—22no—
71Q8×D5—22no—
72Q8×D5D414yescomplemented
73D4×D5—22no—
74D4×D5—22no—
75C2×D20—21no—
76C2×D20—21no—
77C2×D20—21no—
78C2×D20C2311yescharacteristic
79C2×D20C2311yescharacteristic
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×C4×D5C2311yescharacteristic
83C2×Dic10—21no—
84C2×Dic10C2311yescharacteristic
85C5×Q16—22no—
86C5×SD16—22no—
87C2×C5×C8C2311yescharacteristic
88C2×C5×C8C2311yescharacteristic
89C5×C4⋊C4—21no—
90C5×C4⋊C4C2311yescharacteristic
91C5×C22⋊C4—21no—
92C5×C22⋊C4—21no—
93C42×C5—21no—
94C42×C5C2311yescharacteristic
95#689—22no—
96#688—22no—
97#688—22no—
98#687—22no—
99#685—21no—
100#685—21no—
101#685—21no—
102#685D411yescharacteristic
103#685D411yescharacteristic
104C4⋊Dic5—21no—
105C4⋊Dic5C2311yescharacteristic
106#683—21no—
107#683—21no—
108#683D411yescharacteristic
109#683D411yescharacteristic
110C4×Dic5—21no—
111C4×Dic5—21no—
112C4×Dic5—21no—
113C4×Dic5—21no—
114C4×Dic5C2311yescharacteristic
115C2×#168C2311yescharacteristic
116C2×#168C2311yescharacteristic
117#677—22no—
118#677—22no—
119#676—22no—
120C8×D5—22no—
121C2×#137—51no—
122C22×SD16—51no—
123#535—51no—
124#519—51no—
125#464—51no—
126#464—51no—
127#464—51no—
128#464D511yescharacteristic, complemented
129#460—51no—
130#460—51no—
131#460—51no—
132#460—51no—
133#424—51no—
134#418—51no—
135#416—51no—
136C23×C5—21no—
137C22×D5—21no—
138C22×D5—21no—
139C22×D5—42no—
140C22×D5—81no—
141C22×D5—81no—
142C22×D5C2×D411yescharacteristic
143C5×Q8—21no—
144C5×Q8—21no—
145C5×Q8—21no—
146C5×Q8C2×D412yes—
147C5×D4—21no—
148C5×D4—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5C2×D411yescharacteristic
153C2×C4×C5C2×D411yescharacteristic
154C2×C4×C5C2411yescharacteristic
155C22⋊D5—42no—
156C22⋊D5—81no—
157C22⋊D5—81no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5C2×D411yescharacteristic
161C2×Dic5C2×D411yescharacteristic
162C2×Dic5C2×D411yescharacteristic
163D20—21no—
164D20—21no—
165D20—21no—
166D20—21no—
167D20—42no—
168D20—81no—
169D20—81no—
170C4×D5—24no—
171C4×D5—42no—
172C4×D5C2×D412yes—
173C4×D5#4112yes—
174Dic10—21no—
175Dic10—24no—
176Dic10C2×D412yes—
177C5×C8—21no—
178C5×C8—21no—
179#168—21no—
180#168—21no—
181C2×#41—51no—
182C22×Q8—51no—
183C22×D4—51no—
184#137—104no—
185C2×Q16—51no—
186C2×Q16C2×D511yescharacteristic, complemented
187C2×SD16—51no—
188C2×SD16—51no—
189C2×SD16—51no—
190C2×SD16—51no—
191C2×SD16—51no—
192C2×SD16—104no—
193C2×SD16C2×D511yescharacteristic
194C2×M16—51no—
195C22×C8—51no—
196#127—51no—
197#127—51no—
198#124—51no—
199#124C2×D511yescharacteristic
200#121—101no—
201#121—101no—
202#120—101no—
203#120—101no—
204C4×Q8—51no—
205C4×Q8—51no—
206C4×Q8—51no—
207C4×Q8—101no—
208C4×Q8—101no—
209C4×Q8C2×D511yescharacteristic, complemented
210#117—51no—
211#117—51no—
212#117—101no—
213#117—101no—
214C4⋊C8—51no—
215C4⋊C8—51no—
216C4⋊C8—51no—
217C4⋊C8C2×D511yescharacteristic, complemented
218#103—51no—
219#103C2×D511yescharacteristic, complemented
220#102—51no—
221#102—51no—
222#102—51no—
223#102—51no—
224#102—51no—
225#102C2×D511yescharacteristic
226C22×C5—41no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5C22×D411yescharacteristic
230C2×D5—21no—
231C2×D5—21no—
232C2×D5—41no—
233C2×D5—41no—
234C2×D5—41no—
235C2×D5—41no—
236C2×D5—41no—
237C2×D5—41no—
238C2×D5—84no—
239C2×D5#12112yes—
240C4×C5—22no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5C22×D411yescharacteristic
246C4×C5C2×#4111yescharacteristic
247Dic5—22no—
248Dic5—21no—
249Dic5—21no—
250Dic5—41no—
251Dic5#12112yes—
252C24—101no—
253#41—102no—
254#41—102no—
255C2×Q8—54no—
256C2×Q8—51no—
257C2×Q8—101no—
258C2×Q8—102no—
259C2×Q8C22×D511yescharacteristic
260C2×Q8C22×D511yescharacteristic
261C2×D4—51no—
262C2×D4—51no—
263C2×D4—101no—
264C2×D4—102no—
265C2×D4—102no—
266C2×D4—101no—
267C2×D4—101no—
268C2×D4—101no—
269C2×D4—101no—
270C2×D4—101no—
271C2×D4C22×D511yescharacteristic
272C22×C4—51no—
273C22×C4—101no—
274C22×C4—101no—
275Q16—22no—
276Q16—102no—
277SD16—22no—
278SD16—102no—
279SD16—102no—
280SD16—102no—
281SD16—102no—
282SD16—102no—
283M16—102no—
284C2×C8—51no—
285C2×C8—51no—
286C2×C8—102no—
287C2×C8C22×D511yescharacteristic
288C2×C8C22×D511yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—51no—
291C4⋊C4—51no—
292C4⋊C4—51no—
293C4⋊C4—101no—
294C4⋊C4—101no—
295C4⋊C4—101no—
296C4⋊C4C22×D511yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—51no—
300C22⋊C4—51no—
301C22⋊C4—101no—
302C22⋊C4—101no—
303C22⋊C4—101no—
304C42—21no—
305C42—51no—
306C42—101no—
307C42—101no—
308C42—101no—
309C42—101no—
310C42C22×D511yescharacteristic
311C2×C5—81no—
312C2×C5C2×#12111yescharacteristic
313C2×C5#57711yescharacteristic
314C2×C5#57711yescharacteristic
315D5—22no—
316D5—81no—
317D5—81no—
318C23—21no—
319C23—51no—
320C23—101no—
321C23—101no—
322C23—202no—
323C23—401no—
324C23—401no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—52no—
329Q8—104no—
330Q8—101no—
331Q8D4×D512yes—
332D4—21no—
333D4—21no—
334D4—101no—
335D4—101no—
336D4—101no—
337D4—101no—
338D4—202no—
339D4—202no—
340D4—401no—
341D4—401no—
342D4—401no—
343D4—401no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—51no—
348C2×C4—52no—
349C2×C4—52no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—104no—
353C2×C4—101no—
354C2×C4—101no—
355C2×C4—202no—
356C2×C4D4×D511yescharacteristic
357C2×C4D4×D511yescharacteristic
358C2×C4C23×D511yescharacteristic
359C8—21no—
360C8—21no—
361C8—101no—
362C8—101no—
363C5#304311yescharacteristic, complemented, Sylow
364C22—41no—
365C22—41no—
366C22—41no—
367C22—52no—
368C22—101no—
369C22—101no—
370C22—201no—
371C22—201no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22—201no—
376C22—404no—
377C22C2×D4×D511yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—52no—
384C4—101no—
385C4—101no—
386C4—102no—
387C4—201no—
388C4C2×D4×D511yescharacteristic
389C4D5×#4111yescharacteristic
390C2—81no—
391C2—102no—
392C2—401no—
393C2—401no—
394C2D5×#12111yescharacteristic
395C2#6610411yescharacteristic
396C2#6611211yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#464C2
socleC22×C5C22×D4
prime radical#66008C2
hypercenter#464D5
hypocenterC5#3043
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#4064C2semidirect
2. C2×D5×SD16C2semidirect
4. #65906C2semidirect
5. C5×#464C2semidirect
6. #65474C2semidirect
7. #65452C2semidirect
8. #65343C2semidirect
9. #65316C2semidirect
10. #65137C2semidirect
11. #65128C2semidirect
12. #65093C2semidirect
13. #65087C2semidirect
14. #65059C2semidirect
15. #65051C2semidirect
19. C2×C5×Q16C22semidirect
22. C4×C5×Q8C22semidirect
24. Q8×Dic5C22semidirect
25. C2×#689C22semidirect
27. C2×#688C22semidirect
33. C2×#677C22semidirect
39. #4033C22semidirect
48. C4×Dic10C22semidirect
49. C5×C4⋊C8C22semidirect
50. C5×#103C22semidirect
52. #3967C22semidirect
55. #3953C22semidirect
56. #3946C22semidirect
57. #3946C22semidirect
59. #3941C22semidirect
60. C4⋊#168C22semidirect
72. Q8×D5D4semidirect
128. #464D5semidirect
186. C2×Q16C2×D5semidirect
209. C4×Q8C2×D5semidirect
217. C4⋊C8C2×D5semidirect
219. #103C2×D5semidirect
363. C5#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#40642
C2×D5×SD162
#660082
#659062
C5×#4642
#654742
#654522
#653432
#653162
#651372
#651282
#650932
#650872
#650592
#650512
#30435