Finite Group Databasebeta

← #12256271

Subgroups — #12256271

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3280C211yesmaximal, characteristic, complemented
2#10611142C211yesmaximal, characteristic, complemented
3#10602875C211yesmaximal, characteristic, complemented
4#10602871C211yesmaximal, characteristic, complemented
5#10602828C211yesmaximal, characteristic, complemented
6C2×#64782C211yesmaximal, characteristic, complemented
7#10602116C211yesmaximal, characteristic, complemented
8#10602112C211yesmaximal, characteristic, complemented
9#10601875C211yesmaximal, characteristic, complemented
10#10601871C211yesmaximal, characteristic, complemented
11#10601866C211yesmaximal, characteristic, complemented
12#10601862C211yesmaximal, characteristic, complemented
13#10601680C211yesmaximal, characteristic, complemented
14#10601678C211yesmaximal, characteristic, complemented
15#10601650C211yesmaximal, characteristic, complemented
16C2×C5×#135C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C5×#546—21no—
19#65889—21no—
20C5×#495C2211yescharacteristic
21C5×#467C2211yescharacteristic
22C5×#466C2211yescharacteristic
23C5×#463—21no—
24C5×#450—21no—
25C5×#449—21no—
26C4×C5×D8C2211yescharacteristic
27C5×C8×D4C2211yescharacteristic
28C2×#3960C2211yescharacteristic, complemented
29C2×#3958C2211yescharacteristic
30C2×#3958C2211yescharacteristic
31#65404C2211yescharacteristic
32#65404C2211yescharacteristic, complemented
33C2×#3950C2211yescharacteristic
34C2×#3950C2211yescharacteristic, complemented
35C2×#3944C2211yescharacteristic, complemented
36C22×#672C2211yescharacteristic
37#65135—21no—
38#65025—21no—
39#65025—21no—
40C4×D40C2211yescharacteristic, complemented
41#64971C2211yescharacteristic, complemented
42#64784C2211yescharacteristic, complemented
43#64784C2211yescharacteristic, complemented
44#64784C2211yescharacteristic, complemented
45#64782C2211yescharacteristic
46#64782C2211yescharacteristic
47#64782C2211yescharacteristic
48#64782C2211yescharacteristic
49#64782C2211yescharacteristic
50#64782C2211yescharacteristic
51C22⋊#672C2211yescharacteristic
52C22⋊#672C2211yescharacteristic, complemented
53#64711C2211yescharacteristic, complemented
54#64710C2211yescharacteristic, complemented
55#64710C2211yescharacteristic, complemented
56#64710C2211yescharacteristic, complemented
57C4⋊#672C2211yescharacteristic, complemented
58#64681C2211yescharacteristic, complemented
59#33873—51nomaximal, Sylow
60C2×C5×#41—21no—
61C22×C5×D4—21no—
62C2×#711—41no—
63C5×#135—22no—
64C5×#135—41no—
65C2×C5×Q16C2311yescharacteristic
66C2×C5×SD16—21no—
67C2×C5×SD16—21no—
68C2×C5×D8—22no—
69C2×C5×D8—21no—
70C2×C5×D8—41no—
71C2×C5×D8C2311yescharacteristic
72C2×C5×D8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×#124—21no—
76C5×#123—41no—
77C5×C22⋊Q8—21no—
78C5×#121—21no—
79C5×#121—41no—
80C5×#120—41no—
81C4×C5×D4—21no—
82C4×C5×D4D411yescharacteristic
83C2×C5×C22⋊C4—41no—
84#4076—21no—
85#4076—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×D40C2311yescharacteristic
89#4043—41no—
90#4032—41no—
91#4032—41no—
92C4×D20—21no—
93#4015—21no—
94C5×#107C2311yescharacteristic
95C5×C4⋊C8D411yescharacteristic
96C5×#103—21no—
97C5×#102—21no—
98C5×#102—21no—
99C5×C22⋊C8D411yescharacteristic
100C5×C22⋊C8D411yescharacteristic
101C4×C5×C8C2311yescharacteristic
102#3960—41no—
103#3958—22no—
104#3958—41no—
105#3953—21no—
106#3953—21no—
107#3953—21no—
108#3950—21no—
109#3950—21no—
110#3950—21no—
111#3950C2311yescharacteristic
112#3950C2311yescharacteristic
113#3950C2311yescharacteristic
114#3944—41no—
115C2×#672—41no—
116C2×#672C2311yescharacteristic
117C2×#672C2311yescharacteristic
118C2×#672C2311yescharacteristic
119C2×#672C2311yescharacteristic
120#3334—51no—
121#3280D511yescharacteristic, complemented
122#2243—51no—
123#2235—51no—
124#2233—51no—
125#2226—51no—
126#2218—51no—
127#2217—51no—
128#2210—51no—
129#2186—51no—
130#2184—51no—
131#2177—51no—
132#2168—51no—
133#2139—51no—
134C2×#357—51no—
135C24×C5—41no—
136C5×#41—42no—
137C5×#41—81no—
138C2×C5×Q8—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—42no—
142C2×C5×D4—41no—
143C2×C5×D4—41no—
144C2×C5×D4—41no—
145C2×C5×D4—81no—
146C2×C5×D4D811yescharacteristic
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C2×C22⋊D5—41no—
152C2×C22⋊D5—41no—
153C22×Dic5—41no—
154C22×Dic5—41no—
155#711—84no—
156C2×D20—21no—
157C2×C4×D5—41no—
158C2×Dic10—41no—
159C5×Q16—21no—
160C5×Q16—21no—
161C5×SD16—42no—
162C5×SD16—81no—
163C5×D8—21no—
164C5×D8—21no—
165C5×D8—21no—
166C5×D8—42no—
167C5×D8#4112yescomplemented
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8C2×D411yescharacteristic
173C2×C5×C8C2×D411yescharacteristic
174C2×C5×C8C2×D411yescharacteristic
175C2×C5×C8C2411yescharacteristic
176C5×C4⋊C4—21no—
177C5×C4⋊C4—41no—
178C5×C4⋊C4D811yescharacteristic
179C5×C22⋊C4—41no—
180C5×C22⋊C4—41no—
181C5×C22⋊C4—41no—
182C5×C22⋊C4—41no—
183C5×C22⋊C4—41no—
184C5×C22⋊C4D811yescharacteristic
185C5×C22⋊C4D811yescharacteristic
186C42×C5C2×D411yescharacteristic
187#685—41no—
188#685—41no—
189#685—41no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—41no—
194C4⋊Dic5—41no—
195C4⋊Dic5—41no—
196D40—21no—
197D40—21no—
198#672—21no—
199#672—21no—
200#672—21no—
201#672—21no—
202C2×#135C2×D511yescharacteristic
203C22×D8C2×D511yescharacteristic
204#547—101no—
205#546—21no—
206C2×SD32—51no—
207C2×D16—51no—
208C2×D16—51no—
209C2×M32—51no—
210C22×C16—51no—
211#500—51no—
212#495C2×D511yescharacteristic
213#480—101no—
214#480—101no—
215#474—101no—
216#467C2×D511yescharacteristic
217#466—51no—
218#466—51no—
219#466C2×D511yescharacteristic
220#463—21no—
221#450—21no—
222#449—21no—
223C4×D8—51no—
224C4×D8C2×D511yescharacteristic
225C8×D4C2×D511yescharacteristic
226C2×#107—51no—
227C2×#107—51no—
228#367—51no—
229#367—51no—
230#367—51no—
231C4⋊C16—51no—
232#358—51no—
233#358—51no—
234#358—51no—
235#357—51no—
236#357—51no—
237#357—51no—
238#357—51no—
239#357—51no—
240#357—51no—
241#357—51no—
242C22⋊C16—51no—
243C22⋊C16—51no—
244#346—51no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5—82no—
248C23×C5—82no—
249C23×C5—161no—
250C23×C5C2×D811yescharacteristic
251C23×C5C2×D811yescharacteristic
252C22×D5—41no—
253C5×Q8—41no—
254C5×Q8—41no—
255C5×D4—22no—
256C5×D4—22no—
257C5×D4—41no—
258C5×D4—41no—
259C5×D4—41no—
260C5×D4—82no—
261C5×D4—82no—
262C5×D4—161no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—82no—
270C2×C4×C5—161no—
271C2×C4×C5C2×D811yescharacteristic
272C2×C4×C5C2×D811yescharacteristic
273C2×C4×C5C2×D811yescharacteristic
274C2×C4×C5C2×D811yescharacteristic
275C2×C4×C5C22×D411yescharacteristic
276C22⋊D5—82no—
277C22⋊D5—82no—
278C2×Dic5—41no—
279C2×Dic5—41no—
280C2×Dic5—41no—
281C2×Dic5—82no—
282C2×Dic5—82no—
283D20—41no—
284D20—41no—
285C4×D5—82no—
286Dic10—82no—
287C5×C8—21no—
288C5×C8—21no—
289C5×C8—21no—
290C5×C8C2×#4111yescharacteristic
291C5×C8H(5,𝔽2)11yescharacteristic
292C2×#41—21no—
293C2×#41—201no—
294C22×D4—21no—
295#135—22no—
296#135—41no—
297C2×Q16C22×D511yescharacteristic
298C2×SD16—21no—
299C2×SD16—21no—
300C2×D8—22no—
301C2×D8—21no—
302C2×D8—41no—
303C2×D8—51no—
304C2×D8C22×D511yescharacteristic
305C2×D8C22×D511yescharacteristic
306C22×C8C22×D511yescharacteristic
307C22×C8C22×D511yescharacteristic
308C4⋊Q8—101no—
309#124—21no—
310#123—41no—
311#123—201no—
312#123—201no—
313C22⋊Q8—21no—
314C22⋊Q8—201no—
315#121—21no—
316#121—41no—
317#121—101no—
318#121—101no—
319#120—41no—
320C4×D4—21no—
321C4×D4—101no—
322C4×D4C22⋊D511yescharacteristic
323C2×C4⋊C4—101no—
324C2×C4⋊C4—101no—
325C2×C22⋊C4—41no—
326SD32—201no—
327D16—102no—
328D16—201no—
329M32—201no—
330C2×C16—51no—
331C2×C16—51no—
332C2×C16—51no—
333C2×C16—51no—
334C2×C16—201no—
335#107—51no—
336#107—51no—
337#107—51no—
338#107—101no—
339#107—101no—
340#107—101no—
341#107C22×D511yescharacteristic
342C4⋊C8C22⋊D511yescharacteristic
343#103—21no—
344#102—21no—
345#102—21no—
346#102—101no—
347#102—101no—
348#102—101no—
349C22⋊C8C22⋊D511yescharacteristic
350C22⋊C8C22⋊D511yescharacteristic
351C4×C8C22×D511yescharacteristic
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—21no—
355C22×C5—21no—
356C22×C5—21no—
357C22×C5—42no—
358C22×C5—81no—
359C22×C5—81no—
360C22×C5—81no—
361C22×C5—81no—
362C22×C5—81no—
363C22×C5—164no—
364C22×C5#50912yes—
365C22×C5C22×D811yescharacteristic
366C2×D5—81no—
367C2×D5—81no—
368C2×D5—81no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—21no—
372C4×C5—21no—
373C4×C5—81no—
374C4×C5—81no—
375C4×C5#54611yescharacteristic
376C4×C5#57711yescharacteristic
377Dic5—81no—
378Dic5—81no—
379Dic5—81no—
380C24—41no—
381#41—42no—
382#41—81no—
383#41—404no—
384C2×Q8—21no—
385C2×Q8—201no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—81no—
393C2×D4—101no—
394C2×D4—201no—
395C2×D4—201no—
396C2×D4#68611yescharacteristic
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—201no—
400C22×C4—201no—
401C22×C4—201no—
402C22×C4C2×C22⋊D511yescharacteristic
403C22×C4C2×C22⋊D511yescharacteristic
404Q16—21no—
405Q16—21no—
406SD16—42no—
407SD16—81no—
408D8—21no—
409D8—21no—
410D8—21no—
411D8—42no—
412D8—101no—
413D8—101no—
414D8#71112yescomplemented
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8C2×C22⋊D511yescharacteristic
420C2×C8C2×C22⋊D511yescharacteristic
421C2×C8C2×C22⋊D511yescharacteristic
422C2×C8C23×D511yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—101no—
426C4⋊C4—101no—
427C4⋊C4—101no—
428C4⋊C4—201no—
429C4⋊C4—201no—
430C4⋊C4—201no—
431C4⋊C4#68611yescharacteristic
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—201no—
438C22⋊C4—201no—
439C22⋊C4—201no—
440C22⋊C4#68611yescharacteristic
441C22⋊C4#68611yescharacteristic
442C42C2×C22⋊D511yescharacteristic
443C16—101no—
444C16—101no—
445C16—101no—
446C16—101no—
447C2×C5—22no—
448C2×C5—41no—
449C2×C5—82no—
450C2×C5—161no—
451C2×C5#329411yescharacteristic
452C2×C5C2×#50911yescharacteristic
453C2×C5#341611yescharacteristic
454D5—161no—
455C23—41no—
456C23—41no—
457C23—82no—
458C23—82no—
459C23—161no—
460C23—201no—
461C23C2×#68611yescharacteristic
462C23C2×#68611yescharacteristic
463Q8—41no—
464Q8—41no—
465Q8—402no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—82no—
472D4—82no—
473D4—161no—
474D4—201no—
475D4—201no—
476D4—402no—
477D4—402no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—82no—
485C2×C4—161no—
486C2×C4—201no—
487C2×C4—201no—
488C2×C4—201no—
489C2×C4—402no—
490C2×C4—402no—
491C2×C4—402no—
492C2×C4C2×#68611yescharacteristic
493C2×C4C2×#68611yescharacteristic
494C2×C4C2×#68611yescharacteristic
495C2×C4C2×#68611yescharacteristic
496C2×C4C22×C22⋊D511yescharacteristic
497C8—21no—
498C8—21no—
499C8—21no—
500C8C2×#71111yescharacteristic
501C8#414411yescharacteristic
502C5#3387311yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—401no—
516C22—401no—
517C22—401no—
518C22#6548212yes—
519C22C22×#68611yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—401no—
527C4—401no—
528C4—401no—
529C4#6614011yescharacteristic
530C4#6617011yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—801no—
536C2#1061521311yescharacteristic
537C2C2×#6548211yescharacteristic
538C2#1061573911yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC5×#3280C2
socleC22×C5C22×D8
hypercenter#3280D5
hypocenterC5#33873
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C5×#3280C2semidirect
2. #10611142C2semidirect
3. #10602875C2semidirect
4. #10602871C2semidirect
5. #10602828C2semidirect
6. C2×#64782C2semidirect
7. #10602116C2semidirect
8. #10602112C2semidirect
9. #10601875C2semidirect
10. #10601871C2semidirect
11. #10601866C2semidirect
12. #10601862C2semidirect
13. #10601680C2semidirect
14. #10601678C2semidirect
15. #10601650C2semidirect
28. C2×#3960C22semidirect
32. #65404C22semidirect
34. C2×#3950C22semidirect
35. C2×#3944C22semidirect
40. C4×D40C22semidirect
41. #64971C22semidirect
42. #64784C22semidirect
43. #64784C22semidirect
44. #64784C22semidirect
52. C22⋊#672C22semidirect
53. #64711C22semidirect
54. #64710C22semidirect
55. #64710C22semidirect
56. #64710C22semidirect
57. C4⋊#672C22semidirect
58. #64681C22semidirect
121. #3280D5semidirect
167. C5×D8#41semidirect
414. D8#711semidirect
502. C5#33873semidirect

Maximal subgroups

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

subgroupindex
C5×#32802
#106111422
#106028752
#106028712
#106028282
C2×#647822
#106021162
#106021122
#106018752
#106018712
#106018662
#106018622
#106016802
#106016782
#106016502
#338735