Finite Group Databasebeta

← #12256265

Subgroups — #12256265

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×#3334C211yesmaximal, characteristic, complemented
2#10611164C211yesmaximal, characteristic, complemented
3#10602181C211yesmaximal, characteristic, complemented
4#10602176C211yesmaximal, characteristic, complemented
5#10601869C211yesmaximal, characteristic, complemented
6#10601868C211yesmaximal, characteristic, complemented
7#10601866C211yesmaximal, characteristic, complemented
8#10601865C211yesmaximal, characteristic, complemented
9#10601683C211yesmaximal, characteristic, complemented
10#10601678C211yesmaximal, characteristic, complemented
11#10601650C211yesmaximal, characteristic, complemented
12#10601395C211yesmaximal, characteristic, complemented
13#10601393C211yesmaximal, characteristic, complemented
14#10601391C211yesmaximal, characteristic, complemented
15C2×#64711C211yesmaximal, characteristic, complemented
16C5×#547—21no—
17C2×#4050C2211yescharacteristic
18C22×D40C2211yescharacteristic
19#65884—21no—
20C5×#500C2211yescharacteristic, complemented
21C5×#480—21no—
22C5×#480—21no—
23C5×#474—21no—
24C5×#466C2211yescharacteristic
25C5×#466C2211yescharacteristic, complemented
26C4×C5×D8C2211yescharacteristic, complemented
27C5×C8×D4C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic, complemented
30C2×#3959C2211yescharacteristic, complemented
31C2×#3958C2211yescharacteristic
32C2×#3958C2211yescharacteristic
33#65405C2211yescharacteristic
34#65404C2211yescharacteristic
35C2×#3944C2211yescharacteristic, complemented
36C22×#672C2211yescharacteristic
37#65133—21no—
38#65023—21no—
39#65020—21no—
40#64985C2211yescharacteristic
41C4×D40C2211yescharacteristic
42#64782C2211yescharacteristic, complemented
43C22⋊#672C2211yescharacteristic
44C22⋊#672C2211yescharacteristic, complemented
45#64712C2211yescharacteristic, complemented
46#64712C2211yescharacteristic, complemented
47#64712C2211yescharacteristic, complemented
48#64711C2211yescharacteristic
49#64711C2211yescharacteristic
50#64711C2211yescharacteristic
51#64711C2211yescharacteristic
52#64711C2211yescharacteristic
53#64711C2211yescharacteristic
54#64710C2211yescharacteristic, complemented
55#64710C2211yescharacteristic, complemented
56#64710C2211yescharacteristic, complemented
57C4⋊#672C2211yescharacteristic, complemented
58#64681C2211yescharacteristic, complemented
59#33873—51nomaximal, Sylow
60C2×C5×#41—41no—
61C2×#709—21no—
62C22×D20—21no—
63C2×C5×D8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C5×C4⋊Q8—21no—
67C5×#123—41no—
68C5×#123—41no—
69C5×C22⋊Q8—41no—
70C5×#121—21no—
71C5×#121—21no—
72C4×C5×D4—21no—
73C4×C5×D4D411yescharacteristic
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76#4083—41no—
77#4076—21no—
78#4070—21no—
79C2×Dic20C2311yescharacteristic
80#4050—22no—
81#4050—41no—
82C2×D40—22no—
83C2×D40—21no—
84C2×D40—41no—
85C2×D40C2311yescharacteristic
86C2×D40C2311yescharacteristic
87C2×#677—21no—
88C2×#677—21no—
89#4040—41no—
90#4030—41no—
91D5×C22⋊C4—41no—
92#4021—21no—
93C4×D20—21no—
94C5×#107—21no—
95C5×#107—21no—
96C5×#107—21no—
97C5×#107C2311yescharacteristic
98C5×#107C2311yescharacteristic
99C5×#107C2311yescharacteristic
100C5×C4⋊C8D411yescharacteristic
101C5×#102—21no—
102C5×#102—21no—
103C5×#102—21no—
104C5×C22⋊C8D411yescharacteristic
105C5×C22⋊C8D411yescharacteristic
106C4×C5×C8C2311yescharacteristic
107#3959—41no—
108#3958—22no—
109#3958—41no—
110#3953—21no—
111#3953—21no—
112#3950C2311yescharacteristic
113#3948—21no—
114#3944—41no—
115C2×#672—41no—
116C2×#672C2311yescharacteristic
117C2×#672C2311yescharacteristic
118C2×#672C2311yescharacteristic
119C2×#672C2311yescharacteristic
120#3334D511yescharacteristic, complemented
121#3280—51no—
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—
135C23×D5—41no—
136C5×#41—84no—
137C2×C5×Q8—41no—
138C2×C5×D4—21no—
139C2×C5×D4—41no—
140C2×C5×D4—41no—
141C2×C5×D4D811yescharacteristic
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C2×C22⋊D5—41no—
148C2×C22⋊D5—41no—
149#709—42no—
150#709—81no—
151C2×D20—21no—
152C2×D20—21no—
153C2×D20—42no—
154C2×D20—41no—
155C2×D20—81no—
156C2×C4×D5—41no—
157C2×C4×D5—41no—
158C2×Dic10—21no—
159C5×D8—21no—
160C5×D8—21no—
161C2×C5×C8—21no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8C2×D411yescharacteristic
166C2×C5×C8C2×D411yescharacteristic
167C2×C5×C8C2×D411yescharacteristic
168C2×C5×C8C2411yescharacteristic
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—41no—
173C5×C4⋊C4—41no—
174C5×C4⋊C4—41no—
175C5×C4⋊C4D811yescharacteristic
176C5×C22⋊C4—41no—
177C5×C22⋊C4—41no—
178C5×C22⋊C4—41no—
179C5×C22⋊C4D811yescharacteristic
180C5×C22⋊C4D811yescharacteristic
181C42×C5C2×D411yescharacteristic
182C22⋊Dic5—41no—
183#685—41no—
184#685—41no—
185#685—41no—
186#685—41no—
187C4⋊Dic5—21no—
188#683—41no—
189Dic20—21no—
190Dic20—21no—
191D40—21no—
192D40—21no—
193D40—21no—
194D40—42no—
195D40#4112yescomplemented
196#677—42no—
197#677—81no—
198#672—21no—
199#672—21no—
200#672—21no—
201#672—21no—
202C2×#135—51no—
203C22×D8—51no—
204#547—21no—
205#546—101no—
206C2×SD32—51no—
207C2×D16—51no—
208C2×D16—51no—
209C2×M32—51no—
210C22×C16—51no—
211#500C2×D511yescharacteristic, complemented
212#495—51no—
213#480—21no—
214#480—21no—
215#474—21no—
216#467—51no—
217#466—51no—
218#466C2×D511yescharacteristic
219#466C2×D511yescharacteristic, complemented
220#463—101no—
221#450—101no—
222#449—101no—
223C4×D8—51no—
224C4×D8C2×D511yescharacteristic, complemented
225C8×D4C2×D511yescharacteristic
226C2×#107C2×D511yescharacteristic
227C2×#107C2×D511yescharacteristic, complemented
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×C5C2×D811yescharacteristic
247C23×C5C2×D811yescharacteristic
248C22×D5—41no—
249C22×D5—41no—
250C22×D5—82no—
251C22×D5—82no—
252C22×D5—161no—
253C5×Q8—82no—
254C5×D4—22no—
255C5×D4—41no—
256C5×D4—41no—
257C5×D4—82no—
258C5×D4—82no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—82no—
267C2×C4×C5—82no—
268C2×C4×C5—82no—
269C2×C4×C5C2×D811yescharacteristic
270C2×C4×C5C2×D811yescharacteristic
271C2×C4×C5C2×D811yescharacteristic
272C2×C4×C5C2×D811yescharacteristic
273C2×C4×C5C22×D411yescharacteristic
274C22⋊D5—82no—
275C22⋊D5—161no—
276C2×Dic5—41no—
277C2×Dic5—41no—
278D20—22no—
279D20—41no—
280D20—41no—
281D20—41no—
282D20—82no—
283C4×D5—82no—
284C4×D5—161no—
285Dic10—41no—
286Dic10—41no—
287C5×C8—21no—
288C5×C8—21no—
289C5×C8—21no—
290C5×C8C2×#4111yescharacteristic
291C5×C8H(5,𝔽2)11yescharacteristic
292C2×#41—41no—
293C2×#41—101no—
294C22×D4—101no—
295#135—102no—
296#135—201no—
297C2×Q16—51no—
298C2×SD16—101no—
299C2×SD16—101no—
300C2×D8—51no—
301C2×D8—51no—
302C2×D8—102no—
303C2×D8—101no—
304C2×D8—201no—
305C2×D8C22×D511yescharacteristic
306C22×C8C22×D511yescharacteristic
307C22×C8C22×D511yescharacteristic
308C4⋊Q8—21no—
309#124—101no—
310#123—41no—
311#123—41no—
312#123—201no—
313C22⋊Q8—41no—
314C22⋊Q8—101no—
315#121—21no—
316#121—21no—
317#121—101no—
318#121—201no—
319#120—201no—
320C4×D4—21no—
321C4×D4—101no—
322C4×D4C22⋊D511yescharacteristic
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C22⋊C4—201no—
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—21no—
336#107—21no—
337#107—21no—
338#107—51no—
339#107C22×D511yescharacteristic
340#107C22×D511yescharacteristic
341#107C22×D511yescharacteristic
342C4⋊C8C22⋊D511yescharacteristic
343#103—101no—
344#102—21no—
345#102—21no—
346#102—21no—
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—81no—
358C22×C5—81no—
359C22×C5—81no—
360C22×C5#50912yes—
361C22×C5C22×D811yescharacteristic
362C2×D5—42no—
363C2×D5—81no—
364C2×D5—81no—
365C2×D5—81no—
366C2×D5—81no—
367C2×D5—81no—
368C2×D5—164no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—21no—
372C4×C5—21no—
373C4×C5—81no—
374C4×C5—81no—
375C4×C5—81no—
376C4×C5#54611yescharacteristic
377C4×C5#57711yescharacteristic
378Dic5—81no—
379Dic5—81no—
380C24—201no—
381#41—84no—
382#41—202no—
383#41—401no—
384C2×Q8—41no—
385C2×Q8—101no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—101no—
390C2×D4—101no—
391C2×D4—202no—
392C2×D4—201no—
393C2×D4—201no—
394C2×D4—201no—
395C2×D4—401no—
396C2×D4#68611yescharacteristic
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—201no—
401C22×C4—201no—
402C22×C4C2×C22⋊D511yescharacteristic
403C22×C4C2×C22⋊D511yescharacteristic
404Q16—101no—
405Q16—101no—
406SD16—202no—
407SD16—401no—
408D8—21no—
409D8—21no—
410D8—52no—
411D8—101no—
412D8—101no—
413D8—101no—
414D8—202no—
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—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—101no—
430C4⋊C4—201no—
431C4⋊C4#68611yescharacteristic
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—201no—
436C22⋊C4—201no—
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—161no—
450C2×C5#329411yescharacteristic
451C2×C5C2×#50911yescharacteristic
452C2×C5#341611yescharacteristic
453D5—82no—
454D5—161no—
455C23—41no—
456C23—201no—
457C23—201no—
458C23—402no—
459C23—402no—
460C23—801no—
461C23C2×#68611yescharacteristic
462C23C2×#68611yescharacteristic
463Q8—82no—
464Q8—201no—
465Q8—201no—
466D4—22no—
467D4—41no—
468D4—41no—
469D4—82no—
470D4—82no—
471D4—102no—
472D4—201no—
473D4—201no—
474D4—201no—
475D4—402no—
476D4—402no—
477D4—801no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—201no—
489C2×C4—201no—
490C2×C4—402no—
491C2×C4—801no—
492C2×C4C2×#68611yescharacteristic
493C2×C4C2×#68611yescharacteristic
494C2×C4C2×#68611yescharacteristic
495C2×C4C2×#68611yescharacteristic
496C2×C4C22×C22⋊D511yescharacteristic
497C8—21no—
498C8—21no—
499C8—21no—
500C8D5×#4111yescharacteristic
501C8#414911yescharacteristic
502C5#3387311yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—202no—
512C22—401no—
513C22—401no—
514C22—401no—
515C22—401no—
516C22—401no—
517C22—804no—
518C22#6543612yes—
519C22C22×#68611yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—401no—
528C4—401no—
529C4#6616311yescharacteristic
530C4#6617111yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—402no—
535C2—801no—
536C2#1061525611yescharacteristic
537C2C2×#6543611yescharacteristic
538C2#1061574711yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC5×#3334C2
socleC22×C5C22×D8
hypercenter#3334D5
hypocenterC5#33873
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. C5×#3334C2semidirect
2. #10611164C2semidirect
3. #10602181C2semidirect
4. #10602176C2semidirect
5. #10601869C2semidirect
6. #10601868C2semidirect
7. #10601866C2semidirect
8. #10601865C2semidirect
9. #10601683C2semidirect
10. #10601678C2semidirect
11. #10601650C2semidirect
12. #10601395C2semidirect
13. #10601393C2semidirect
14. #10601391C2semidirect
15. C2×#64711C2semidirect
20. C5×#500C22semidirect
25. C5×#466C22semidirect
26. C4×C5×D8C22semidirect
29. C2×C5×#107C22semidirect
30. C2×#3959C22semidirect
35. C2×#3944C22semidirect
42. #64782C22semidirect
44. C22⋊#672C22semidirect
45. #64712C22semidirect
46. #64712C22semidirect
47. #64712C22semidirect
54. #64710C22semidirect
55. #64710C22semidirect
56. #64710C22semidirect
57. C4⋊#672C22semidirect
58. #64681C22semidirect
120. #3334D5semidirect
195. D40#41semidirect
211. #500C2×D5semidirect
219. #466C2×D5semidirect
224. C4×D8C2×D5semidirect
227. C2×#107C2×D5semidirect
502. C5#33873semidirect

Maximal subgroups

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

subgroupindex
C5×#33342
#106111642
#106021812
#106021762
#106018692
#106018682
#106018662
#106018652
#106016832
#106016782
#106016502
#106013952
#106013932
#106013912
C2×#647112
#338735