Finite Group Databasebeta

← #12256160

Subgroups — #12256160

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3280C211yesmaximal, characteristic, complemented
2#10611147C211yesmaximal, characteristic, complemented
3#10602875C211yesmaximal, characteristic, complemented
4#10602870C211yesmaximal, characteristic, complemented
5#10602828C211yesmaximal, characteristic, complemented
6C2×#64782C211yesmaximal, characteristic, complemented
7#10602116C211yesmaximal, characteristic, complemented
8#10602111C211yesmaximal, characteristic, complemented
9#10601875C211yesmaximal, characteristic, complemented
10#10601872C211yesmaximal, characteristic, complemented
11#10601864C211yesmaximal, characteristic, complemented
12#10601863C211yesmaximal, characteristic, complemented
13#10601681C211yesmaximal, characteristic, complemented
14C4×#3958C211yesmaximal, characteristic, complemented
15D4×#672C211yesmaximal, characteristic, complemented
16C2×C5×#135C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C5×#546—21no—
19#65899—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
33#65395C2211yescharacteristic, complemented
34C2×#3950C2211yescharacteristic
35C22×#672C2211yescharacteristic
36C22×#672C2211yescharacteristic, complemented
37#65136—21no—
38#65026—21no—
39#65024—21no—
40C4×D40C2211yescharacteristic, complemented
41#64972C2211yescharacteristic, 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#64709C2211yescharacteristic, complemented
56#64709C2211yescharacteristic, complemented
57C4⋊#672C2211yescharacteristic, complemented
58C4×#672C2211yescharacteristic, complemented
59#33864—51nomaximal, Sylow
60C2×C5×#41—21no—
61C22×C5×D4—21no—
62C5×#135—22no—
63C5×#135—41no—
64C2×C5×Q16C2311yescharacteristic
65C2×C5×SD16—21no—
66C2×C5×SD16—21no—
67C2×C5×D8—22no—
68C2×C5×D8—21no—
69C2×C5×D8—41no—
70C2×C5×D8C2311yescharacteristic
71C2×C5×D8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×#124—21no—
75C5×#123—41no—
76C5×C22⋊Q8—21no—
77C5×#121—21no—
78C5×#121—41no—
79C5×#120—41no—
80C4×C5×D4—21no—
81C4×C5×D4D411yescharacteristic
82C2×C5×C22⋊C4—41no—
83#4085—41no—
84#4076—21no—
85#4076—21no—
86#4072—21no—
87C2×C4⋊Dic5—21no—
88C2×D40C2311yescharacteristic
89#4044—41no—
90#4029—41no—
91#4027—41no—
92C4×D20—21no—
93#4016—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#3950C2311yescharacteristic
110#3950C2311yescharacteristic
111#3950C2311yescharacteristic
112#3949—21no—
113#3949—21no—
114C2×#672—41no—
115C2×#672—41no—
116C2×#672C2311yescharacteristic
117C2×#672C2311yescharacteristic
118C2×#672C2311yescharacteristic
119C2×#672C2311yescharacteristic
120#3339—51no—
121#3280D511yescharacteristic, complemented
122#2242—51no—
123#2236—51no—
124#2234—51no—
125#2228—51no—
126#2217—51no—
127#2215—51no—
128#2210—51no—
129#2186—51no—
130#2184—51no—
131C4×D16—51no—
132D4×C16—51no—
133#2138—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—
154C2×D20—21no—
155C2×C4×D5—41no—
156C5×Q16—21no—
157C5×Q16—21no—
158C5×SD16—42no—
159C5×SD16—81no—
160C5×D8—21no—
161C5×D8—21no—
162C5×D8—21no—
163C5×D8—42no—
164C5×D8#4112yes—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8C2×D411yescharacteristic
170C2×C5×C8C2×D411yescharacteristic
171C2×C5×C8C2×D411yescharacteristic
172C2×C5×C8C2411yescharacteristic
173C5×C4⋊C4—21no—
174C5×C4⋊C4—41no—
175C5×C4⋊C4D811yescharacteristic
176C5×C22⋊C4—41no—
177C5×C22⋊C4—41no—
178C5×C22⋊C4—41no—
179C5×C22⋊C4—41no—
180C5×C22⋊C4—41no—
181C5×C22⋊C4D811yescharacteristic
182C5×C22⋊C4D811yescharacteristic
183C42×C5C2×D411yescharacteristic
184C22⋊Dic5—41no—
185#685—41no—
186#685—41no—
187#685—41no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—41no—
192#683—41no—
193#683—41no—
194C4×Dic5—41no—
195D40—21no—
196D40—21no—
197#672—21no—
198#672—21no—
199#672—21no—
200#672—21no—
201C2×#135C2×D511yescharacteristic
202C22×D8C2×D511yescharacteristic
203#553—101no—
204#546—21no—
205C2×SD32—51no—
206C2×D16—51no—
207C2×D16—51no—
208C22×C16—51no—
209C22×C16—51no—
210#499—51no—
211#495C2×D511yescharacteristic
212#482—101no—
213#481—101no—
214#478—101no—
215#467C2×D511yescharacteristic
216#466—51no—
217#466—51no—
218#466C2×D511yescharacteristic
219#463—21no—
220#450—21no—
221#449—21no—
222C4×D8—51no—
223C4×D8C2×D511yescharacteristic
224C8×D4C2×D511yescharacteristic
225#427—51no—
226C2×#107—51no—
227#367—51no—
228#366—51no—
229#366—51no—
230C4⋊C16—51no—
231#358—51no—
232#358—51no—
233#358—51no—
234#357—51no—
235#357—51no—
236#357—51no—
237#357—51no—
238#357—51no—
239#357—51no—
240#357—51no—
241C22⋊C16—51no—
242C22⋊C16—51no—
243C4×C16—51no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—82no—
247C23×C5—82no—
248C23×C5—161no—
249C23×C5C2×D811yescharacteristic
250C23×C5C2×D811yescharacteristic
251C22×D5—41no—
252C5×Q8—41no—
253C5×Q8—41no—
254C5×D4—22no—
255C5×D4—22no—
256C5×D4—41no—
257C5×D4—41no—
258C5×D4—41no—
259C5×D4—82no—
260C5×D4—82no—
261C5×D4—161no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—82no—
269C2×C4×C5—161no—
270C2×C4×C5C2×D811yescharacteristic
271C2×C4×C5C2×D811yescharacteristic
272C2×C4×C5C2×D811yescharacteristic
273C2×C4×C5C2×D811yescharacteristic
274C2×C4×C5C22×D411yescharacteristic
275C22⋊D5—82no—
276C22⋊D5—161no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279C2×Dic5—41no—
280C2×Dic5—161no—
281D20—41no—
282D20—41no—
283C4×D5—161no—
284C5×C8—21no—
285C5×C8—21no—
286C5×C8—21no—
287C5×C8C2×#4111yescharacteristic
288C5×C8H(5,𝔽2)11yescharacteristic
289C2×#41—21no—
290C22×D4—21no—
291#135—22no—
292#135—41no—
293C2×Q16C22×D511yescharacteristic
294C2×SD16—21no—
295C2×SD16—21no—
296C2×D8—22no—
297C2×D8—21no—
298C2×D8—41no—
299C2×D8—51no—
300C2×D8C22×D511yescharacteristic
301C2×D8C22×D511yescharacteristic
302C22×C8C22×D511yescharacteristic
303C22×C8C22×D511yescharacteristic
304#126—201no—
305#125—101no—
306#124—21no—
307#123—41no—
308#123—201no—
309C22⋊Q8—21no—
310#121—21no—
311#121—41no—
312#121—101no—
313#121—101no—
314#121—201no—
315#120—41no—
316C4×D4—21no—
317C4×D4—101no—
318C4×D4—201no—
319C4×D4C22⋊D511yescharacteristic
320#117—101no—
321C2×C4⋊C4—101no—
322C2×C22⋊C4—41no—
323SD32—201no—
324D16—102no—
325D16—201no—
326C2×C16—51no—
327C2×C16—51no—
328C2×C16—51no—
329C2×C16—51no—
330C2×C16—201no—
331C2×C16—201no—
332#107—51no—
333#107—51no—
334#107—51no—
335#107—101no—
336#107C22×D511yescharacteristic
337#106—101no—
338#106—101no—
339C4⋊C8C22⋊D511yescharacteristic
340#103—21no—
341#102—21no—
342#102—21no—
343#102—101no—
344#102—101no—
345#102—101no—
346C22⋊C8C22⋊D511yescharacteristic
347C22⋊C8C22⋊D511yescharacteristic
348C4×C8C22×D511yescharacteristic
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—42no—
355C22×C5—81no—
356C22×C5—81no—
357C22×C5—81no—
358C22×C5—81no—
359C22×C5—81no—
360C22×C5—164no—
361C22×C5#50812yes—
362C22×C5C22×D811yescharacteristic
363C2×D5—81no—
364C2×D5—81no—
365C2×D5—81no—
366C4×C5—21no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—21no—
370C4×C5—81no—
371C4×C5—81no—
372C4×C5#54611yescharacteristic
373C4×C5#57711yescharacteristic
374Dic5—81no—
375Dic5—81no—
376Dic5—81no—
377C24—41no—
378#41—42no—
379#41—81no—
380C2×Q8—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—42no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—81no—
388C2×D4—101no—
389C2×D4—201no—
390C2×D4—201no—
391C2×D4#68611yescharacteristic
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—201no—
395C22×C4—201no—
396C22×C4C2×C22⋊D511yescharacteristic
397C22×C4C2×C22⋊D511yescharacteristic
398Q16—21no—
399Q16—21no—
400SD16—42no—
401SD16—81no—
402D8—21no—
403D8—21no—
404D8—21no—
405D8—42no—
406D8—101no—
407D8—101no—
408D8#71112yes—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D511yescharacteristic
414C2×C8C2×C22⋊D511yescharacteristic
415C2×C8C2×C22⋊D511yescharacteristic
416C2×C8C23×D511yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—101no—
420C4⋊C4—101no—
421C4⋊C4—101no—
422C4⋊C4—201no—
423C4⋊C4—201no—
424C4⋊C4—201no—
425C4⋊C4#68611yescharacteristic
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—201no—
432C22⋊C4—201no—
433C22⋊C4—201no—
434C22⋊C4—201no—
435C22⋊C4#68611yescharacteristic
436C22⋊C4#68611yescharacteristic
437C42—201no—
438C42C2×C22⋊D511yescharacteristic
439C16—101no—
440C16—101no—
441C16—101no—
442C16—101no—
443C2×C5—22no—
444C2×C5—41no—
445C2×C5—82no—
446C2×C5—161no—
447C2×C5#329411yescharacteristic
448C2×C5C2×#50811yescharacteristic
449C2×C5#341511yescharacteristic
450D5—161no—
451C23—41no—
452C23—41no—
453C23—82no—
454C23—82no—
455C23—161no—
456C23—201no—
457C23C2×#68611yescharacteristic
458C23C2×#68611yescharacteristic
459Q8—41no—
460Q8—41no—
461D4—22no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—82no—
467D4—82no—
468D4—161no—
469D4—201no—
470D4—201no—
471D4—402no—
472D4—801no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—161no—
481C2×C4—201no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—801no—
485C2×C4—801no—
486C2×C4C2×#68611yescharacteristic
487C2×C4C2×#68611yescharacteristic
488C2×C4C2×#68611yescharacteristic
489C2×C4C2×#68611yescharacteristic
490C2×C4C22×C22⋊D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8C2×#71111yescharacteristic
495C8#414411yescharacteristic
496C5#3386411yescharacteristic, complemented, Sylow
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—164no—
509C22—401no—
510C22—401no—
511C22—401no—
512C22#6548312yes—
513C22C22×#68611yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—401no—
521C4—401no—
522C4—401no—
523C4#6614011yescharacteristic
524C4#6617011yescharacteristic
525C2—22no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—801no—
530C2#1061521311yescharacteristic
531C2C2×#6548311yescharacteristic
532C2#1061573811yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC5×#3280C2
socleC22×C5C22×D8
hypercenter#3280D5
hypocenterC5#33864
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. #10611147C2semidirect
3. #10602875C2semidirect
4. #10602870C2semidirect
5. #10602828C2semidirect
6. C2×#64782C2semidirect
7. #10602116C2semidirect
8. #10602111C2semidirect
9. #10601875C2semidirect
10. #10601872C2semidirect
11. #10601864C2semidirect
12. #10601863C2semidirect
13. #10601681C2semidirect
14. C4×#3958C2semidirect
15. D4×#672C2semidirect
28. C2×#3960C22semidirect
32. #65404C22semidirect
33. #65395C22semidirect
36. C22×#672C22semidirect
40. C4×D40C22semidirect
41. #64972C22semidirect
42. #64784C22semidirect
43. #64784C22semidirect
44. #64784C22semidirect
52. C22⋊#672C22semidirect
53. #64711C22semidirect
54. #64710C22semidirect
55. #64709C22semidirect
56. #64709C22semidirect
57. C4⋊#672C22semidirect
58. C4×#672C22semidirect
121. #3280D5semidirect
496. C5#33864semidirect

Maximal subgroups

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

subgroupindex
C5×#32802
#106111472
#106028752
#106028702
#106028282
C2×#647822
#106021162
#106021112
#106018752
#106018722
#106018642
#106018632
#106016812
C4×#39582
D4×#6722
#338645