Finite Group Databasebeta

← #12070461

Subgroups — #12070461

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611679C211yesmaximal, characteristic, complemented
2#10611385C211yesmaximal, characteristic
3#10611273C211yesmaximal, characteristic, complemented
4C5×#1590C211yesmaximal, characteristic, complemented
5#10601747C211yesmaximal, characteristic, complemented
6#10601691C211yesmaximal, characteristic, complemented
7#10601656C211yesmaximal, characteristic, complemented
8#10599327C211yesmaximal, characteristic, complemented
9#10599314C211yesmaximal, characteristic, complemented
10#10599034C211yesmaximal, characteristic, complemented
11#10599005C211yesmaximal, characteristic, complemented
12D5×D4⋊C8C211yesmaximal, characteristic, complemented
13#10598953C211yesmaximal, characteristic, complemented
14C8×D40C211yesmaximal, characteristic, complemented
15#10598840C211yesmaximal, characteristic, complemented
16#65914C2211yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C5×#446C2211yescharacteristic, complemented
19C4×C5×SD16C2211yescharacteristic
20C5×#436C2211yescharacteristic
21#65458C411yescharacteristic
22#65454C411yescharacteristic
23#65416—21no—
24#65415—21no—
25C4×#688C2211yescharacteristic
26Q8×#168C2211yescharacteristic, complemented
27C4×#686C2211yescharacteristic
28#65301C2211yescharacteristic
29#65160C411yescharacteristic
30#65152C411yescharacteristic
31#65128—21no—
32#65127C2211yescharacteristic, complemented
33#65124C2211yescharacteristic
34#65123—21no—
35#65123C2211yescharacteristic
36D5×C4⋊C8C2211yescharacteristic
37#65108C411yescharacteristic
38#65098C411yescharacteristic
39#65062C411yescharacteristic
40#65055C411yescharacteristic
41#65017—21no—
42D5×C22⋊C8—21no—
43#64998—21no—
44#64995—21no—
45C4×D40C2211yescharacteristic
46C8×D20C2211yescharacteristic
47C8×D20C2211yescharacteristic, complemented
48#64974C2211yescharacteristic
49#64974C2211yescharacteristic
50C4×C8×D5C2211yescharacteristic
51C5×#334C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic
54C5×C82C2211yescharacteristic, complemented
55Q8⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic
57#64703C2211yescharacteristic
58#64703C2211yescharacteristic, complemented
59#64700C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64679C2211yescharacteristic, complemented
63#64678C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#18014—51nomaximal, Sylow
68C2×D4×D5C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×SD16C2×C411yescharacteristic
71C2×C5×M16—21no—
72C4×C5×Q8C2311yescharacteristic
73C4×C5×D4C2311yescharacteristic
74#4093C2×C411yescharacteristic
75#4092C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#686C2×C411yescharacteristic
79C4×C22⋊D5—21no—
80C2×#681—21no—
81C2×D40C2×C411yescharacteristic
82C2×#676—21no—
83C2×C8×D5—21no—
84C2×C8×D5—21no—
85C2×C8×D5—21no—
86C2×C8×D5—21no—
87C2×C8×D5—21no—
88#4044—21no—
89#4041C2×C411yescharacteristic
90#4040—21no—
91#4039C2×C411yescharacteristic
92D5×C4⋊C4C2×C411yescharacteristic
93#4036C2×C411yescharacteristic
94#4027—21no—
95D5×C22⋊C4—21no—
96C4×D20—21no—
97C4×D20C2311yescharacteristic
98C4×D20C2311yescharacteristic
99#4018—21no—
100C42×D5C2311yescharacteristic
101C5×#106C2×C411yescharacteristic
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#102C2×C411yescharacteristic
107C5×C22⋊C8—21no—
108C5×#97—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112#3967C2×C411yescharacteristic
113#3964C2×C411yescharacteristic
114C22⋊#168—21no—
115#3953C2×C411yescharacteristic
116#3953C2×C411yescharacteristic
117#3952—21no—
118#3952—21no—
119#3952—21no—
120#3952—21no—
121#3952—21no—
122#3952C2×C411yescharacteristic
123#3952C2×C411yescharacteristic
124#3952D411yescharacteristic
125#3952D411yescharacteristic
126#3950C2×C411yescharacteristic
127#3947—21no—
128#3946—21no—
129#3946C2×C411yescharacteristic
130#3946C2×C411yescharacteristic
131#3946D411yescharacteristic
132#3946D411yescharacteristic
133C8×Dic5—21no—
134#3941C2×C411yescharacteristic
135#3941C2×C411yescharacteristic
136#3940C2×C411yescharacteristic
137#3939C2×C411yescharacteristic
138C4⋊#168—21no—
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105—51no—
146#2994—51no—
147#2974—51no—
148#1590D511yescharacteristic, complemented
149#1589—51no—
150#1588—51no—
151#1586—51no—
152#1586—51no—
153#1585—51no—
154C8×SD16—51no—
155C8×D8—51no—
156#1573—51no—
157#1494—51no—
158C2×D4⋊C8—51no—
159#1450—51no—
160C23×D5—21no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C2×C22⋊D5—21no—
165C22×Dic5—21no—
166D4×D5—22no—
167D4×D5—41no—
168C2×D20—21no—
169C2×D20C22×C411yescharacteristic
170C2×D20C22×C411yescharacteristic
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5—21no—
175C2×C4×D5—81no—
176C2×C4×D5—81no—
177C2×C4×D5C22×C411yescharacteristic
178C2×C4×D5C2×D411yescharacteristic
179C2×C4×D5#4111yescharacteristic
180C5×SD16—41no—
181C5×M16—81no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C22×C411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C22⋊C4—21no—
193C42×C5—21no—
194C42×C5C2411yescharacteristic
195C22⋊Dic5—21no—
196#688—22no—
197#686—41no—
198#685—21no—
199#685—21no—
200#685—21no—
201#685—21no—
202#685—21no—
203#685—21no—
204#685—21no—
205C4⋊Dic5—21no—
206C4⋊Dic5C22×C411yescharacteristic
207C4⋊Dic5C22×C411yescharacteristic
208#683—21no—
209#683—21no—
210#683—21no—
211C4×Dic5C22×C411yescharacteristic
212C4×Dic5C2×D411yescharacteristic
213C4×Dic5#4111yescharacteristic
214#681—81no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222D40—22no—
223#676—81no—
224C8×D5—24no—
225C8×D5—81no—
226C8×D5—81no—
227C8×D5—81no—
228C8×D5—81no—
229#529—51no—
230C2×C4×D4—51no—
231#484—51no—
232#481—51no—
233#478—51no—
234#478—51no—
235#463—51no—
236#463—51no—
237#450—51no—
238#447—51no—
239#446C2×D511yescharacteristic, complemented
240C8×Q8—51no—
241C4×SD16—51no—
242C4×SD16C2×D511yescharacteristic
243C4×D8—51no—
244C4×D8—51no—
245#436—51no—
246#436—51no—
247#436C2×D511yescharacteristic
248#435—101no—
249#435—101no—
250#435—101no—
251C8×D4—51no—
252C8×D4—51no—
253C8×D4—51no—
254C8×D4—101no—
255#433—101no—
256#432—51no—
257#431—51no—
258#431—51no—
259#424—101no—
260C2×C4⋊C8—51no—
261#407—101no—
262C2×C22⋊C8—101no—
263C2×C4×C8—51no—
264#335—51no—
265#335—51no—
266#334—51no—
267#334C2×D511yescharacteristic, complemented
268Q8⋊C8—51no—
269Q8⋊C8C2×D511yescharacteristic, complemented
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275D4⋊C8C2×D511yescharacteristic
276#322—51no—
277#322—51no—
278C82—51no—
279C82C2×D511yescharacteristic, complemented
280C23×C5—21no—
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—81no—
286C22×D5C4×D411yescharacteristic
287C5×Q8—21no—
288C5×Q8—21no—
289C5×D4—21no—
290C5×D4—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5C23×C411yescharacteristic
297C2×C4×C5C22×D411yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C22⋊D5—42no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—81no—
303C2×Dic5C4×D411yescharacteristic
304C2×Dic5C4×D411yescharacteristic
305C2×Dic5C4×D411yescharacteristic
306D20—21no—
307D20—21no—
308D20—21no—
309D20—42no—
310D20#13112yes—
311C4×D5—22no—
312C4×D5—21no—
313C4×D5—21no—
314C4×D5—21no—
315C4×D5—21no—
316C4×D5—41no—
317C4×D5—41no—
318C4×D5—41no—
319C4×D5—41no—
320C4×D5—81no—
321C4×D5—81no—
322C5×C8—22no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—21no—
326C5×C8—21no—
327C5×C8—41no—
328C5×C8—41no—
329#168—22no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—21no—
334#168—41no—
335#168—41no—
336C22×D4—51no—
337C23×C4—101no—
338C2×SD16—51no—
339C2×SD16C4×D511yescharacteristic
340C2×D8—51no—
341C2×D8—51no—
342C2×M16—21no—
343C2×M16—101no—
344C2×M16—101no—
345C22×C8—101no—
346C22×C8—101no—
347C22×C8—101no—
348C22×C8—101no—
349C22×C8—101no—
350#126—101no—
351#125—51no—
352#124—51no—
353#123—101no—
354C22⋊Q8—51no—
355#121—51no—
356C4×Q8C22×D511yescharacteristic
357C4×D4—51no—
358C4×D4—51no—
359C4×D4—51no—
360C4×D4—51no—
361C4×D4—101no—
362C4×D4—101no—
363C4×D4—101no—
364C4×D4C22×D511yescharacteristic
365#117—101no—
366C2×C4⋊C4—51no—
367C2×C22⋊C4—101no—
368C2×C42—51no—
369#107—51no—
370#107—51no—
371#106—51no—
372#106C4×D511yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—51no—
375C4⋊C8—51no—
376C4⋊C8—51no—
377C4⋊C8—51no—
378C4⋊C8—51no—
379C4⋊C8—51no—
380C4⋊C8—101no—
381C4⋊C8—101no—
382C4⋊C8C22×D511yescharacteristic
383C4⋊C8C22×D511yescharacteristic
384#103—51no—
385#103C4×D511yescharacteristic
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102—51no—
391#102C4×D511yescharacteristic
392C22⋊C8—21no—
393C22⋊C8—51no—
394C22⋊C8—51no—
395C22⋊C8—51no—
396C22⋊C8—51no—
397C22⋊C8—101no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403#97—21no—
404#97—101no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—101no—
409C4×C8—101no—
410C4×C8C22×D511yescharacteristic
411C4×C8C22×D511yescharacteristic
412C4×C8C22×D511yescharacteristic
413C22×C5—41no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5C2×C4×D411yescharacteristic
417C2×D5—21no—
418C2×D5—21no—
419C2×D5—22no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C2×D5—84no—
426C2×D5#44312yes—
427C4×C5—21no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5—41no—
431C4×C5C2×#13111yescharacteristic
432C4×C5#56811yescharacteristic
433C4×C5#57611yescharacteristic
434C4×C5#57711yescharacteristic
435Dic5—21no—
436Dic5—21no—
437Dic5—21no—
438Dic5—41no—
439Dic5—41no—
440C24—101no—
441C2×Q8C2×C4×D511yescharacteristic
442C2×D4—51no—
443C2×D4—51no—
444C2×D4—101no—
445C2×D4—101no—
446C2×D4—102no—
447C2×D4—201no—
448C2×D4C2×C4×D511yescharacteristic
449C22×C4—21no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—401no—
459C22×C4—401no—
460SD16—41no—
461SD16—102no—
462D8—102no—
463D8—201no—
464M16—81no—
465M16—401no—
466M16—401no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—104no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—401no—
479C2×C8—401no—
480C2×C8—401no—
481C2×C8—401no—
482C2×C8C2×C4×D511yescharacteristic
483C2×C8C2×C4×D511yescharacteristic
484C2×C8D4×D511yescharacteristic
485C2×C8D4×D511yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—51no—
488C4⋊C4—51no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4C2×C4×D511yescharacteristic
494C4⋊C4C2×C4×D511yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—101no—
497C22⋊C4—101no—
498C22⋊C4—101no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C22⋊C4—101no—
504C42—21no—
505C42—51no—
506C42—51no—
507C42—51no—
508C42C23×D511yescharacteristic
509C2×C5—81no—
510C2×C5#293311yescharacteristic
511C2×C5#294611yescharacteristic
512C2×C5C2×#44311yescharacteristic
513D5—22no—
514D5—42no—
515D5—81no—
516C23—21no—
517C23—51no—
518C23—101no—
519C23—101no—
520C23—202no—
521C23—202no—
522C23—401no—
523Q8—21no—
524Q8—21no—
525D4—21no—
526D4—21no—
527D4—52no—
528D4—101no—
529D4—101no—
530D4—101no—
531D4—202no—
532D4—202no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—51no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—102no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—401no—
553C2×C4—401no—
554C2×C4—401no—
555C2×C4C22×C4×D511yescharacteristic
556C2×C4C2×D4×D511yescharacteristic
557C2×C4D5×#4111yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—102no—
566C8—101no—
567C8—101no—
568C8—101no—
569C8—101no—
570C8—201no—
571C8—201no—
572C5#1801411yescharacteristic, complemented, Sylow
573C22—41no—
574C22—41no—
575C22—41no—
576C22—52no—
577C22—101no—
578C22—101no—
579C22—102no—
580C22—201no—
581C22—201no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22—404no—
586C22C4×D4×D511yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—101no—
592C4—101no—
593C4—101no—
594C4—201no—
595C4—201no—
596C4#6607911yescharacteristic
597C4D5×#13111yescharacteristic
598C4#6609611yescharacteristic
599C4#6610311yescharacteristic
600C2—81no—
601C2—102no—
602C2—202no—
603C2—401no—
604C2#1061127011yescharacteristic
605C2#1061137811yescharacteristic
606C2D5×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1590C2
socleC22×C5C2×C4×D4
prime radical#65062C4
cosocleC42×C5C24
hypercenter#1590D5
hypocenterC5#18014
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #10611679C2semidirect
3. #10611273C2semidirect
4. C5×#1590C2semidirect
5. #10601747C2semidirect
6. #10601691C2semidirect
7. #10601656C2semidirect
8. #10599327C2semidirect
9. #10599314C2semidirect
10. #10599034C2semidirect
11. #10599005C2semidirect
12. D5×D4⋊C8C2semidirect
13. #10598953C2semidirect
14. C8×D40C2semidirect
15. #10598840C2semidirect
18. C5×#446C22semidirect
26. Q8×#168C22semidirect
32. #65127C22semidirect
47. C8×D20C22semidirect
51. C5×#334C22semidirect
52. C5×Q8⋊C8C22semidirect
54. C5×C82C22semidirect
55. Q8⋊#168C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64699C22semidirect
62. #64679C22semidirect
63. #64678C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
148. #1590D5semidirect
239. #446C2×D5semidirect
267. #334C2×D5semidirect
269. Q8⋊C8C2×D5semidirect
279. C82C2×D5semidirect
572. C5#18014semidirect

Maximal subgroups

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

subgroupindex
#106116792
#106113852
#106112732
C5×#15902
#106017472
#106016912
#106016562
#105993272
#105993142
#105990342
#105990052
D5×D4⋊C82
#105989532
C8×D402
#105988402
#180145