Finite Group Databasebeta

← #12069437

Subgroups — #12069437

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611696C211yesmaximal, characteristic, complemented
2#10611382C211yesmaximal, characteristic
3#10611157C211yesmaximal, characteristic
4C5×#1585C211yesmaximal, characteristic, complemented
5#10601746C211yesmaximal, characteristic, complemented
6SD16⋊#168C211yesmaximal, characteristic, complemented
7#10601635C211yesmaximal, characteristic, complemented
8#10599366C211yesmaximal, characteristic, complemented
9#10599351C211yesmaximal, characteristic, complemented
10#10599028C211yesmaximal, characteristic, complemented
11#10599005C211yesmaximal, characteristic, complemented
12#10598968C211yesmaximal, characteristic
13#10598942C211yesmaximal, characteristic, complemented
14#10598873C211yesmaximal, characteristic, complemented
15#10598866C211yesmaximal, characteristic, complemented
16#65912C2211yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C5×#446C2211yescharacteristic, complemented
19C4×C5×SD16C2211yescharacteristic
20C5×C8×D4C2211yescharacteristic
21#65458C411yescharacteristic
22#65451C411yescharacteristic
23C8×C22⋊D5—21no—
24C2×#3952—21no—
25C4×#688C2211yescharacteristic
26Q8×#168C2211yescharacteristic, complemented
27C4×#687C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65159C411yescharacteristic
30#65151C411yescharacteristic
31#65129—21no—
32#65124C2211yescharacteristic
33#65123C2211yescharacteristic
34#65122C2211yescharacteristic
35#65120—21no—
36#65119C2211yescharacteristic, complemented
37#65107C411yescharacteristic
38#65094C411yescharacteristic
39#65065C411yescharacteristic
40#65050C411yescharacteristic
41#65014—21no—
42D5×C22⋊C8—21no—
43#64998—21no—
44#64990—21no—
45C4×#677C2211yescharacteristic
46C4×#676C2211yescharacteristic
47C8×D20C2211yescharacteristic
48#64974C2211yescharacteristic
49#64974C2211yescharacteristic
50#64968C2211yescharacteristic, complemented
51C5×#335C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic, complemented
55Q8⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic, complemented
58#64703C2211yescharacteristic
59#64700C2211yescharacteristic, complemented
60#64700C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64678C2211yescharacteristic, complemented
63#64676C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64675C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#17924—51nomaximal, Sylow
68C2×D4×D5C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×SD16C2×C411yescharacteristic
71C22×C5×C8—21no—
72C4×C5×Q8C2311yescharacteristic
73C4×C5×D4C2311yescharacteristic
74#4092C2×C411yescharacteristic
75#4090C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#687C2×C411yescharacteristic
79C4×C22⋊D5—21no—
80C22×#168—21no—
81C2×#677C2×C411yescharacteristic
82C2×#676—21no—
83C2×C8×D5—21no—
84C2×C8×D5—21no—
85#4043C2×C411yescharacteristic
86#4042—21no—
87#4039C2×C411yescharacteristic
88D5×C4⋊C4C2×C411yescharacteristic
89#4035—21no—
90#4034C2×C411yescharacteristic
91#4027—21no—
92D5×C22⋊C4—21no—
93C4×D20C2311yescharacteristic
94#4018—21no—
95C42×D5C2311yescharacteristic
96C4×Dic10—21no—
97C4×Dic10C2311yescharacteristic
98C5×#106C2×C411yescharacteristic
99C5×C4⋊C8—21no—
100C5×C4⋊C8C2311yescharacteristic
101C5×C4⋊C8C2311yescharacteristic
102C5×#103C2×C411yescharacteristic
103C5×#102C2×C411yescharacteristic
104C5×C22⋊C8—21no—
105C5×#97—21no—
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109#3967C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111C22⋊#168—21no—
112#3953C2×C411yescharacteristic
113#3952—21no—
114#3952—21no—
115#3952—21no—
116#3952—21no—
117#3952C2×C411yescharacteristic
118#3952C2×C411yescharacteristic
119#3952D411yescharacteristic
120#3952D411yescharacteristic
121#3949C2×C411yescharacteristic
122#3948C2×C411yescharacteristic
123#3947—21no—
124#3947—21no—
125#3947—21no—
126#3946—21no—
127#3946—21no—
128#3946C2×C411yescharacteristic
129#3946C2×C411yescharacteristic
130#3946D411yescharacteristic
131#3946D411yescharacteristic
132C8×Dic5—21no—
133C8×Dic5—21no—
134#3942C2×C411yescharacteristic
135#3941C2×C411yescharacteristic
136#3940C2×C411yescharacteristic
137#3940C2×C411yescharacteristic
138C4⋊#168—21no—
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3101—51no—
146#2985—51no—
147#2972—51no—
148#1585—51no—
149#1585D511yescharacteristic, complemented
150#1582—51no—
151#1582—51no—
152SD16⋊C8—51no—
153SD16⋊C8—51no—
154C8×SD16—51no—
155C8×SD16—51no—
156#1572—51no—
157#1490—51no—
158#1485—51no—
159#1453—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—22no—
168C2×D20C22×C411yescharacteristic
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—81no—
173C2×C4×D5—81no—
174C2×C4×D5C22×C411yescharacteristic
175C2×C4×D5C2×D411yescharacteristic
176C2×C4×D5#4111yescharacteristic
177C2×Dic10—21no—
178C2×Dic10C22×C411yescharacteristic
179C5×SD16—22no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—81no—
184C2×C5×C8C22×C411yescharacteristic
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C2×D411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C5×C4⋊C4—21no—
189C5×C4⋊C4C22×C411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C22⋊C4—21no—
192C42×C5—21no—
193C42×C5C2411yescharacteristic
194C22⋊Dic5—21no—
195#688—22no—
196#687—22no—
197#685—21no—
198#685—21no—
199#685—21no—
200#685—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5C22×C411yescharacteristic
203C4⋊Dic5C22×C411yescharacteristic
204#683—21no—
205#683—21no—
206#683—21no—
207#683—21no—
208#683—21no—
209#683—21no—
210C4×Dic5—21no—
211C4×Dic5C22×C411yescharacteristic
212C4×Dic5C2×D411yescharacteristic
213C4×Dic5#4111yescharacteristic
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—81no—
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222#677—22no—
223#676—42no—
224C8×D5—81no—
225C8×D5—81no—
226#533—51no—
227C2×C4×D4—51no—
228#483—51no—
229#483—51no—
230#476—51no—
231#476—51no—
232#461—51no—
233#461—51no—
234#450—51no—
235#450—51no—
236#446—51no—
237#446—101no—
238#446—101no—
239#446C2×D511yescharacteristic, complemented
240C8×Q8—51no—
241C8×Q8—51no—
242C4×SD16—51no—
243C4×SD16—51no—
244C4×SD16—51no—
245C4×SD16C2×D511yescharacteristic
246C8×D4—51no—
247C8×D4—51no—
248C8×D4—51no—
249C8×D4—101no—
250C8×D4—101no—
251C8×D4C2×D511yescharacteristic
252#433—101no—
253#433—101no—
254#432—51no—
255#431—51no—
256#431—51no—
257#431—51no—
258C2×C22⋊C8—101no—
259C2×C22⋊C8—101no—
260C4×M16—51no—
261#335—51no—
262#335C2×D511yescharacteristic, complemented
263#334—51no—
264#334—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8C2×D511yescharacteristic, complemented
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8C2×D511yescharacteristic
273#322—51no—
274#322—51no—
275#322C2×D511yescharacteristic, complemented
276C82—51no—
277C23×C5—21no—
278C22×D5—21no—
279C22×D5—24no—
280C22×D5—81no—
281C22×D5—81no—
282C22×D5C4×D411yescharacteristic
283C5×Q8—21no—
284C5×Q8—21no—
285C5×D4—21no—
286C5×D4#13112yes—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5C23×C411yescharacteristic
293C2×C4×C5C22×D411yescharacteristic
294C2×C4×C5C2×#4111yescharacteristic
295C22⋊D5—24no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—81no—
300C2×Dic5C4×D411yescharacteristic
301C2×Dic5C4×D411yescharacteristic
302C2×Dic5C4×D411yescharacteristic
303D20—21no—
304D20#13112yes—
305C4×D5—21no—
306C4×D5—21no—
307C4×D5—21no—
308C4×D5—21no—
309C4×D5—41no—
310C4×D5—41no—
311C4×D5—41no—
312C4×D5—81no—
313C4×D5—81no—
314Dic10—21no—
315Dic10—21no—
316Dic10—81no—
317C5×C8—22no—
318C5×C8—21no—
319C5×C8—21no—
320C5×C8—21no—
321C5×C8—21no—
322C5×C8—41no—
323C5×C8—41no—
324#168—21no—
325#168—21no—
326#168—21no—
327#168—21no—
328#168—41no—
329#168—41no—
330#168—41no—
331C22×D4—51no—
332C23×C4—101no—
333C2×SD16—51no—
334C2×SD16—51no—
335C2×SD16—51no—
336C2×SD16C4×D511yescharacteristic
337C2×M16—101no—
338C22×C8—21no—
339C22×C8—101no—
340C22×C8—101no—
341C22×C8—101no—
342C4⋊Q8—51no—
343C4⋊Q8—51no—
344#125—101no—
345C22⋊Q8—51no—
346C22⋊Q8—51no—
347C22⋊Q8—101no—
348C4×Q8—51no—
349C4×Q8—101no—
350C4×Q8C22×D511yescharacteristic
351C4×D4—51no—
352C4×D4—51no—
353C4×D4—51no—
354C4×D4—101no—
355C4×D4—101no—
356C4×D4C22×D511yescharacteristic
357#117—101no—
358C2×C4⋊C4—51no—
359C2×C22⋊C4—101no—
360C2×C42—51no—
361#106—51no—
362#106—51no—
363#106—51no—
364#106C4×D511yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—51no—
367C4⋊C8—51no—
368C4⋊C8—51no—
369C4⋊C8—51no—
370C4⋊C8—51no—
371C4⋊C8—51no—
372C4⋊C8—101no—
373C4⋊C8—101no—
374C4⋊C8—101no—
375C4⋊C8C22×D511yescharacteristic
376C4⋊C8C22×D511yescharacteristic
377#103—51no—
378#103—51no—
379#103—51no—
380#103C4×D511yescharacteristic
381#102—51no—
382#102—51no—
383#102—51no—
384#102C4×D511yescharacteristic
385C22⋊C8—21no—
386C22⋊C8—51no—
387C22⋊C8—51no—
388C22⋊C8—51no—
389C22⋊C8—51no—
390C22⋊C8—101no—
391C22⋊C8—101no—
392C22⋊C8—101no—
393C22⋊C8—101no—
394C22⋊C8—101no—
395#97—21no—
396#97—101no—
397#97—101no—
398#97—101no—
399C4×C8—51no—
400C4×C8—51no—
401C4×C8—51no—
402C4×C8—101no—
403C4×C8—101no—
404C4×C8—101no—
405C4×C8C22×D511yescharacteristic
406C4×C8C22×D511yescharacteristic
407C4×C8C22×D511yescharacteristic
408C22×C5—22no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5C2×C4×D411yescharacteristic
412C2×D5—21no—
413C2×D5—22no—
414C2×D5—21no—
415C2×D5—21no—
416C2×D5—41no—
417C2×D5—41no—
418C2×D5—84no—
419C4×C5—21no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5C2×#13111yescharacteristic
424C4×C5C2×#13111yescharacteristic
425C4×C5#57711yescharacteristic
426C4×C5#57711yescharacteristic
427Dic5—21no—
428Dic5—21no—
429Dic5—21no—
430Dic5—41no—
431Dic5—41no—
432Dic5—41no—
433C24—101no—
434C2×Q8—51no—
435C2×Q8—101no—
436C2×Q8C2×C4×D511yescharacteristic
437C2×D4—51no—
438C2×D4—101no—
439C2×D4—102no—
440C2×D4—102no—
441C2×D4C2×C4×D511yescharacteristic
442C22×C4—21no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—401no—
451C22×C4—401no—
452SD16—22no—
453SD16—102no—
454SD16—102no—
455SD16—102no—
456M16—202no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—51no—
461C2×C8—51no—
462C2×C8—51no—
463C2×C8—51no—
464C2×C8—81no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—401no—
469C2×C8—401no—
470C2×C8—401no—
471C2×C8C2×C4×D511yescharacteristic
472C2×C8C2×C4×D511yescharacteristic
473C2×C8D4×D511yescharacteristic
474C2×C8D4×D511yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—51no—
477C4⋊C4—51no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4—101no—
481C4⋊C4—101no—
482C4⋊C4—101no—
483C4⋊C4—101no—
484C4⋊C4—101no—
485C4⋊C4C2×C4×D511yescharacteristic
486C4⋊C4C2×C4×D511yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—101no—
489C22⋊C4—101no—
490C22⋊C4—101no—
491C22⋊C4—101no—
492C22⋊C4—101no—
493C42—21no—
494C42—51no—
495C42—51no—
496C42—51no—
497C42—101no—
498C42C23×D511yescharacteristic
499C2×C5—42no—
500C2×C5#292911yescharacteristic
501C2×C5#294911yescharacteristic
502C2×C5#295611yescharacteristic
503D5—41no—
504D5—42no—
505C23—21no—
506C23—51no—
507C23—104no—
508C23—101no—
509C23—401no—
510C23—401no—
511Q8—21no—
512Q8—21no—
513Q8—101no—
514Q8—101no—
515Q8—401no—
516D4—21no—
517D4—52no—
518D4—104no—
519D4—101no—
520D4#405312yes—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—51no—
527C2×C4—51no—
528C2×C4—51no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—401no—
540C2×C4—401no—
541C2×C4—401no—
542C2×C4C22×C4×D511yescharacteristic
543C2×C4C2×D4×D511yescharacteristic
544C2×C4D5×#4111yescharacteristic
545C8—22no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—101no—
553C8—101no—
554C8—101no—
555C8—101no—
556C8—201no—
557C8—201no—
558C8—201no—
559C5#1792411yescharacteristic, complemented, Sylow
560C22—22no—
561C22—41no—
562C22—41no—
563C22—101no—
564C22—102no—
565C22—101no—
566C22—101no—
567C22—201no—
568C22—201no—
569C22—404no—
570C22C4×D4×D511yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—101no—
576C4—101no—
577C4—101no—
578C4—201no—
579C4—201no—
580C4—201no—
581C4C2×#405311yescharacteristic
582C4D5×#13111yescharacteristic
583C4#6610911yescharacteristic
584C4#6611211yescharacteristic
585C2—42no—
586C2—201no—
587C2—202no—
588C2#1061120911yescharacteristic
589C2#1061150811yescharacteristic
590C2#1061162011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1585C2
socleC22×C5C2×C4×D4
prime radicalC2×D4×D5C2×C4
cosocleC42×C5C24
hypercenter#1585D5
hypocenterC5#17924
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
1. #10611696C2semidirect
4. C5×#1585C2semidirect
5. #10601746C2semidirect
6. SD16⋊#168C2semidirect
7. #10601635C2semidirect
8. #10599366C2semidirect
9. #10599351C2semidirect
10. #10599028C2semidirect
11. #10599005C2semidirect
13. #10598942C2semidirect
14. #10598873C2semidirect
15. #10598866C2semidirect
18. C5×#446C22semidirect
26. Q8×#168C22semidirect
36. #65119C22semidirect
50. #64968C22semidirect
51. C5×#335C22semidirect
52. C5×Q8⋊C8C22semidirect
54. C5×#322C22semidirect
55. Q8⋊#168C22semidirect
57. #64704C22semidirect
59. #64700C22semidirect
60. #64700C22semidirect
62. #64678C22semidirect
63. #64676C22semidirect
64. #64675C22semidirect
65. #64675C22semidirect
66. C8×#168C22semidirect
149. #1585D5semidirect
239. #446C2×D5semidirect
262. #335C2×D5semidirect
268. Q8⋊C8C2×D5semidirect
275. #322C2×D5semidirect
559. C5#17924semidirect

Maximal subgroups

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

subgroupindex
#106116962
#106113822
#106111572
C5×#15852
#106017462
SD16⋊#1682
#106016352
#105993662
#105993512
#105990282
#105990052
#105989682
#105989422
#105988732
#105988662
#179245