Finite Group Databasebeta

← #12069359

Subgroups — #12069359

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611678C211yesmaximal, characteristic, complemented
2#10611385C211yesmaximal, characteristic
3#10611157C211yesmaximal, characteristic, complemented
4C5×#1585C211yesmaximal, characteristic, complemented
5#10601746C211yesmaximal, characteristic, complemented
6SD16×#168C211yesmaximal, characteristic, complemented
7#10601634C211yesmaximal, characteristic, complemented
8#10599368C211yesmaximal, characteristic, complemented
9#10599349C211yesmaximal, characteristic, complemented
10#10599026C211yesmaximal, characteristic, complemented
11#10599007C211yesmaximal, characteristic, complemented
12#10598965C211yesmaximal, characteristic, complemented
13#10598944C211yesmaximal, characteristic, complemented
14#10598874C211yesmaximal, characteristic, complemented
15#10598867C211yesmaximal, characteristic, complemented
16#65914C2211yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C5×#446C2211yescharacteristic, complemented
19C4×C5×SD16C2211yescharacteristic
20C5×C8×D4C2211yescharacteristic
21#65458C411yescharacteristic
22#65454C411yescharacteristic
23C8×C22⋊D5—21no—
24C2×#3952—21no—
25C4×#688C2211yescharacteristic
26Q8×#168C2211yescharacteristic, complemented
27C4×#686C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65160C411yescharacteristic
30#65152C411yescharacteristic
31#65128—21no—
32#65127—21no—
33#65126C2211yescharacteristic
34#65123C2211yescharacteristic
35#65123C2211yescharacteristic, complemented
36#65122C2211yescharacteristic
37#65108C411yescharacteristic
38#65098C411yescharacteristic
39#65062C411yescharacteristic
40#65055C411yescharacteristic
41#65014—21no—
42D5×C22⋊C8—21no—
43#64998—21no—
44#64995—21no—
45C4×D40C2211yescharacteristic
46#64977C2211yescharacteristic, complemented
47C8×D20C2211yescharacteristic
48#64974C2211yescharacteristic
49#64974C2211yescharacteristic
50#64974C2211yescharacteristic
51C5×#335C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic, complemented
55Q8⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic
57#64703C2211yescharacteristic
58#64703C2211yescharacteristic, complemented
59#64700C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64679C2211yescharacteristic, complemented
63#64677C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#17918—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#4093C2×C411yescharacteristic
75#4092C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#686C2×C411yescharacteristic
79C4×C22⋊D5—21no—
80C22×#168—21no—
81C2×D40C2×C411yescharacteristic
82C2×#676—21no—
83C2×#676—21no—
84C2×C8×D5—21no—
85C2×C8×D5—21no—
86C2×C8×D5—21no—
87#4044—21no—
88#4041C2×C411yescharacteristic
89#4040—21no—
90#4039C2×C411yescharacteristic
91D5×C4⋊C4C2×C411yescharacteristic
92#4036C2×C411yescharacteristic
93#4027—21no—
94D5×C22⋊C4—21no—
95C4×D20—21no—
96C4×D20C2311yescharacteristic
97C4×D20C2311yescharacteristic
98#4018—21no—
99C42×D5C2311yescharacteristic
100C5×#106C2×C411yescharacteristic
101C5×C4⋊C8—21no—
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×#103C2×C411yescharacteristic
105C5×#102C2×C411yescharacteristic
106C5×C22⋊C8—21no—
107C5×#97—21no—
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111#3967C2×C411yescharacteristic
112#3964C2×C411yescharacteristic
113C22⋊#168—21no—
114#3953C2×C411yescharacteristic
115#3953C2×C411yescharacteristic
116#3952—21no—
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#3946—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#2993—51no—
147#2972—51no—
148#1586—51no—
149#1585D511yescharacteristic, complemented
150#1582—51no—
151#1581—51no—
152#1580—51no—
153SD16⋊C8—51no—
154C8×SD16—51no—
155C8×D8—51no—
156#1574—51no—
157#1486—51no—
158#1482—51no—
159#1454—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×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—22no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—81no—
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—22no—
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
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—81no—
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222D40—22no—
223#676—81no—
224#676—81no—
225C8×D5—81no—
226C8×D5—81no—
227C8×D5—81no—
228#529—51no—
229C2×C4×D4—51no—
230#484—51no—
231#481—51no—
232#478—51no—
233#478—51no—
234#463—51no—
235#463—51no—
236#450—51no—
237#447—51no—
238#446C2×D511yescharacteristic, complemented
239C8×Q8—51no—
240C4×SD16—51no—
241C4×SD16C2×D511yescharacteristic
242C4×D8—51no—
243C4×D8—51no—
244#436—51no—
245#436—101no—
246#435—101no—
247C8×D4—51no—
248C8×D4—51no—
249C8×D4—51no—
250C8×D4—51no—
251C8×D4—101no—
252C8×D4—101no—
253C8×D4C2×D511yescharacteristic
254#433—101no—
255#431—51no—
256#431—51no—
257#431—51no—
258#431—51no—
259#424—101no—
260#423—51no—
261C2×C22⋊C8—101no—
262C2×C22⋊C8—101no—
263#335—51no—
264#335C2×D511yescharacteristic, complemented
265#334—51no—
266#334—51no—
267Q8⋊C8—51no—
268Q8⋊C8C2×D511yescharacteristic, complemented
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8C2×D511yescharacteristic
275#322—51no—
276#322—51no—
277#322C2×D511yescharacteristic, complemented
278C82—51no—
279C23×C5—21no—
280C22×D5—21no—
281C22×D5—24no—
282C22×D5—21no—
283C22×D5—81no—
284C22×D5—81no—
285C22×D5C4×D411yescharacteristic
286C5×Q8—21no—
287C5×Q8—21no—
288C5×D4—21no—
289C5×D4#13112yes—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5C23×C411yescharacteristic
296C2×C4×C5C22×D411yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C22⋊D5—24no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—81no—
302C2×Dic5C4×D411yescharacteristic
303C2×Dic5C4×D411yescharacteristic
304C2×Dic5C4×D411yescharacteristic
305D20—21no—
306D20—21no—
307D20—21no—
308D20—81no—
309D20#13112yes—
310C4×D5—21no—
311C4×D5—21no—
312C4×D5—21no—
313C4×D5—21no—
314C4×D5—41no—
315C4×D5—41no—
316C4×D5—41no—
317C4×D5—41no—
318C4×D5—41no—
319C4×D5—81no—
320C4×D5—81no—
321C5×C8—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—41no—
333#168—41no—
334#168—41no—
335C22×D4—51no—
336C23×C4—101no—
337C2×SD16—51no—
338C2×SD16C4×D511yescharacteristic
339C2×D8—51no—
340C2×D8—51no—
341C2×M16—101no—
342C2×M16—101no—
343C22×C8—21no—
344C22×C8—101no—
345C22×C8—101no—
346C22×C8—101no—
347C22×C8—101no—
348#126—101no—
349#125—51no—
350#124—51no—
351#123—101no—
352C22⋊Q8—51no—
353#121—51no—
354C4×Q8C22×D511yescharacteristic
355C4×D4—51no—
356C4×D4—51no—
357C4×D4—51no—
358C4×D4—51no—
359C4×D4—101no—
360C4×D4—101no—
361C4×D4—101no—
362C4×D4C22×D511yescharacteristic
363#117—101no—
364C2×C4⋊C4—51no—
365C2×C22⋊C4—101no—
366C2×C42—51no—
367#107—51no—
368#107—51no—
369#106—51no—
370#106C4×D511yescharacteristic
371C4⋊C8—21no—
372C4⋊C8—51no—
373C4⋊C8—51no—
374C4⋊C8—51no—
375C4⋊C8—51no—
376C4⋊C8—51no—
377C4⋊C8—51no—
378C4⋊C8—101no—
379C4⋊C8—101no—
380C4⋊C8—101no—
381C4⋊C8C22×D511yescharacteristic
382C4⋊C8C22×D511yescharacteristic
383#103—51no—
384#103C4×D511yescharacteristic
385#102—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102C4×D511yescharacteristic
391C22⋊C8—21no—
392C22⋊C8—51no—
393C22⋊C8—51no—
394C22⋊C8—51no—
395C22⋊C8—51no—
396C22⋊C8—101no—
397C22⋊C8—101no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403#97—21no—
404C4×C8—51no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—101no—
408C4×C8—101no—
409C4×C8C22×D511yescharacteristic
410C4×C8C22×D511yescharacteristic
411C4×C8C22×D511yescharacteristic
412C22×C5—22no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5C2×C4×D411yescharacteristic
416C2×D5—21no—
417C2×D5—22no—
418C2×D5—21no—
419C2×D5—21no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C2×D5—84no—
426C4×C5—21no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5C2×#13111yescharacteristic
431C4×C5C2×#13111yescharacteristic
432C4×C5#57611yescharacteristic
433C4×C5#57711yescharacteristic
434Dic5—21no—
435Dic5—21no—
436Dic5—21no—
437Dic5—41no—
438Dic5—41no—
439C24—101no—
440C2×Q8C2×C4×D511yescharacteristic
441C2×D4—51no—
442C2×D4—51no—
443C2×D4—101no—
444C2×D4—101no—
445C2×D4—102no—
446C2×D4—102no—
447C2×D4C2×C4×D511yescharacteristic
448C22×C4—21no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—401no—
458C22×C4—401no—
459SD16—22no—
460SD16—102no—
461D8—102no—
462D8—102no—
463M16—401no—
464M16—401no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—51no—
469C2×C8—51no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—81no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—401no—
477C2×C8—401no—
478C2×C8—401no—
479C2×C8—401no—
480C2×C8C2×C4×D511yescharacteristic
481C2×C8C2×C4×D511yescharacteristic
482C2×C8D4×D511yescharacteristic
483C2×C8D4×D511yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—51no—
486C4⋊C4—51no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4C2×C4×D511yescharacteristic
492C4⋊C4C2×C4×D511yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—101no—
495C22⋊C4—101no—
496C22⋊C4—101no—
497C22⋊C4—101no—
498C22⋊C4—101no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C42—21no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42C23×D511yescharacteristic
507C2×C5—42no—
508C2×C5#292911yescharacteristic
509C2×C5#294611yescharacteristic
510C2×C5#295711yescharacteristic
511D5—41no—
512D5—42no—
513D5—81no—
514C23—21no—
515C23—51no—
516C23—104no—
517C23—101no—
518C23—101no—
519C23—401no—
520C23—401no—
521Q8—21no—
522Q8—21no—
523D4—21no—
524D4—52no—
525D4—104no—
526D4—101no—
527D4—101no—
528D4—101no—
529D4—401no—
530D4#405312yes—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—51no—
537C2×C4—51no—
538C2×C4—51no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—401no—
551C2×C4—401no—
552C2×C4—401no—
553C2×C4C22×C4×D511yescharacteristic
554C2×C4C2×D4×D511yescharacteristic
555C2×C4D5×#4111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—201no—
568C8—201no—
569C8—201no—
570C5#1791811yescharacteristic, complemented, Sylow
571C22—22no—
572C22—41no—
573C22—41no—
574C22—101no—
575C22—102no—
576C22—101no—
577C22—101no—
578C22—201no—
579C22—201no—
580C22—201no—
581C22—201no—
582C22—201no—
583C22—404no—
584C22C4×D4×D511yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—101no—
590C4—101no—
591C4—101no—
592C4—201no—
593C4—201no—
594C4C2×#405311yescharacteristic
595C4D5×#13111yescharacteristic
596C4#6610811yescharacteristic
597C4#6611211yescharacteristic
598C2—42no—
599C2—201no—
600C2—202no—
601C2—401no—
602C2#1061120911yescharacteristic
603C2#1061150611yescharacteristic
604C2#1061162111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1585C2
socleC22×C5C2×C4×D4
prime radical#65062C4
cosocleC42×C5C24
hypercenter#1585D5
hypocenterC5#17918
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. #10611678C2semidirect
3. #10611157C2semidirect
4. C5×#1585C2semidirect
5. #10601746C2semidirect
6. SD16×#168C2semidirect
7. #10601634C2semidirect
8. #10599368C2semidirect
9. #10599349C2semidirect
10. #10599026C2semidirect
11. #10599007C2semidirect
12. #10598965C2semidirect
13. #10598944C2semidirect
14. #10598874C2semidirect
15. #10598867C2semidirect
18. C5×#446C22semidirect
26. Q8×#168C22semidirect
35. #65123C22semidirect
46. #64977C22semidirect
51. C5×#335C22semidirect
52. C5×Q8⋊C8C22semidirect
54. C5×#322C22semidirect
55. Q8⋊#168C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64699C22semidirect
62. #64679C22semidirect
63. #64677C22semidirect
64. #64675C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
149. #1585D5semidirect
238. #446C2×D5semidirect
264. #335C2×D5semidirect
268. Q8⋊C8C2×D5semidirect
277. #322C2×D5semidirect
570. C5#17918semidirect

Maximal subgroups

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

subgroupindex
#106116782
#106113852
#106111572
C5×#15852
#106017462
SD16×#1682
#106016342
#105993682
#105993492
#105990262
#105990072
#105989652
#105989442
#105988742
#105988672
#179185