Finite Group Databasebeta

← #12070525

Subgroups — #12070525

Order 1280.

642 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#10611323C211yesmaximal, characteristic
2#10611158C211yesmaximal, characteristic, complemented
3#10611141C211yesmaximal, characteristic, complemented
4C5×#1580C211yesmaximal, characteristic, complemented
5#10601672C211yesmaximal, characteristic, complemented
6#10601635C211yesmaximal, characteristic, complemented
7#10601634C211yesmaximal, characteristic, complemented
8#10599327C211yesmaximal, characteristic, complemented
9#10599313C211yesmaximal, characteristic, complemented
10#10598970C211yesmaximal, characteristic, complemented
11D5×D4⋊C8C211yesmaximal, characteristic, complemented
12#10598956C211yesmaximal, characteristic, complemented
13#10598943C211yesmaximal, characteristic, complemented
14#10598875C211yesmaximal, characteristic, complemented
15#10598864C211yesmaximal, characteristic, complemented
16#65891C2211yescharacteristic
17C4×D4×D5C2211yescharacteristic
18C4×C5×D8C2211yescharacteristic
19C5×C8×D4C2211yescharacteristic
20C5×C8×D4C2211yescharacteristic, complemented
21#65445C411yescharacteristic
22#65442C411yescharacteristic
23#65400—21no—
24C8×C22⋊D5—21no—
25C2×#3952—21no—
26#65391—21no—
27C4×#687C2211yescharacteristic
28C4×#686C2211yescharacteristic
29#65301C2211yescharacteristic, complemented
30D4×#168C2211yescharacteristic
31#65180C411yescharacteristic
32#65173C411yescharacteristic
33#65127C2211yescharacteristic
34#65124C2211yescharacteristic
35D5×C4⋊C8C2211yescharacteristic
36#65119C2211yescharacteristic, complemented
37#65076C411yescharacteristic
38#65066C411yescharacteristic
39#65065C411yescharacteristic
40#65052C411yescharacteristic
41#65019—21no—
42#65017—21no—
43#65015—21no—
44#65009—21no—
45C4×#677C2211yescharacteristic
46#64977C2211yescharacteristic
47#64974C2211yescharacteristic
48#64974C2211yescharacteristic
49C4×C8×D5C2211yescharacteristic
50#64968C2211yescharacteristic, complemented
51C5×#334C2211yescharacteristic, complemented
52C5×D4⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic, complemented
54C5×#322C2211yescharacteristic, complemented
55D4⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic, complemented
57#64704C2211yescharacteristic, complemented
58#64703C2211yescharacteristic
59#64700C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64678C2211yescharacteristic, complemented
63#64676C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18020—51nomaximal, Sylow
68C2×D4×D5C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×D8C2×C411yescharacteristic
71C22×C5×C8—21no—
72C22×C5×C8—21no—
73C4×C5×D4C2311yescharacteristic
74C4×C5×D4C2311yescharacteristic
75#4084C2×C411yescharacteristic
76#4082C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#687C2×C411yescharacteristic
79C2×#686C2×C411yescharacteristic
80C4×C22⋊D5—21no—
81C4×C22⋊D5—21no—
82#4072—21no—
83C2×#681—21no—
84C22×#168—21no—
85C2×#677C2×C411yescharacteristic
86C2×#676—21no—
87C2×#676—21no—
88C2×C8×D5—21no—
89C2×C8×D5—21no—
90#4043C2×C411yescharacteristic
91#4039C2×C411yescharacteristic
92D5×C4⋊C4C2×C411yescharacteristic
93#4036C2×C411yescharacteristic
94#4029—21no—
95#4027—21no—
96D5×C22⋊C4—21no—
97#4025—21no—
98C4×D20C2311yescharacteristic
99C42×D5C2311yescharacteristic
100C4×Dic10C2311yescharacteristic
101C5×#107C2×C411yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×#102C2×C411yescharacteristic
105C5×#102C2×C411yescharacteristic
106C5×C22⋊C8—21no—
107C5×C22⋊C8—21no—
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111#3964C2×C411yescharacteristic
112#3964C2×C411yescharacteristic
113C22⋊#168—21no—
114C22⋊#168—21no—
115#3953C2×C411yescharacteristic
116#3952—21no—
117#3952—21no—
118#3952—21no—
119#3952C2×C411yescharacteristic
120#3952C2×C411yescharacteristic
121#3952D411yescharacteristic
122#3952D411yescharacteristic
123#3949C2×C411yescharacteristic
124#3948C2×C411yescharacteristic
125#3947—21no—
126#3947—21no—
127#3946—21no—
128#3946—21no—
129#3946—21no—
130#3946C2×C411yescharacteristic
131#3946C2×C411yescharacteristic
132#3946D411yescharacteristic
133#3946D411yescharacteristic
134C8×Dic5—21no—
135C8×Dic5—21no—
136#3942C2×C411yescharacteristic
137#3941C2×C411yescharacteristic
138#3940C2×C411yescharacteristic
139#3939C2×C411yescharacteristic
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105—51no—
146#2994—51no—
147#2974—51no—
148#1594—51no—
149#1592—51no—
150#1583—51no—
151#1582—51no—
152#1581—51no—
153#1581—51no—
154#1580D511yescharacteristic, complemented
155SD16⋊C8—51no—
156#1573—51no—
157#1494—51no—
158C2×D4⋊C8—51no—
159#1452—51no—
160C23×D5—21no—
161C2×C5×D4C22×C411yescharacteristic
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C2×C22⋊D5—21no—
166C2×C22⋊D5—21no—
167C22×Dic5—21no—
168D4×D5—22no—
169D4×D5—41no—
170C2×D20C22×C411yescharacteristic
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5—81no—
175C2×C4×D5—81no—
176C2×C4×D5C22×C411yescharacteristic
177C2×C4×D5C2×D411yescharacteristic
178C2×C4×D5#4111yescharacteristic
179C2×Dic10C22×C411yescharacteristic
180C5×D8—22no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—81no—
185C2×C5×C8—81no—
186C2×C5×C8C22×C411yescharacteristic
187C2×C5×C8C22×C411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C42×C5C2411yescharacteristic
195C22⋊Dic5—21no—
196C22⋊Dic5—21no—
197C22⋊Dic5—21no—
198C22⋊Dic5—21no—
199#687—22no—
200#686—41no—
201#685—21no—
202#685—21no—
203#685—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5—21no—
206C4⋊Dic5C22×C411yescharacteristic
207C4⋊Dic5C22×C411yescharacteristic
208#683—21no—
209#683—21no—
210#683—21no—
211C4×Dic5—21no—
212C4×Dic5C22×C411yescharacteristic
213C4×Dic5C2×D411yescharacteristic
214C4×Dic5#4111yescharacteristic
215#681—81no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—81no—
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C2×D411yescharacteristic
223C2×#168C2×D411yescharacteristic
224#677—41no—
225#676—81no—
226#676—81no—
227C8×D5—42no—
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#446—51no—
240C8×Q8—51no—
241C4×SD16—51no—
242C4×SD16—51no—
243C4×D8—51no—
244C4×D8C2×D511yescharacteristic
245#436—51no—
246#436—51no—
247#436—51no—
248#435—101no—
249#435—101no—
250#435—101no—
251C8×D4—51no—
252C8×D4—101no—
253C8×D4C2×D511yescharacteristic
254C8×D4C2×D511yescharacteristic, complemented
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⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8C2×D511yescharacteristic
275D4⋊C8C2×D511yescharacteristic, complemented
276#322—51no—
277#322—51no—
278#322—51no—
279#322C2×D511yescharacteristic, complemented
280C23×C5—21no—
281C23×C5—21no—
282C22×D5—21no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—81no—
286C22×D5C4×D411yescharacteristic
287C5×D4—21no—
288C5×D4—21no—
289C5×D4—21no—
290C5×D4#13112yes—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5C23×C411yescharacteristic
298C2×C4×C5C22×D411yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C22⋊D5—42no—
301C22⋊D5—42no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—81no—
306C2×Dic5C4×D411yescharacteristic
307C2×Dic5C4×D411yescharacteristic
308C2×Dic5C4×D411yescharacteristic
309D20—21no—
310D20—21no—
311C4×D5—22no—
312C4×D5—21no—
313C4×D5—21no—
314C4×D5—21no—
315C4×D5—21no—
316C4×D5—41no—
317C4×D5—41no—
318C4×D5—81no—
319C4×D5—81no—
320Dic10—21no—
321Dic10—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—21no—
326C5×C8—41no—
327C5×C8—41no—
328C5×C8—41no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—41no—
334#168—41no—
335#168—41no—
336C22×D4—51no—
337C23×C4—101no—
338C2×SD16—51no—
339C2×SD16—51no—
340C2×D8—51no—
341C2×D8C4×D511yescharacteristic
342C2×M16—101no—
343C2×M16—101no—
344C2×M16—101no—
345C22×C8—21no—
346C22×C8—21no—
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×Q8—51no—
357C4×D4—51no—
358C4×D4—51no—
359C4×D4—51no—
360C4×D4—101no—
361C4×D4—101no—
362C4×D4—101no—
363C4×D4C22×D511yescharacteristic
364C4×D4C22×D511yescharacteristic
365#117—101no—
366C2×C4⋊C4—51no—
367C2×C22⋊C4—101no—
368C2×C42—51no—
369#107—51no—
370#107C4×D511yescharacteristic
371#106—51no—
372#106—51no—
373C4⋊C8—51no—
374C4⋊C8—51no—
375C4⋊C8—51no—
376C4⋊C8—51no—
377C4⋊C8—51no—
378C4⋊C8—51no—
379C4⋊C8—101no—
380C4⋊C8—101no—
381C4⋊C8—101no—
382C4⋊C8C22×D511yescharacteristic
383C4⋊C8C22×D511yescharacteristic
384#103—51no—
385#103—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102C4×D511yescharacteristic
391#102C4×D511yescharacteristic
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—51no—
395C22⋊C8—51no—
396C22⋊C8—51no—
397C22⋊C8—51no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403#97—101no—
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—22no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5C2×C4×D411yescharacteristic
420C2×D5—21no—
421C2×D5—21no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C2×D5—84no—
426C2×D5#44412yes—
427C4×C5—21no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5C2×#13111yescharacteristic
431C4×C5#56811yescharacteristic
432C4×C5#57611yescharacteristic
433C4×C5#57711yescharacteristic
434Dic5—21no—
435Dic5—21no—
436Dic5—21no—
437Dic5—41no—
438Dic5—41no—
439Dic5—41no—
440C24—101no—
441C2×Q8—51no—
442C2×D4—51no—
443C2×D4—101no—
444C2×D4—102no—
445C2×D4—101no—
446C2×D4—201no—
447C2×D4C2×C4×D511yescharacteristic
448C2×D4C2×C4×D511yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—401no—
459C22×C4—401no—
460SD16—102no—
461SD16—201no—
462D8—22no—
463D8—201no—
464M16—401no—
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—81no—
475C2×C8—81no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—202no—
480C2×C8—401no—
481C2×C8—401no—
482C2×C8C2×C4×D511yescharacteristic
483C2×C8C2×C4×D511yescharacteristic
484C2×C8D4×D511yescharacteristic
485C2×C8D4×D511yescharacteristic
486C4⋊C4—51no—
487C4⋊C4—51no—
488C4⋊C4—101no—
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—21no—
497C22⋊C4—101no—
498C22⋊C4—101no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C22⋊C4—101no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—101no—
508C42C23×D511yescharacteristic
509C2×C5—42no—
510C2×C5—81no—
511C2×C5#293311yescharacteristic
512C2×C5#294611yescharacteristic
513C2×C5C2×#44411yescharacteristic
514D5—22no—
515D5—81no—
516C23—21no—
517C23—21no—
518C23—51no—
519C23—101no—
520C23—202no—
521C23—202no—
522C23—401no—
523Q8—101no—
524Q8—101no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—101no—
529D4—101no—
530D4—202no—
531D4—202no—
532D4#404712yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—51no—
542C2×C4—102no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
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—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—101no—
566C8—101no—
567C8—101no—
568C8—101no—
569C8—201no—
570C8—201no—
571C8—201no—
572C5#1802011yescharacteristic, complemented, Sylow
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—52no—
580C22—101no—
581C22—101no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22—404no—
586C22C4×D4×D511yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—101no—
591C4—101no—
592C4—101no—
593C4—201no—
594C4—201no—
595C4—201no—
596C4C2×#404711yescharacteristic
597C4#6608411yescharacteristic
598C4#6610811yescharacteristic
599C4#6610911yescharacteristic
600C2—42no—
601C2—81no—
602C2—102no—
603C2—401no—
604C2#1061115411yescharacteristic
605C2#1061159711yescharacteristic
606C2D5×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1580C2
socleC22×C5C2×C4×D4
prime radical#65445C4
cosocleC42×C5C24
hypercenter#1580D5
hypocenterC5#18020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #10611158C2semidirect
3. #10611141C2semidirect
4. C5×#1580C2semidirect
5. #10601672C2semidirect
6. #10601635C2semidirect
7. #10601634C2semidirect
8. #10599327C2semidirect
9. #10599313C2semidirect
10. #10598970C2semidirect
11. D5×D4⋊C8C2semidirect
12. #10598956C2semidirect
13. #10598943C2semidirect
14. #10598875C2semidirect
15. #10598864C2semidirect
20. C5×C8×D4C22semidirect
29. #65301C22semidirect
36. #65119C22semidirect
50. #64968C22semidirect
51. C5×#334C22semidirect
53. C5×D4⋊C8C22semidirect
54. C5×#322C22semidirect
56. D4⋊#168C22semidirect
57. #64704C22semidirect
59. #64700C22semidirect
60. #64699C22semidirect
62. #64678C22semidirect
63. #64676C22semidirect
64. #64675C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
154. #1580D5semidirect
254. C8×D4C2×D5semidirect
267. #334C2×D5semidirect
275. D4⋊C8C2×D5semidirect
279. #322C2×D5semidirect
572. C5#18020semidirect

Maximal subgroups

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

subgroupindex
#106113232
#106111582
#106111412
C5×#15802
#106016722
#106016352
#106016342
#105993272
#105993132
#105989702
D5×D4⋊C82
#105989562
#105989432
#105988752
#105988642
#180205