Finite Group Databasebeta

← #12070524

Subgroups — #12070524

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#10614040C211yesmaximal, characteristic
2#10614034C211yesmaximal, characteristic, complemented
3#10610748C211yesmaximal, characteristic, complemented
4C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5#10601216C211yesmaximal, characteristic, complemented
6#10600529C211yesmaximal, characteristic, complemented
7#10600519C211yesmaximal, characteristic, complemented
8#10598956C211yesmaximal, characteristic, complemented
9#10598955C211yesmaximal, characteristic, complemented
10#10598948C211yesmaximal, characteristic, complemented
11#10598947C211yesmaximal, characteristic, complemented
12#10598946C211yesmaximal, characteristic, complemented
13#10598945C211yesmaximal, characteristic, complemented
14#10598944C211yesmaximal, characteristic, complemented
15#10598943C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17#65813C2211yescharacteristic
18C2×C5×C4⋊C8C2211yescharacteristic
19C2×C4×C5×C8C2211yescharacteristic
20#65507C411yescharacteristic
21#65506C411yescharacteristic
22#65496—21no—
23C2×C22⋊#168—21no—
24#65400—21no—
25C8×C22⋊D5—21no—
26C4×#687C2211yescharacteristic
27C4×#687C2211yescharacteristic
28#65305C411yescharacteristic
29#65305C411yescharacteristic
30C4×#686C2211yescharacteristic
31C4×#686C2211yescharacteristic
32#65301C2211yescharacteristic
33#65301C2211yescharacteristic
34#65300—21no—
35#65300—21no—
36D4×#168C2211yescharacteristic
37D4×#168C2211yescharacteristic
38#65298C411yescharacteristic
39#65298C411yescharacteristic
40#65259C411yescharacteristic
41#65257C411yescharacteristic
42#65215C2211yescharacteristic
43#65214C2211yescharacteristic
44#65214C2211yescharacteristic
45#65129—21no—
46#65128—21no—
47#65127C2211yescharacteristic, complemented
48#65123C2211yescharacteristic, complemented
49#65120C2211yescharacteristic, complemented
50#65119C2211yescharacteristic, complemented
51C5×D4⋊C8C2211yescharacteristic
52C5×D4⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×D4⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic, complemented
56#64700C2211yescharacteristic, complemented
57#64699C2211yescharacteristic, complemented
58#64699C2211yescharacteristic, complemented
59#64679C2211yescharacteristic, complemented
60#64679C2211yescharacteristic, complemented
61#64676C2211yescharacteristic, complemented
62#64676C2211yescharacteristic, complemented
63#64674C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18020—51nomaximal, Sylow
68C22×C5×D4C2×C411yescharacteristic
69C23×C4×C5—21no—
70C22×C5×C8—21no—
71C22×C5×C8—21no—
72C4×C5×D4—21no—
73C4×C5×D4—21no—
74C4×C5×D4C2×C411yescharacteristic
75C4×C5×D4C2×C411yescharacteristic
76C4×C5×D4C2311yescharacteristic
77C4×C5×D4C2311yescharacteristic
78C2×C5×C4⋊C4C2×C411yescharacteristic
79C2×C5×C22⋊C4—21no—
80C2×C42×C5C2311yescharacteristic
81C2×#687C2×C411yescharacteristic
82C2×#687C2×C411yescharacteristic
83C2×#686C2×C411yescharacteristic
84C2×#686C2×C411yescharacteristic
85#4076C2×C411yescharacteristic
86#4075—21no—
87C4×C22⋊D5—21no—
88#4070C2×C411yescharacteristic
89C2×#681—21no—
90C2×#681—21no—
91C22×#168—21no—
92C22×#168—21no—
93C2×#676—21no—
94C2×C8×D5—21no—
95#4022—21no—
96#4021C2×C411yescharacteristic
97C4×D20C2311yescharacteristic
98#4018—21no—
99#4016C2×C411yescharacteristic
100C4×Dic10C2311yescharacteristic
101C5×C4⋊C8—21no—
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C4×C5×C8—21no—
105C4×C5×C8C2311yescharacteristic
106C4×C5×C8C2311yescharacteristic
107#3964C2×C411yescharacteristic
108#3964C2×C411yescharacteristic
109#3964C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111C22⋊#168—21no—
112C22⋊#168—21no—
113C22⋊#168—21no—
114C22⋊#168—21no—
115C22⋊#168—21no—
116C22⋊#168C2×C411yescharacteristic
117C22⋊#168C2×C411yescharacteristic
118C22⋊#168D411yescharacteristic
119C22⋊#168D411yescharacteristic
120#3952—21no—
121#3952—21no—
122#3947—21no—
123#3946—21no—
124#3946—21no—
125C8×Dic5—21no—
126#3942C2×C411yescharacteristic
127#3942C2×C411yescharacteristic
128#3941C2×C411yescharacteristic
129#3941C2×C411yescharacteristic
130#3940C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3939C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134C4⋊#168C2×C411yescharacteristic
135C4⋊#168C2×C411yescharacteristic
136C4⋊#168D411yescharacteristic
137C4⋊#168D411yescharacteristic
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140#3935—21no—
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#1580—51no—
155SD16⋊C8—51no—
156#1573—51no—
157#1494—51no—
158C2×D4⋊C8D511yescharacteristic, complemented
159#1452—51no—
160C24×C5—21no—
161C2×C5×D4—22no—
162C2×C5×D4—21no—
163C2×C5×D4—41no—
164C2×C5×D4C22×C411yescharacteristic
165C2×C5×D4C22×C411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—81no—
172C22×C4×C5—81no—
173C22×C4×C5C22×C411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C2×C22⋊D5—21no—
177C2×D20C22×C411yescharacteristic
178C2×C4×D5—21no—
179C2×Dic10C22×C411yescharacteristic
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—42no—
185C2×C5×C8—81no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4C22×C411yescharacteristic
188C5×C4⋊C4C22×C411yescharacteristic
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C42×C5C22×C411yescharacteristic
194C42×C5C2×D411yescharacteristic
195C42×C5#4111yescharacteristic
196C42×C5C2411yescharacteristic
197C22⋊Dic5—21no—
198#687—22no—
199#687—41no—
200#686—22no—
201#686—41no—
202#685—21no—
203#685—21no—
204#685—21no—
205#685—21no—
206C4⋊Dic5C22×C411yescharacteristic
207C4⋊Dic5C22×C411yescharacteristic
208#683—21no—
209#683—21no—
210#683—21no—
211#683—21no—
212C4×Dic5—21no—
213#681—81no—
214#681—81no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—81no—
218C2×#168—81no—
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C2×#168C2×D411yescharacteristic
225C2×#168C2×D411yescharacteristic
226C2×#168C2×D411yescharacteristic
227#676—81no—
228C8×D5—81no—
229#529—51no—
230C2×C4×D4C2×D511yescharacteristic
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×D8—51no—
245#436—51no—
246#436—51no—
247#436—51no—
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⋊C8C2×D511yescharacteristic
261#407—101no—
262C2×C22⋊C8—101no—
263C2×C4×C8C2×D511yescharacteristic
264#335—51no—
265#335—51no—
266#334—51no—
267#334—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8C2×D511yescharacteristic
273D4⋊C8C2×D511yescharacteristic
274D4⋊C8C2×D511yescharacteristic
275D4⋊C8C2×D511yescharacteristic
276#322—51no—
277#322—51no—
278#322—51no—
279#322—51no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—42no—
283C23×C5—42no—
284C23×C5—81no—
285C23×C5C4×D411yescharacteristic
286C22×D5—21no—
287C5×D4—21no—
288C5×D4—21no—
289C5×D4—21no—
290C5×D4—42no—
291C5×D4#13112yes—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—81no—
304C2×C4×C5—81no—
305C2×C4×C5—81no—
306C2×C4×C5C4×D411yescharacteristic
307C2×C4×C5C4×D411yescharacteristic
308C2×C4×C5C4×D411yescharacteristic
309C2×C4×C5C23×C411yescharacteristic
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C22⋊D5—42no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316D20—21no—
317D20—21no—
318C4×D5—41no—
319C4×D5—41no—
320Dic10—21no—
321Dic10—21no—
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325C5×C8—41no—
326#168—21no—
327#168—21no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—21no—
334#168—41no—
335#168—41no—
336C22×D4C4×D511yescharacteristic
337C23×C4—21no—
338C2×SD16—51no—
339C2×SD16—51no—
340C2×D8—51no—
341C2×D8—51no—
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—21no—
358C4×D4—21no—
359C4×D4—51no—
360C4×D4—101no—
361C4×D4C4×D511yescharacteristic
362C4×D4C4×D511yescharacteristic
363C4×D4C22×D511yescharacteristic
364C4×D4C22×D511yescharacteristic
365#117—101no—
366C2×C4⋊C4C4×D511yescharacteristic
367C2×C22⋊C4—21no—
368C2×C42C22×D511yescharacteristic
369#107—51no—
370#107—51no—
371#106—51no—
372#106—51no—
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#103—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102—51no—
391#102—51no—
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—101no—
404#97—101no—
405C4×C8—21no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—51no—
410C4×C8—101no—
411C4×C8C22×D511yescharacteristic
412C4×C8C22×D511yescharacteristic
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—22no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—84no—
422C22×C5#44412yes—
423C22×C5C2×C4×D411yescharacteristic
424C2×D5—41no—
425C2×D5—41no—
426C2×D5—41no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5C2×#13111yescharacteristic
434C4×C5#56811yescharacteristic
435C4×C5#57611yescharacteristic
436C4×C5#57711yescharacteristic
437Dic5—41no—
438Dic5—41no—
439Dic5—41no—
440C24—21no—
441C2×Q8—51no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—51no—
446C2×D4—101no—
447C2×D4C2×C4×D511yescharacteristic
448C2×D4C2×C4×D511yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—101no—
457C22×C4C2×C4×D511yescharacteristic
458C22×C4D4×D511yescharacteristic
459C22×C4#71111yescharacteristic
460SD16—102no—
461SD16—201no—
462D8—102no—
463D8—201no—
464M16—401no—
465M16—401no—
466M16—401no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—51no—
475C2×C8—51no—
476C2×C8—51no—
477C2×C8—51no—
478C2×C8—51no—
479C2×C8—51no—
480C2×C8—81no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—401no—
484C2×C8—401no—
485C2×C8—401no—
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—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C22⋊C4—101no—
504C42—101no—
505C42C2×C4×D511yescharacteristic
506C42D4×D511yescharacteristic
507C42#71111yescharacteristic
508C42C23×D511yescharacteristic
509C2×C5—22no—
510C2×C5—42no—
511C2×C5—81no—
512C2×C5#293311yescharacteristic
513C2×C5#294611yescharacteristic
514C2×C5C2×#44411yescharacteristic
515D5—81no—
516C23—21no—
517C23—21no—
518C23—42no—
519C23—42no—
520C23—81no—
521C23—101no—
522C23#402711yescharacteristic
523Q8—101no—
524Q8—101no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—101no—
530D4—101no—
531D4—202no—
532D4#404712yes—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4#402711yescharacteristic
553C2×C4#402711yescharacteristic
554C2×C4#402711yescharacteristic
555C2×C4C22×C4×D511yescharacteristic
556C2×C4C2×D4×D511yescharacteristic
557C2×C4C2×#71111yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—101no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—101no—
568C8—101no—
569C8—101no—
570C8—201no—
571C8—201no—
572C5#1802011yescharacteristic, complemented, Sylow
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22#6511212yes—
586C22C2×#402711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—201no—
594C4—201no—
595C4—201no—
596C4C2×#404711yescharacteristic
597C4#6607911yescharacteristic
598C4#6609111yescharacteristic
599C4#6609611yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—401no—
604C2#1061032711yescharacteristic
605C2#1061045711yescharacteristic
606C2C2×#6511211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC2×C5×D4⋊C8C2
socleC22×C5C2×C4×D4
prime radical#65506C4
cosocleC42×C5C24
hypercenterC2×D4⋊C8D5
hypocenterC5#18020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10614034C2semidirect
3. #10610748C2semidirect
4. C2×C5×D4⋊C8C2semidirect
5. #10601216C2semidirect
6. #10600529C2semidirect
7. #10600519C2semidirect
8. #10598956C2semidirect
9. #10598955C2semidirect
10. #10598948C2semidirect
11. #10598947C2semidirect
12. #10598946C2semidirect
13. #10598945C2semidirect
14. #10598944C2semidirect
15. #10598943C2semidirect
47. #65127C22semidirect
48. #65123C22semidirect
49. #65120C22semidirect
50. #65119C22semidirect
55. #64700C22semidirect
56. #64700C22semidirect
57. #64699C22semidirect
58. #64699C22semidirect
59. #64679C22semidirect
60. #64679C22semidirect
61. #64676C22semidirect
62. #64676C22semidirect
63. #64674C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
158. C2×D4⋊C8D5semidirect
572. C5#18020semidirect

Maximal subgroups

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

subgroupindex
#106140402
#106140342
#106107482
C2×C5×D4⋊C82
#106012162
#106005292
#106005192
#105989562
#105989552
#105989482
#105989472
#105989462
#105989452
#105989442
#105989432
#180205