Finite Group Databasebeta

← #12070330

Subgroups — #12070330

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614040C211yesmaximal, characteristic
2D4×#681C211yesmaximal, characteristic, complemented
3#10611011C211yesmaximal, characteristic, complemented
4C5×#1478C211yesmaximal, characteristic, complemented
5#10601557C211yesmaximal, characteristic, complemented
6#10601541C211yesmaximal, characteristic, complemented
7#10601536C211yesmaximal, characteristic, complemented
8#10598956C211yesmaximal, characteristic, complemented
9#10598954C211yesmaximal, characteristic, complemented
10#10598952C211yesmaximal, characteristic, complemented
11#10598950C211yesmaximal, characteristic, complemented
12#10598947C211yesmaximal, characteristic, complemented
13#10598946C211yesmaximal, characteristic, complemented
14#10598943C211yesmaximal, characteristic, complemented
15#10598941C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C22×#681—21no—
18#65813C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C5×#431C2211yescharacteristic
21#65507C411yescharacteristic
22#65506C411yescharacteristic
23#65496—21no—
24C4×#687C2211yescharacteristic
25C4×#687C2211yescharacteristic
26#65305C411yescharacteristic
27#65305C411yescharacteristic
28C4×#686C2211yescharacteristic
29C4×#686C2211yescharacteristic
30#65301C2211yescharacteristic
31#65301C2211yescharacteristic
32#65300—21no—
33#65300—21no—
34D4×#168C2211yescharacteristic
35D4×#168C2211yescharacteristic
36#65298C411yescharacteristic
37#65298C411yescharacteristic
38#65259C411yescharacteristic
39#65257C411yescharacteristic
40#65214C2211yescharacteristic
41#65213C2211yescharacteristic
42C4×#681C2211yescharacteristic
43#65127C2211yescharacteristic, complemented
44#65123C2211yescharacteristic, complemented
45#65120C2211yescharacteristic, complemented
46#65119C2211yescharacteristic, complemented
47#65018—21no—
48#65017—21no—
49#64979—21no—
50#64978—21no—
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#64675C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#18006—51nomaximal, Sylow
68C22×C5×D4C2×C411yescharacteristic
69C23×C4×C5—21no—
70C4×C5×D4—21no—
71C4×C5×D4—21no—
72C4×C5×D4C2×C411yescharacteristic
73C4×C5×D4C2×C411yescharacteristic
74C4×C5×D4C2311yescharacteristic
75C4×C5×D4C2311yescharacteristic
76C2×C5×C4⋊C4C2×C411yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C42×C5C2311yescharacteristic
79C2×#687C2×C411yescharacteristic
80C2×#687C2×C411yescharacteristic
81C2×#686C2×C411yescharacteristic
82C2×#686C2×C411yescharacteristic
83#4076C2×C411yescharacteristic
84#4075—21no—
85C4×C22⋊D5—21no—
86#4070C2×C411yescharacteristic
87C2×#681—21no—
88C2×#681—21no—
89C2×#681—21no—
90C2×#681—44no—
91C2×#681D411yescharacteristic
92C2×#681D411yescharacteristic
93C22×#168—21no—
94C22×#168—21no—
95C2×#676—21no—
96C2×C8×D5—21no—
97#4022—21no—
98#4021C2×C411yescharacteristic
99C4×D20C2311yescharacteristic
100#4018—21no—
101#4016C2×C411yescharacteristic
102C4×Dic10C2311yescharacteristic
103C5×C4⋊C8—21no—
104C5×C4⋊C8C2311yescharacteristic
105C5×C4⋊C8C2311yescharacteristic
106C5×C22⋊C8—21no—
107C5×C22⋊C8—21no—
108C4×C5×C8—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111#3964C2×C411yescharacteristic
112#3964C2×C411yescharacteristic
113#3964C2×C411yescharacteristic
114#3964C2×C411yescharacteristic
115C22⋊#168—21no—
116C22⋊#168—21no—
117C22⋊#168—21no—
118C22⋊#168—21no—
119C22⋊#168C2×C411yescharacteristic
120C22⋊#168C2×C411yescharacteristic
121#3952—21no—
122#3952—21no—
123#3947—21no—
124#3946—21no—
125#3946—21no—
126C8×Dic5—21no—
127#3942C2×C411yescharacteristic
128#3942C2×C411yescharacteristic
129#3941C2×C411yescharacteristic
130#3941C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3940C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134#3939C2×C411yescharacteristic
135C4⋊#168—21no—
136C4⋊#168C2×C411yescharacteristic
137C4⋊#168C2×C411yescharacteristic
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140#3935D411yescharacteristic
141#3935D411yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#3105—51no—
147#2969—51no—
148D4×M16—51no—
149#1594—51no—
150#1590—51no—
151#1588—51no—
152#1586—51no—
153#1582—51no—
154#1581—51no—
155SD16⋊C8—51no—
156C8×D8—51no—
157#1574—51no—
158#1495—51no—
159#1478D511yescharacteristic, complemented
160#1453—51no—
161C24×C5—21no—
162C2×C5×D4—22no—
163C2×C5×D4—21no—
164C2×C5×D4—41no—
165C2×C5×D4C22×C411yescharacteristic
166C2×C5×D4C22×C411yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—42no—
173C22×C4×C5—42no—
174C22×C4×C5C22×C411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5#4111yescharacteristic
177C2×C22⋊D5—21no—
178C2×D20C22×C411yescharacteristic
179C2×C4×D5—21no—
180C2×Dic10C22×C411yescharacteristic
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4C22×C411yescharacteristic
187C5×C4⋊C4C22×C411yescharacteristic
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C42×C5C22×C411yescharacteristic
193C42×C5C2×D411yescharacteristic
194C42×C5#4111yescharacteristic
195C42×C5C2411yescharacteristic
196C22⋊Dic5—21no—
197#687—22no—
198#687—41no—
199#686—22no—
200#686—41no—
201#685—21no—
202#685—21no—
203#685—21no—
204#685—21no—
205C4⋊Dic5C22×C411yescharacteristic
206C4⋊Dic5C22×C411yescharacteristic
207#683—21no—
208#683—21no—
209#683—21no—
210#683—21no—
211C4×Dic5—21no—
212#681—22no—
213#681—41no—
214#681—42no—
215#681—42no—
216#681—42no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—42no—
220C2×#168—42no—
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C22×C411yescharacteristic
224C2×#168C22×C411yescharacteristic
225C2×#168C2×D411yescharacteristic
226C2×#168C2×D411yescharacteristic
227C2×#168C2×D411yescharacteristic
228C2×#168C2×D411yescharacteristic
229#676—42no—
230C8×D5—42no—
231C22×M16—101no—
232#529—51no—
233C2×C4×D4C2×D511yescharacteristic
234#484—51no—
235#481—51no—
236#478—51no—
237#478—51no—
238#463—51no—
239#463—51no—
240#450—51no—
241#447—51no—
242#446—51no—
243C8×Q8—51no—
244C4×SD16—51no—
245C4×SD16—51no—
246C4×D8—51no—
247C4×D8—51no—
248#436—51no—
249#436—51no—
250#436—51no—
251#436—101no—
252#435—101no—
253#435—101no—
254#435—101no—
255C8×D4—51no—
256C8×D4—51no—
257C8×D4—51no—
258#433—101no—
259#431—51no—
260#431C2×D511yescharacteristic
261#431C2×D511yescharacteristic
262#423—51no—
263#407—101no—
264#405—101no—
265C4×M16—51no—
266#335—51no—
267#335—51no—
268#334—51no—
269#334—51no—
270Q8⋊C8—51no—
271Q8⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8C2×D511yescharacteristic
275D4⋊C8C2×D511yescharacteristic
276D4⋊C8C2×D511yescharacteristic
277D4⋊C8C2×D511yescharacteristic
278#322—51no—
279#322—51no—
280#322—51no—
281C82—51no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—42no—
285C23×C5—42no—
286C23×C5—81no—
287C23×C5C4×D411yescharacteristic
288C22×D5—21no—
289C5×D4—21no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—42no—
293C5×D4#13112yes—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5C4×D411yescharacteristic
309C2×C4×C5C4×D411yescharacteristic
310C2×C4×C5C4×D411yescharacteristic
311C2×C4×C5C23×C411yescharacteristic
312C2×C4×C5C22×D411yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C22⋊D5—81no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318D20—21no—
319D20—21no—
320C4×D5—41no—
321C4×D5—41no—
322Dic10—21no—
323Dic10—21no—
324C5×C8—41no—
325C5×C8—41no—
326C5×C8—41no—
327C5×C8—41no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—21no—
334#168—21no—
335#168—41no—
336#168—41no—
337#168AGL(1,ℤ/8)12yes—
338C22×D4C4×D511yescharacteristic
339C23×C4—21no—
340C2×SD16—51no—
341C2×SD16—51no—
342C2×D8—51no—
343C2×D8—51no—
344C2×M16—51no—
345C2×M16—51no—
346C2×M16—101no—
347C2×M16—101no—
348C2×M16—101no—
349C2×M16—101no—
350C2×M16—204no—
351C22×C8—101no—
352C22×C8—101no—
353C22×C8—101no—
354#126—101no—
355#125—51no—
356#124—51no—
357#123—101no—
358C22⋊Q8—51no—
359#121—51no—
360C4×Q8—51no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—51no—
364C4×D4—101no—
365C4×D4C4×D511yescharacteristic
366C4×D4C4×D511yescharacteristic
367C4×D4C22×D511yescharacteristic
368C4×D4C22×D511yescharacteristic
369#117—101no—
370C2×C4⋊C4C4×D511yescharacteristic
371C2×C22⋊C4—21no—
372C2×C42C22×D511yescharacteristic
373#107—51no—
374#107—51no—
375#106—51no—
376#106—51no—
377C4⋊C8—21no—
378C4⋊C8—51no—
379C4⋊C8—51no—
380C4⋊C8—51no—
381C4⋊C8—51no—
382C4⋊C8—101no—
383C4⋊C8—101no—
384C4⋊C8—101no—
385C4⋊C8C22×D511yescharacteristic
386C4⋊C8C22×D511yescharacteristic
387#103—51no—
388#103—51no—
389#102—51no—
390#102—51no—
391#102—51no—
392#102—51no—
393#102—51no—
394#102—51no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—51no—
398C22⋊C8—51no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403C22⋊C8—101no—
404C22⋊C8—101no—
405#97—51no—
406#97—51no—
407#97—101no—
408C4×C8—21no—
409C4×C8—51no—
410C4×C8—51no—
411C4×C8—51no—
412C4×C8—51no—
413C4×C8—101no—
414C4×C8C22×D511yescharacteristic
415C4×C8C22×D511yescharacteristic
416C22×C5—21no—
417C22×C5—22no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—84no—
426C22×C5C2×C4×D411yescharacteristic
427C2×D5—41no—
428C2×D5—41no—
429C2×D5—41no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—21no—
433C4×C5—21no—
434C4×C5—41no—
435C4×C5—41no—
436C4×C5C2×#13111yescharacteristic
437C4×C5#56811yescharacteristic
438C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
439C4×C5#57511yescharacteristic
440Dic5—41no—
441Dic5—41no—
442Dic5—41no—
443C24—21no—
444C2×Q8—51no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—51no—
449C2×D4—101no—
450C2×D4C2×C4×D511yescharacteristic
451C2×D4C2×C4×D511yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—101no—
460C22×C4C2×C4×D511yescharacteristic
461C22×C4D4×D511yescharacteristic
462C22×C4#71111yescharacteristic
463SD16—102no—
464SD16—201no—
465D8—102no—
466D8—201no—
467M16—102no—
468M16—202no—
469M16—202no—
470M16—201no—
471M16—202no—
472M16—202no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—51no—
478C2×C8—51no—
479C2×C8—51no—
480C2×C8—51no—
481C2×C8—51no—
482C2×C8—51no—
483C2×C8—51no—
484C2×C8—51no—
485C2×C8—101no—
486C2×C8—101no—
487C2×C8—202no—
488C2×C8—202no—
489C2×C8—202no—
490C4⋊C4—21no—
491C4⋊C4—51no—
492C4⋊C4—51no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4C2×C4×D511yescharacteristic
498C4⋊C4C2×C4×D511yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—101no—
504C22⋊C4—101no—
505C22⋊C4—101no—
506C22⋊C4—101no—
507C22⋊C4—101no—
508C42—101no—
509C42C2×C4×D511yescharacteristic
510C42D4×D511yescharacteristic
511C42#71111yescharacteristic
512C42C23×D511yescharacteristic
513C2×C5—41no—
514C2×C5—42no—
515C2×C5—81no—
516C2×C5#293311yescharacteristic
517C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
518C2×C5#295711yescharacteristic
519D5—81no—
520C23—21no—
521C23—21no—
522C23—42no—
523C23—42no—
524C23—81no—
525C23—101no—
526C23#402711yescharacteristic
527Q8—101no—
528Q8—101no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—42no—
533D4—101no—
534D4—101no—
535D4—401no—
536D4#404712yes—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4#402711yescharacteristic
557C2×C4#402711yescharacteristic
558C2×C4#402711yescharacteristic
559C2×C4C22×C4×D511yescharacteristic
560C2×C4C2×D4×D511yescharacteristic
561C2×C4C2×#71111yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—52no—
567C8—101no—
568C8—101no—
569C8—101no—
570C8—101no—
571C8—101no—
572C8—101no—
573C8—101no—
574C8—201no—
575C8—201no—
576C5#1800611yescharacteristic, complemented, Sylow
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—201no—
588C22—201no—
589C22—201no—
590C22C2×#402711yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—201no—
598C4—201no—
599C4—201no—
600C4C2×#404711yescharacteristic
601C4#6607911yescharacteristic
602C4D5×AGL(1,ℤ/8)11yescharacteristic
603C4#6610711yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—401no—
608C2#1061032711yescharacteristic
609C2#1061064511yescharacteristic
610C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1478C2
socleC22×C5C2×C4×D4
prime radical#65506C4
cosocleC42×C5C24
hypercenter#1478D5
hypocenterC5#18006
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. D4×#681C2semidirect
3. #10611011C2semidirect
4. C5×#1478C2semidirect
5. #10601557C2semidirect
6. #10601541C2semidirect
7. #10601536C2semidirect
8. #10598956C2semidirect
9. #10598954C2semidirect
10. #10598952C2semidirect
11. #10598950C2semidirect
12. #10598947C2semidirect
13. #10598946C2semidirect
14. #10598943C2semidirect
15. #10598941C2semidirect
43. #65127C22semidirect
44. #65123C22semidirect
45. #65120C22semidirect
46. #65119C22semidirect
55. #64700C22semidirect
56. #64700C22semidirect
57. #64699C22semidirect
58. #64699C22semidirect
59. #64679C22semidirect
60. #64679C22semidirect
61. #64676C22semidirect
62. #64676C22semidirect
63. #64675C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
159. #1478D5semidirect
576. C5#18006semidirect

Maximal subgroups

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

subgroupindex
#106140402
D4×#6812
#106110112
C5×#14782
#106015572
#106015412
#106015362
#105989562
#105989542
#105989522
#105989502
#105989472
#105989462
#105989432
#105989412
#180065