Finite Group Databasebeta

← #12069358

Subgroups — #12069358

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#10611031C211yesmaximal, characteristic
2#10611017C211yesmaximal, characteristic, complemented
3#10610784C211yesmaximal, characteristic, complemented
4C5×#1574C211yesmaximal, characteristic, complemented
5#10601552C211yesmaximal, characteristic, complemented
6#10601537C211yesmaximal, characteristic, complemented
7#10601289C211yesmaximal, characteristic, complemented
8#10599354C211yesmaximal, characteristic, complemented
9#10599352C211yesmaximal, characteristic, complemented
10#10599351C211yesmaximal, characteristic, complemented
11#10599349C211yesmaximal, characteristic, complemented
12#10599314C211yesmaximal, characteristic, complemented
13#10599312C211yesmaximal, characteristic, complemented
14#10599311C211yesmaximal, characteristic, complemented
15#10599309C211yesmaximal, characteristic, complemented
16#65813C2211yescharacteristic
17C2×C4×D20C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C5×#423C2211yescharacteristic
21#65417—21no—
22#65416—21no—
23#65214C2211yescharacteristic
24#65214C2211yescharacteristic
25#65136C411yescharacteristic
26#65136C411yescharacteristic
27#65133C411yescharacteristic
28#65133C411yescharacteristic
29#65129—21no—
30#65128—21no—
31#65127C2211yescharacteristic, complemented
32#65123C2211yescharacteristic
33#65123C2211yescharacteristic
34#65123C2211yescharacteristic
35#65123C2211yescharacteristic
36#65123C2211yescharacteristic, complemented
37#65120C2211yescharacteristic, complemented
38#65119C2211yescharacteristic, complemented
39#65024C411yescharacteristic
40#65021C411yescharacteristic
41#65020C411yescharacteristic
42D5×C22⋊C8—21no—
43D5×C22⋊C8—21no—
44#65011C411yescharacteristic
45C4×D40C2211yescharacteristic
46C4×D40C2211yescharacteristic
47C4×#677C2211yescharacteristic
48C4×#677C2211yescharacteristic
49C8×D20—21no—
50C8×D20—21no—
51C5×#335C2211yescharacteristic, complemented
52C5×#335C2211yescharacteristic, complemented
53C5×#334C2211yescharacteristic, complemented
54C5×#334C2211yescharacteristic, complemented
55#64704C2211yescharacteristic, complemented
56#64704C2211yescharacteristic, complemented
57#64703C2211yescharacteristic
58#64703C2211yescharacteristic
59#64703C2211yescharacteristic
60#64703C2211yescharacteristic
61#64703C2211yescharacteristic, complemented
62#64703C2211yescharacteristic, complemented
63#64675C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#17918—51nomaximal, Sylow
68C22×D20C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×M16—21no—
71C2×C42×C5C2311yescharacteristic
72#4076C2×C411yescharacteristic
73#4075—21no—
74C4×C22⋊D5—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C2×C411yescharacteristic
77#4070C2×C411yescharacteristic
78C2×D40C2×C411yescharacteristic
79C2×D40C2×C411yescharacteristic
80C2×#677C2×C411yescharacteristic
81C2×#677C2×C411yescharacteristic
82C2×#676—21no—
83C2×C8×D5—21no—
84C2×C8×D5—21no—
85C2×C8×D5—21no—
86C2×C8×D5—21no—
87C2×C8×D5—21no—
88#4022—21no—
89#4021C2×C411yescharacteristic
90C4×D20—21no—
91C4×D20—21no—
92C4×D20C2×C411yescharacteristic
93C4×D20C2×C411yescharacteristic
94C4×D20C2311yescharacteristic
95C4×D20C2311yescharacteristic
96C4×D20C2311yescharacteristic
97#4018—21no—
98#4016C2×C411yescharacteristic
99C4×Dic10C2311yescharacteristic
100C5×C4⋊C8—21no—
101C5×C4⋊C8C2×C411yescharacteristic
102C5×C4⋊C8C2×C411yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×C4⋊C8C2311yescharacteristic
106C5×C4⋊C8C2311yescharacteristic
107C5×C22⋊C8—21no—
108C5×C22⋊C8C2×C411yescharacteristic
109C5×C22⋊C8C2×C411yescharacteristic
110C4×C5×C8—21no—
111C4×C5×C8C2311yescharacteristic
112C4×C5×C8C2311yescharacteristic
113C22⋊#168—21no—
114C22⋊#168D411yescharacteristic
115C22⋊#168D411yescharacteristic
116#3953C2×C411yescharacteristic
117#3953C2×C411yescharacteristic
118#3953C2×C411yescharacteristic
119#3953C2×C411yescharacteristic
120#3953C2×C411yescharacteristic
121#3953C2×C411yescharacteristic
122#3952—21no—
123#3952—21no—
124#3952—21no—
125#3952—21no—
126#3952—21no—
127#3952—21no—
128#3950C2×C411yescharacteristic
129#3950C2×C411yescharacteristic
130#3949C2×C411yescharacteristic
131#3949C2×C411yescharacteristic
132#3948C2×C411yescharacteristic
133#3948C2×C411yescharacteristic
134#3947—21no—
135#3946—21no—
136#3946—21no—
137C8×Dic5—21no—
138C4⋊#168—21no—
139C4⋊#168D411yescharacteristic
140C4⋊#168D411yescharacteristic
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105—51no—
146#2993—51no—
147#2972—51no—
148#1586—51no—
149#1585—51no—
150#1582—51no—
151#1581—51no—
152#1580—51no—
153SD16⋊C8—51no—
154C8×SD16—51no—
155C8×D8—51no—
156#1574D511yescharacteristic, complemented
157#1486—51no—
158#1482—51no—
159#1454—51no—
160C23×D5—21no—
161C22×C4×C5C22×C411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C2×C22⋊D5—21no—
165C22×Dic5—21no—
166C2×D20—21no—
167C2×D20—22no—
168C2×D20—22no—
169C2×D20C22×C411yescharacteristic
170C2×D20C22×C411yescharacteristic
171C2×D20C22×C411yescharacteristic
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—81no—
178C2×C4×D5—81no—
179C2×Dic10C22×C411yescharacteristic
180C5×M16—81no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C22×C411yescharacteristic
187C2×C5×C8C22×C411yescharacteristic
188C2×C5×C8C22×C411yescharacteristic
189C42×C5C22×C411yescharacteristic
190C42×C5C2×D411yescharacteristic
191C42×C5#4111yescharacteristic
192C42×C5C2411yescharacteristic
193C22⋊Dic5—21no—
194#685—21no—
195#685—21no—
196#685—21no—
197#685—21no—
198#685—21no—
199#685—21no—
200#685—21no—
201#685—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5C22×C411yescharacteristic
204C4⋊Dic5C22×C411yescharacteristic
205C4⋊Dic5C22×C411yescharacteristic
206C4⋊Dic5C22×C411yescharacteristic
207#683—21no—
208#683—21no—
209#683—21no—
210#683—21no—
211C4×Dic5—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168C2×D411yescharacteristic
215C2×#168C2×D411yescharacteristic
216C2×#168C2×D411yescharacteristic
217C2×#168C2×D411yescharacteristic
218D40—22no—
219D40—22no—
220#677—22no—
221#677—22no—
222#676—81no—
223C8×D5—81no—
224C8×D5—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#446—51no—
239C8×Q8—51no—
240C4×SD16—51no—
241C4×SD16—51no—
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—51no—
252C8×D4—101no—
253C8×D4—101no—
254#433—101no—
255#431—51no—
256#431—51no—
257#431C2×D511yescharacteristic
258#431C2×D511yescharacteristic
259#424—101no—
260#423C2×D511yescharacteristic
261C2×C22⋊C8—101no—
262C2×C22⋊C8—101no—
263#335C2×D511yescharacteristic, complemented
264#335C2×D511yescharacteristic, complemented
265#334C2×D511yescharacteristic, complemented
266#334C2×D511yescharacteristic, complemented
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275#322—51no—
276#322—51no—
277#322—51no—
278C82—51no—
279C23×C5C4×D411yescharacteristic
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—24no—
283C22×D5—21no—
284C22×D5—81no—
285C22×D5—81no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—41no—
291C2×C4×C5C4×D411yescharacteristic
292C2×C4×C5C4×D411yescharacteristic
293C2×C4×C5C4×D411yescharacteristic
294C2×C4×C5C23×C411yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C2×#4111yescharacteristic
297C22⋊D5—81no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—81no—
304D20—24no—
305D20—21no—
306D20—21no—
307D20—21no—
308D20—21no—
309D20#13112yes—
310D20#13112yes—
311C4×D5—41no—
312C4×D5—41no—
313C4×D5—41no—
314C4×D5—41no—
315C4×D5—41no—
316C4×D5—41no—
317C4×D5—81no—
318C4×D5—81no—
319Dic10—21no—
320Dic10—21no—
321C5×C8—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—41no—
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—
335C22×D4—51no—
336C23×C4—101no—
337C2×SD16—51no—
338C2×SD16—51no—
339C2×D8—51no—
340C2×D8—51no—
341C2×M16—21no—
342C2×M16—101no—
343C22×C8—101no—
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×Q8—51no—
355C4×D4—51no—
356C4×D4—51no—
357C4×D4—51no—
358C4×D4—51no—
359C4×D4—51no—
360C4×D4—101no—
361C4×D4—101no—
362C4×D4—101no—
363#117—101no—
364C2×C4⋊C4—51no—
365C2×C22⋊C4—101no—
366C2×C42C22×D511yescharacteristic
367#107—51no—
368#107—51no—
369#106—51no—
370#106—51no—
371C4⋊C8—21no—
372C4⋊C8—51no—
373C4⋊C8—51no—
374C4⋊C8—101no—
375C4⋊C8—101no—
376C4⋊C8—101no—
377C4⋊C8C4×D511yescharacteristic
378C4⋊C8C4×D511yescharacteristic
379C4⋊C8C22×D511yescharacteristic
380C4⋊C8C22×D511yescharacteristic
381C4⋊C8C22×D511yescharacteristic
382C4⋊C8C22×D511yescharacteristic
383#103—51no—
384#103—51no—
385#102—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102—51no—
391C22⋊C8—21no—
392C22⋊C8—51no—
393C22⋊C8—51no—
394C22⋊C8—101no—
395C22⋊C8—101no—
396C22⋊C8—101no—
397C22⋊C8—101no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8C4×D511yescharacteristic
402C22⋊C8C4×D511yescharacteristic
403#97—101no—
404C4×C8—21no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—101no—
410C4×C8C22×D511yescharacteristic
411C4×C8C22×D511yescharacteristic
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5C2×C4×D411yescharacteristic
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—41no—
419C2×D5—41no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C2×D5—84no—
426C4×C5—21no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5C2×#13111yescharacteristic
431C4×C5C2×#13111yescharacteristic
432C4×C5#57611yescharacteristic
433C4×C5#57711yescharacteristic
434Dic5—41no—
435Dic5—41no—
436Dic5—41no—
437Dic5—41no—
438Dic5—41no—
439C24—101no—
440C2×Q8—51no—
441C2×D4—51no—
442C2×D4—51no—
443C2×D4—51no—
444C2×D4—102no—
445C2×D4—102no—
446C2×D4—101no—
447C2×D4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—401no—
455C22×C4—401no—
456C22×C4C2×C4×D511yescharacteristic
457C22×C4D4×D511yescharacteristic
458C22×C4#71311yescharacteristic
459SD16—102no—
460SD16—102no—
461D8—102no—
462D8—102no—
463M16—81no—
464M16—401no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—51no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—401no—
476C2×C8—401no—
477C2×C8—401no—
478C2×C8—401no—
479C2×C8—401no—
480C2×C8C2×C4×D511yescharacteristic
481C2×C8C2×C4×D511yescharacteristic
482C2×C8C2×C4×D511yescharacteristic
483C2×C8C2×C4×D511yescharacteristic
484C4⋊C4—51no—
485C4⋊C4—51no—
486C4⋊C4—51no—
487C4⋊C4—51no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C22⋊C4—101no—
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—101no—
503C42C2×C4×D511yescharacteristic
504C42D4×D511yescharacteristic
505C42#71311yescharacteristic
506C42C23×D511yescharacteristic
507C2×C5—41no—
508C2×C5#292911yescharacteristic
509C2×C5#294611yescharacteristic
510C2×C5#295711yescharacteristic
511D5—42no—
512D5—42no—
513D5—81no—
514C23—104no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23—401no—
519C23—401no—
520C23#403911yescharacteristic
521Q8—101no—
522Q8—101no—
523D4—52no—
524D4—52no—
525D4—104no—
526D4—101no—
527D4—101no—
528D4—101no—
529D4—101no—
530D4—401no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—401no—
548C2×C4—401no—
549C2×C4—401no—
550C2×C4#403911yescharacteristic
551C2×C4#403911yescharacteristic
552C2×C4#403911yescharacteristic
553C2×C4C22×C4×D511yescharacteristic
554C2×C4C2×D4×D511yescharacteristic
555C2×C4C2×#71311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—101no—
568C8—201no—
569C8—201no—
570C5#1791811yescharacteristic, complemented, Sylow
571C22—21no—
572C22—21no—
573C22—21no—
574C22—102no—
575C22—102no—
576C22—201no—
577C22—201no—
578C22—201no—
579C22—201no—
580C22—201no—
581C22—201no—
582C22—201no—
583C22—404no—
584C22C2×#403911yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—201no—
590C4—201no—
591C4—201no—
592C4—201no—
593C4—201no—
594C4D5×#13111yescharacteristic
595C4D5×#13111yescharacteristic
596C4#6610811yescharacteristic
597C4#6611211yescharacteristic
598C2—41no—
599C2—202no—
600C2—202no—
601C2—401no—
602C2#1061080411yescharacteristic
603C2#1061093211yescharacteristic
604C2#1061098011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1574C2
socleC22×C5C2×C4×D4
prime radical#65021C4
cosocleC42×C5C24
hypercenter#1574D5
hypocenterC5#17918
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #10611017C2semidirect
3. #10610784C2semidirect
4. C5×#1574C2semidirect
5. #10601552C2semidirect
6. #10601537C2semidirect
7. #10601289C2semidirect
8. #10599354C2semidirect
9. #10599352C2semidirect
10. #10599351C2semidirect
11. #10599349C2semidirect
12. #10599314C2semidirect
13. #10599312C2semidirect
14. #10599311C2semidirect
15. #10599309C2semidirect
31. #65127C22semidirect
36. #65123C22semidirect
37. #65120C22semidirect
38. #65119C22semidirect
51. C5×#335C22semidirect
52. C5×#335C22semidirect
53. C5×#334C22semidirect
54. C5×#334C22semidirect
55. #64704C22semidirect
56. #64704C22semidirect
61. #64703C22semidirect
62. #64703C22semidirect
63. #64675C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
156. #1574D5semidirect
263. #335C2×D5semidirect
264. #335C2×D5semidirect
265. #334C2×D5semidirect
266. #334C2×D5semidirect
570. C5#17918semidirect

Maximal subgroups

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

subgroupindex
#106110312
#106110172
#106107842
C5×#15742
#106015522
#106015372
#106012892
#105993542
#105993522
#105993512
#105993492
#105993142
#105993122
#105993112
#105993092
#179185