Finite Group Databasebeta

← #12070431

Subgroups — #12070431

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611693C211yesmaximal, characteristic, complemented
2#10611387C211yesmaximal, characteristic
3#10611252C211yesmaximal, characteristic
4C5×#1590C211yesmaximal, characteristic, complemented
5#10601749C211yesmaximal, characteristic, complemented
6#10601690C211yesmaximal, characteristic, complemented
7#10601657C211yesmaximal, characteristic, complemented
8#10599328C211yesmaximal, characteristic, complemented
9#10599315C211yesmaximal, characteristic, complemented
10#10599024C211yesmaximal, characteristic, complemented
11#10599020C211yesmaximal, characteristic, complemented
12#10598971C211yesmaximal, characteristic
13#10598943C211yesmaximal, characteristic, complemented
14C8×Dic20C211yesmaximal, characteristic, complemented
15#10598841C211yesmaximal, characteristic, complemented
16C4×Q8×D5C2211yescharacteristic
17#65891C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C4×C5×SD16C2211yescharacteristic
20C5×#436C2211yescharacteristic
21#65459C411yescharacteristic
22#65455C411yescharacteristic
23#65417—21no—
24#65411—21no—
25C4×#689C2211yescharacteristic
26#65313C2211yescharacteristic
27C4×#687C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65151C411yescharacteristic
30#65146C411yescharacteristic
31#65126—21no—
32#65126C2211yescharacteristic
33#65122C2211yescharacteristic
34#65120C2211yescharacteristic
35#65119C2211yescharacteristic
36#65117—21no—
37#65097C411yescharacteristic
38#65085C411yescharacteristic
39#65063C411yescharacteristic
40#65056C411yescharacteristic
41#65019—21no—
42#65009—21no—
43#64996—21no—
44#64990—21no—
45C4×Dic20C2211yescharacteristic
46C4×#676C2211yescharacteristic
47#64974C2211yescharacteristic
48#64974C2211yescharacteristic
49C8×Dic10C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#334C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×C82C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64700C2211yescharacteristic
60#64699C2211yescharacteristic
61#64678C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#18012—51nomaximal, Sylow
68C2×Q8×D5C2×C411yescharacteristic
69C2×C5×SD16C2×C411yescharacteristic
70C2×C5×M16—21no—
71C4×C5×Q8C2311yescharacteristic
72C4×C5×D4C2311yescharacteristic
73Q8×Dic5C2×C411yescharacteristic
74C2×#689C2×C411yescharacteristic
75#4084C2×C411yescharacteristic
76#4082C2×C411yescharacteristic
77C2×#687C2×C411yescharacteristic
78C4×C22⋊D5—21no—
79#4072—21no—
80C22×#168—21no—
81C2×Dic20C2×C411yescharacteristic
82C2×#676—21no—
83C2×#676D411yescharacteristic
84C2×#676D411yescharacteristic
85#4043C2×C411yescharacteristic
86D5×C4⋊C4—21no—
87D5×C4⋊C4C2×C411yescharacteristic
88#4036C2×C411yescharacteristic
89#4033—21no—
90#4033C2×C411yescharacteristic
91#4029—21no—
92#4025—21no—
93C42×D5—21no—
94C42×D5C2311yescharacteristic
95C4×Dic10—21no—
96C4×Dic10C2311yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×#106C2×C411yescharacteristic
99C5×C4⋊C8—21no—
100C5×C4⋊C8C2311yescharacteristic
101C5×C4⋊C8C2311yescharacteristic
102C5×#103C2×C411yescharacteristic
103C5×#102C2×C411yescharacteristic
104C5×C22⋊C8—21no—
105C5×#97—21no—
106C4×C5×C8C2311yescharacteristic
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109#3967C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111C22⋊#168—21no—
112#3952—21no—
113#3952—21no—
114#3952C2×C411yescharacteristic
115#3952C2×C411yescharacteristic
116#3950C2×C411yescharacteristic
117#3948C2×C411yescharacteristic
118#3948C2×C411yescharacteristic
119#3947—21no—
120#3947D411yescharacteristic
121#3947D411yescharacteristic
122#3946—21no—
123#3946—21no—
124#3946—21no—
125#3946—21no—
126#3946—21no—
127#3946—21no—
128#3946C2×C411yescharacteristic
129#3946C2×C411yescharacteristic
130C8×Dic5—21no—
131C8×Dic5—21no—
132C8×Dic5—21no—
133C8×Dic5—21no—
134#3942C2×C411yescharacteristic
135#3942C2×C411yescharacteristic
136#3940C2×C411yescharacteristic
137#3939C2×C411yescharacteristic
138C4⋊#168—21no—
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141#3935—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108—51no—
146#2969—51no—
147Q8×M16—51no—
148#1593—51no—
149#1590D511yescharacteristic, complemented
150#1587—51no—
151#1585—51no—
152#1584—51no—
153#1583—51no—
154SD16⋊C8—51no—
155C8×Q16—51no—
156#1574—51no—
157#1495—51no—
158#1479—51no—
159#1453—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×D4C22×C411yescharacteristic
162C22×C4×C5—21no—
163C2×C22⋊D5—21no—
164Q8×D5—22no—
165Q8×D5—41no—
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5C22×C411yescharacteristic
169C2×C4×D5C2×D411yescharacteristic
170C2×C4×D5#4111yescharacteristic
171C2×Dic10—21no—
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C5×SD16—41no—
175C5×M16—42no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C5×C22⋊C4—21no—
187C42×C5—21no—
188C42×C5C2411yescharacteristic
189C22⋊Dic5—21no—
190C22⋊Dic5—21no—
191C22⋊Dic5—21no—
192#689—41no—
193#687—22no—
194#685—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5C22×C411yescharacteristic
199C4⋊Dic5C22×C411yescharacteristic
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5C22×C411yescharacteristic
210C4×Dic5C2×D411yescharacteristic
211C4×Dic5#4111yescharacteristic
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—42no—
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C2×D411yescharacteristic
219C2×#168C2×D411yescharacteristic
220Dic20—22no—
221#676—22no—
222#676—41no—
223#676—42no—
224#529—51no—
225C2×C4×Q8—51no—
226#483—51no—
227#480—51no—
228#479—51no—
229#479—51no—
230#464—51no—
231#464—51no—
232#451—51no—
233#448—51no—
234#446—51no—
235#446—51no—
236#446—101no—
237#446—101no—
238#446C2×D511yescharacteristic
239C8×Q8—51no—
240C8×Q8—51no—
241C8×Q8—51no—
242C4×Q16—51no—
243C4×Q16—51no—
244C4×SD16—51no—
245C4×SD16C2×D511yescharacteristic
246#436—101no—
247#436C2×D511yescharacteristic
248#435—101no—
249C8×D4—51no—
250#433—101no—
251#431—51no—
252#431—51no—
253#431—51no—
254#423—51no—
255#423—101no—
256#405—101no—
257C4×M16—51no—
258C4×M16—101no—
259#335—51no—
260#335—51no—
261#334—51no—
262#334C2×D511yescharacteristic
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8C2×D511yescharacteristic
269D4⋊C8—51no—
270D4⋊C8C2×D511yescharacteristic
271#322—51no—
272#322—51no—
273#322—51no—
274C82C2×D511yescharacteristic
275C23×C5—21no—
276C22×D5C4×D411yescharacteristic
277C5×Q8—21no—
278C5×Q8—21no—
279C5×D4—21no—
280C5×D4—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5C23×C411yescharacteristic
287C2×C4×C5C22×D411yescharacteristic
288C2×C4×C5C2×#4111yescharacteristic
289C22⋊D5—81no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5C4×D411yescharacteristic
295C2×Dic5C4×D411yescharacteristic
296C2×Dic5C4×D411yescharacteristic
297C4×D5—21no—
298C4×D5—21no—
299C4×D5—21no—
300C4×D5—21no—
301C4×D5—41no—
302C4×D5—42no—
303C4×D5—81no—
304Dic10—21no—
305Dic10—21no—
306Dic10—21no—
307Dic10—42no—
308Dic10#13112yes—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8#13712yes—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322#168—41no—
323C22×Q8—51no—
324C2×Q16—51no—
325C2×Q16—51no—
326C2×SD16—51no—
327C2×SD16C4×D511yescharacteristic
328C2×M16—21no—
329C2×M16—51no—
330C2×M16—51no—
331C2×M16—101no—
332C22×C8—101no—
333#126—101no—
334#125—51no—
335#124—51no—
336#123—101no—
337C22⋊Q8—51no—
338#121—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8—51no—
343C4×Q8—101no—
344C4×Q8—101no—
345C4×Q8C22×D511yescharacteristic
346C4×D4—101no—
347C4×D4C22×D511yescharacteristic
348#117—101no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—101no—
351C2×C42—51no—
352C2×C42—101no—
353#107—51no—
354#107—51no—
355#106—51no—
356#106C4×D511yescharacteristic
357C4⋊C8—21no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—51no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8C22×D511yescharacteristic
370C4⋊C8C22×D511yescharacteristic
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#103C4×D511yescharacteristic
377#102—51no—
378#102C4×D511yescharacteristic
379C22⋊C8—21no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386#97—51no—
387#97—51no—
388#97—101no—
389#97—101no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8C22×D511yescharacteristic
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5C2×C4×D411yescharacteristic
404C2×D5—21no—
405C2×D5—21no—
406C2×D5—21no—
407C4×C5—21no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5C2×#13111yescharacteristic
412C4×C5#56811yescharacteristic
413C4×C5C2×#13711yescharacteristic
414C4×C5#57511yescharacteristic
415Dic5—22no—
416Dic5—21no—
417Dic5—21no—
418Dic5—21no—
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—101no—
425C2×Q8—102no—
426C2×Q8—201no—
427C2×Q8C2×C4×D511yescharacteristic
428C2×D4—101no—
429C2×D4C2×C4×D511yescharacteristic
430C22×C4—21no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—101no—
435C22×C4—101no—
436Q16—102no—
437Q16—201no—
438SD16—41no—
439SD16—102no—
440M16—42no—
441M16—102no—
442M16—201no—
443M16—202no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—202no—
455C2×C8C2×C4×D511yescharacteristic
456C2×C8C2×C4×D511yescharacteristic
457C2×C8D4×D511yescharacteristic
458C2×C8D4×D511yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—51no—
461C4⋊C4—51no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4C2×C4×D511yescharacteristic
471C4⋊C4C2×C4×D511yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—101no—
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C42—21no—
478C42—51no—
479C42—51no—
480C42—51no—
481C42—101no—
482C42—101no—
483C42—101no—
484C42—101no—
485C42C23×D511yescharacteristic
486C2×C5—81no—
487C2×C5#293311yescharacteristic
488C2×C5C4×#13711yescharacteristic
489C2×C5#295711yescharacteristic
490D5—41no—
491C23—21no—
492C23—51no—
493Q8—21no—
494Q8—21no—
495Q8—52no—
496Q8—101no—
497Q8—101no—
498Q8—101no—
499Q8—202no—
500D4—21no—
501D4—21no—
502D4—401no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—51no—
509C2×C4—51no—
510C2×C4—51no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—201no—
520C2×C4—202no—
521C2×C4—401no—
522C2×C4C22×C4×D511yescharacteristic
523C2×C4C2×D4×D511yescharacteristic
524C2×C4D5×#4111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—101no—
532C8—101no—
533C8—101no—
534C8—101no—
535C8—201no—
536C8—201no—
537C8—201no—
538C8#406112yes—
539C5#1801211yescharacteristic, complemented, Sylow
540C22—41no—
541C22—41no—
542C22—41no—
543C22—101no—
544C22—101no—
545C22—101no—
546C22C4×D4×D511yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—101no—
552C4—102no—
553C4—101no—
554C4—101no—
555C4—201no—
556C4—201no—
557C4—201no—
558C4#6607911yescharacteristic
559C4D5×#13111yescharacteristic
560C4C2×#406111yescharacteristic
561C4#6610211yescharacteristic
562C2—81no—
563C2—201no—
564C2#1061127011yescharacteristic
565C2C4×#406111yescharacteristic
566C2#1061162111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1590C2
socleC22×C5C2×C4×D4
prime radical#4084C2×C4
cosocleC42×C5C24
hypercenter#1590D5
hypocenterC5#18012
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #10611693C2semidirect
4. C5×#1590C2semidirect
5. #10601749C2semidirect
6. #10601690C2semidirect
7. #10601657C2semidirect
8. #10599328C2semidirect
9. #10599315C2semidirect
10. #10599024C2semidirect
11. #10599020C2semidirect
13. #10598943C2semidirect
14. C8×Dic20C2semidirect
15. #10598841C2semidirect
149. #1590D5semidirect
539. C5#18012semidirect

Maximal subgroups

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

subgroupindex
#106116932
#106113872
#106112522
C5×#15902
#106017492
#106016902
#106016572
#105993282
#105993152
#105990242
#105990202
#105989712
#105989432
C8×Dic202
#105988412
#180125