Finite Group Databasebeta

← #12070019

Subgroups — #12070019

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611689C211yesmaximal, characteristic
2#10611648C211yesmaximal, characteristic
3#10611456C211yesmaximal, characteristic
4C5×#1584C211yesmaximal, characteristic, complemented
5#10601749C211yesmaximal, characteristic, complemented
6#10601727C211yesmaximal, characteristic, complemented
7#10601696C211yesmaximal, characteristic, complemented
8#10599362C211yesmaximal, characteristic
9#10599353C211yesmaximal, characteristic, complemented
10#10599033C211yesmaximal, characteristic
11#10599033C211yesmaximal, characteristic
12#10599012C211yesmaximal, characteristic, complemented
13#10599011C211yesmaximal, characteristic, complemented
14#10598879C211yesmaximal, characteristic, complemented
15D5×#322C211yesmaximal, characteristic
16#65912C2211yescharacteristic
17#65912C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic
20C4×C5×Q16C2211yescharacteristic
21#65477C411yescharacteristic
22#65470C411yescharacteristic
23C4×#689C2211yescharacteristic
24C4×#689C2211yescharacteristic
25#65313C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27#65176C411yescharacteristic
28#65163C411yescharacteristic
29#65128—21no—
30#65128—21no—
31#65126C2211yescharacteristic
32#65126C2211yescharacteristic
33#65120C2211yescharacteristic
34#65119—21no—
35#65119C2211yescharacteristic
36#65117—21no—
37#65102C411yescharacteristic
38#65102C411yescharacteristic
39#65081C411yescharacteristic
40#65081C411yescharacteristic
41#64997—21no—
42#64990—21no—
43C4×Dic20C2211yescharacteristic
44#64978—21no—
45C4×C8×D5C2211yescharacteristic
46C4×C8×D5C2211yescharacteristic
47C4×C8×D5C2211yescharacteristic
48#64968C2211yescharacteristic
49C8×Dic10—21no—
50C8×Dic10C2211yescharacteristic
51C5×#335C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64699C2211yescharacteristic
60#64699C2211yescharacteristic
61#64678C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#17977—51nomaximal, Sylow
68C2×C5×Q16C2×C411yescharacteristic
69C4×C5×Q8C2311yescharacteristic
70C4×C5×Q8C2311yescharacteristic
71#4092C2×C411yescharacteristic
72#4092C2×C411yescharacteristic
73#4090C2×C411yescharacteristic
74#4090C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76C2×#689C2×C411yescharacteristic
77C2×Dic20C2×C411yescharacteristic
78C2×#676—21no—
79C2×#676—21no—
80C2×C8×D5—21no—
81C2×C8×D5C2×C411yescharacteristic
82C2×C8×D5C2×C411yescharacteristic
83C2×C8×D5D411yescharacteristic
84C2×C8×D5D411yescharacteristic
85#4043C2×C411yescharacteristic
86#4043C2×C411yescharacteristic
87#4042—21no—
88#4042—21no—
89#4035—21no—
90#4035—21no—
91#4034C2×C411yescharacteristic
92#4034C2×C411yescharacteristic
93#4018—21no—
94#4018—21no—
95C42×D5C2311yescharacteristic
96C4×Dic10—21no—
97C4×Dic10—21no—
98C4×Dic10C2311yescharacteristic
99C4×Dic10C2311yescharacteristic
100C5×#107C2×C411yescharacteristic
101C5×C4⋊C8—21no—
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#103C2×C411yescharacteristic
107C5×#97—21no—
108C4×C5×C8—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112#3967C2×C411yescharacteristic
113#3967C2×C411yescharacteristic
114#3950C2×C411yescharacteristic
115#3948C2×C411yescharacteristic
116#3948C2×C411yescharacteristic
117#3947—21no—
118#3947—21no—
119#3946—21no—
120#3946—21no—
121#3946—21no—
122#3946—21no—
123#3946—21no—
124#3946—21no—
125C8×Dic5—21no—
126C8×Dic5—21no—
127C8×Dic5—21no—
128C8×Dic5C2×C411yescharacteristic
129C8×Dic5C2×C411yescharacteristic
130C8×Dic5D411yescharacteristic
131C8×Dic5D411yescharacteristic
132#3942C2×C411yescharacteristic
133#3942C2×C411yescharacteristic
134#3939C2×C411yescharacteristic
135#3939C2×C411yescharacteristic
136C4⋊#168—21no—
137C4⋊#168—21no—
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140#3935—21no—
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3170—51no—
146#2960—51no—
147#2960—51no—
148#1584—51no—
149#1584—51no—
150#1584—51no—
151#1584—51no—
152#1584—51no—
153#1584—51no—
154#1584—51no—
155#1584D511yescharacteristic, complemented
156#1567—51no—
157#1493—51no—
158#1493—51no—
159C2×#322—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×Q8C22×C411yescharacteristic
162C2×C4×D5C22×C411yescharacteristic
163C2×C4×D5C2×D411yescharacteristic
164C2×C4×D5#4111yescharacteristic
165C2×Dic10—21no—
166C2×Dic10—21no—
167C2×Dic10C22×C411yescharacteristic
168C2×Dic10C22×C411yescharacteristic
169C5×Q16—41no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8C22×C411yescharacteristic
174C2×C5×C8C22×C411yescharacteristic
175C2×C5×C8C2×D411yescharacteristic
176C2×C5×C8C2×D411yescharacteristic
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4C22×C411yescharacteristic
180C5×C4⋊C4C22×C411yescharacteristic
181C42×C5—21no—
182C42×C5—21no—
183C42×C5C2411yescharacteristic
184#689—41no—
185#689—41no—
186#685—21no—
187#685—21no—
188#685—21no—
189#685—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5C22×C411yescharacteristic
193C4⋊Dic5C22×C411yescharacteristic
194#683—21no—
195#683—21no—
196#683—21no—
197#683—21no—
198#683—21no—
199#683—21no—
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204C4×Dic5—21no—
205C4×Dic5—21no—
206C4×Dic5C22×C411yescharacteristic
207C4×Dic5C2×D411yescharacteristic
208C4×Dic5#4111yescharacteristic
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168C22×C411yescharacteristic
213C2×#168C22×C411yescharacteristic
214C2×#168C2×D411yescharacteristic
215C2×#168C2×D411yescharacteristic
216Dic20—41no—
217#676—42no—
218#676—42no—
219C8×D5—22no—
220C8×D5—41no—
221C8×D5—41no—
222C8×D5—42no—
223C8×D5Q1614yescomplemented
224#533—51no—
225#533—51no—
226#500—51no—
227#494—51no—
228#487—51no—
229#487—51no—
230#467—51no—
231#467—51no—
232#467—51no—
233#467—51no—
234#446—51no—
235#446—51no—
236#446—51no—
237#446—101no—
238#446—101no—
239#446C2×D511yescharacteristic
240C8×Q8—51no—
241C8×Q8—51no—
242C8×Q8—51no—
243C8×Q8—101no—
244C8×Q8—101no—
245C8×Q8C2×D511yescharacteristic
246C4×Q16—51no—
247C4×Q16—51no—
248C4×Q16—51no—
249C4×Q16C2×D511yescharacteristic
250#424—101no—
251#424—101no—
252#423—51no—
253#423—51no—
254#405—101no—
255#405—101no—
256C2×C4×C8—51no—
257C2×C4×C8—51no—
258C2×C4×C8—51no—
259#335—51no—
260#335—51no—
261#335—51no—
262#335C2×D511yescharacteristic
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269Q8⋊C8C2×D511yescharacteristic
270Q8⋊C8C2×D511yescharacteristic
271#322—51no—
272#322—51no—
273#322—51no—
274#322C2×D511yescharacteristic
275C22×D5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5C23×C411yescharacteristic
285C2×C4×C5C22×D411yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5C4×D411yescharacteristic
292C2×Dic5C4×D411yescharacteristic
293C2×Dic5C4×D411yescharacteristic
294C4×D5—21no—
295C4×D5—21no—
296C4×D5—22no—
297C4×D5C2×Q1612yes—
298C4×D5#13512yes—
299Dic10—21no—
300Dic10—21no—
301Dic10—21no—
302Dic10—21no—
303Dic10—42no—
304Dic10—42no—
305C5×C8—21no—
306C5×C8—21no—
307C5×C8—21no—
308C5×C8—41no—
309C5×C8—41no—
310C5×C8—41no—
311C5×C8C2×Q1612yes—
312#168—21no—
313#168—21no—
314#168—21no—
315#168—41no—
316#168—41no—
317#168—41no—
318#168C2×Q1612yes—
319C2×Q16—51no—
320C2×Q16—51no—
321C2×Q16—51no—
322C2×Q16C4×D511yescharacteristic
323C2×M16—101no—
324C2×M16—101no—
325C22×C8—51no—
326C22×C8—51no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8—101no—
330C4⋊Q8—51no—
331C4⋊Q8—51no—
332C4⋊Q8—51no—
333C4⋊Q8—51no—
334#125—101no—
335#125—101no—
336C22⋊Q8—51no—
337C22⋊Q8—51no—
338C22⋊Q8—51no—
339C22⋊Q8—51no—
340C22⋊Q8—101no—
341C22⋊Q8—101no—
342C4×Q8—51no—
343C4×Q8—51no—
344C4×Q8—101no—
345C4×Q8—101no—
346C4×Q8C22×D511yescharacteristic
347C4×Q8C22×D511yescharacteristic
348#117—101no—
349#117—101no—
350C2×C42—51no—
351#107—51no—
352#107—51no—
353#107—51no—
354#107C4×D511yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—101no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8C22×D511yescharacteristic
368C4⋊C8C22×D511yescharacteristic
369#103—51no—
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103C4×D511yescharacteristic
376#103C4×D511yescharacteristic
377#97—21no—
378#97—101no—
379#97—101no—
380#97—101no—
381C4×C8—21no—
382C4×C8—51no—
383C4×C8—51no—
384C4×C8—51no—
385C4×C8—51no—
386C4×C8—51no—
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—101no—
390C4×C8—101no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8C22×D511yescharacteristic
394C4×C8C22×D511yescharacteristic
395C4×C8C22×D511yescharacteristic
396C22×C5C2×C4×D411yescharacteristic
397C2×D5—21no—
398C2×D5—21no—
399C2×D5C4×Q1612yes—
400C4×C5—21no—
401C4×C5—41no—
402C4×C5—41no—
403C4×C5—41no—
404C4×C5—41no—
405C4×C5#56811yescharacteristic
406C4×C5#56811yescharacteristic
407C4×C5C22×Q1611yescharacteristic
408C4×C5C2×#13511yescharacteristic
409Dic5—21no—
410Dic5—41no—
411Dic5—41no—
412Dic5—41no—
413Dic5—41no—
414Dic5C4×Q1612yes—
415Dic5#44412yes—
416C2×Q8—51no—
417C2×Q8—51no—
418C2×Q8—101no—
419C2×Q8—101no—
420C2×Q8C2×C4×D511yescharacteristic
421C2×Q8C2×C4×D511yescharacteristic
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—51no—
425Q16—41no—
426Q16—201no—
427Q16—201no—
428Q16—201no—
429M16—202no—
430M16—202no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—51no—
435C2×C8—54no—
436C2×C8—51no—
437C2×C8—51no—
438C2×C8—51no—
439C2×C8—102no—
440C2×C8—101no—
441C2×C8—101no—
442C2×C8—101no—
443C2×C8—201no—
444C2×C8—201no—
445C2×C8—202no—
446C2×C8C2×C4×D511yescharacteristic
447C2×C8C2×C4×D511yescharacteristic
448C2×C8D4×D511yescharacteristic
449C2×C8D4×D511yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—51no—
453C4⋊C4—51no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—101no—
457C4⋊C4—101no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4C2×C4×D511yescharacteristic
467C4⋊C4C2×C4×D511yescharacteristic
468C22⋊C4—101no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C42—21no—
473C42—21no—
474C42—51no—
475C42—51no—
476C42—51no—
477C42—101no—
478C42—101no—
479C42C23×D511yescharacteristic
480C2×C5#293211yescharacteristic
481C2×C5C2×C4×Q1611yescharacteristic
482C2×C5C2×#44411yescharacteristic
483D5—22no—
484C23—51no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—101no—
490Q8—101no—
491Q8—101no—
492Q8—101no—
493Q8—202no—
494Q8—202no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—51no—
500C2×C4—51no—
501C2×C4—52no—
502C2×C4—52no—
503C2×C4—51no—
504C2×C4—102no—
505C2×C4—101no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4C22×C4×D511yescharacteristic
512C2×C4C2×D4×D511yescharacteristic
513C2×C4D5×#4111yescharacteristic
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—52no—
521C8—101no—
522C8—101no—
523C8—101no—
524C8—201no—
525C8—201no—
526C8—201no—
527C8D5×Q1612yes—
528C5#1797711yescharacteristic, complemented, Sylow
529C22—52no—
530C22—101no—
531C22—101no—
532C22C4×D4×D511yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—52no—
539C4—52no—
540C4—101no—
541C4—201no—
542C4—201no—
543C4—201no—
544C4—201no—
545C4#6607911yescharacteristic
546C4#6608411yescharacteristic
547C4C2×D5×Q1611yescharacteristic
548C4D5×#13511yescharacteristic
549C2—102no—
550C2#1061121111yescharacteristic
551C2C4×D5×Q1611yescharacteristic
552C2D5×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1584C2
socleC22×C5C2×C4×D4
prime radicalC22×D5C4×D4
cosocleC42×C5C24
hypercenter#1584D5
hypocenterC5#17977
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. C5×#1584C2semidirect
5. #10601749C2semidirect
6. #10601727C2semidirect
7. #10601696C2semidirect
9. #10599353C2semidirect
12. #10599012C2semidirect
13. #10599011C2semidirect
14. #10598879C2semidirect
155. #1584D5semidirect
223. C8×D5Q16semidirect
528. C5#17977semidirect

Maximal subgroups

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

subgroupindex
#106116892
#106116482
#106114562
C5×#15842
#106017492
#106017272
#106016962
#105993622
#105993532
#105990332
#105990122
#105990112
#105988792
D5×#3222
#179775