Finite Group Databasebeta

← #12070437

Subgroups — #12070437

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
1C5×#2962C211yesmaximal, characteristic, complemented
2#10615083C211yesmaximal, characteristic
3#10610243C211yesmaximal, characteristic
4#10602620C211yesmaximal, characteristic, complemented
5#10601750C211yesmaximal, characteristic, complemented
6#10601749C211yesmaximal, characteristic, complemented
7#10601748C211yesmaximal, characteristic, complemented
8#10601743C211yesmaximal, characteristic, complemented
9#10601729C211yesmaximal, characteristic, complemented
10#10601726C211yesmaximal, characteristic, complemented
11#10601725C211yesmaximal, characteristic, complemented
12C8×#689C211yesmaximal, characteristic, complemented
13#10601218C211yesmaximal, characteristic
14#10601216C211yesmaximal, characteristic, complemented
15#10600641C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C4×#709C2211yescharacteristic
18C5×#446—21no—
19C5×#446—21no—
20C5×#446C2211yescharacteristic
21C5×#446C2211yescharacteristic
22C5×C8×Q8C2211yescharacteristic
23C5×C8×Q8C2211yescharacteristic
24C5×#424—21no—
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#405—21no—
27C4×C5×M16C2211yescharacteristic
28#65417—21no—
29#65417—21no—
30#65383C411yescharacteristic
31#65379C411yescharacteristic
32#65376C411yescharacteristic
33#65372C411yescharacteristic
34#65336C411yescharacteristic
35#65336C411yescharacteristic
36#65334C411yescharacteristic
37#65334C411yescharacteristic
38C4×#689C2211yescharacteristic
39C4×#689C2211yescharacteristic
40C4×#688C2211yescharacteristic
41C4×#688C2211yescharacteristic
42#65215C2211yescharacteristic
43#65214C2211yescharacteristic
44#65214C2211yescharacteristic
45#64996—21no—
46#64994—21no—
47#64977C2211yescharacteristic
48#64977C2211yescharacteristic
49C8×Dic10C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic
52Q8⋊#168C2211yescharacteristic
53Q8⋊#168C2211yescharacteristic
54Q8⋊#168C2211yescharacteristic
55#64704C2211yescharacteristic
56#64704C2211yescharacteristic
57#64703C2211yescharacteristic
58#64703C2211yescharacteristic
59#64700C2211yescharacteristic
60#64700C2211yescharacteristic
61#64699C2211yescharacteristic
62#64699C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18013—51nomaximal, Sylow
68C2×#709C2×C411yescharacteristic
69C2×C5×M16D411yescharacteristic
70C2×C5×M16D411yescharacteristic
71C22×C5×C8—21no—
72C5×C4⋊Q8C2×C411yescharacteristic
73C5×C4⋊Q8C2×C411yescharacteristic
74C5×#125—21no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8C2×C411yescharacteristic
77C5×C22⋊Q8C2×C411yescharacteristic
78C4×C5×Q8—21no—
79C4×C5×Q8C2311yescharacteristic
80C4×C5×Q8C2311yescharacteristic
81C5×#117—21no—
82C2×C42×C5C2311yescharacteristic
83C2×#689C2×C411yescharacteristic
84C2×#689C2×C411yescharacteristic
85C2×#688C2×C411yescharacteristic
86C2×#688C2×C411yescharacteristic
87C4×C22⋊D5—21no—
88C4×C22⋊D5—21no—
89#4072C2×C411yescharacteristic
90C2×#676—21no—
91C2×#676—21no—
92C4×D20C2×C411yescharacteristic
93C4×D20C2311yescharacteristic
94#4018—21no—
95C42×D5—21no—
96C4×Dic10C2×C411yescharacteristic
97C4×Dic10C2311yescharacteristic
98C5×C4⋊C8—21no—
99C5×C4⋊C8—21no—
100C5×C4⋊C8—21no—
101C5×C4⋊C8—21no—
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×#97—21no—
106C5×#97—21no—
107C5×#97D411yescharacteristic
108C5×#97D411yescharacteristic
109C4×C5×C8—21no—
110C4×C5×C8—21no—
111C4×C5×C8C2311yescharacteristic
112C4×C5×C8C2311yescharacteristic
113#3967C2×C411yescharacteristic
114#3967C2×C411yescharacteristic
115#3967C2×C411yescharacteristic
116#3967C2×C411yescharacteristic
117C22⋊#168—21no—
118C22⋊#168—21no—
119C22⋊#168C2×C411yescharacteristic
120C22⋊#168C2×C411yescharacteristic
121#3952—21no—
122#3952—21no—
123#3946—21no—
124#3946—21no—
125C8×Dic5—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#3935—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107—51no—
146#2971—51no—
147#2962D511yescharacteristic, complemented
148#1592—51no—
149#1590—51no—
150#1588—51no—
151#1587—51no—
152#1584—51no—
153#1583—51no—
154#1579—51no—
155C8×Q16—51no—
156#1573—51no—
157#1497—51no—
158#1477—51no—
159#1453—51no—
160C2×C5×Q8—21no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×Q8C22×C411yescharacteristic
163C22×C4×C5C22×C411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5#4111yescharacteristic
166C2×C22⋊D5—21no—
167#709—22no—
168#709—41no—
169C2×D20C22×C411yescharacteristic
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×Dic10C22×C411yescharacteristic
174C5×M16—22no—
175C5×M16—41no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—42no—
179C2×C5×C8C2×D411yescharacteristic
180C2×C5×C8C2×D411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C42×C5—21no—
195C42×C5—21no—
196C42×C5C22×C411yescharacteristic
197C42×C5C2×D411yescharacteristic
198C42×C5#4111yescharacteristic
199C42×C5C2411yescharacteristic
200C22⋊Dic5—21no—
201#689—22no—
202#689—22no—
203#688—41no—
204#688—41no—
205#685—21no—
206#685—21no—
207C4⋊Dic5C22×C411yescharacteristic
208C4⋊Dic5C22×C411yescharacteristic
209#683—21no—
210#683—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222#676—42no—
223#676—42no—
224#533C2×D511yescharacteristic
225C4×#41—51no—
226#485—51no—
227#485—51no—
228#475—51no—
229#474—51no—
230#462—51no—
231#461—51no—
232#452—51no—
233#452—51no—
234#446—21no—
235#446—21no—
236#446C2×D511yescharacteristic
237#446C2×D511yescharacteristic
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8C2×D511yescharacteristic
241C8×Q8C2×D511yescharacteristic
242C4×Q16—51no—
243C4×Q16—51no—
244C4×SD16—51no—
245C4×SD16—51no—
246#436—51no—
247#436—51no—
248#436—101no—
249#436—101no—
250#432—51no—
251#432—101no—
252#431—51no—
253#431—51no—
254#424—21no—
255C2×C4⋊C8C2×D511yescharacteristic
256#405—21no—
257C4×M16—101no—
258C4×M16C2×D511yescharacteristic
259#335—51no—
260#335—51no—
261#334—51no—
262#334—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8—51no—
271#322—51no—
272#322—51no—
273#322—51no—
274C82—51no—
275C23×C5C4×D411yescharacteristic
276C22×D5—21no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—81no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
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—42no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301D20—21no—
302D20—21no—
303C4×D5—42no—
304C4×D5—41no—
305C4×D5—41no—
306C4×D5—81no—
307Dic10—21no—
308Dic10#13112yes—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8#13712yes—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—41no—
320#168—41no—
321#168—41no—
322#168—41no—
323C2×#41—51no—
324C2×Q16—51no—
325C2×Q16—51no—
326C2×SD16—51no—
327C2×SD16—51no—
328C2×M16—101no—
329C2×M16—101no—
330C2×M16C22⋊D511yescharacteristic
331C2×M16C22⋊D511yescharacteristic
332C22×C8—21no—
333C4⋊Q8C4×D511yescharacteristic
334C4⋊Q8C4×D511yescharacteristic
335#125—21no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D511yescharacteristic
338C22⋊Q8C4×D511yescharacteristic
339C4×Q8—21no—
340C4×Q8—51no—
341C4×Q8—51no—
342C4×Q8C22×D511yescharacteristic
343C4×Q8C22×D511yescharacteristic
344C4×D4—51no—
345C4×D4—51no—
346C4×D4—101no—
347C4×D4—101no—
348#117—21no—
349#117—51no—
350#117—101no—
351C2×C42—101no—
352C2×C42C22×D511yescharacteristic
353#107—51no—
354#107—51no—
355#106—51no—
356#106—51no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—51no—
363C4⋊C8—51no—
364C4⋊C8—51no—
365C4⋊C8—51no—
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#103—51no—
377#102—51no—
378#102—51no—
379C22⋊C8—51no—
380C22⋊C8—51no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—21no—
386#97—21no—
387#97—101no—
388#97C22⋊D511yescharacteristic
389#97C22⋊D511yescharacteristic
390C4×C8—21no—
391C4×C8—21no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—51no—
395C4×C8—51no—
396C4×C8—101no—
397C4×C8—101no—
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—21no—
403C22×C5C2×C4×D411yescharacteristic
404C2×D5—41no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5C2×#13111yescharacteristic
416C4×C5#56811yescharacteristic
417C4×C5C2×#13711yescharacteristic
418C4×C5#57511yescharacteristic
419Dic5—22no—
420Dic5—41no—
421Dic5—41no—
422#41—102no—
423#41—201no—
424C2×Q8—21no—
425C2×Q8—51no—
426C2×Q8C2×C4×D511yescharacteristic
427C2×Q8C2×C4×D511yescharacteristic
428C2×D4—51no—
429C2×D4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4C2×C4×D511yescharacteristic
434C22×C4#70911yescharacteristic
435C22×C4C2×C22⋊D511yescharacteristic
436Q16—102no—
437Q16—102no—
438SD16—201no—
439SD16—201no—
440M16—22no—
441M16—41no—
442M16—202no—
443M16—202no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8C2×C22⋊D511yescharacteristic
456C2×C8C2×C22⋊D511yescharacteristic
457C2×C8C2×C22⋊D511yescharacteristic
458C2×C8C2×C22⋊D511yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—51no—
467C4⋊C4—51no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4C2×C4×D511yescharacteristic
471C4⋊C4C2×C4×D511yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—101no—
477C42—21no—
478C42—21no—
479C42—101no—
480C42—101no—
481C42—101no—
482C42C2×C4×D511yescharacteristic
483C42#70911yescharacteristic
484C42C2×C22⋊D511yescharacteristic
485C42C23×D511yescharacteristic
486C2×C5—41no—
487C2×C5#293311yescharacteristic
488C2×C5C4×#13711yescharacteristic
489C2×C5#295711yescharacteristic
490D5—81no—
491C23—101no—
492C23C4×C22⋊D511yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—52no—
498Q8—81no—
499Q8—101no—
500D4—101no—
501D4—101no—
502D4—202no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—202no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—401no—
519C2×C4C4×C22⋊D511yescharacteristic
520C2×C4C4×C22⋊D511yescharacteristic
521C2×C4C4×C22⋊D511yescharacteristic
522C2×C4C22×C4×D511yescharacteristic
523C2×C4C2×#70911yescharacteristic
524C2×C4C22×C22⋊D511yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—101no—
534C8—201no—
535C8—201no—
536C8—201no—
537C8—201no—
538C8#408812yes—
539C5#1801311yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—201no—
544C22—201no—
545C22—201no—
546C22C2×C4×C22⋊D511yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—102no—
556C4—201no—
557C4—201no—
558C4D5×#13111yescharacteristic
559C4#6608411yescharacteristic
560C4C2×#408811yescharacteristic
561C4#6615611yescharacteristic
562C2—41no—
563C2—401no—
564C2C4×#408811yescharacteristic
565C2#1061552711yescharacteristic
566C2#1061554311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#2962C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenter#2962D5
hypocenterC5#18013
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. C5×#2962C2semidirect
4. #10602620C2semidirect
5. #10601750C2semidirect
6. #10601749C2semidirect
7. #10601748C2semidirect
8. #10601743C2semidirect
9. #10601729C2semidirect
10. #10601726C2semidirect
11. #10601725C2semidirect
12. C8×#689C2semidirect
14. #10601216C2semidirect
15. #10600641C2semidirect
147. #2962D5semidirect
539. C5#18013semidirect

Maximal subgroups

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

subgroupindex
C5×#29622
#106150832
#106102432
#106026202
#106017502
#106017492
#106017482
#106017432
#106017292
#106017262
#106017252
C8×#6892
#106012182
#106012162
#106006412
#180135