Finite Group Databasebeta

← #12070489

Subgroups — #12070489

Order 1280.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2994C211yesmaximal, characteristic
2#10614883C211yesmaximal, characteristic
3#10610996C211yesmaximal, characteristic, complemented
4#10602545C211yesmaximal, characteristic
5#10601750C211yesmaximal, characteristic, complemented
6#10601744C211yesmaximal, characteristic, complemented
7#10601728C211yesmaximal, characteristic, complemented
8C8×#689C211yesmaximal, characteristic, complemented
9#10601659C211yesmaximal, characteristic, complemented
10#10601658C211yesmaximal, characteristic, complemented
11C8×#687C211yesmaximal, characteristic, complemented
12#10601636C211yesmaximal, characteristic, complemented
13#10601533C211yesmaximal, characteristic, complemented
14C2×#64704C211yesmaximal, characteristic, complemented
15#10601216C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C2×C4×Dic10C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic
20C5×#436C2211yescharacteristic
21C5×#435—21no—
22C5×C8×D4—21no—
23C5×C8×D4C2211yescharacteristic
24C5×#433—21no—
25C5×#431C2211yescharacteristic
26C5×#424—21no—
27C2×C5×C4⋊C8C2211yescharacteristic
28#65352C411yescharacteristic
29#65352C411yescharacteristic
30#65343C411yescharacteristic
31#65343C411yescharacteristic
32#65339C411yescharacteristic
33#65332C411yescharacteristic
34#65329C411yescharacteristic
35#65322C411yescharacteristic
36C4×#689C2211yescharacteristic
37C4×#689C2211yescharacteristic
38C4×#687C2211yescharacteristic
39C4×#687C2211yescharacteristic
40#65215C2211yescharacteristic
41#65214C2211yescharacteristic
42C2×C4×#168C2211yescharacteristic
43#65117—21no—
44#65117—21no—
45#65008—21no—
46#65007—21no—
47#64968C2211yescharacteristic
48#64968C2211yescharacteristic
49C8×Dic10C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic
52Q8⋊#168C2211yescharacteristic
53D4⋊#168C2211yescharacteristic
54D4⋊#168C2211yescharacteristic
55#64704C2211yescharacteristic
56#64704C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64700C2211yescharacteristic
60#64700C2211yescharacteristic
61#64699C2211yescharacteristic
62#64699C2211yescharacteristic
63#64674C2211yescharacteristic
64#64674C2211yescharacteristic
65C8×#168C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18017—51nomaximal, Sylow
68C22×Dic10C2×C411yescharacteristic
69C2×C5×M16—21no—
70C22×C5×C8—21no—
71C22×C5×C8—21no—
72C5×#126—21no—
73C5×#125C2×C411yescharacteristic
74C5×#124C2×C411yescharacteristic
75C5×#123—21no—
76C5×C22⋊Q8C2×C411yescharacteristic
77C5×#121C2×C411yescharacteristic
78C4×C5×Q8C2311yescharacteristic
79C4×C5×D4—21no—
80C4×C5×D4C2311yescharacteristic
81C5×#117—21no—
82C2×C42×C5C2311yescharacteristic
83C2×#689C2×C411yescharacteristic
84C2×#689C2×C411yescharacteristic
85C2×#687C2×C411yescharacteristic
86C2×#687C2×C411yescharacteristic
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×#683—21no—
89C2×C4×Dic5—21no—
90C22×#168—21no—
91C4×Dic10—21no—
92C4×Dic10—21no—
93C4×Dic10C2×C411yescharacteristic
94C4×Dic10C2×C411yescharacteristic
95C4×Dic10C2311yescharacteristic
96C4×Dic10C2311yescharacteristic
97C5×C4⋊C8—21no—
98C5×C4⋊C8—21no—
99C5×C4⋊C8—21no—
100C5×C4⋊C8D411yescharacteristic
101C5×C4⋊C8D411yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C22⋊C8—21no—
105C5×C22⋊C8—21no—
106C5×C22⋊C8D411yescharacteristic
107C5×C22⋊C8D411yescharacteristic
108C5×#97—21no—
109C4×C5×C8—21no—
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112#3967C2×C411yescharacteristic
113#3967C2×C411yescharacteristic
114#3964C2×C411yescharacteristic
115#3964C2×C411yescharacteristic
116C22⋊#168—21no—
117C22⋊#168C2×C411yescharacteristic
118C22⋊#168C2×C411yescharacteristic
119#3947—21no—
120#3947—21no—
121#3946—21no—
122#3946—21no—
123#3946—21no—
124#3946—21no—
125C8×Dic5—21no—
126C8×Dic5—21no—
127#3942C2×C411yescharacteristic
128#3942C2×C411yescharacteristic
129#3942C2×C411yescharacteristic
130#3942C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3940C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134#3939C2×C411yescharacteristic
135C4⋊#168C2×C411yescharacteristic
136C4⋊#168C2×C411yescharacteristic
137C4⋊#168C2311yescharacteristic
138C4⋊#168C2311yescharacteristic
139#3935—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108—51no—
146#2994D511yescharacteristic
147#2984—51no—
148#1591—51no—
149#1590—51no—
150#1588—51no—
151#1587—51no—
152#1587—51no—
153#1585—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1573—51no—
157#1494—51no—
158C2×Q8⋊C8—51no—
159#1450—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C22×C411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5#4111yescharacteristic
167C22×Dic5—21no—
168C22×Dic5—21no—
169C2×Dic10—22no—
170C2×Dic10—21no—
171C2×Dic10—41no—
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C5×M16—81no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—81no—
178C2×C5×C8—81no—
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⋊C4C22×C411yescharacteristic
188C5×C4⋊C4C22×C411yescharacteristic
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C42×C5—21no—
195C42×C5C22×C411yescharacteristic
196C42×C5C2×D411yescharacteristic
197C42×C5#4111yescharacteristic
198C42×C5C2411yescharacteristic
199#689—22no—
200#689—41no—
201#687—22no—
202#687—41no—
203C4⋊Dic5—21no—
204C4⋊Dic5C22×C411yescharacteristic
205C4⋊Dic5C22×C411yescharacteristic
206#683—21no—
207#683—21no—
208#683—21no—
209#683—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C2×#168—24no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223#529C2×D511yescharacteristic
224C2×C4×Q8—51no—
225#483—51no—
226#480—51no—
227#479—51no—
228#479—51no—
229#464—51no—
230#464—51no—
231#451—51no—
232#448—51no—
233#446—51no—
234#446—51no—
235#446—101no—
236#446—101no—
237#446C2×D511yescharacteristic
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8C2×D511yescharacteristic
241C4×Q16—51no—
242C4×Q16—51no—
243C4×SD16—51no—
244C4×SD16—51no—
245#436C2×D511yescharacteristic
246#435—21no—
247C8×D4—21no—
248C8×D4C2×D511yescharacteristic
249#433—21no—
250#432—51no—
251#432—101no—
252#431—51no—
253#431—101no—
254#431C2×D511yescharacteristic
255#424—21no—
256C2×C4⋊C8C2×D511yescharacteristic
257C2×C4×C8—51no—
258#335—51no—
259#335—51no—
260#334—51no—
261#334—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268D4⋊C8—51no—
269D4⋊C8—51no—
270#322—51no—
271#322—51no—
272C82—51no—
273C82—51no—
274C23×C5—21no—
275C23×C5C4×D411yescharacteristic
276C5×Q8—21no—
277C5×Q8—21no—
278C5×D4—21no—
279C5×D4—21no—
280C5×D4—42no—
281C2×C4×C5—22no—
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—41no—
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
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303Dic10—21no—
304Dic10—21no—
305Dic10—21no—
306Dic10—42no—
307Dic10#13112yes—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—41no—
313C5×C8—41no—
314#168—22no—
315#168—22no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—41no—
321#168—41no—
322C22×Q8—51no—
323C2×Q16—51no—
324C2×Q16—51no—
325C2×SD16—51no—
326C2×SD16—51no—
327C2×M16—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—101no—
331#126—21no—
332#125C4×D511yescharacteristic
333#124C4×D511yescharacteristic
334#123—21no—
335C22⋊Q8C4×D511yescharacteristic
336#121C4×D511yescharacteristic
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—101no—
342C4×Q8—101no—
343C4×Q8C22×D511yescharacteristic
344C4×D4—21no—
345C4×D4C22×D511yescharacteristic
346#117—21no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—101no—
349C2×C42—101no—
350C2×C42C22×D511yescharacteristic
351#107—51no—
352#107—51no—
353#106—51no—
354#106—51no—
355C4⋊C8—21no—
356C4⋊C8—21no—
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⋊C8C22⋊D511yescharacteristic
367C4⋊C8C22⋊D511yescharacteristic
368C4⋊C8C22×D511yescharacteristic
369C4⋊C8C22×D511yescharacteristic
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#103—51no—
376#102—51no—
377#102—51no—
378C22⋊C8—21no—
379C22⋊C8—21no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—101no—
383C22⋊C8C22⋊D511yescharacteristic
384C22⋊C8C22⋊D511yescharacteristic
385#97—21no—
386#97—101no—
387#97—101no—
388#97—101no—
389C4×C8—21no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8C22×D511yescharacteristic
398C4×C8C22×D511yescharacteristic
399C22×C5—21no—
400C22×C5—21no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5#44312yes—
405C22×C5C2×C4×D411yescharacteristic
406C4×C5—21no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—41no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5C2×#13111yescharacteristic
414C4×C5#56811yescharacteristic
415C4×C5#57711yescharacteristic
416C4×C5#57811yescharacteristic
417Dic5—22no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421C2×Q8—51no—
422C2×Q8—51no—
423C2×Q8—102no—
424C2×Q8—101no—
425C2×Q8—201no—
426C2×Q8C2×C4×D511yescharacteristic
427C2×D4—21no—
428C2×D4C2×C4×D511yescharacteristic
429C22×C4—21no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4C2×C4×D511yescharacteristic
433C22×C4#70911yescharacteristic
434C22×C4C2×C22⋊D511yescharacteristic
435Q16—102no—
436Q16—201no—
437SD16—102no—
438SD16—201no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—51no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—104no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8C2×C22⋊D511yescharacteristic
454C2×C8C2×C22⋊D511yescharacteristic
455C2×C8C2×C22⋊D511yescharacteristic
456C2×C8C2×C22⋊D511yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—51no—
462C4⋊C4—51no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4C2×C4×D511yescharacteristic
469C4⋊C4C2×C4×D511yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C42—21no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42C2×C4×D511yescharacteristic
481C42#70911yescharacteristic
482C42C2×C22⋊D511yescharacteristic
483C42C23×D511yescharacteristic
484C2×C5—22no—
485C2×C5—81no—
486C2×C5#293311yescharacteristic
487C2×C5#294711yescharacteristic
488C2×C5C2×#44311yescharacteristic
489C23—21no—
490C23C4×C22⋊D511yescharacteristic
491Q8—21no—
492Q8—21no—
493Q8—52no—
494Q8—101no—
495Q8—101no—
496Q8—101no—
497Q8—202no—
498D4—21no—
499D4—21no—
500D4—42no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—202no—
516C2×C4—202no—
517C2×C4C4×C22⋊D511yescharacteristic
518C2×C4C4×C22⋊D511yescharacteristic
519C2×C4C4×C22⋊D511yescharacteristic
520C2×C4C22×C4×D511yescharacteristic
521C2×C4C2×#70911yescharacteristic
522C2×C4C22×C22⋊D511yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—102no—
530C8—102no—
531C8—101no—
532C8—101no—
533C8—101no—
534C8—101no—
535C8—201no—
536C8—201no—
537C5#1801711yescharacteristic, complemented, Sylow
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#6543312yes—
544C22C2×C4×C22⋊D511yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—102no—
553C4—201no—
554C4—201no—
555C4—201no—
556C4D5×#13111yescharacteristic
557C4#6608411yescharacteristic
558C4#6617011yescharacteristic
559C4#6617211yescharacteristic
560C2—22no—
561C2—81no—
562C2#1061430211yescharacteristic
563C2C2×#6543311yescharacteristic
564C2#1061552711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#2994C2
socleC22×C5C2×C4×D4
prime radicalC5×#121C2×C4
cosocleC42×C5C24
hypercenter#2994D5
hypocenterC5#18017
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
3. #10610996C2semidirect
5. #10601750C2semidirect
6. #10601744C2semidirect
7. #10601728C2semidirect
8. C8×#689C2semidirect
9. #10601659C2semidirect
10. #10601658C2semidirect
11. C8×#687C2semidirect
12. #10601636C2semidirect
13. #10601533C2semidirect
14. C2×#64704C2semidirect
15. #10601216C2semidirect
537. C5#18017semidirect

Maximal subgroups

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

subgroupindex
C5×#29942
#106148832
#106109962
#106025452
#106017502
#106017442
#106017282
C8×#6892
#106016592
#106016582
C8×#6872
#106016362
#106015332
C2×#647042
#106012162
#180175