Finite Group Databasebeta

← #12070443

Subgroups — #12070443

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×#3107C211yesmaximal, characteristic
2#10615061C211yesmaximal, characteristic, complemented
3#10614250C211yesmaximal, characteristic
4#10602620C211yesmaximal, characteristic, complemented
5#10602432C211yesmaximal, characteristic
6#10601697C211yesmaximal, characteristic, complemented
7#10601696C211yesmaximal, characteristic, complemented
8#10601695C211yesmaximal, characteristic, complemented
9Q16×#168C211yesmaximal, characteristic, complemented
10#10601693C211yesmaximal, characteristic, complemented
11#10601692C211yesmaximal, characteristic, complemented
12#10601691C211yesmaximal, characteristic, complemented
13#10601689C211yesmaximal, characteristic, complemented
14#10601545C211yesmaximal, characteristic, complemented
15#10601536C211yesmaximal, characteristic, complemented
16C5×#533C2211yescharacteristic
17C4×C5×#41C2211yescharacteristic
18C5×#485C411yescharacteristic
19C5×#485C411yescharacteristic
20C5×#475C411yescharacteristic
21C5×#474C411yescharacteristic
22C5×#462C411yescharacteristic
23C5×#461C411yescharacteristic
24C5×#452C411yescharacteristic
25C5×#452C411yescharacteristic
26C4×C5×Q16C2211yescharacteristic
27C4×C5×Q16C2211yescharacteristic
28C4×C5×SD16C2211yescharacteristic
29C4×C5×SD16C2211yescharacteristic
30C5×#431C2211yescharacteristic
31#65313—21no—
32#65313—21no—
33#65313C2211yescharacteristic
34#65313C2211yescharacteristic
35Q8×#168C2211yescharacteristic
36Q8×#168C2211yescharacteristic
37Q8×#168C2211yescharacteristic
38Q8×#168C2211yescharacteristic
39#65301—21no—
40#65301—21no—
41#65301C2211yescharacteristic
42#65301C2211yescharacteristic
43#65288—21no—
44#65286—21no—
45#65215—21no—
46#65215C2211yescharacteristic
47#65214C2211yescharacteristic
48C2×C4⋊#168C2211yescharacteristic
49C4×#681—21no—
50C4×#681C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic
52Q8⋊#168C2211yescharacteristic
53Q8⋊#168C2211yescharacteristic
54Q8⋊#168C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56Q8⋊#168C2211yescharacteristic
57D4⋊#168C2211yescharacteristic
58D4⋊#168C2211yescharacteristic
59#64678C2211yescharacteristic
60#64678C2211yescharacteristic
61#64677C2211yescharacteristic
62#64677C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#18013—51nomaximal, Sylow
68C2×C5×#41C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C2×C5×Q16C2×C411yescharacteristic
71C2×C5×SD16C2×C411yescharacteristic
72C2×C5×SD16C2×C411yescharacteristic
73C5×C4⋊Q8C2×C411yescharacteristic
74C5×C4⋊Q8C2×C411yescharacteristic
75C5×#125—21no—
76C5×C22⋊Q8—21no—
77C5×C22⋊Q8C2×C411yescharacteristic
78C5×C22⋊Q8C2×C411yescharacteristic
79C4×C5×Q8—21no—
80C4×C5×Q8C2×C411yescharacteristic
81C4×C5×Q8C2311yescharacteristic
82C4×C5×Q8C2311yescharacteristic
83C4×C5×Q8C2311yescharacteristic
84C4×C5×D4—21no—
85C4×C5×D4—21no—
86C4×C5×D4C2×C411yescharacteristic
87C4×C5×D4C2311yescharacteristic
88C5×#117—21no—
89C5×#117—21no—
90C5×#117C2×C411yescharacteristic
91C2×C42×C5—21no—
92C2×C42×C5C2311yescharacteristic
93C2×#681—21no—
94C2×#681—21no—
95C2×#681D411yescharacteristic
96C2×#681D411yescharacteristic
97C22×#168—21no—
98C5×#107C2×C411yescharacteristic
99C5×#107C2×C411yescharacteristic
100C5×#106C2×C411yescharacteristic
101C5×#106C2×C411yescharacteristic
102C5×C4⋊C8C2×C411yescharacteristic
103C5×C4⋊C8C2×C411yescharacteristic
104C5×#103C2×C411yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#103C2×C411yescharacteristic
107C5×#103C2×C411yescharacteristic
108C5×#103C2×C411yescharacteristic
109C5×#103C2×C411yescharacteristic
110C5×#102C2×C411yescharacteristic
111C5×#102C2×C411yescharacteristic
112C5×C22⋊C8C2×C411yescharacteristic
113C5×C22⋊C8C2×C411yescharacteristic
114C4×C5×C8C2311yescharacteristic
115C4×C5×C8C2311yescharacteristic
116C22⋊#168—21no—
117C22⋊#168—21no—
118C22⋊#168—21no—
119C22⋊#168—21no—
120C4⋊#168—21no—
121C4⋊#168—21no—
122C4⋊#168—21no—
123C4⋊#168—21no—
124C4⋊#168—21no—
125C4⋊#168—21no—
126C4⋊#168—21no—
127C4⋊#168—21no—
128C4⋊#168C2311yescharacteristic
129C4⋊#168C2311yescharacteristic
130C4⋊#168C2311yescharacteristic
131C4⋊#168C2311yescharacteristic
132#3935—21no—
133#3935—21no—
134#3935—21no—
135#3935D411yescharacteristic
136#3935D411yescharacteristic
137C4×#168—21no—
138C4×#168—21no—
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107D511yescharacteristic
146#2971—51no—
147#2962—51no—
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—
160C5×#41—22no—
161C5×#41—41no—
162C2×C5×Q8—21no—
163C2×C5×Q8C22×C411yescharacteristic
164C2×C5×Q8C22×C411yescharacteristic
165C2×C5×Q8C22×C411yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4C22×C411yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5C22×C411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C5×Q16—22no—
175C5×Q16—22no—
176C5×SD16—41no—
177C5×SD16—41no—
178C2×C5×C8C22×C411yescharacteristic
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C5×C4⋊C4—21no—
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⋊C4—21no—
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C4⋊C4C22×C411yescharacteristic
193C5×C4⋊C4C22×C411yescharacteristic
194C5×C4⋊C4C22×C411yescharacteristic
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5C22×C411yescharacteristic
206C42×C5C2×D411yescharacteristic
207C42×C5#4111yescharacteristic
208C42×C5C2411yescharacteristic
209#681—22no—
210#681—41no—
211#681—42no—
212#681—42no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—42no—
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223C2×#168C2×D411yescharacteristic
224#533C2×D511yescharacteristic
225C4×#41C2×D511yescharacteristic
226#485Dic511yescharacteristic
227#485Dic511yescharacteristic
228#475Dic511yescharacteristic
229#474Dic511yescharacteristic
230#462Dic511yescharacteristic
231#461Dic511yescharacteristic
232#452Dic511yescharacteristic
233#452Dic511yescharacteristic
234#446—51no—
235#446—51no—
236#446—101no—
237#446—101no—
238C8×Q8—51no—
239C8×Q8—51no—
240C8×Q8—51no—
241C8×Q8—51no—
242C4×Q16C2×D511yescharacteristic
243C4×Q16C2×D511yescharacteristic
244C4×SD16C2×D511yescharacteristic
245C4×SD16C2×D511yescharacteristic
246#436—51no—
247#436—51no—
248#436—101no—
249#436—101no—
250#432—51no—
251#432—101no—
252#431—51no—
253#431C2×D511yescharacteristic
254#424—101no—
255C2×C4⋊C8—51no—
256#405—101no—
257C4×M16—51no—
258C4×M16—101no—
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×C5—21no—
276C23×C5C4×D411yescharacteristic
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—21no—
280C5×Q8—21no—
281C5×Q8—21no—
282C5×Q8—81no—
283C5×Q8#13112yes—
284C5×D4—21no—
285C5×D4—21no—
286C5×D4—42no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—41no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—81no—
303C2×C4×C5C4×D411yescharacteristic
304C2×C4×C5C4×D411yescharacteristic
305C2×C4×C5C4×D411yescharacteristic
306C2×C4×C5C23×C411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—21no—
312C5×C8—21no—
313#168—21no—
314#168—21no—
315#168—21no—
316#168—41no—
317#168—41no—
318#168—41no—
319#168—41no—
320#168—41no—
321#168—41no—
322#168#13712yes—
323C2×#41C2×Dic511yescharacteristic
324C2×Q16C2×Dic511yescharacteristic
325C2×Q16C2×Dic511yescharacteristic
326C2×SD16C2×Dic511yescharacteristic
327C2×SD16C2×Dic511yescharacteristic
328C2×M16—51no—
329C2×M16—51no—
330C2×M16—101no—
331C2×M16—101no—
332C22×C8—101no—
333C4⋊Q8C2×Dic511yescharacteristic
334C4⋊Q8C2×Dic511yescharacteristic
335#125—21no—
336C22⋊Q8—21no—
337C22⋊Q8C2×Dic511yescharacteristic
338C22⋊Q8C2×Dic511yescharacteristic
339C4×Q8—21no—
340C4×Q8C2×Dic511yescharacteristic
341C4×Q8C22×D511yescharacteristic
342C4×Q8C22×D511yescharacteristic
343C4×Q8C22×D511yescharacteristic
344C4×D4—21no—
345C4×D4—21no—
346C4×D4C2×Dic511yescharacteristic
347C4×D4C22×D511yescharacteristic
348#117—21no—
349#117—21no—
350#117C2×Dic511yescharacteristic
351C2×C42—21no—
352C2×C42C22×D511yescharacteristic
353#107C2×Dic511yescharacteristic
354#107C2×Dic511yescharacteristic
355#106C2×Dic511yescharacteristic
356#106C2×Dic511yescharacteristic
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—51no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8—101no—
364C4⋊C8—101no—
365C4⋊C8—101no—
366C4⋊C8—101no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8C2×Dic511yescharacteristic
370C4⋊C8C2×Dic511yescharacteristic
371#103C2×Dic511yescharacteristic
372#103C2×Dic511yescharacteristic
373#103C2×Dic511yescharacteristic
374#103C2×Dic511yescharacteristic
375#103C2×Dic511yescharacteristic
376#103C2×Dic511yescharacteristic
377#102C2×Dic511yescharacteristic
378#102C2×Dic511yescharacteristic
379C22⋊C8—101no—
380C22⋊C8—101no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8C2×Dic511yescharacteristic
384C22⋊C8C2×Dic511yescharacteristic
385#97—51no—
386#97—51no—
387#97—101no—
388#97—101no—
389#97—101no—
390C4×C8—51no—
391C4×C8—51no—
392C4×C8—51no—
393C4×C8—51no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8—101no—
397C4×C8—101no—
398C4×C8C22×D511yescharacteristic
399C4×C8C22×D511yescharacteristic
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—21no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5C2×C4×D411yescharacteristic
407C4×C5—21no—
408C4×C5—22no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—21no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5—41no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5C2×#13111yescharacteristic
419C4×C5#56811yescharacteristic
420C4×C5C2×#13711yescharacteristic
421C4×C5#57511yescharacteristic
422#41—22no—
423#41—41no—
424C2×Q8—21no—
425C2×Q8C22×Dic511yescharacteristic
426C2×Q8C22×Dic511yescharacteristic
427C2×Q8C22×Dic511yescharacteristic
428C2×D4—21no—
429C2×D4C22×Dic511yescharacteristic
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4D4×D511yescharacteristic
434C22×C4#71111yescharacteristic
435C22×C4C22×Dic511yescharacteristic
436Q16—22no—
437Q16—22no—
438SD16—41no—
439SD16—41no—
440M16—102no—
441M16—202no—
442M16—201no—
443M16—202no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—202no—
455C2×C8C22×Dic511yescharacteristic
456C2×C8C22×Dic511yescharacteristic
457C2×C8C22×Dic511yescharacteristic
458C2×C8C22×Dic511yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4C22×Dic511yescharacteristic
469C4⋊C4C22×Dic511yescharacteristic
470C4⋊C4C22×Dic511yescharacteristic
471C4⋊C4C22×Dic511yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42D4×D511yescharacteristic
483C42#71111yescharacteristic
484C42C22×Dic511yescharacteristic
485C42C23×D511yescharacteristic
486C2×C5—41no—
487C2×C5—81no—
488C2×C5#293311yescharacteristic
489C2×C5C4×#13711yescharacteristic
490C2×C5#295711yescharacteristic
491C23—21no—
492C23D4×Dic511yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8#409412yes—
500D4—21no—
501D4—21no—
502D4—42no—
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—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—81no—
519C2×C4D4×Dic511yescharacteristic
520C2×C4D4×Dic511yescharacteristic
521C2×C4D4×Dic511yescharacteristic
522C2×C4C2×D4×D511yescharacteristic
523C2×C4C2×#71111yescharacteristic
524C2×C4C23×Dic511yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—52no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—201no—
534C8—201no—
535C8—201no—
536C8—201no—
537C8—201no—
538C8—201no—
539C5#1801311yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×D4×Dic511yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—22no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4D5×#13711yescharacteristic
559C4#6611111yescharacteristic
560C4C2×#409411yescharacteristic
561C4#6615311yescharacteristic
562C2—41no—
563C2—81no—
564C2#1061464911yescharacteristic
565C2#1061564111yescharacteristic
566C2Dic5×#13711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#3107C2
socleC22×C5C2×C4×D4
prime radicalC2×C5×#41C2×C4
cosocleC42×C5C24
hypercenter#3107D5
hypocenterC5#18013
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #10615061C2semidirect
4. #10602620C2semidirect
6. #10601697C2semidirect
7. #10601696C2semidirect
8. #10601695C2semidirect
9. Q16×#168C2semidirect
10. #10601693C2semidirect
11. #10601692C2semidirect
12. #10601691C2semidirect
13. #10601689C2semidirect
14. #10601545C2semidirect
15. #10601536C2semidirect
539. C5#18013semidirect

Maximal subgroups

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

subgroupindex
C5×#31072
#106150612
#106142502
#106026202
#106024322
#106016972
#106016962
#106016952
Q16×#1682
#106016932
#106016922
#106016912
#106016892
#106015452
#106015362
#180135