Finite Group Databasebeta

← #12070323

Subgroups — #12070323

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3102C211yesmaximal, characteristic
2#10614860C211yesmaximal, characteristic, complemented
3#10614250C211yesmaximal, characteristic, complemented
4#10602545C211yesmaximal, characteristic, complemented
5#10602431C211yesmaximal, characteristic, complemented
6#10601697C211yesmaximal, characteristic, complemented
7#10601695C211yesmaximal, characteristic, complemented
8#10601693C211yesmaximal, characteristic, complemented
9#10601691C211yesmaximal, characteristic, complemented
10#10601691C211yesmaximal, characteristic, complemented
11SD16⋊#168C211yesmaximal, characteristic, complemented
12#10601675C211yesmaximal, characteristic, complemented
13#10601673C211yesmaximal, characteristic, complemented
14#10601544C211yesmaximal, characteristic, complemented
15#10601534C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C4×C5×#41C2211yescharacteristic
18C5×#485C411yescharacteristic
19C5×#482C411yescharacteristic
20C5×#479C411yescharacteristic
21C5×#478C411yescharacteristic
22C5×#464C411yescharacteristic
23C5×#463C411yescharacteristic
24C5×#452C411yescharacteristic
25C5×#449C411yescharacteristic
26C4×C5×Q16C2211yescharacteristic
27C4×C5×SD16C2211yescharacteristic
28C4×C5×SD16C2211yescharacteristic
29C4×C5×D8C2211yescharacteristic
30C5×#431C2211yescharacteristic
31#65313C2211yescharacteristic
32Q8×#168C2211yescharacteristic
33Q8×#168C2211yescharacteristic
34Q8×#168C2211yescharacteristic
35#65301—21no—
36#65301—21no—
37#65301—21no—
38#65301C2211yescharacteristic
39#65301C2211yescharacteristic
40#65301C2211yescharacteristic
41#65300—21no—
42D4×#168C2211yescharacteristic
43#65289—21no—
44#65286—21no—
45#65215—21no—
46#65215C2211yescharacteristic
47#65214C2211yescharacteristic
48C4×#681—21no—
49C4×#681C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic
52Q8⋊#168C2211yescharacteristic
53Q8⋊#168C2211yescharacteristic
54Q8⋊#168C2211yescharacteristic
55D4⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic
57D4⋊#168C2211yescharacteristic
58D4⋊#168C2211yescharacteristic
59#64678C2211yescharacteristic
60#64678C2211yescharacteristic
61#64677C2211yescharacteristic
62#64677C2211yescharacteristic
63#64675C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#18005—51nomaximal, Sylow
68C2×C5×#41C2×C411yescharacteristic
69C2×C5×Q16C2×C411yescharacteristic
70C2×C5×SD16C2×C411yescharacteristic
71C2×C5×SD16C2×C411yescharacteristic
72C2×C5×D8C2×C411yescharacteristic
73C5×#126—21no—
74C5×#125C2×C411yescharacteristic
75C5×#124C2×C411yescharacteristic
76C5×#123—21no—
77C5×C22⋊Q8C2×C411yescharacteristic
78C5×#121C2×C411yescharacteristic
79C4×C5×Q8C2×C411yescharacteristic
80C4×C5×Q8C2311yescharacteristic
81C4×C5×Q8C2311yescharacteristic
82C4×C5×D4—21no—
83C4×C5×D4—21no—
84C4×C5×D4—21no—
85C4×C5×D4C2×C411yescharacteristic
86C4×C5×D4C2311yescharacteristic
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×#681—21no—
96C2×#681D411yescharacteristic
97C2×#681D411yescharacteristic
98C22×#168—21no—
99C22×#168—21no—
100C5×#107C2×C411yescharacteristic
101C5×#107C2×C411yescharacteristic
102C5×#106C2×C411yescharacteristic
103C5×#106C2×C411yescharacteristic
104C5×C4⋊C8C2×C411yescharacteristic
105C5×C4⋊C8C2×C411yescharacteristic
106C5×#103C2×C411yescharacteristic
107C5×#103C2×C411yescharacteristic
108C5×#103C2×C411yescharacteristic
109C5×#103C2×C411yescharacteristic
110C5×#102C2×C411yescharacteristic
111C5×#102C2×C411yescharacteristic
112C5×#102C2×C411yescharacteristic
113C5×#102C2×C411yescharacteristic
114C5×C22⋊C8C2×C411yescharacteristic
115C5×C22⋊C8C2×C411yescharacteristic
116C4×C5×C8C2311yescharacteristic
117C4×C5×C8C2311yescharacteristic
118C22⋊#168—21no—
119C22⋊#168—21no—
120C22⋊#168—21no—
121C22⋊#168—21no—
122C22⋊#168—21no—
123C22⋊#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#3935D411yescharacteristic
135#3935D411yescharacteristic
136C4×#168—21no—
137C4×#168—21no—
138C4×#168—21no—
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3102D511yescharacteristic
146#2971—51no—
147#2969—51no—
148#1594—51no—
149#1592—51no—
150#1588—51no—
151#1588—51no—
152#1587—51no—
153#1586—51no—
154#1579—51no—
155SD16⋊C8—51no—
156#1572—51no—
157#1494—51no—
158#1476—51no—
159#1451—51no—
160C5×#41—22no—
161C5×#41—41no—
162C2×C5×Q8C22×C411yescharacteristic
163C2×C5×Q8C22×C411yescharacteristic
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C22×C411yescharacteristic
167C2×C5×D4C22×C411yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5C22×C411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5#4111yescharacteristic
175C5×Q16—22no—
176C5×SD16—22no—
177C5×SD16—41no—
178C5×D8—41no—
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C2×C5×C8C22×C411yescharacteristic
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⋊C4C22×C411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C4⋊C4C22×C411yescharacteristic
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—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—41no—
210#681—41no—
211#681—42no—
212#681—42no—
213#681—42no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—42no—
221C2×#168—42no—
222C2×#168C2×D411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C2×#168C2×D411yescharacteristic
225C2×#168C2×D411yescharacteristic
226#529C2×D511yescharacteristic
227C4×#41C2×D511yescharacteristic
228#485Dic511yescharacteristic
229#482Dic511yescharacteristic
230#479Dic511yescharacteristic
231#478Dic511yescharacteristic
232#464Dic511yescharacteristic
233#463Dic511yescharacteristic
234#452Dic511yescharacteristic
235#449Dic511yescharacteristic
236#446—51no—
237C8×Q8—51no—
238C8×Q8—51no—
239C8×Q8—51no—
240C4×Q16C2×D511yescharacteristic
241C4×SD16C2×D511yescharacteristic
242C4×SD16C2×D511yescharacteristic
243C4×D8C2×D511yescharacteristic
244#436—51no—
245#436—51no—
246#436—51no—
247#436—101no—
248#436—101no—
249#436—101no—
250#435—101no—
251C8×D4—51no—
252#433—101no—
253#432—51no—
254#432—101no—
255#431—51no—
256#431C2×D511yescharacteristic
257#405—101no—
258C4×M16—51no—
259C4×M16—101no—
260C2×C4×C8—51no—
261#335—51no—
262#335—51no—
263#334—51no—
264#334—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273#322—51no—
274#322—51no—
275#322—51no—
276#322—51no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5C4×D411yescharacteristic
280C5×Q8—21no—
281C5×Q8—21no—
282C5×Q8—21no—
283C5×Q8#13112yes—
284C5×D4—21no—
285C5×D4—21no—
286C5×D4—21no—
287C5×D4—21no—
288C5×D4—42no—
289C5×D4—81no—
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—21no—
299C2×C4×C5—21no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—81no—
307C2×C4×C5C4×D411yescharacteristic
308C2×C4×C5C4×D411yescharacteristic
309C2×C4×C5C4×D411yescharacteristic
310C2×C4×C5C23×C411yescharacteristic
311C2×C4×C5C22×D411yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C5×C8—21no—
314C5×C8—21no—
315C5×C8—21no—
316C5×C8—21no—
317#168—22no—
318#168—21no—
319#168—21no—
320#168—21no—
321#168—21no—
322#168—41no—
323#168—41no—
324#168—41no—
325#168—41no—
326#168—41no—
327C2×#41C2×Dic511yescharacteristic
328C2×Q16C2×Dic511yescharacteristic
329C2×SD16C2×Dic511yescharacteristic
330C2×SD16C2×Dic511yescharacteristic
331C2×D8C2×Dic511yescharacteristic
332C2×M16—51no—
333C2×M16—51no—
334C2×M16—101no—
335C2×M16—101no—
336C2×M16—101no—
337C22×C8—101no—
338C22×C8—101no—
339#126—21no—
340#125C2×Dic511yescharacteristic
341#124C2×Dic511yescharacteristic
342#123—21no—
343C22⋊Q8C2×Dic511yescharacteristic
344#121C2×Dic511yescharacteristic
345C4×Q8C2×Dic511yescharacteristic
346C4×Q8C22×D511yescharacteristic
347C4×Q8C22×D511yescharacteristic
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4C2×Dic511yescharacteristic
352C4×D4C22×D511yescharacteristic
353C4×D4C22×D511yescharacteristic
354#117—21no—
355#117—21no—
356#117C2×Dic511yescharacteristic
357C2×C42—21no—
358C2×C42C22×D511yescharacteristic
359#107C2×Dic511yescharacteristic
360#107C2×Dic511yescharacteristic
361#106C2×Dic511yescharacteristic
362#106C2×Dic511yescharacteristic
363C4⋊C8—51no—
364C4⋊C8—51no—
365C4⋊C8—51no—
366C4⋊C8—51no—
367C4⋊C8—101no—
368C4⋊C8—101no—
369C4⋊C8—101no—
370C4⋊C8—101no—
371C4⋊C8C2×Dic511yescharacteristic
372C4⋊C8C2×Dic511yescharacteristic
373#103C2×Dic511yescharacteristic
374#103C2×Dic511yescharacteristic
375#103C2×Dic511yescharacteristic
376#103C2×Dic511yescharacteristic
377#102C2×Dic511yescharacteristic
378#102C2×Dic511yescharacteristic
379#102C2×Dic511yescharacteristic
380#102C2×Dic511yescharacteristic
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385C22⋊C8—101no—
386C22⋊C8—101no—
387C22⋊C8C2×Dic511yescharacteristic
388C22⋊C8C2×Dic511yescharacteristic
389#97—51no—
390#97—51no—
391#97—101no—
392#97—101no—
393C4×C8—51no—
394C4×C8—51no—
395C4×C8—51no—
396C4×C8—51no—
397C4×C8—101no—
398C4×C8—101no—
399C4×C8—101no—
400C4×C8—101no—
401C4×C8—101no—
402C4×C8C22×D511yescharacteristic
403C4×C8C22×D511yescharacteristic
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—21no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5C2×C4×D411yescharacteristic
414C4×C5—21no—
415C4×C5—22no—
416C4×C5—21no—
417C4×C5—21no—
418C4×C5—21no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424C4×C5C2×#13111yescharacteristic
425C4×C5#56811yescharacteristic
426C4×C5#57511yescharacteristic
427C4×C5#57511yescharacteristic
428#41—22no—
429#41—41no—
430C2×Q8C22×Dic511yescharacteristic
431C2×Q8C22×Dic511yescharacteristic
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C22×Dic511yescharacteristic
435C2×D4C22×Dic511yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4D4×D511yescharacteristic
441C22×C4#71111yescharacteristic
442C22×C4C22×Dic511yescharacteristic
443Q16—22no—
444SD16—22no—
445SD16—41no—
446D8—41no—
447M16—201no—
448M16—201no—
449M16—202no—
450M16—202no—
451M16—202no—
452C2×C8—51no—
453C2×C8—51no—
454C2×C8—51no—
455C2×C8—51no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—202no—
463C2×C8—202no—
464C2×C8C22×Dic511yescharacteristic
465C2×C8C22×Dic511yescharacteristic
466C2×C8C22×Dic511yescharacteristic
467C2×C8C22×Dic511yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×Dic511yescharacteristic
475C4⋊C4C22×Dic511yescharacteristic
476C4⋊C4C22×Dic511yescharacteristic
477C4⋊C4C22×Dic511yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42D4×D511yescharacteristic
491C42#71111yescharacteristic
492C42C22×Dic511yescharacteristic
493C42C23×D511yescharacteristic
494C2×C5—41no—
495C2×C5—81no—
496C2×C5—81no—
497C2×C5#293311yescharacteristic
498C2×C5#294311yescharacteristic
499C2×C5#295611yescharacteristic
500C23—21no—
501C23—21no—
502C23D4×Dic511yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8#409412yes—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—42no—
512D4—81no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—81no—
530C2×C4D4×Dic511yescharacteristic
531C2×C4D4×Dic511yescharacteristic
532C2×C4D4×Dic511yescharacteristic
533C2×C4C2×D4×D511yescharacteristic
534C2×C4C2×#71111yescharacteristic
535C2×C4C23×Dic511yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—102no—
541C8—101no—
542C8—101no—
543C8—101no—
544C8—101no—
545C8—201no—
546C8—201no—
547C8—201no—
548C8—201no—
549C8—201no—
550C5#1800511yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic511yescharacteristic
561C4—21no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4#6610211yescharacteristic
572C4#6610211yescharacteristic
573C4C2×#409411yescharacteristic
574C4#6615311yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2#1061464911yescharacteristic
579C2#1061562811yescharacteristic
580C2#1061573111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#3102C2
socleC22×C5C2×C4×D4
prime radicalC5×#449C4
cosocleC42×C5C24
hypercenter#3102D5
hypocenterC5#18005
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
2. #10614860C2semidirect
3. #10614250C2semidirect
4. #10602545C2semidirect
5. #10602431C2semidirect
6. #10601697C2semidirect
7. #10601695C2semidirect
8. #10601693C2semidirect
9. #10601691C2semidirect
10. #10601691C2semidirect
11. SD16⋊#168C2semidirect
12. #10601675C2semidirect
13. #10601673C2semidirect
14. #10601544C2semidirect
15. #10601534C2semidirect
550. C5#18005semidirect

Maximal subgroups

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

subgroupindex
C5×#31022
#106148602
#106142502
#106025452
#106024312
#106016972
#106016952
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