Finite Group Databasebeta

← #12070290

Subgroups — #12070290

Order 1280.

610 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
1#10614871C211yesmaximal, characteristic
2#10614860C211yesmaximal, characteristic, complemented
3#10611059C211yesmaximal, characteristic, complemented
4C5×#1494C211yesmaximal, characteristic, complemented
5#10601589C211yesmaximal, characteristic, complemented
6#10600527C211yesmaximal, characteristic, complemented
7#10600518C211yesmaximal, characteristic, complemented
8#10599020C211yesmaximal, characteristic, complemented
9#10599014C211yesmaximal, characteristic, complemented
10#10599013C211yesmaximal, characteristic, complemented
11#10599007C211yesmaximal, characteristic, complemented
12#10598955C211yesmaximal, characteristic, complemented
13#10598951C211yesmaximal, characteristic, complemented
14#10598949C211yesmaximal, characteristic, complemented
15#10598944C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C4×#709C2211yescharacteristic
18C5×#432C2211yescharacteristic
19C2×C4×C5×C8C2211yescharacteristic
20#65355C411yescharacteristic
21#65352C411yescharacteristic
22#65346C411yescharacteristic
23#65343C411yescharacteristic
24#65336C411yescharacteristic
25#65334C411yescharacteristic
26#65326C411yescharacteristic
27#65324C411yescharacteristic
28C4×#689C2211yescharacteristic
29C4×#688C2211yescharacteristic
30#65313C2211yescharacteristic
31Q8×#168C2211yescharacteristic
32C4×#687C2211yescharacteristic
33C4×#686C2211yescharacteristic
34#65301—21no—
35#65301C2211yescharacteristic
36#65300—21no—
37D4×#168C2211yescharacteristic
38#65289—21no—
39#65286—21no—
40#65214C2211yescharacteristic
41#65214C2211yescharacteristic
42C4×#681C2211yescharacteristic
43#65123C2211yescharacteristic
44#65123C2211yescharacteristic
45#65120C2211yescharacteristic
46#65120C2211yescharacteristic
47#65017—21no—
48#65017—21no—
49#64994—21no—
50D5×#97—21no—
51C5×Q8⋊C8C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×D4⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64675C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#18002—51nomaximal, Sylow
68C2×#709C2×C411yescharacteristic
69C22×C5×C8—21no—
70C5×#126—21no—
71C5×#125C2×C411yescharacteristic
72C5×#124C2×C411yescharacteristic
73C5×#123—21no—
74C5×C22⋊Q8C2×C411yescharacteristic
75C5×#121C2×C411yescharacteristic
76C4×C5×Q8C2311yescharacteristic
77C4×C5×D4—21no—
78C4×C5×D4C2311yescharacteristic
79C5×#117—21no—
80C2×C42×C5C2311yescharacteristic
81C2×#689C2×C411yescharacteristic
82C2×#688C2×C411yescharacteristic
83C2×#687C2×C411yescharacteristic
84C2×#686C2×C411yescharacteristic
85C4×C22⋊D5—21no—
86C4×C22⋊D5—21no—
87#4072C2×C411yescharacteristic
88C2×#681—21no—
89C2×#681D411yescharacteristic
90C2×#681D411yescharacteristic
91C22×#168—21no—
92C2×C8×D5—21no—
93C2×C8×D5—21no—
94C4×D20C2×C411yescharacteristic
95C4×D20C2311yescharacteristic
96#4018—21no—
97C42×D5—21no—
98C4×Dic10C2×C411yescharacteristic
99C4×Dic10C2311yescharacteristic
100C5×C4⋊C8C2311yescharacteristic
101C5×C4⋊C8C2311yescharacteristic
102C5×C22⋊C8—21no—
103C5×#97—21no—
104C4×C5×C8—21no—
105C4×C5×C8C2311yescharacteristic
106C4×C5×C8C2311yescharacteristic
107#3967C2×C411yescharacteristic
108#3967C2×C411yescharacteristic
109#3964C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111C22⋊#168—21no—
112C22⋊#168—21no—
113C22⋊#168—21no—
114C22⋊#168C2×C411yescharacteristic
115C22⋊#168C2×C411yescharacteristic
116#3952—21no—
117#3952—21no—
118#3947—21no—
119#3947—21no—
120#3946—21no—
121#3946—21no—
122#3942C2×C411yescharacteristic
123#3942C2×C411yescharacteristic
124#3941C2×C411yescharacteristic
125#3941C2×C411yescharacteristic
126#3940C2×C411yescharacteristic
127#3940C2×C411yescharacteristic
128#3939C2×C411yescharacteristic
129#3939C2×C411yescharacteristic
130C4⋊#168—21no—
131C4⋊#168—21no—
132C4⋊#168C2×C411yescharacteristic
133C4⋊#168C2×C411yescharacteristic
134C4⋊#168C2311yescharacteristic
135C4⋊#168C2311yescharacteristic
136#3935—21no—
137#3935D411yescharacteristic
138#3935D411yescharacteristic
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3102—51no—
146#2970—51no—
147#2969—51no—
148#1593—51no—
149#1592—51no—
150#1587—51no—
151#1586—51no—
152#1585—51no—
153#1585—51no—
154#1580—51no—
155SD16⋊C8—51no—
156#1572—51no—
157#1494D511yescharacteristic, complemented
158#1476—51no—
159#1451—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
167C2×C22⋊D5—21no—
168#709—22no—
169#709—41no—
170C2×D20C22×C411yescharacteristic
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×Dic10C22×C411yescharacteristic
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—42no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C5×C22⋊C4—21no—
187C5×C22⋊C4—21no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C42×C5—21no—
192C42×C5C22×C411yescharacteristic
193C42×C5C2×D411yescharacteristic
194C42×C5#4111yescharacteristic
195C42×C5C2411yescharacteristic
196C22⋊Dic5—21no—
197#689—41no—
198#688—22no—
199#687—41no—
200#686—22no—
201#685—21no—
202#685—21no—
203C4⋊Dic5C22×C411yescharacteristic
204C4⋊Dic5C22×C411yescharacteristic
205#683—21no—
206#683—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210#681—41no—
211#681—41no—
212#681—42no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—42no—
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C2×D411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C8×D5—42no—
225C8×D5—42no—
226#529C2×D511yescharacteristic
227C4×#41—51no—
228#485—51no—
229#482—51no—
230#479—51no—
231#478—51no—
232#464—51no—
233#463—51no—
234#452—51no—
235#449—51no—
236#446—51no—
237#446—51no—
238#446—51no—
239C8×Q8—51no—
240C4×Q16—51no—
241C4×SD16—51no—
242C4×SD16—51no—
243C4×D8—51no—
244#436—51no—
245#436—101no—
246#435—101no—
247#435—101no—
248#435—101no—
249C8×D4—51no—
250C8×D4—51no—
251C8×D4—51no—
252#433—101no—
253#432—101no—
254#432C2×D511yescharacteristic
255#431—51no—
256#431—51no—
257#405—101no—
258C4×M16—51no—
259C2×#97—101no—
260C2×C4×C8C2×D511yescharacteristic
261#335—51no—
262#335—51no—
263#334—51no—
264#334—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267Q8⋊C8C2×D511yescharacteristic
268Q8⋊C8C2×D511yescharacteristic
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8C2×D511yescharacteristic
272D4⋊C8C2×D511yescharacteristic
273#322—51no—
274#322—51no—
275#322—51no—
276#322—51no—
277C23×C5—21no—
278C23×C5C4×D411yescharacteristic
279C22×D5—21no—
280C5×Q8—21no—
281C5×Q8—21no—
282C5×D4—21no—
283C5×D4—21no—
284C5×D4—81no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5C4×D411yescharacteristic
296C2×C4×C5C4×D411yescharacteristic
297C2×C4×C5C4×D411yescharacteristic
298C2×C4×C5C23×C411yescharacteristic
299C2×C4×C5C22×D411yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C22⋊D5—42no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305D20—21no—
306D20#13112yes—
307C4×D5—42no—
308C4×D5—41no—
309C4×D5—41no—
310C4×D5—81no—
311Dic10—21no—
312Dic10—21no—
313C5×C8—22no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317#168—21no—
318#168—21no—
319#168—21no—
320#168—21no—
321#168—21no—
322#168—21no—
323#168—21no—
324#168—21no—
325#168—41no—
326#168—41no—
327C2×#41—51no—
328C2×Q16—51no—
329C2×SD16—51no—
330C2×SD16—51no—
331C2×D8—51no—
332C2×M16—51no—
333C2×M16—51no—
334C2×M16—101no—
335C22×C8—21no—
336C22×C8—101no—
337C22×C8—101no—
338C22×C8—101no—
339#126—21no—
340#125C4×D511yescharacteristic
341#124C4×D511yescharacteristic
342#123—21no—
343C22⋊Q8C4×D511yescharacteristic
344#121C4×D511yescharacteristic
345C4×Q8—51no—
346C4×Q8—51no—
347C4×Q8C22×D511yescharacteristic
348C4×D4—21no—
349C4×D4—51no—
350C4×D4—51no—
351C4×D4—101no—
352C4×D4—101no—
353C4×D4C22×D511yescharacteristic
354#117—21no—
355#117—51no—
356#117—101no—
357C2×C42—101no—
358C2×C42C22×D511yescharacteristic
359#107—51no—
360#107—51no—
361#106—51no—
362#106—51no—
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⋊C8C22×D511yescharacteristic
372C4⋊C8C22×D511yescharacteristic
373#103—51no—
374#103—51no—
375#103—51no—
376#103—51no—
377#102—51no—
378#102—51no—
379#102—51no—
380#102—51no—
381C22⋊C8—21no—
382C22⋊C8—51no—
383C22⋊C8—51no—
384C22⋊C8—101no—
385C22⋊C8—101no—
386C22⋊C8—101no—
387C22⋊C8—101no—
388C22⋊C8—101no—
389#97—21no—
390#97—51no—
391#97—51no—
392#97—101no—
393#97—101no—
394#97—101no—
395C4×C8—21no—
396C4×C8—51no—
397C4×C8—51no—
398C4×C8—51no—
399C4×C8—51no—
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×C5C2×C4×D411yescharacteristic
411C2×D5—22no—
412C2×D5—41no—
413C2×D5—41no—
414C4×C5—21no—
415C4×C5—21no—
416C4×C5—21no—
417C4×C5—21no—
418C4×C5—41no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5C2×#13111yescharacteristic
422C4×C5#56811yescharacteristic
423C4×C5#57511yescharacteristic
424C4×C5#57511yescharacteristic
425Dic5—41no—
426Dic5—41no—
427Dic5—41no—
428#41—102no—
429#41—201no—
430C2×Q8—51no—
431C2×Q8C2×C4×D511yescharacteristic
432C2×D4—21no—
433C2×D4—51no—
434C2×D4—101no—
435C2×D4C2×C4×D511yescharacteristic
436C22×C4—21no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4C2×C4×D511yescharacteristic
441C22×C4D4×D511yescharacteristic
442C22×C4#71111yescharacteristic
443Q16—201no—
444SD16—102no—
445SD16—201no—
446D8—102no—
447M16—201no—
448M16—201no—
449M16—202no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—51no—
456C2×C8—51no—
457C2×C8—51no—
458C2×C8—51no—
459C2×C8—51no—
460C2×C8—51no—
461C2×C8—51no—
462C2×C8—51no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—202no—
466C2×C8—202no—
467C2×C8—202no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—51no—
473C4⋊C4—51no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4C2×C4×D511yescharacteristic
477C4⋊C4C2×C4×D511yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—101no—
484C22⋊C4—101no—
485C22⋊C4—101no—
486C42—21no—
487C42—101no—
488C42—101no—
489C42—101no—
490C42C2×C4×D511yescharacteristic
491C42D4×D511yescharacteristic
492C42#71111yescharacteristic
493C42C23×D511yescharacteristic
494C2×C5—41no—
495C2×C5—81no—
496C2×C5#293311yescharacteristic
497C2×C5#294311yescharacteristic
498C2×C5#295611yescharacteristic
499D5—42no—
500C23—21no—
501C23—101no—
502C23#402711yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—101no—
506Q8—101no—
507D4—21no—
508D4—21no—
509D4—52no—
510D4—81no—
511D4—101no—
512D4—202no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—202no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—401no—
530C2×C4#402711yescharacteristic
531C2×C4#402711yescharacteristic
532C2×C4#402711yescharacteristic
533C2×C4C22×C4×D511yescharacteristic
534C2×C4C2×D4×D511yescharacteristic
535C2×C4C2×#71111yescharacteristic
536C8—22no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—101no—
541C8—101no—
542C8—101no—
543C8—101no—
544C8—101no—
545C8—101no—
546C8—101no—
547C8—101no—
548C8—201no—
549C8—201no—
550C5#1800211yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—102no—
558C22—201no—
559C22—201no—
560C22C2×#402711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—201no—
569C4—201no—
570C4—201no—
571C4D5×#13111yescharacteristic
572C4#6608411yescharacteristic
573C4#6610211yescharacteristic
574C4#6610211yescharacteristic
575C2—41no—
576C2—81no—
577C2—202no—
578C2#1061039011yescharacteristic
579C2#1061055011yescharacteristic
580C2#1061071111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1494C2
socleC22×C5C2×C4×D4
prime radical#65326C4
cosocleC42×C5C24
hypercenter#1494D5
hypocenterC5#18002
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #10614860C2semidirect
3. #10611059C2semidirect
4. C5×#1494C2semidirect
5. #10601589C2semidirect
6. #10600527C2semidirect
7. #10600518C2semidirect
8. #10599020C2semidirect
9. #10599014C2semidirect
10. #10599013C2semidirect
11. #10599007C2semidirect
12. #10598955C2semidirect
13. #10598951C2semidirect
14. #10598949C2semidirect
15. #10598944C2semidirect
157. #1494D5semidirect
550. C5#18002semidirect

Maximal subgroups

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

subgroupindex
#106148712
#106148602
#106110592
C5×#14942
#106015892
#106005272
#106005182
#105990202
#105990142
#105990132
#105990072
#105989552
#105989512
#105989492
#105989442
#180025