Finite Group Databasebeta

← #12069369

Subgroups — #12069369

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614174C211yesmaximal, characteristic
2#10614166C211yesmaximal, characteristic, complemented
3#10610784C211yesmaximal, characteristic
4C5×#1487C211yesmaximal, characteristic, complemented
5#10601553C211yesmaximal, characteristic
6#10601537C211yesmaximal, characteristic, complemented
7#10601288C211yesmaximal, characteristic, complemented
8#10599016C211yesmaximal, characteristic, complemented
9#10599014C211yesmaximal, characteristic, complemented
10#10599011C211yesmaximal, characteristic, complemented
11#10599010C211yesmaximal, characteristic, complemented
12#10599008C211yesmaximal, characteristic, complemented
13#10599007C211yesmaximal, characteristic, complemented
14#10599006C211yesmaximal, characteristic, complemented
15#10599005C211yesmaximal, characteristic, complemented
16C2×C4×C5×Q8C2211yescharacteristic
17#65813C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#423C2211yescharacteristic
20#65517C411yescharacteristic
21#65516C411yescharacteristic
22#65417—21no—
23#65416—21no—
24C4×#689C2211yescharacteristic
25C4×#689C2211yescharacteristic
26#65317C411yescharacteristic
27#65317C411yescharacteristic
28C4×#688C2211yescharacteristic
29C4×#688C2211yescharacteristic
30Q8×#168—21no—
31Q8×#168—21no—
32Q8×#168C2211yescharacteristic
33Q8×#168C2211yescharacteristic
34Q8×#168C2211yescharacteristic
35Q8×#168C2211yescharacteristic
36#65311C411yescharacteristic
37#65311C411yescharacteristic
38#65260C411yescharacteristic
39#65256C411yescharacteristic
40#65214—21no—
41#65214—21no—
42#65214C2211yescharacteristic
43#65214C2211yescharacteristic
44#65214C2211yescharacteristic
45#65129—21no—
46#65128—21no—
47#65127C2211yescharacteristic
48#65123C2211yescharacteristic
49#65120C2211yescharacteristic
50#65119C2211yescharacteristic
51C5×Q8⋊C8C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×Q8⋊C8C2211yescharacteristic
54C5×Q8⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17919—51nomaximal, Sylow
68C22×C5×Q8C2×C411yescharacteristic
69C2×C5×M16—21no—
70C4×C5×Q8—21no—
71C4×C5×Q8—21no—
72C4×C5×Q8C2×C411yescharacteristic
73C4×C5×Q8C2×C411yescharacteristic
74C4×C5×Q8C2311yescharacteristic
75C4×C5×Q8C2311yescharacteristic
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4C2×C411yescharacteristic
78C2×C42×C5—21no—
79C2×C42×C5C2311yescharacteristic
80C2×#689C2×C411yescharacteristic
81C2×#689C2×C411yescharacteristic
82C2×#688C2×C411yescharacteristic
83C2×#688C2×C411yescharacteristic
84#4076C2×C411yescharacteristic
85#4075—21no—
86C4×C22⋊D5—21no—
87#4070C2×C411yescharacteristic
88C2×#676—21no—
89C2×C8×D5—21no—
90#4022—21no—
91#4021C2×C411yescharacteristic
92C4×D20C2311yescharacteristic
93#4018—21no—
94#4016C2×C411yescharacteristic
95C4×Dic10C2311yescharacteristic
96C5×C4⋊C8—21no—
97C5×C4⋊C8—21no—
98C5×C4⋊C8C2311yescharacteristic
99C5×C4⋊C8C2311yescharacteristic
100C5×C22⋊C8—21no—
101C4×C5×C8C2311yescharacteristic
102C4×C5×C8C2311yescharacteristic
103#3967C2×C411yescharacteristic
104#3967C2×C411yescharacteristic
105#3967C2×C411yescharacteristic
106#3967C2×C411yescharacteristic
107C22⋊#168—21no—
108C22⋊#168C2×C411yescharacteristic
109C22⋊#168C2×C411yescharacteristic
110C22⋊#168D411yescharacteristic
111C22⋊#168D411yescharacteristic
112#3952—21no—
113#3952—21no—
114#3947—21no—
115#3946—21no—
116#3946—21no—
117C8×Dic5—21no—
118#3942C2×C411yescharacteristic
119#3942C2×C411yescharacteristic
120#3941C2×C411yescharacteristic
121#3941C2×C411yescharacteristic
122#3940C2×C411yescharacteristic
123#3940C2×C411yescharacteristic
124#3939C2×C411yescharacteristic
125#3939C2×C411yescharacteristic
126C4⋊#168—21no—
127C4⋊#168—21no—
128C4⋊#168—21no—
129C4⋊#168—21no—
130C4⋊#168C2×C411yescharacteristic
131C4⋊#168C2×C411yescharacteristic
132C4⋊#168D411yescharacteristic
133C4⋊#168D411yescharacteristic
134C4⋊#168C2311yescharacteristic
135C4⋊#168C2311yescharacteristic
136C4×#168—21no—
137C4×#168—21no—
138C4×#168—21no—
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3108—51no—
146#2993—51no—
147#2982—51no—
148#1588—51no—
149#1587—51no—
150#1584—51no—
151#1583—51no—
152#1579—51no—
153SD16⋊C8—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1574—51no—
157#1487D511yescharacteristic, complemented
158#1482—51no—
159#1454—51no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—21no—
163C2×C5×Q8C22×C411yescharacteristic
164C2×C5×Q8C22×C411yescharacteristic
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5C22×C411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5#4111yescharacteristic
170C2×C22⋊D5—21no—
171C2×D20C22×C411yescharacteristic
172C2×C4×D5—21no—
173C2×Dic10C22×C411yescharacteristic
174C5×M16—81no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C42×C5—21no—
187C42×C5—21no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5C22×C411yescharacteristic
191C42×C5C2×D411yescharacteristic
192C42×C5#4111yescharacteristic
193C42×C5C2411yescharacteristic
194C22⋊Dic5—21no—
195#689—22no—
196#689—22no—
197#688—22no—
198#688—22no—
199#685—21no—
200#685—21no—
201#685—21no—
202#685—21no—
203C4⋊Dic5C22×C411yescharacteristic
204C4⋊Dic5C22×C411yescharacteristic
205#683—21no—
206#683—21no—
207#683—21no—
208#683—21no—
209C4×Dic5—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168C22×C411yescharacteristic
213C2×#168C22×C411yescharacteristic
214C2×#168C22×C411yescharacteristic
215C2×#168C22×C411yescharacteristic
216C2×#168C2×D411yescharacteristic
217C2×#168C2×D411yescharacteristic
218C2×#168C2×D411yescharacteristic
219C2×#168C2×D411yescharacteristic
220#676—81no—
221C8×D5—81no—
222#529—51no—
223C2×C4×Q8C2×D511yescharacteristic
224#483—51no—
225#480—51no—
226#479—51no—
227#479—51no—
228#464—51no—
229#464—51no—
230#451—51no—
231#448—51no—
232#446—51no—
233C8×Q8—51no—
234C8×Q8—51no—
235C8×Q8—51no—
236C8×Q8—51no—
237C8×Q8—51no—
238C8×Q8—101no—
239C8×Q8—101no—
240C4×Q16—51no—
241C4×Q16—51no—
242C4×SD16—51no—
243C4×SD16—51no—
244#436—51no—
245#436—101no—
246#435—101no—
247C8×D4—51no—
248#433—101no—
249#431—51no—
250#431—51no—
251#431—51no—
252#431—101no—
253#431—101no—
254#431C2×D511yescharacteristic
255#424—101no—
256#423C2×D511yescharacteristic
257#335—51no—
258#335—51no—
259#334—51no—
260#334—51no—
261Q8⋊C8—51no—
262Q8⋊C8—51no—
263Q8⋊C8C2×D511yescharacteristic
264Q8⋊C8C2×D511yescharacteristic
265Q8⋊C8C2×D511yescharacteristic
266Q8⋊C8C2×D511yescharacteristic
267D4⋊C8—51no—
268D4⋊C8—51no—
269#322—51no—
270#322—51no—
271#322—51no—
272C82—51no—
273C23×C5C4×D411yescharacteristic
274C22×D5—21no—
275C5×Q8—24no—
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8#13112yes—
279C5×Q8#13112yes—
280C2×C4×C5—24no—
281C2×C4×C5—21no—
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—81no—
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—81no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301D20—21no—
302D20—21no—
303C4×D5—41no—
304C4×D5—41no—
305Dic10—21no—
306Dic10—21no—
307C5×C8—41no—
308C5×C8—41no—
309C5×C8—41no—
310C5×C8—41no—
311#168—21no—
312#168—21no—
313#168—21no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—41no—
320#168—41no—
321C22×Q8C4×D511yescharacteristic
322C2×Q16—51no—
323C2×Q16—51no—
324C2×SD16—51no—
325C2×SD16—51no—
326C2×M16—21no—
327C2×M16—101no—
328C22×C8—101no—
329#126—101no—
330#125—51no—
331#124—51no—
332#123—101no—
333C22⋊Q8—51no—
334#121—51no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—51no—
338C4×Q8C4×D511yescharacteristic
339C4×Q8C4×D511yescharacteristic
340C4×Q8C22×D511yescharacteristic
341C4×Q8C22×D511yescharacteristic
342C4×D4—51no—
343C4×D4—101no—
344#117—101no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4C4×D511yescharacteristic
347C2×C42—21no—
348C2×C42C22×D511yescharacteristic
349#107—51no—
350#107—51no—
351#106—51no—
352#106—51no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—51no—
356C4⋊C8—51no—
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⋊C8C22×D511yescharacteristic
368C4⋊C8C22×D511yescharacteristic
369#103—51no—
370#103—51no—
371#103—51no—
372#103—51no—
373#103—51no—
374#103—51no—
375#102—51no—
376#102—51no—
377C22⋊C8—21no—
378C22⋊C8—51no—
379C22⋊C8—51no—
380C22⋊C8—51no—
381C22⋊C8—51no—
382C22⋊C8—101no—
383C22⋊C8—101no—
384C22⋊C8—101no—
385#97—101no—
386C4×C8—51no—
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—101no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8—101no—
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C22×C5—21no—
399C22×C5—21no—
400C22×C5—21no—
401C22×C5C2×C4×D411yescharacteristic
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5—21no—
410C4×C5—21no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5C2×#13111yescharacteristic
414C4×C5C2×#13111yescharacteristic
415C4×C5#57711yescharacteristic
416C4×C5#57811yescharacteristic
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—51no—
424C2×Q8C2×C4×D511yescharacteristic
425C2×Q8C2×C4×D511yescharacteristic
426C2×D4—51no—
427C2×D4—101no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—101no—
431C22×C4C2×C4×D511yescharacteristic
432C22×C4D4×D511yescharacteristic
433C22×C4#71111yescharacteristic
434Q16—102no—
435Q16—102no—
436SD16—102no—
437SD16—102no—
438M16—81no—
439M16—401no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—51no—
447C2×C8—51no—
448C2×C8—51no—
449C2×C8—51no—
450C2×C8—51no—
451C2×C8—51no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—401no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—51no—
461C4⋊C4—51no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4C2×C4×D511yescharacteristic
467C4⋊C4C2×C4×D511yescharacteristic
468C22⋊C4—101no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—101no—
478C42C2×C4×D511yescharacteristic
479C42D4×D511yescharacteristic
480C42#71111yescharacteristic
481C42C23×D511yescharacteristic
482C2×C5—41no—
483C2×C5#292911yescharacteristic
484C2×C5#294711yescharacteristic
485C2×C5#295711yescharacteristic
486D5—81no—
487C23—101no—
488C23#402711yescharacteristic
489Q8—24no—
490Q8—21no—
491Q8—21no—
492Q8—101no—
493Q8—101no—
494Q8#405312yes—
495Q8#405312yes—
496D4—101no—
497D4—101no—
498D4—401no—
499C2×C4—24no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—201no—
514C2×C4—201no—
515C2×C4#402711yescharacteristic
516C2×C4#402711yescharacteristic
517C2×C4#402711yescharacteristic
518C2×C4C22×C4×D511yescharacteristic
519C2×C4C2×D4×D511yescharacteristic
520C2×C4C2×#71111yescharacteristic
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—101no—
526C8—101no—
527C8—101no—
528C8—101no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—101no—
533C8—201no—
534C8—201no—
535C5#1791911yescharacteristic, complemented, Sylow
536C22—21no—
537C22—21no—
538C22—21no—
539C22—201no—
540C22—201no—
541C22—201no—
542C22C2×#402711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—201no—
552C4—201no—
553C4—201no—
554C4C2×#405311yescharacteristic
555C4C2×#405311yescharacteristic
556C4#6609611yescharacteristic
557C4#6610011yescharacteristic
558C2—41no—
559C2—401no—
560C2#1061035711yescharacteristic
561C2#1061050511yescharacteristic
562C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1487C2
socleC22×C5C2×C4×D4
prime radical#4076C2×C4
cosocleC42×C5C24
hypercenter#1487D5
hypocenterC5#17919
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #10614166C2semidirect
4. C5×#1487C2semidirect
6. #10601537C2semidirect
7. #10601288C2semidirect
8. #10599016C2semidirect
9. #10599014C2semidirect
10. #10599011C2semidirect
11. #10599010C2semidirect
12. #10599008C2semidirect
13. #10599007C2semidirect
14. #10599006C2semidirect
15. #10599005C2semidirect
157. #1487D5semidirect
535. C5#17919semidirect

Maximal subgroups

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

subgroupindex
#106141742
#106141662
#106107842
C5×#14872
#106015532
#106015372
#106012882
#105990162
#105990142
#105990112
#105990102
#105990082
#105990072
#105990062
#105990052
#179195