Finite Group Databasebeta

← #12069373

Subgroups — #12069373

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#10611042C211yesmaximal, characteristic
2#10610994C211yesmaximal, characteristic, complemented
3#10610784C211yesmaximal, characteristic
4C5×#1574C211yesmaximal, characteristic, complemented
5#10601552C211yesmaximal, characteristic
6#10601537C211yesmaximal, characteristic, complemented
7#10601293C211yesmaximal, characteristic, complemented
8#10599355C211yesmaximal, characteristic, complemented
9#10599353C211yesmaximal, characteristic, complemented
10#10599351C211yesmaximal, characteristic, complemented
11#10599350C211yesmaximal, characteristic, complemented
12#10599315C211yesmaximal, characteristic, complemented
13#10599313C211yesmaximal, characteristic, complemented
14#10599310C211yesmaximal, characteristic, complemented
15#10599309C211yesmaximal, characteristic, complemented
16#65813C2211yescharacteristic
17C2×C4×Dic10C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#431C2211yescharacteristic
20C5×#423C2211yescharacteristic
21#65417—21no—
22#65416—21no—
23#65214C2211yescharacteristic
24#65214C2211yescharacteristic
25#65134C411yescharacteristic
26#65134C411yescharacteristic
27#65129—21no—
28#65128—21no—
29#65127C2211yescharacteristic
30#65123C2211yescharacteristic
31#65120C2211yescharacteristic
32#65119C2211yescharacteristic
33#65119C2211yescharacteristic
34#65119C2211yescharacteristic
35#65119C2211yescharacteristic
36#65119C2211yescharacteristic
37#65118C411yescharacteristic
38#65118C411yescharacteristic
39#65028C411yescharacteristic
40#65027C411yescharacteristic
41#65025C411yescharacteristic
42#65010C411yescharacteristic
43#65007—21no—
44#65007—21no—
45C4×Dic20C2211yescharacteristic
46C4×Dic20C2211yescharacteristic
47C4×#677C2211yescharacteristic
48C4×#677C2211yescharacteristic
49C8×Dic10—21no—
50C8×Dic10—21no—
51C5×#335C2211yescharacteristic
52C5×#335C2211yescharacteristic
53C5×#334C2211yescharacteristic
54C5×#334C2211yescharacteristic
55#64704C2211yescharacteristic
56#64704C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64704C2211yescharacteristic
60#64704C2211yescharacteristic
61#64703C2211yescharacteristic
62#64703C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17919—51nomaximal, Sylow
68C22×Dic10C2×C411yescharacteristic
69C2×C5×M16—21no—
70C2×C42×C5C2311yescharacteristic
71#4076C2×C411yescharacteristic
72#4075—21no—
73C4×C22⋊D5—21no—
74C2×C4⋊Dic5C2×C411yescharacteristic
75#4070C2×C411yescharacteristic
76C2×#683—21no—
77C2×C4×Dic5—21no—
78C2×Dic20C2×C411yescharacteristic
79C2×Dic20C2×C411yescharacteristic
80C2×#677C2×C411yescharacteristic
81C2×#677C2×C411yescharacteristic
82C2×#676—21no—
83C2×C8×D5—21no—
84#4022—21no—
85#4021C2×C411yescharacteristic
86C4×D20C2311yescharacteristic
87#4018—21no—
88#4016C2×C411yescharacteristic
89C4×Dic10—21no—
90C4×Dic10—21no—
91C4×Dic10C2×C411yescharacteristic
92C4×Dic10C2×C411yescharacteristic
93C4×Dic10C2311yescharacteristic
94C4×Dic10C2311yescharacteristic
95C4×Dic10C2311yescharacteristic
96C5×C4⋊C8—21no—
97C5×C4⋊C8C2×C411yescharacteristic
98C5×C4⋊C8C2×C411yescharacteristic
99C5×C4⋊C8C2311yescharacteristic
100C5×C4⋊C8C2311yescharacteristic
101C5×C4⋊C8C2311yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×C22⋊C8—21no—
104C5×C22⋊C8C2×C411yescharacteristic
105C5×C22⋊C8C2×C411yescharacteristic
106C4×C5×C8—21no—
107C4×C5×C8C2311yescharacteristic
108C4×C5×C8C2311yescharacteristic
109C22⋊#168—21no—
110C22⋊#168D411yescharacteristic
111C22⋊#168D411yescharacteristic
112#3953C2×C411yescharacteristic
113#3953C2×C411yescharacteristic
114#3952—21no—
115#3952—21no—
116#3950C2×C411yescharacteristic
117#3950C2×C411yescharacteristic
118#3949C2×C411yescharacteristic
119#3949C2×C411yescharacteristic
120#3948C2×C411yescharacteristic
121#3948C2×C411yescharacteristic
122#3948C2×C411yescharacteristic
123#3948C2×C411yescharacteristic
124#3948C2×C411yescharacteristic
125#3948C2×C411yescharacteristic
126#3947—21no—
127#3946—21no—
128#3946—21no—
129#3946—21no—
130#3946—21no—
131#3946—21no—
132#3946—21no—
133C8×Dic5—21no—
134C8×Dic5—21no—
135C8×Dic5—21no—
136C8×Dic5—21no—
137C8×Dic5—21no—
138C4⋊#168—21no—
139C4⋊#168D411yescharacteristic
140C4⋊#168D411yescharacteristic
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#1574D511yescharacteristic, complemented
157#1487—51no—
158#1482—51no—
159#1454—51no—
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C2×C22⋊D5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C2×D20C22×C411yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10—21no—
169C2×Dic10—22no—
170C2×Dic10—22no—
171C2×Dic10C22×C411yescharacteristic
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C5×M16—81no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C22×C411yescharacteristic
182C2×C5×C8C22×C411yescharacteristic
183C42×C5C22×C411yescharacteristic
184C42×C5C2×D411yescharacteristic
185C42×C5#4111yescharacteristic
186C42×C5C2411yescharacteristic
187C22⋊Dic5—21no—
188#685—21no—
189#685—21no—
190#685—21no—
191#685—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5C22×C411yescharacteristic
194C4⋊Dic5C22×C411yescharacteristic
195C4⋊Dic5C22×C411yescharacteristic
196C4⋊Dic5C22×C411yescharacteristic
197#683—21no—
198#683—21no—
199#683—21no—
200#683—21no—
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168C2×D411yescharacteristic
213C2×#168C2×D411yescharacteristic
214C2×#168C2×D411yescharacteristic
215C2×#168C2×D411yescharacteristic
216Dic20—22no—
217Dic20—22no—
218#677—22no—
219#677—22no—
220#676—81no—
221C8×D5—81no—
222#529—51no—
223C2×C4×Q8—51no—
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—101no—
252#431—101no—
253#431C2×D511yescharacteristic
254#431C2×D511yescharacteristic
255#424—101no—
256#423C2×D511yescharacteristic
257#335C2×D511yescharacteristic
258#335C2×D511yescharacteristic
259#334C2×D511yescharacteristic
260#334C2×D511yescharacteristic
261Q8⋊C8—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8—51no—
267D4⋊C8—51no—
268D4⋊C8—51no—
269#322—51no—
270#322—51no—
271#322—51no—
272C82—51no—
273C23×C5C4×D411yescharacteristic
274C22×D5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—41no—
280C2×C4×C5C4×D411yescharacteristic
281C2×C4×C5C4×D411yescharacteristic
282C2×C4×C5C4×D411yescharacteristic
283C2×C4×C5C23×C411yescharacteristic
284C2×C4×C5C22×D411yescharacteristic
285C2×C4×C5C2×#4111yescharacteristic
286C22⋊D5—81no—
287C2×Dic5—24no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—81no—
296D20—21no—
297D20—21no—
298C4×D5—41no—
299C4×D5—41no—
300Dic10—24no—
301Dic10—21no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10#13112yes—
306Dic10#13112yes—
307C5×C8—21no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—21no—
319#168—41no—
320#168—41no—
321C22×Q8—51no—
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—51no—
336C4×Q8—51no—
337C4×Q8—51no—
338C4×Q8—51no—
339C4×Q8—51no—
340C4×Q8—101no—
341C4×Q8—101no—
342C4×D4—51no—
343C4×D4—101no—
344#117—101no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—101no—
347C2×C42—101no—
348C2×C42C22×D511yescharacteristic
349#107—51no—
350#107—51no—
351#106—51no—
352#106—51no—
353C4⋊C8—21no—
354C4⋊C8—51no—
355C4⋊C8—51no—
356C4⋊C8—101no—
357C4⋊C8—101no—
358C4⋊C8—101no—
359C4⋊C8—101no—
360C4⋊C8—101no—
361C4⋊C8—101no—
362C4⋊C8—101no—
363C4⋊C8C4×D511yescharacteristic
364C4⋊C8C4×D511yescharacteristic
365C4⋊C8C22×D511yescharacteristic
366C4⋊C8C22×D511yescharacteristic
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—101no—
381C22⋊C8—101no—
382C22⋊C8—101no—
383C22⋊C8C4×D511yescharacteristic
384C22⋊C8C4×D511yescharacteristic
385#97—101no—
386C4×C8—21no—
387C4×C8—51no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
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—21no—
406C4×C5—21no—
407C4×C5—21no—
408C4×C5—21no—
409C4×C5C2×#13111yescharacteristic
410C4×C5C2×#13111yescharacteristic
411C4×C5#57711yescharacteristic
412C4×C5#57811yescharacteristic
413Dic5—22no—
414Dic5—22no—
415Dic5—41no—
416Dic5—41no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420C2×Q8—51no—
421C2×Q8—51no—
422C2×Q8—51no—
423C2×Q8—102no—
424C2×Q8—102no—
425C2×Q8—101no—
426C2×D4—51no—
427C2×D4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4C2×C4×D511yescharacteristic
432C22×C4D4×D511yescharacteristic
433C22×C4#71311yescharacteristic
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—101no—
449C2×C8—101no—
450C2×C8—401no—
451C2×C8C2×C4×D511yescharacteristic
452C2×C8C2×C4×D511yescharacteristic
453C2×C8C2×C4×D511yescharacteristic
454C2×C8C2×C4×D511yescharacteristic
455C4⋊C4—51no—
456C4⋊C4—51no—
457C4⋊C4—51no—
458C4⋊C4—51no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C22⋊C4—101no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C42—101no—
474C42—101no—
475C42—101no—
476C42—101no—
477C42—101no—
478C42C2×C4×D511yescharacteristic
479C42D4×D511yescharacteristic
480C42#71311yescharacteristic
481C42C23×D511yescharacteristic
482C2×C5—41no—
483C2×C5#292911yescharacteristic
484C2×C5#294711yescharacteristic
485C2×C5#295711yescharacteristic
486D5—81no—
487C23—101no—
488C23#403911yescharacteristic
489Q8—52no—
490Q8—52no—
491Q8—104no—
492Q8—101no—
493Q8—101no—
494Q8—101no—
495Q8—101no—
496D4—101no—
497D4—101no—
498D4—401no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—104no—
505C2×C4—101no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—201no—
513C2×C4—201no—
514C2×C4—401no—
515C2×C4#403911yescharacteristic
516C2×C4#403911yescharacteristic
517C2×C4#403911yescharacteristic
518C2×C4C22×C4×D511yescharacteristic
519C2×C4C2×D4×D511yescharacteristic
520C2×C4C2×#71311yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
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×#403911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—102no—
548C4—102no—
549C4—201no—
550C4—201no—
551C4—201no—
552C4—201no—
553C4—201no—
554C4D5×#13111yescharacteristic
555C4D5×#13111yescharacteristic
556C4#6610911yescharacteristic
557C4#6611311yescharacteristic
558C2—41no—
559C2—401no—
560C2#1061080411yescharacteristic
561C2#1061093311yescharacteristic
562C2#1061098011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1574C2
socleC22×C5C2×C4×D4
prime radical#4076C2×C4
cosocleC42×C5C24
hypercenter#1574D5
hypocenterC5#17919
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #10610994C2semidirect
4. C5×#1574C2semidirect
6. #10601537C2semidirect
7. #10601293C2semidirect
8. #10599355C2semidirect
9. #10599353C2semidirect
10. #10599351C2semidirect
11. #10599350C2semidirect
12. #10599315C2semidirect
13. #10599313C2semidirect
14. #10599310C2semidirect
15. #10599309C2semidirect
156. #1574D5semidirect
535. C5#17919semidirect

Maximal subgroups

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

subgroupindex
#106110422
#106109942
#106107842
C5×#15742
#106015522
#106015372
#106012932
#105993552
#105993532
#105993512
#105993502
#105993152
#105993132
#105993102
#105993092
#179195