Finite Group Databasebeta

← #12069400

Subgroups — #12069400

Order 1280.

598 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#10611696C211yesmaximal, characteristic, complemented
2#10611386C211yesmaximal, characteristic
3#10611136C211yesmaximal, characteristic
4C5×#1582C211yesmaximal, characteristic, complemented
5#10601750C211yesmaximal, characteristic, complemented
6SD16⋊#168C211yesmaximal, characteristic, complemented
7#10601636C211yesmaximal, characteristic, complemented
8#10599327C211yesmaximal, characteristic, complemented
9#10599310C211yesmaximal, characteristic, complemented
10#10599025C211yesmaximal, characteristic, complemented
11#10599006C211yesmaximal, characteristic, complemented
12#10598966C211yesmaximal, characteristic
13#10598942C211yesmaximal, characteristic, complemented
14#10598879C211yesmaximal, characteristic, complemented
15#10598867C211yesmaximal, characteristic, complemented
16#65912C2211yescharacteristic
17C4×#711C2211yescharacteristic
18C5×#446C2211yescharacteristic
19C4×C5×SD16C2211yescharacteristic
20C5×C8×D4C2211yescharacteristic
21#65462C411yescharacteristic
22#65451C411yescharacteristic
23C8×C22⋊D5—21no—
24C2×#3946—21no—
25C4×#689C2211yescharacteristic
26Q8×#168C2211yescharacteristic
27C4×#687C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65156C411yescharacteristic
30#65143C411yescharacteristic
31#65129—21no—
32#65124C2211yescharacteristic
33D5×C4⋊C8C2211yescharacteristic
34#65120—21no—
35#65119C2211yescharacteristic
36#65119C2211yescharacteristic
37#65103C411yescharacteristic
38#65082C411yescharacteristic
39#65072C411yescharacteristic
40#65048C411yescharacteristic
41#65014—21no—
42#65007—21no—
43#64998—21no—
44#64990—21no—
45C4×Dic20C2211yescharacteristic
46#64974C2211yescharacteristic
47#64974C2211yescharacteristic
48#64974C2211yescharacteristic
49#64968C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#334C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64700C2211yescharacteristic
60#64699C2211yescharacteristic
61#64678C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64675C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17921—51nomaximal, Sylow
68C2×#711C2×C411yescharacteristic
69C2×C5×SD16C2×C411yescharacteristic
70C22×C5×C8—21no—
71C4×C5×Q8C2311yescharacteristic
72C4×C5×D4C2311yescharacteristic
73#4092C2×C411yescharacteristic
74#4090C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76D4×Dic5C2×C411yescharacteristic
77C2×#687C2×C411yescharacteristic
78C4×C22⋊D5—21no—
79C2×C4×Dic5—21no—
80C22×#168—21no—
81C2×Dic20C2×C411yescharacteristic
82C2×C8×D5—21no—
83#4043C2×C411yescharacteristic
84#4042—21no—
85#4038C2×C411yescharacteristic
86#4035—21no—
87#4034C2×C411yescharacteristic
88#4033C2×C411yescharacteristic
89#4027—21no—
90#4023—21no—
91#4018—21no—
92C42×D5C2311yescharacteristic
93C4×Dic10—21no—
94C4×Dic10C2311yescharacteristic
95C4×Dic10C2311yescharacteristic
96C5×#106C2×C411yescharacteristic
97C5×C4⋊C8—21no—
98C5×C4⋊C8C2311yescharacteristic
99C5×C4⋊C8C2311yescharacteristic
100C5×#103C2×C411yescharacteristic
101C5×#102C2×C411yescharacteristic
102C5×C22⋊C8—21no—
103C5×#97—21no—
104C4×C5×C8C2311yescharacteristic
105C4×C5×C8C2311yescharacteristic
106C4×C5×C8C2311yescharacteristic
107#3967C2×C411yescharacteristic
108#3964C2×C411yescharacteristic
109C22⋊#168—21no—
110#3952—21no—
111#3952—21no—
112#3952C2×C411yescharacteristic
113#3952C2×C411yescharacteristic
114#3952D411yescharacteristic
115#3952D411yescharacteristic
116#3950C2×C411yescharacteristic
117#3948C2×C411yescharacteristic
118#3948C2×C411yescharacteristic
119#3947—21no—
120#3947—21no—
121#3946—21no—
122#3946—21no—
123#3946—21no—
124#3946—21no—
125#3946—21no—
126#3946—21no—
127#3946C2×C411yescharacteristic
128#3946C2×C411yescharacteristic
129#3946D411yescharacteristic
130#3946D411yescharacteristic
131C8×Dic5—21no—
132C8×Dic5—21no—
133C8×Dic5—21no—
134#3942C2×C411yescharacteristic
135#3942C2×C411yescharacteristic
136#3940C2×C411yescharacteristic
137#3939C2×C411yescharacteristic
138C4⋊#168—21no—
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141C4×#168—21no—
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3107—51no—
146#2988—51no—
147#2985—51no—
148#1587—51no—
149#1585—51no—
150#1584—51no—
151#1582D511yescharacteristic, complemented
152#1579—51no—
153SD16⋊C8—51no—
154C8×Q16—51no—
155C8×SD16—51no—
156#1573—51no—
157#1488—51no—
158#1481—51no—
159#1454—51no—
160C2×C5×Q8C22×C411yescharacteristic
161C2×C5×D4C22×C411yescharacteristic
162C22×C4×C5—21no—
163C2×C22⋊D5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166#711—22no—
167#711—22no—
168C2×C4×D5C22×C411yescharacteristic
169C2×C4×D5C2×D411yescharacteristic
170C2×C4×D5#4111yescharacteristic
171C2×Dic10—21no—
172C2×Dic10C22×C411yescharacteristic
173C2×Dic10C22×C411yescharacteristic
174C5×SD16—22no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—81no—
179C2×C5×C8C22×C411yescharacteristic
180C2×C5×C8C22×C411yescharacteristic
181C2×C5×C8C2×D411yescharacteristic
182C2×C5×C8C2×D411yescharacteristic
183C5×C4⋊C4—21no—
184C5×C4⋊C4C22×C411yescharacteristic
185C5×C4⋊C4C22×C411yescharacteristic
186C5×C22⋊C4—21no—
187C42×C5—21no—
188C42×C5C2411yescharacteristic
189C22⋊Dic5—21no—
190#689—22no—
191#687—22no—
192#685—21no—
193#685—21no—
194#685—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5C22×C411yescharacteristic
197C4⋊Dic5C22×C411yescharacteristic
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×Dic5C22×C411yescharacteristic
210C4×Dic5C2×D411yescharacteristic
211C4×Dic5#4111yescharacteristic
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—81no—
216C2×#168C22×C411yescharacteristic
217C2×#168C22×C411yescharacteristic
218C2×#168C2×D411yescharacteristic
219C2×#168C2×D411yescharacteristic
220Dic20—22no—
221C8×D5—81no—
222#533—51no—
223C4×#41—51no—
224#485—51no—
225#485—51no—
226#475—51no—
227#474—51no—
228#462—51no—
229#461—51no—
230#452—51no—
231#452—51no—
232#446—51no—
233#446—101no—
234#446—101no—
235#446C2×D511yescharacteristic
236C8×Q8—51no—
237C8×Q8—51no—
238C8×Q8—51no—
239C8×Q8—51no—
240C4×Q16—51no—
241C4×Q16—51no—
242C4×SD16—51no—
243C4×SD16C2×D511yescharacteristic
244C8×D4—51no—
245C8×D4—101no—
246C8×D4—101no—
247C8×D4C2×D511yescharacteristic
248#433—101no—
249#433—101no—
250#432—51no—
251#431—51no—
252#431—51no—
253#431—51no—
254#431—101no—
255C2×C4⋊C8—51no—
256C2×C4⋊C8—101no—
257#335—51no—
258#335—51no—
259#334—51no—
260#334C2×D511yescharacteristic
261Q8⋊C8—51no—
262Q8⋊C8—51no—
263Q8⋊C8—51no—
264Q8⋊C8—51no—
265Q8⋊C8—51no—
266Q8⋊C8C2×D511yescharacteristic
267D4⋊C8—51no—
268D4⋊C8C2×D511yescharacteristic
269#322—51no—
270#322—51no—
271#322C2×D511yescharacteristic
272C82—51no—
273C23×C5—21no—
274C22×D5C4×D411yescharacteristic
275C5×Q8—21no—
276C5×Q8—21no—
277C5×D4—21no—
278C5×D4#13112yes—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5C23×C411yescharacteristic
285C2×C4×C5C22×D411yescharacteristic
286C2×C4×C5C2×#4111yescharacteristic
287C22⋊D5—24no—
288C2×Dic5—24no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—81no—
294C2×Dic5C4×D411yescharacteristic
295C2×Dic5C4×D411yescharacteristic
296C2×Dic5C4×D411yescharacteristic
297C4×D5—21no—
298C4×D5—21no—
299C4×D5—21no—
300C4×D5—21no—
301C4×D5—41no—
302Dic10—21no—
303Dic10—21no—
304Dic10—21no—
305Dic10—81no—
306Dic10#13112yes—
307C5×C8—21no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314#168—21no—
315#168—21no—
316#168—21no—
317#168—21no—
318#168—41no—
319#168—41no—
320#168—41no—
321C2×#41—51no—
322C2×Q16—51no—
323C2×Q16—51no—
324C2×SD16—51no—
325C2×SD16C4×D511yescharacteristic
326C22×C8—21no—
327C22×C8—101no—
328C22×C8—101no—
329C4⋊Q8—51no—
330C4⋊Q8—51no—
331#125—101no—
332C22⋊Q8—51no—
333C22⋊Q8—51no—
334C22⋊Q8—101no—
335C4×Q8—51no—
336C4×Q8—51no—
337C4×Q8—51no—
338C4×Q8—101no—
339C4×Q8C22×D511yescharacteristic
340C4×D4—51no—
341C4×D4—101no—
342C4×D4—101no—
343C4×D4C22×D511yescharacteristic
344#117—51no—
345#117—101no—
346#117—101no—
347C2×C42—51no—
348C2×C42—101no—
349#107—51no—
350#107—51no—
351#106—51no—
352#106C4×D511yescharacteristic
353C4⋊C8—21no—
354C4⋊C8—51no—
355C4⋊C8—51no—
356C4⋊C8—51no—
357C4⋊C8—51no—
358C4⋊C8—51no—
359C4⋊C8—51no—
360C4⋊C8—101no—
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#103C4×D511yescharacteristic
375#102—51no—
376#102C4×D511yescharacteristic
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—21no—
386#97—101no—
387#97—101no—
388C4×C8—51no—
389C4×C8—51no—
390C4×C8—51no—
391C4×C8—101no—
392C4×C8—101no—
393C4×C8—101no—
394C4×C8—101no—
395C4×C8C22×D511yescharacteristic
396C4×C8C22×D511yescharacteristic
397C4×C8C22×D511yescharacteristic
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5C2×C4×D411yescharacteristic
402C2×D5—21no—
403C2×D5—21no—
404C2×D5—21no—
405C4×C5—21no—
406C4×C5—41no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5C2×#13111yescharacteristic
410C4×C5C2×#13111yescharacteristic
411C4×C5#57711yescharacteristic
412C4×C5#57811yescharacteristic
413Dic5—22no—
414Dic5—21no—
415Dic5—21no—
416Dic5—21no—
417Dic5—41no—
418Dic5—41no—
419Dic5—41no—
420#41—102no—
421#41—102no—
422C2×Q8—51no—
423C2×Q8—51no—
424C2×Q8—101no—
425C2×Q8C2×C4×D511yescharacteristic
426C2×D4—101no—
427C2×D4C2×C4×D511yescharacteristic
428C22×C4—21no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—101no—
433C22×C4—101no—
434Q16—102no—
435Q16—102no—
436SD16—22no—
437SD16—102no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—51no—
442C2×C8—51no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—81no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—401no—
450C2×C8—401no—
451C2×C8C2×C4×D511yescharacteristic
452C2×C8C2×C4×D511yescharacteristic
453C2×C8D4×D511yescharacteristic
454C2×C8D4×D511yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—51no—
457C4⋊C4—51no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4C2×C4×D511yescharacteristic
467C4⋊C4C2×C4×D511yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—101no—
470C22⋊C4—101no—
471C22⋊C4—101no—
472C22⋊C4—101no—
473C42—21no—
474C42—51no—
475C42—51no—
476C42—51no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42C23×D511yescharacteristic
482C2×C5—42no—
483C2×C5#292911yescharacteristic
484C2×C5#294711yescharacteristic
485C2×C5#295711yescharacteristic
486D5—41no—
487C23—21no—
488C23—51no—
489Q8—21no—
490Q8—21no—
491Q8—52no—
492Q8—101no—
493Q8—101no—
494Q8—101no—
495Q8—401no—
496D4—21no—
497D4—104no—
498D4#405312yes—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—51no—
507C2×C4—104no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—201no—
517C2×C4—401no—
518C2×C4C22×C4×D511yescharacteristic
519C2×C4C2×D4×D511yescharacteristic
520C2×C4D5×#4111yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—101no—
529C8—101no—
530C8—101no—
531C8—101no—
532C8—201no—
533C8—201no—
534C8—201no—
535C5#1792111yescharacteristic, complemented, Sylow
536C22—22no—
537C22—41no—
538C22—41no—
539C22—101no—
540C22—101no—
541C22—101no—
542C22C4×D4×D511yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—101no—
548C4—102no—
549C4—101no—
550C4—101no—
551C4—201no—
552C4—201no—
553C4—201no—
554C4C2×#405311yescharacteristic
555C4D5×#13111yescharacteristic
556C4#6609611yescharacteristic
557C4#6610511yescharacteristic
558C2—42no—
559C2—201no—
560C2#1061120911yescharacteristic
561C2#1061137911yescharacteristic
562C2#1061163011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1582C2
socleC22×C5C2×C4×D4
prime radicalC2×#711C2×C4
cosocleC42×C5C24
hypercenter#1582D5
hypocenterC5#17921
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #10611696C2semidirect
4. C5×#1582C2semidirect
5. #10601750C2semidirect
6. SD16⋊#168C2semidirect
7. #10601636C2semidirect
8. #10599327C2semidirect
9. #10599310C2semidirect
10. #10599025C2semidirect
11. #10599006C2semidirect
13. #10598942C2semidirect
14. #10598879C2semidirect
15. #10598867C2semidirect
151. #1582D5semidirect
535. C5#17921semidirect

Maximal subgroups

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

subgroupindex
#106116962
#106113862
#106111362
C5×#15822
#106017502
SD16⋊#1682
#106016362
#105993272
#105993102
#105990252
#105990062
#105989662
#105989422
#105988792
#105988672
#179215