Finite Group Databasebeta

← #12068913

Subgroups — #12068913

Order 1280.

662 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
1D5×#446C211yesmaximal, characteristic, complemented
2C4×#4061C211yesmaximal, characteristic
3C8×#711C211yesmaximal, characteristic
4C5×#1585C211yesmaximal, characteristic, complemented
5#10601750C211yesmaximal, characteristic, complemented
6#10601688C211yesmaximal, characteristic, complemented
7#10601636C211yesmaximal, characteristic, complemented
8#10599361C211yesmaximal, characteristic, complemented
9#10599353C211yesmaximal, characteristic, complemented
10#10599024C211yesmaximal, characteristic, complemented
11#10599012C211yesmaximal, characteristic, complemented
12#10598959C211yesmaximal, characteristic
13#10598947C211yesmaximal, characteristic, complemented
14#10598880C211yesmaximal, characteristic, complemented
15#10598863C211yesmaximal, characteristic, complemented
16C2×#4061C411yescharacteristic
17C4×Q8×D5C2211yescharacteristic
18C4×#711C2211yescharacteristic
19C5×#446C2211yescharacteristic
20C4×C5×SD16C2211yescharacteristic
21C5×C8×D4C2211yescharacteristic
22#65453C411yescharacteristic
23C8×C22⋊D5—21no—
24C2×C8×Dic5—21no—
25C4×#689C2211yescharacteristic
26#65313C2211yescharacteristic
27C4×#687C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65150C411yescharacteristic
30#65142C411yescharacteristic
31#65122C2211yescharacteristic
32D5×C4⋊C8—21no—
33D5×C4⋊C8C2211yescharacteristic
34#65120C2211yescharacteristic
35#65119C2211yescharacteristic
36#65117—21no—
37#65091C411yescharacteristic
38#65078C411yescharacteristic
39#65060C411yescharacteristic
40#65046C411yescharacteristic
41#65014—21no—
42#65007—21no—
43D5×#97—21no—
44#64990—21no—
45C4×Dic20C2211yescharacteristic
46C4×#676C2211yescharacteristic
47#64974C2211yescharacteristic
48C4×C8×D5C2211yescharacteristic
49#64968C2211yescharacteristic
50C8×Dic10C2211yescharacteristic
51C5×#335C2211yescharacteristic
52C5×Q8⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic
55Q8⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic
58#64704C2211yescharacteristic
59#64700C2211yescharacteristic
60#64699C2211yescharacteristic
61#64677C2211yescharacteristic
62#64676C2211yescharacteristic
63#64676C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66#64674C2211yescharacteristic
67#17872—51nomaximal, Sylow
68C2×Q8×D5C2×C411yescharacteristic
69C2×#711C2×C411yescharacteristic
70C2×C5×SD16C2×C411yescharacteristic
71C22×C5×C8—21no—
72C4×C5×Q8C2311yescharacteristic
73C4×C5×D4C2311yescharacteristic
74Q8×Dic5C2×C411yescharacteristic
75C2×#689C2×C411yescharacteristic
76D4×Dic5C2×C411yescharacteristic
77C2×#687C2×C411yescharacteristic
78C4×C22⋊D5—21no—
79C2×C4×Dic5—21no—
80C22×#168—21no—
81#4061—24no—
82C2×Dic20C2×C411yescharacteristic
83C2×#676C2×C411yescharacteristic
84C2×#676C2×C411yescharacteristic
85C2×C8×D5—21no—
86C2×C8×D5D411yescharacteristic
87C2×C8×D5D411yescharacteristic
88#4038C2×C411yescharacteristic
89D5×C4⋊C4—21no—
90D5×C4⋊C4C2×C411yescharacteristic
91#4033—21no—
92#4033C2×C411yescharacteristic
93#4033C2×C411yescharacteristic
94#4027—21no—
95#4023—21no—
96C42×D5—21no—
97C42×D5C2311yescharacteristic
98C4×Dic10—21no—
99C4×Dic10C2311yescharacteristic
100C4×Dic10C2311yescharacteristic
101C5×#106C2×C411yescharacteristic
102C5×C4⋊C8—21no—
103C5×C4⋊C8C2311yescharacteristic
104C5×C4⋊C8C2311yescharacteristic
105C5×#103C2×C411yescharacteristic
106C5×#102C2×C411yescharacteristic
107C5×C22⋊C8—21no—
108C5×#97—21no—
109C4×C5×C8C2311yescharacteristic
110C4×C5×C8C2311yescharacteristic
111C4×C5×C8C2311yescharacteristic
112#3967C2×C411yescharacteristic
113#3964C2×C411yescharacteristic
114C22⋊#168—21no—
115#3952—21no—
116#3952—21no—
117#3950C2×C411yescharacteristic
118#3948C2×C411yescharacteristic
119#3948C2×C411yescharacteristic
120#3947—21no—
121#3947—21no—
122#3947C2×C411yescharacteristic
123#3947C2×C411yescharacteristic
124#3946—21no—
125#3946—21no—
126#3946—21no—
127#3946—21no—
128#3946—21no—
129#3946—21no—
130C8×Dic5—21no—
131C8×Dic5—21no—
132C8×Dic5—21no—
133C8×Dic5D411yescharacteristic
134C8×Dic5D411yescharacteristic
135#3942C2×C411yescharacteristic
136#3942C2×C411yescharacteristic
137#3940C2×C411yescharacteristic
138#3939C2×C411yescharacteristic
139C4⋊#168—21no—
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142#3935—21no—
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146C8×#41—51no—
147C2×#446—51no—
148C4×#137—51no—
149#1587—51no—
150#1587—51no—
151#1585—51no—
152#1585D511yescharacteristic, complemented
153#1584—51no—
154#1584—51no—
155#1582—51no—
156#1582—51no—
157#1565—51no—
158#1479—51no—
159#1477—51no—
160#1451—51no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×D4C22×C411yescharacteristic
163C22×C4×C5—21no—
164C2×C22⋊D5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167Q8×D5—22no—
168Q8×D5—22no—
169#711—22no—
170#711M1614yes—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5C22×C411yescharacteristic
174C2×C4×D5C2×D411yescharacteristic
175C2×C4×D5#4111yescharacteristic
176C2×Dic10—21no—
177C2×Dic10C22×C411yescharacteristic
178C2×Dic10C22×C411yescharacteristic
179C5×SD16—22no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—42no—
184C2×C5×C8C22×C411yescharacteristic
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C2×D411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C5×C4⋊C4—21no—
189C5×C4⋊C4C22×C411yescharacteristic
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C22⋊C4—21no—
192C42×C5—21no—
193C42×C5C2411yescharacteristic
194C22⋊Dic5—21no—
195#689—22no—
196#687—22no—
197#685—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5C22×C411yescharacteristic
200C4⋊Dic5C22×C411yescharacteristic
201#683—21no—
202#683—21no—
203#683—21no—
204#683—21no—
205#683—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5C22×C411yescharacteristic
213C4×Dic5C2×D411yescharacteristic
214C4×Dic5#4111yescharacteristic
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—42no—
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223Dic20—22no—
224#676—22no—
225#676—22no—
226C8×D5—22no—
227C8×D5—41no—
228C8×D5—42no—
229C2×#137—51no—
230C4×#41—51no—
231C2×C4×Q8—51no—
232#446—51no—
233#446—51no—
234#446—51no—
235#446—101no—
236#446—101no—
237#446C2×D511yescharacteristic
238C8×Q8—51no—
239C8×Q8—51no—
240#441—51no—
241#441—51no—
242#440—51no—
243#440—51no—
244C4×Q16—51no—
245C4×Q16—51no—
246C4×SD16—51no—
247C4×SD16C2×D511yescharacteristic
248C8×D4—51no—
249C8×D4—101no—
250C8×D4—101no—
251C8×D4C2×D511yescharacteristic
252#431—51no—
253#431—51no—
254#431—101no—
255#428—51no—
256C2×C4⋊C8—51no—
257C2×C4⋊C8—101no—
258#419—51no—
259#417—51no—
260C4×M16—51no—
261C2×#97—101no—
262C2×C4×C8—51no—
263C2×C4×C8—101no—
264#335—51no—
265#335C2×D511yescharacteristic
266#334—51no—
267#334—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270Q8⋊C8—51no—
271Q8⋊C8—51no—
272Q8⋊C8—51no—
273Q8⋊C8C2×D511yescharacteristic
274D4⋊C8—51no—
275D4⋊C8C2×D511yescharacteristic
276#322—51no—
277#322—51no—
278#322—51no—
279#322C2×D511yescharacteristic
280C23×C5—21no—
281C22×D5C4×D411yescharacteristic
282C5×Q8—21no—
283C5×Q8—21no—
284C5×D4—21no—
285C5×D4C2×M1612yes—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5C23×C411yescharacteristic
292C2×C4×C5C22×D411yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C22⋊D5—24no—
295C2×Dic5—21no—
296C2×Dic5—24no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—42no—
301C2×Dic5C4×D411yescharacteristic
302C2×Dic5C4×D411yescharacteristic
303C2×Dic5C4×D411yescharacteristic
304C4×D5—21no—
305C4×D5—21no—
306C4×D5—41no—
307C4×D5—42no—
308C4×D5—42no—
309C4×D5C2×M1612yes—
310C4×D5#13112yes—
311Dic10—21no—
312Dic10—21no—
313Dic10—21no—
314Dic10—42no—
315Dic10C2×M1612yes—
316C5×C8—21no—
317C5×C8—21no—
318C5×C8—21no—
319C5×C8—21no—
320C5×C8—41no—
321C5×C8—41no—
322C5×C8—41no—
323#168—21no—
324#168—21no—
325#168—21no—
326#168—41no—
327#168—41no—
328#168—41no—
329#168#13712yescomplemented
330C2×#41—51no—
331C22×Q8—51no—
332#137—104no—
333C2×Q16—51no—
334C2×Q16—51no—
335C2×SD16—51no—
336C2×SD16C4×D511yescharacteristic
337C2×M16—51no—
338C2×M16—51no—
339C22×C8—21no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—101no—
343C22×C8—101no—
344C4×Q8—51no—
345C4×Q8—51no—
346C4×Q8—51no—
347C4×Q8—51no—
348C4×Q8—51no—
349C4×Q8—101no—
350C4×Q8—101no—
351C4×Q8C22×D511yescharacteristic
352C4×D4—51no—
353C4×D4—101no—
354C4×D4—101no—
355C4×D4C22×D511yescharacteristic
356#117—51no—
357#117—101no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—101no—
360C2×C42—51no—
361C2×C42—101no—
362C2×C42—101no—
363#107—51no—
364#107—51no—
365#106—51no—
366#106C4×D511yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—51no—
369C4⋊C8—51no—
370C4⋊C8—101no—
371C4⋊C8—101no—
372C4⋊C8—101no—
373C4⋊C8—101no—
374C4⋊C8—101no—
375C4⋊C8—101no—
376C4⋊C8—101no—
377C4⋊C8C22×D511yescharacteristic
378C4⋊C8C22×D511yescharacteristic
379#103—51no—
380#103—51no—
381#103—51no—
382#103—51no—
383#103—51no—
384#103C4×D511yescharacteristic
385#102—51no—
386#102C4×D511yescharacteristic
387C22⋊C8—21no—
388C22⋊C8—101no—
389C22⋊C8—101no—
390C22⋊C8—101no—
391#97—21no—
392#97—51no—
393#97—51no—
394#97—101no—
395#97—101no—
396#97—101no—
397C4×C8—51no—
398C4×C8—51no—
399C4×C8—51no—
400C4×C8—51no—
401C4×C8—51no—
402C4×C8—101no—
403C4×C8—101no—
404C4×C8—101no—
405C4×C8C22×D511yescharacteristic
406C4×C8C22×D511yescharacteristic
407C4×C8C22×D511yescharacteristic
408C22×C5—22no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5C2×C4×D411yescharacteristic
412C2×D5—21no—
413C2×D5—21no—
414C2×D5#43512yes—
415C4×C5—21no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5C22×M1611yescharacteristic
420C4×C5C2×#13111yescharacteristic
421C4×C5C2×#13711yescharacteristic
422C4×C5#57511yescharacteristic
423Dic5—22no—
424Dic5—21no—
425Dic5—21no—
426Dic5—41no—
427Dic5—41no—
428Dic5—41no—
429Dic5#43512yes—
430#41—54no—
431#41—102no—
432C2×Q8—51no—
433C2×Q8—51no—
434C2×Q8—101no—
435C2×Q8—102no—
436C2×Q8—102no—
437C2×Q8C2×C4×D511yescharacteristic
438C2×D4—101no—
439C2×D4C2×C4×D511yescharacteristic
440C22×C4—21no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448Q16—102no—
449Q16—102no—
450SD16—22no—
451SD16—102no—
452M16—102no—
453M16—102no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8—51no—
459C2×C8—51no—
460C2×C8—51no—
461C2×C8—51no—
462C2×C8—102no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—201no—
467C2×C8—202no—
468C2×C8—202no—
469C2×C8C2×C4×D511yescharacteristic
470C2×C8C2×C4×D511yescharacteristic
471C2×C8D4×D511yescharacteristic
472C2×C8D4×D511yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—51no—
475C4⋊C4—51no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4—101no—
481C4⋊C4—101no—
482C4⋊C4C2×C4×D511yescharacteristic
483C4⋊C4C2×C4×D511yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—101no—
486C22⋊C4—101no—
487C42—21no—
488C42—51no—
489C42—51no—
490C42—51no—
491C42—101no—
492C42—101no—
493C42—101no—
494C42—101no—
495C42—101no—
496C42—101no—
497C42C23×D511yescharacteristic
498C2×C5—42no—
499C2×C5C2×#43511yescharacteristic
500C2×C5C4×#13711yescharacteristic
501C2×C5#295511yescharacteristic
502D5—22no—
503C23—21no—
504C23—51no—
505Q8—21no—
506Q8—21no—
507Q8—52no—
508Q8—101no—
509Q8—101no—
510Q8—101no—
511Q8—202no—
512D4—21no—
513D4—104no—
514D4D5×M1612yes—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—51no—
521C2×C4—52no—
522C2×C4—52no—
523C2×C4—51no—
524C2×C4—51no—
525C2×C4—104no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—201no—
533C2×C4—202no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4C22×C4×D511yescharacteristic
537C2×C4C2×D4×D511yescharacteristic
538C2×C4D5×#4111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—52no—
547C8—101no—
548C8—101no—
549C8—101no—
550C8—201no—
551C8—201no—
552C8—201no—
553C5#1787211yescharacteristic, complemented, Sylow
554C22—22no—
555C22—41no—
556C22—41no—
557C22—52no—
558C22—101no—
559C22—101no—
560C22C4×D4×D511yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—52no—
566C4—102no—
567C4—101no—
568C4—101no—
569C4—201no—
570C4—201no—
571C4—201no—
572C4C2×D5×M1611yescharacteristic
573C4D5×#13111yescharacteristic
574C4#6610711yescharacteristic
575C4D5×#13711yescharacteristic
576C2—42no—
577C2—102no—
578C2D5×#43511yescharacteristic
579C2#1061150511yescharacteristic
580C2#1061161911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1585C2
socleC22×C5C2×C4×D4
prime radicalC2×#711C2×C4
cosocleC42×C5C24
hypercenter#1585D5
hypocenterC5#17872
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
1. D5×#446C2semidirect
4. C5×#1585C2semidirect
5. #10601750C2semidirect
6. #10601688C2semidirect
7. #10601636C2semidirect
8. #10599361C2semidirect
9. #10599353C2semidirect
10. #10599024C2semidirect
11. #10599012C2semidirect
13. #10598947C2semidirect
14. #10598880C2semidirect
15. #10598863C2semidirect
152. #1585D5semidirect
329. #168#137semidirect
553. C5#17872semidirect

Maximal subgroups

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

subgroupindex
D5×#4462
C4×#40612
C8×#7112
C5×#15852
#106017502
#106016882
#106016362
#105993612
#105993532
#105990242
#105990122
#105989592
#105989472
#105988802
#105988632
#178725