Finite Group Databasebeta

← #12068953

Subgroups — #12068953

Order 1280.

698 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611637C211yesmaximal, characteristic, complemented
2C4×#4060C211yesmaximal, characteristic
3#10611274C211yesmaximal, characteristic, complemented
4C5×#1583C211yesmaximal, characteristic, complemented
5#10601729C211yesmaximal, characteristic, complemented
6#10601691C211yesmaximal, characteristic, complemented
7#10601656C211yesmaximal, characteristic, complemented
8#10599321C211yesmaximal, characteristic, complemented
9#10599314C211yesmaximal, characteristic, complemented
10#10599022C211yesmaximal, characteristic, complemented
11#10599010C211yesmaximal, characteristic, complemented
12D5×D4⋊C8C211yesmaximal, characteristic, complemented
13#10598946C211yesmaximal, characteristic, complemented
14#10598871C211yesmaximal, characteristic, complemented
15#10598863C211yesmaximal, characteristic, complemented
16C2×#4060C411yescharacteristic
17C4×#713C2211yescharacteristic
18C4×D4×D5C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic, complemented
20C4×C5×SD16C2211yescharacteristic
21C5×#436C2211yescharacteristic
22#65453C411yescharacteristic
23#65417—21no—
24#65415—21no—
25C4×#688C2211yescharacteristic
26Q8×#168C2211yescharacteristic, complemented
27C4×#686C2211yescharacteristic
28#65301C2211yescharacteristic
29#65158C411yescharacteristic
30#65150C411yescharacteristic
31#65127C2211yescharacteristic
32#65123—21no—
33#65123C2211yescharacteristic, complemented
34#65122C2211yescharacteristic
35D5×C4⋊C8—21no—
36D5×C4⋊C8C2211yescharacteristic
37#65106C411yescharacteristic
38#65092C411yescharacteristic
39#65074C411yescharacteristic
40#65059C411yescharacteristic
41#65018—21no—
42#65015—21no—
43C4×D40C2211yescharacteristic
44#64977C2211yescharacteristic
45C4×#676C2211yescharacteristic
46C8×D20—21no—
47C8×D20C2211yescharacteristic, complemented
48#64974—21no—
49#64974C2211yescharacteristic
50C4×C8×D5C2211yescharacteristic
51C5×#334C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic, complemented
55Q8⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic
57#64703C2211yescharacteristic
58#64703C2211yescharacteristic, complemented
59#64700C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64679C2211yescharacteristic, complemented
63#64678C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#17875—51nomaximal, Sylow
68C2×#713C2×C411yescharacteristic
69C2×D4×D5C2×C411yescharacteristic
70C22×C4×D5—21no—
71C2×C5×SD16C2×C411yescharacteristic
72C2×C5×M16—21no—
73C4×C5×Q8C2311yescharacteristic
74C4×C5×D4C2311yescharacteristic
75Q8×Dic5C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#686C2×C411yescharacteristic
79C4×C22⋊D5—21no—
80C2×#681—21no—
81#4060—24no—
82C2×D40C2×C411yescharacteristic
83C2×#676—21no—
84C2×#676—21no—
85C2×#676C2×C411yescharacteristic
86C2×#676C2×C411yescharacteristic
87C2×C8×D5—21no—
88C2×C8×D5—21no—
89C2×C8×D5—21no—
90C2×C8×D5—21no—
91#4039—21no—
92#4039C2×C411yescharacteristic
93#4039C2×C411yescharacteristic
94#4038—21no—
95#4038C2×C411yescharacteristic
96D5×C4⋊C4C2×C411yescharacteristic
97#4027—21no—
98D5×C22⋊C4—21no—
99C4×D20—21no—
100C4×D20C2311yescharacteristic
101C4×D20C2311yescharacteristic
102C42×D5—21no—
103C42×D5C2311yescharacteristic
104C5×#106C2×C411yescharacteristic
105C5×C4⋊C8—21no—
106C5×C4⋊C8C2311yescharacteristic
107C5×C4⋊C8C2311yescharacteristic
108C5×#103C2×C411yescharacteristic
109C5×#102C2×C411yescharacteristic
110C5×C22⋊C8—21no—
111C4×C5×C8—21no—
112C4×C5×C8C2311yescharacteristic
113C4×C5×C8C2311yescharacteristic
114C4×C5×C8C2311yescharacteristic
115#3967C2×C411yescharacteristic
116#3964C2×C411yescharacteristic
117C22⋊#168—21no—
118#3953C2×C411yescharacteristic
119#3953C2×C411yescharacteristic
120#3952—21no—
121#3952—21no—
122#3952—21no—
123#3952—21no—
124#3952—21no—
125#3952D411yescharacteristic
126#3952D411yescharacteristic
127#3950C2×C411yescharacteristic
128#3947C2×C411yescharacteristic
129#3947C2×C411yescharacteristic
130#3946—21no—
131#3946D411yescharacteristic
132#3946D411yescharacteristic
133C8×Dic5—21no—
134C8×Dic5—21no—
135#3941C2×C411yescharacteristic
136#3941C2×C411yescharacteristic
137#3940C2×C411yescharacteristic
138#3939C2×C411yescharacteristic
139C4⋊#168—21no—
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142C4×#168—21no—
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#2988—51no—
147#2975—51no—
148C4×AGL(1,ℤ/8)—51no—
149#1588—51no—
150#1588—51no—
151#1586—51no—
152#1586—51no—
153#1583—51no—
154#1583D511yescharacteristic, complemented
155#1581—51no—
156#1581—51no—
157#1565—51no—
158#1476—51no—
159C2×D4⋊C8—51no—
160#1451—51no—
161C23×D5—21no—
162C2×C5×Q8C22×C411yescharacteristic
163C2×C5×D4C22×C411yescharacteristic
164C22×C4×C5—21no—
165C2×C22⋊D5—21no—
166C22×Dic5—21no—
167#713—22no—
168#713M1614yescomplemented
169D4×D5—22no—
170D4×D5—22no—
171C2×D20—21no—
172C2×D20C22×C411yescharacteristic
173C2×D20C22×C411yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—81no—
181C2×C4×D5—81no—
182C2×C4×D5C22×C411yescharacteristic
183C2×C4×D5C2×D411yescharacteristic
184C2×C4×D5#4111yescharacteristic
185C5×SD16—22no—
186C5×M16—81no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8C22×C411yescharacteristic
191C2×C5×C8C22×C411yescharacteristic
192C2×C5×C8C2×D411yescharacteristic
193C2×C5×C8C2×D411yescharacteristic
194C5×C4⋊C4—21no—
195C5×C4⋊C4C22×C411yescharacteristic
196C5×C4⋊C4C22×C411yescharacteristic
197C5×C22⋊C4—21no—
198C42×C5—21no—
199C42×C5C2411yescharacteristic
200C22⋊Dic5—21no—
201#688—22no—
202#686—22no—
203#685—21no—
204#685—21no—
205#685—21no—
206#685—21no—
207#685—21no—
208C4⋊Dic5—21no—
209C4⋊Dic5C22×C411yescharacteristic
210C4⋊Dic5C22×C411yescharacteristic
211#683—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5C22×C411yescharacteristic
215C4×Dic5C2×D411yescharacteristic
216C4×Dic5#4111yescharacteristic
217#681—81no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168C22×C411yescharacteristic
222C2×#168C22×C411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C2×#168C2×D411yescharacteristic
225D40—22no—
226#676—22no—
227#676—22no—
228#676—81no—
229#676—81no—
230C8×D5—42no—
231C8×D5—81no—
232C8×D5—81no—
233C8×D5—81no—
234C2×AGL(1,ℤ/8)—51no—
235C4×#41—51no—
236C2×C4×D4—51no—
237C8×Q8—51no—
238C8×Q8C2×D511yescharacteristic, complemented
239#442—51no—
240#442—51no—
241#440—51no—
242#440—51no—
243C4×SD16—51no—
244C4×SD16C2×D511yescharacteristic
245C4×D8—51no—
246C4×D8—51no—
247#436—51no—
248#436—51no—
249#436—51no—
250#436—101no—
251#436—101no—
252#436C2×D511yescharacteristic
253C8×D4—51no—
254C8×D4—51no—
255C8×D4—101no—
256C8×D4—101no—
257#431—51no—
258#431—51no—
259#431—101no—
260#428—51no—
261C2×C4⋊C8—51no—
262C2×C4⋊C8—101no—
263#418—51no—
264#417—51no—
265#407—101no—
266#407—101no—
267C4×M16—51no—
268C2×C4×C8—51no—
269#335—51no—
270#335—51no—
271#334—51no—
272#334C2×D511yescharacteristic, complemented
273Q8⋊C8—51no—
274Q8⋊C8C2×D511yescharacteristic, complemented
275D4⋊C8—51no—
276D4⋊C8—51no—
277D4⋊C8—51no—
278D4⋊C8—51no—
279D4⋊C8—51no—
280D4⋊C8C2×D511yescharacteristic
281#322—51no—
282#322—51no—
283#322—51no—
284#322C2×D511yescharacteristic, complemented
285C23×C5—21no—
286C22×D5—21no—
287C22×D5—21no—
288C22×D5—42no—
289C22×D5—81no—
290C22×D5—81no—
291C22×D5C4×D411yescharacteristic
292C5×Q8—21no—
293C5×Q8C2×M1612yes—
294C5×D4—21no—
295C5×D4—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5C23×C411yescharacteristic
302C2×C4×C5C22×D411yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C22⋊D5—42no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—81no—
308C2×Dic5C4×D411yescharacteristic
309C2×Dic5C4×D411yescharacteristic
310C2×Dic5C4×D411yescharacteristic
311D20—24no—
312D20—21no—
313D20—21no—
314D20—21no—
315D20C2×M1612yes—
316C4×D5—21no—
317C4×D5—21no—
318C4×D5—24no—
319C4×D5—41no—
320C4×D5—41no—
321C4×D5—41no—
322C4×D5—41no—
323C4×D5—41no—
324C4×D5—81no—
325C4×D5—81no—
326C4×D5—81no—
327C4×D5C2×M1612yes—
328C4×D5#13112yes—
329C5×C8—21no—
330C5×C8—21no—
331C5×C8—21no—
332C5×C8—21no—
333C5×C8—41no—
334C5×C8—41no—
335C5×C8—41no—
336#168—22no—
337#168—21no—
338#168—21no—
339#168—21no—
340#168—21no—
341#168—41no—
342#168—41no—
343C2×#41—51no—
344C22×D4—51no—
345C23×C4—101no—
346AGL(1,ℤ/8)—104no—
347C2×SD16—51no—
348C2×SD16C4×D511yescharacteristic
349C2×D8—51no—
350C2×D8—51no—
351C2×M16—21no—
352C2×M16—51no—
353C2×M16—51no—
354C2×M16—101no—
355C2×M16—101no—
356C2×M16—101no—
357C22×C8—101no—
358C22×C8—101no—
359C22×C8—101no—
360C22×C8—101no—
361C4×Q8—51no—
362C4×Q8C22×D511yescharacteristic
363C4×D4—51no—
364C4×D4—51no—
365C4×D4—51no—
366C4×D4—51no—
367C4×D4—51no—
368C4×D4—101no—
369C4×D4—101no—
370C4×D4—101no—
371C4×D4—101no—
372C4×D4C22×D511yescharacteristic
373#117—51no—
374#117—101no—
375C2×C4⋊C4—51no—
376C2×C22⋊C4—101no—
377C2×C42—51no—
378C2×C42—101no—
379#107—51no—
380#107—51no—
381#106—51no—
382#106C4×D511yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—51no—
385C4⋊C8—51no—
386C4⋊C8—51no—
387C4⋊C8—51no—
388C4⋊C8—101no—
389C4⋊C8—101no—
390C4⋊C8C22×D511yescharacteristic
391C4⋊C8C22×D511yescharacteristic
392#103—51no—
393#103C4×D511yescharacteristic
394#102—51no—
395#102—51no—
396#102—51no—
397#102—51no—
398#102—51no—
399#102C4×D511yescharacteristic
400C22⋊C8—21no—
401C22⋊C8—51no—
402C22⋊C8—51no—
403C22⋊C8—101no—
404C22⋊C8—101no—
405C22⋊C8—101no—
406C22⋊C8—101no—
407C22⋊C8—101no—
408C22⋊C8—101no—
409#97—51no—
410#97—51no—
411C4×C8—21no—
412C4×C8—51no—
413C4×C8—51no—
414C4×C8—51no—
415C4×C8—101no—
416C4×C8—101no—
417C4×C8—101no—
418C4×C8C22×D511yescharacteristic
419C4×C8C22×D511yescharacteristic
420C4×C8C22×D511yescharacteristic
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5C2×C4×D411yescharacteristic
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—22no—
428C2×D5—41no—
429C2×D5—41no—
430C2×D5—41no—
431C2×D5—41no—
432C2×D5—41no—
433C2×D5—84no—
434C2×D5#43512yes—
435C4×C5—22no—
436C4×C5—21no—
437C4×C5—41no—
438C4×C5—41no—
439C4×C5C22×M1611yescharacteristic
440C4×C5C2×#13111yescharacteristic
441C4×C5#57611yescharacteristic
442C4×C5#57711yescharacteristic
443Dic5—21no—
444Dic5—21no—
445Dic5—41no—
446Dic5—41no—
447Dic5#43512yes—
448C24—101no—
449#41—54no—
450#41—102no—
451C2×Q8C2×C4×D511yescharacteristic
452C2×D4—51no—
453C2×D4—51no—
454C2×D4—101no—
455C2×D4—102no—
456C2×D4—102no—
457C2×D4—101no—
458C2×D4C2×C4×D511yescharacteristic
459C22×C4—21no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—51no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—101no—
467C22×C4—101no—
468C22×C4—101no—
469C22×C4—101no—
470C22×C4—401no—
471C22×C4—401no—
472SD16—22no—
473SD16—102no—
474D8—102no—
475D8—102no—
476M16—81no—
477M16—102no—
478M16—102no—
479M16—401no—
480M16—401no—
481M16—401no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—51no—
486C2×C8—51no—
487C2×C8—51no—
488C2×C8—51no—
489C2×C8—101no—
490C2×C8—101no—
491C2×C8—101no—
492C2×C8—202no—
493C2×C8—401no—
494C2×C8—401no—
495C2×C8—401no—
496C2×C8C2×C4×D511yescharacteristic
497C2×C8C2×C4×D511yescharacteristic
498C2×C8D4×D511yescharacteristic
499C2×C8D4×D511yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—51no—
502C4⋊C4—51no—
503C4⋊C4—101no—
504C4⋊C4—101no—
505C4⋊C4C2×C4×D511yescharacteristic
506C4⋊C4C2×C4×D511yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—101no—
509C22⋊C4—101no—
510C22⋊C4—101no—
511C22⋊C4—101no—
512C22⋊C4—101no—
513C22⋊C4—101no—
514C42—21no—
515C42—51no—
516C42—51no—
517C42—51no—
518C42—101no—
519C42—101no—
520C42C23×D511yescharacteristic
521C2×C5—81no—
522C2×C5C2×#43511yescharacteristic
523C2×C5#294611yescharacteristic
524C2×C5#295611yescharacteristic
525D5—22no—
526D5—42no—
527D5—81no—
528C23—21no—
529C23—51no—
530C23—101no—
531C23—101no—
532C23—202no—
533C23—401no—
534C23—401no—
535Q8—21no—
536Q8D5×M1612yes—
537D4—21no—
538D4—21no—
539D4—52no—
540D4—104no—
541D4—101no—
542D4—101no—
543D4—101no—
544D4—202no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—51no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—104no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4—401no—
566C2×C4—401no—
567C2×C4—401no—
568C2×C4—401no—
569C2×C4C22×C4×D511yescharacteristic
570C2×C4C2×D4×D511yescharacteristic
571C2×C4D5×#4111yescharacteristic
572C8—21no—
573C8—21no—
574C8—21no—
575C8—21no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—102no—
580C8—101no—
581C8—101no—
582C8—101no—
583C8—101no—
584C8—201no—
585C8—201no—
586C5#1787511yescharacteristic, complemented, Sylow
587C22—41no—
588C22—41no—
589C22—41no—
590C22—52no—
591C22—101no—
592C22—101no—
593C22—102no—
594C22—201no—
595C22—201no—
596C22—201no—
597C22—201no—
598C22—201no—
599C22—404no—
600C22C4×D4×D511yescharacteristic
601C4—22no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—52no—
606C4—101no—
607C4—101no—
608C4—201no—
609C4—201no—
610C4C2×D5×M1611yescharacteristic
611C4D5×#13111yescharacteristic
612C4#6609611yescharacteristic
613C4#6610311yescharacteristic
614C2—81no—
615C2—102no—
616C2—202no—
617C2—401no—
618C2D5×#43511yescharacteristic
619C2#1061137811yescharacteristic
620C2#1061162911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1583C2
socleC22×C5C2×C4×D4
prime radicalC2×#4060C4
cosocleC42×C5C24
hypercenter#1583D5
hypocenterC5#17875
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
1. #10611637C2semidirect
3. #10611274C2semidirect
4. C5×#1583C2semidirect
5. #10601729C2semidirect
6. #10601691C2semidirect
7. #10601656C2semidirect
8. #10599321C2semidirect
9. #10599314C2semidirect
10. #10599022C2semidirect
11. #10599010C2semidirect
12. D5×D4⋊C8C2semidirect
13. #10598946C2semidirect
14. #10598871C2semidirect
15. #10598863C2semidirect
19. C5×C8×Q8C22semidirect
26. Q8×#168C22semidirect
33. #65123C22semidirect
47. C8×D20C22semidirect
51. C5×#334C22semidirect
52. C5×Q8⋊C8C22semidirect
54. C5×#322C22semidirect
55. Q8⋊#168C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64699C22semidirect
62. #64679C22semidirect
63. #64678C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
154. #1583D5semidirect
168. #713M16semidirect
238. C8×Q8C2×D5semidirect
272. #334C2×D5semidirect
274. Q8⋊C8C2×D5semidirect
284. #322C2×D5semidirect
586. C5#17875semidirect

Maximal subgroups

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

subgroupindex
#106116372
C4×#40602
#106112742
C5×#15832
#106017292
#106016912
#106016562
#105993212
#105993142
#105990222
#105990102
D5×D4⋊C82
#105989462
#105988712
#105988632
#178755