Finite Group Databasebeta

← #12069360

Subgroups — #12069360

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2972C211yesmaximal, characteristic, complemented
2#10614040C211yesmaximal, characteristic
3#10611026C211yesmaximal, characteristic, complemented
4#10602391C211yesmaximal, characteristic, complemented
5C8×#687C211yesmaximal, characteristic, complemented
6#10601637C211yesmaximal, characteristic, complemented
7#10601636C211yesmaximal, characteristic, complemented
8#10601635C211yesmaximal, characteristic, complemented
9#10601634C211yesmaximal, characteristic, complemented
10#10601633C211yesmaximal, characteristic, complemented
11#10601632C211yesmaximal, characteristic, complemented
12C8×#686C211yesmaximal, characteristic, complemented
13#10601552C211yesmaximal, characteristic, complemented
14#10601541C211yesmaximal, characteristic, complemented
15#10601537C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17#65813C2211yescharacteristic
18C5×C8×D4—21no—
19C5×C8×D4—21no—
20C5×C8×D4C2211yescharacteristic
21C5×C8×D4C2211yescharacteristic
22C5×C8×D4C2211yescharacteristic
23C5×C8×D4C2211yescharacteristic
24C5×#431C2211yescharacteristic
25C5×#431C2211yescharacteristic
26C2×C5×C22⋊C8—21no—
27C2×C5×C22⋊C8—21no—
28#65507C411yescharacteristic
29#65506C411yescharacteristic
30C4×#687C2211yescharacteristic
31C4×#687C2211yescharacteristic
32#65305C411yescharacteristic
33#65305C411yescharacteristic
34C4×#686C2211yescharacteristic
35C4×#686C2211yescharacteristic
36#65298C411yescharacteristic
37#65298C411yescharacteristic
38#65259C411yescharacteristic
39#65257C411yescharacteristic
40#65214C2211yescharacteristic
41#65214C2211yescharacteristic
42#65213C2211yescharacteristic
43#65129—21no—
44#65128—21no—
45#65018—21no—
46#65017—21no—
47#64977C2211yescharacteristic, complemented
48C8×D20C2211yescharacteristic, complemented
49#64968C2211yescharacteristic, complemented
50C8×Dic10C2211yescharacteristic, complemented
51D4⋊#168C2211yescharacteristic
52D4⋊#168C2211yescharacteristic
53D4⋊#168C2211yescharacteristic
54D4⋊#168C2211yescharacteristic
55#64704C2211yescharacteristic, complemented
56#64704C2211yescharacteristic, complemented
57#64703C2211yescharacteristic, complemented
58#64703C2211yescharacteristic, complemented
59#64700C2211yescharacteristic, complemented
60#64700C2211yescharacteristic, complemented
61#64699C2211yescharacteristic, complemented
62#64699C2211yescharacteristic, complemented
63#64675C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66C8×#168C2211yescharacteristic, complemented
67#17918—51nomaximal, Sylow
68C22×C5×D4C2×C411yescharacteristic
69C23×C4×C5—21no—
70C22×C5×C8—21no—
71C22×C5×C8—21no—
72C22×C5×C8—21no—
73C22×C5×C8—21no—
74C4×C5×D4—21no—
75C4×C5×D4—21no—
76C4×C5×D4C2×C411yescharacteristic
77C4×C5×D4C2×C411yescharacteristic
78C4×C5×D4C2311yescharacteristic
79C4×C5×D4C2311yescharacteristic
80C2×C5×C4⋊C4C2×C411yescharacteristic
81C2×C5×C22⋊C4—21no—
82C2×C42×C5C2311yescharacteristic
83C2×#687C2×C411yescharacteristic
84C2×#687C2×C411yescharacteristic
85C2×#686C2×C411yescharacteristic
86C2×#686C2×C411yescharacteristic
87#4076C2×C411yescharacteristic
88#4075—21no—
89C4×C22⋊D5—21no—
90#4070C2×C411yescharacteristic
91C2×#681—21no—
92C2×#676—21no—
93C2×C8×D5—21no—
94#4022—21no—
95#4021C2×C411yescharacteristic
96C4×D20C2311yescharacteristic
97#4018—21no—
98#4016C2×C411yescharacteristic
99C4×Dic10C2311yescharacteristic
100C5×C4⋊C8D411yescharacteristic
101C5×C4⋊C8D411yescharacteristic
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C22⋊C8—21no—
105C5×C22⋊C8—21no—
106C5×C22⋊C8—21no—
107C5×C22⋊C8—21no—
108C5×C22⋊C8—21no—
109C5×C22⋊C8D411yescharacteristic
110C5×C22⋊C8D411yescharacteristic
111C4×C5×C8—21no—
112C4×C5×C8C2311yescharacteristic
113C4×C5×C8C2311yescharacteristic
114#3964C2×C411yescharacteristic
115#3964C2×C411yescharacteristic
116#3964C2×C411yescharacteristic
117#3964C2×C411yescharacteristic
118C22⋊#168—21no—
119C22⋊#168C2×C411yescharacteristic
120C22⋊#168C2×C411yescharacteristic
121#3952—21no—
122#3952—21no—
123#3947—21no—
124#3946—21no—
125#3946—21no—
126C8×Dic5—21no—
127#3942C2×C411yescharacteristic
128#3942C2×C411yescharacteristic
129#3941C2×C411yescharacteristic
130#3941C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3940C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134#3939C2×C411yescharacteristic
135C4⋊#168—21no—
136C4⋊#168—21no—
137C4⋊#168C2×C411yescharacteristic
138C4⋊#168C2×C411yescharacteristic
139C4⋊#168C2311yescharacteristic
140C4⋊#168C2311yescharacteristic
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105—51no—
146#2993—51no—
147#2972D511yescharacteristic, complemented
148#1586—51no—
149#1585—51no—
150#1582—51no—
151#1581—51no—
152#1580—51no—
153SD16⋊C8—51no—
154C8×SD16—51no—
155C8×D8—51no—
156#1574—51no—
157#1486—51no—
158#1482—51no—
159#1454—51no—
160C24×C5—21no—
161C2×C5×D4—22no—
162C2×C5×D4—22no—
163C2×C5×D4—21no—
164C2×C5×D4C22×C411yescharacteristic
165C2×C5×D4C22×C411yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—81no—
172C22×C4×C5—81no—
173C22×C4×C5C22×C411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C2×C22⋊D5—21no—
177C2×D20C22×C411yescharacteristic
178C2×C4×D5—21no—
179C2×Dic10C22×C411yescharacteristic
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—81no—
183C2×C5×C8—81no—
184C2×C5×C8—81no—
185C2×C5×C8—81no—
186C2×C5×C8C2×D411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C5×C4⋊C4—21no—
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C4⋊C4C22×C411yescharacteristic
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C42×C5C22×C411yescharacteristic
198C42×C5C2×D411yescharacteristic
199C42×C5#4111yescharacteristic
200C42×C5C2411yescharacteristic
201C22⋊Dic5—21no—
202#687—22no—
203#687—22no—
204#686—22no—
205#686—22no—
206#685—21no—
207#685—21no—
208#685—21no—
209#685—21no—
210C4⋊Dic5C22×C411yescharacteristic
211C4⋊Dic5C22×C411yescharacteristic
212#683—21no—
213#683—21no—
214#683—21no—
215#683—21no—
216C4×Dic5—21no—
217#681—81no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168C22×C411yescharacteristic
223C2×#168C22×C411yescharacteristic
224C2×#168C22×C411yescharacteristic
225C2×#168C22×C411yescharacteristic
226#676—81no—
227C8×D5—81no—
228#529—51no—
229C2×C4×D4C2×D511yescharacteristic
230#484—51no—
231#481—51no—
232#478—51no—
233#478—51no—
234#463—51no—
235#463—51no—
236#450—51no—
237#447—51no—
238#446—51no—
239C8×Q8—51no—
240C4×SD16—51no—
241C4×SD16—51no—
242C4×D8—51no—
243C4×D8—51no—
244#436—51no—
245#436—101no—
246#435—101no—
247C8×D4—21no—
248C8×D4—21no—
249C8×D4—51no—
250C8×D4C2×D511yescharacteristic
251C8×D4C2×D511yescharacteristic
252C8×D4C2×D511yescharacteristic
253C8×D4C2×D511yescharacteristic
254#433—101no—
255#431—51no—
256#431—51no—
257#431C2×D511yescharacteristic
258#431C2×D511yescharacteristic
259#424—101no—
260#423—51no—
261C2×C22⋊C8—21no—
262C2×C22⋊C8—21no—
263#335—51no—
264#335—51no—
265#334—51no—
266#334—51no—
267Q8⋊C8—51no—
268Q8⋊C8—51no—
269D4⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275#322—51no—
276#322—51no—
277#322—51no—
278C82—51no—
279C23×C5—24no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—81no—
283C23×C5—81no—
284C23×C5C4×D411yescharacteristic
285C22×D5—21no—
286C5×D4—24no—
287C5×D4—21no—
288C5×D4—21no—
289C5×D4#13112yes—
290C5×D4#13112yes—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—81no—
303C2×C4×C5—81no—
304C2×C4×C5—81no—
305C2×C4×C5C4×D411yescharacteristic
306C2×C4×C5C4×D411yescharacteristic
307C2×C4×C5C4×D411yescharacteristic
308C2×C4×C5C23×C411yescharacteristic
309C2×C4×C5C22×D411yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C22⋊D5—81no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315D20—21no—
316D20—21no—
317C4×D5—41no—
318C4×D5—41no—
319Dic10—21no—
320Dic10—21no—
321C5×C8—21no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—41no—
326C5×C8—41no—
327#168—21no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—41no—
332#168—41no—
333#168—41no—
334#168—41no—
335C22×D4C4×D511yescharacteristic
336C23×C4—21no—
337C2×SD16—51no—
338C2×SD16—51no—
339C2×D8—51no—
340C2×D8—51no—
341C2×M16—101no—
342C2×M16—101no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—101no—
348#126—101no—
349#125—51no—
350#124—51no—
351#123—101no—
352C22⋊Q8—51no—
353#121—51no—
354C4×Q8—51no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—51no—
358C4×D4—101no—
359C4×D4C4×D511yescharacteristic
360C4×D4C4×D511yescharacteristic
361C4×D4C22×D511yescharacteristic
362C4×D4C22×D511yescharacteristic
363#117—101no—
364C2×C4⋊C4C4×D511yescharacteristic
365C2×C22⋊C4—21no—
366C2×C42C22×D511yescharacteristic
367#107—51no—
368#107—51no—
369#106—51no—
370#106—51no—
371C4⋊C8—51no—
372C4⋊C8—51no—
373C4⋊C8—51no—
374C4⋊C8—51no—
375C4⋊C8—101no—
376C4⋊C8—101no—
377C4⋊C8—101no—
378C4⋊C8—101no—
379C4⋊C8C22⋊D511yescharacteristic
380C4⋊C8C22⋊D511yescharacteristic
381C4⋊C8C22×D511yescharacteristic
382C4⋊C8C22×D511yescharacteristic
383#103—51no—
384#103—51no—
385#102—51no—
386#102—51no—
387#102—51no—
388#102—51no—
389#102—51no—
390#102—51no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—51no—
397C22⋊C8—51no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8C22⋊D511yescharacteristic
402C22⋊C8C22⋊D511yescharacteristic
403#97—101no—
404C4×C8—21no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—101no—
410C4×C8C22×D511yescharacteristic
411C4×C8C22×D511yescharacteristic
412C22×C5—21no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—84no—
422C22×C5C2×C4×D411yescharacteristic
423C2×D5—41no—
424C2×D5—41no—
425C2×D5—41no—
426C4×C5—21no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—41no—
431C4×C5—41no—
432C4×C5C2×#13111yescharacteristic
433C4×C5C2×#13111yescharacteristic
434C4×C5#57611yescharacteristic
435C4×C5#57711yescharacteristic
436Dic5—41no—
437Dic5—41no—
438Dic5—41no—
439C24—21no—
440C2×Q8—51no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—51no—
445C2×D4—101no—
446C2×D4C2×C4×D511yescharacteristic
447C2×D4C2×C4×D511yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—101no—
456C22×C4C2×C4×D511yescharacteristic
457C22×C4#70911yescharacteristic
458C22×C4C2×C22⋊D511yescharacteristic
459SD16—102no—
460SD16—102no—
461D8—102no—
462D8—102no—
463M16—401no—
464M16—401no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—51no—
468C2×C8—51no—
469C2×C8—51no—
470C2×C8—51no—
471C2×C8—81no—
472C2×C8—81no—
473C2×C8—81no—
474C2×C8—81no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—401no—
480C2×C8C2×C22⋊D511yescharacteristic
481C2×C8C2×C22⋊D511yescharacteristic
482C2×C8C2×C22⋊D511yescharacteristic
483C2×C8C2×C22⋊D511yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—51no—
486C4⋊C4—51no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4C2×C4×D511yescharacteristic
492C4⋊C4C2×C4×D511yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—101no—
498C22⋊C4—101no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C42—101no—
503C42C2×C4×D511yescharacteristic
504C42#70911yescharacteristic
505C42C2×C22⋊D511yescharacteristic
506C42C23×D511yescharacteristic
507C2×C5—41no—
508C2×C5—42no—
509C2×C5—42no—
510C2×C5#292911yescharacteristic
511C2×C5#294611yescharacteristic
512C2×C5#295711yescharacteristic
513D5—81no—
514C23—24no—
515C23—21no—
516C23—21no—
517C23—81no—
518C23—81no—
519C23—101no—
520C23C4×C22⋊D511yescharacteristic
521Q8—101no—
522Q8—101no—
523D4—24no—
524D4—21no—
525D4—21no—
526D4—101no—
527D4—101no—
528D4—401no—
529D4#404712yes—
530D4#404712yes—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4C4×C22⋊D511yescharacteristic
551C2×C4C4×C22⋊D511yescharacteristic
552C2×C4C4×C22⋊D511yescharacteristic
553C2×C4C22×C4×D511yescharacteristic
554C2×C4C2×#70911yescharacteristic
555C2×C4C22×C22⋊D511yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—101no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—201no—
567C8—201no—
568C8—201no—
569C8—201no—
570C5#1791811yescharacteristic, complemented, Sylow
571C22—21no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—201no—
582C22—201no—
583C22—201no—
584C22C2×C4×C22⋊D511yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—201no—
592C4—201no—
593C4—201no—
594C4C2×#404711yescharacteristic
595C4C2×#404711yescharacteristic
596C4#6616911yescharacteristic
597C4#6617011yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—401no—
602C2#1061426811yescharacteristic
603C2#1061546511yescharacteristic
604C2#1061554311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#2972C2
socleC22×C5C2×C4×D4
prime radical#65506C4
cosocleC42×C5C24
hypercenter#2972D5
hypocenterC5#17918
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. C5×#2972C2semidirect
3. #10611026C2semidirect
4. #10602391C2semidirect
5. C8×#687C2semidirect
6. #10601637C2semidirect
7. #10601636C2semidirect
8. #10601635C2semidirect
9. #10601634C2semidirect
10. #10601633C2semidirect
11. #10601632C2semidirect
12. C8×#686C2semidirect
13. #10601552C2semidirect
14. #10601541C2semidirect
15. #10601537C2semidirect
47. #64977C22semidirect
48. C8×D20C22semidirect
49. #64968C22semidirect
50. C8×Dic10C22semidirect
55. #64704C22semidirect
56. #64704C22semidirect
57. #64703C22semidirect
58. #64703C22semidirect
59. #64700C22semidirect
60. #64700C22semidirect
61. #64699C22semidirect
62. #64699C22semidirect
63. #64675C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. C8×#168C22semidirect
147. #2972D5semidirect
570. C5#17918semidirect

Maximal subgroups

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

subgroupindex
C5×#29722
#106140402
#106110262
#106023912
C8×#6872
#106016372
#106016362
#106016352
#106016342
#106016332
#106016322
C8×#6862
#106015522
#106015412
#106015372
#179185