Finite Group Databasebeta

← #12069396

Subgroups — #12069396

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615030C211yesmaximal, characteristic
2#10615011C211yesmaximal, characteristic, complemented
3#10610744C211yesmaximal, characteristic, complemented
4C5×#1480C211yesmaximal, characteristic, complemented
5#10601556C211yesmaximal, characteristic, complemented
6#10601537C211yesmaximal, characteristic, complemented
7#10601216C211yesmaximal, characteristic, complemented
8#10598952C211yesmaximal, characteristic, complemented
9#10598951C211yesmaximal, characteristic, complemented
10#10598948C211yesmaximal, characteristic, complemented
11#10598946C211yesmaximal, characteristic, complemented
12#10598944C211yesmaximal, characteristic, complemented
13#10598943C211yesmaximal, characteristic, complemented
14#10598942C211yesmaximal, characteristic, complemented
15#10598941C211yesmaximal, characteristic, complemented
16C5×#532C2211yescharacteristic
17C4×#709C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20#65523—21no—
21#65523—21no—
22C8×C22⋊D5—21no—
23C8×C22⋊D5—21no—
24#65380C411yescharacteristic
25#65373C411yescharacteristic
26#65364C411yescharacteristic
27#65361C411yescharacteristic
28#65326C411yescharacteristic
29#65326C411yescharacteristic
30#65324C411yescharacteristic
31#65324C411yescharacteristic
32C4×#687C2211yescharacteristic
33C4×#687C2211yescharacteristic
34C4×#686C2211yescharacteristic
35C4×#686C2211yescharacteristic
36#65301C2211yescharacteristic
37#65301C2211yescharacteristic
38#65300—21no—
39#65300—21no—
40D4×#168C2211yescharacteristic
41D4×#168C2211yescharacteristic
42#65215C2211yescharacteristic
43#65214C2211yescharacteristic
44#65214C2211yescharacteristic
45#65123C2211yescharacteristic
46#65123C2211yescharacteristic
47#65122—21no—
48D5×C4⋊C8—21no—
49#65119C2211yescharacteristic
50#65119C2211yescharacteristic
51C5×D4⋊C8C2211yescharacteristic
52C5×D4⋊C8C2211yescharacteristic
53C5×D4⋊C8C2211yescharacteristic
54C5×D4⋊C8C2211yescharacteristic
55#64700C2211yescharacteristic
56#64700C2211yescharacteristic
57#64699C2211yescharacteristic
58#64699C2211yescharacteristic
59#64679C2211yescharacteristic
60#64679C2211yescharacteristic
61#64676C2211yescharacteristic
62#64676C2211yescharacteristic
63#64675C2211yescharacteristic
64#64674C2211yescharacteristic
65#64674C2211yescharacteristic
66C8×#168C2211yescharacteristic
67#17920—51nomaximal, Sylow
68C2×C5×#41—21no—
69C2×#709C2×C411yescharacteristic
70C22×C5×C8—21no—
71C5×C4⋊Q8C2×C411yescharacteristic
72C5×#127C2×C411yescharacteristic
73C5×#124—21no—
74C5×#121—21no—
75C5×#121C2×C411yescharacteristic
76C5×#121C2×C411yescharacteristic
77C4×C5×D4—21no—
78C4×C5×D4C2311yescharacteristic
79C4×C5×D4C2311yescharacteristic
80C2×C42×C5C2311yescharacteristic
81C2×#687C2×C411yescharacteristic
82C2×#687C2×C411yescharacteristic
83C2×#686C2×C411yescharacteristic
84C2×#686C2×C411yescharacteristic
85C4×C22⋊D5—21no—
86C4×C22⋊D5—21no—
87#4072C2×C411yescharacteristic
88C2×#681—21no—
89C2×#681—21no—
90C22×#168—21no—
91C22×#168—21no—
92C2×C8×D5—21no—
93C2×C8×D5—21no—
94C4×D20C2×C411yescharacteristic
95C4×D20C2311yescharacteristic
96#4018—21no—
97C42×D5—21no—
98C4×Dic10C2×C411yescharacteristic
99C4×Dic10C2311yescharacteristic
100C5×C4⋊C8—21no—
101C5×C4⋊C8—21no—
102C5×C4⋊C8C2311yescharacteristic
103C5×C4⋊C8C2311yescharacteristic
104C5×C22⋊C8—21no—
105C4×C5×C8C2311yescharacteristic
106C4×C5×C8C2311yescharacteristic
107#3964C2×C411yescharacteristic
108#3964C2×C411yescharacteristic
109#3964C2×C411yescharacteristic
110#3964C2×C411yescharacteristic
111C22⋊#168—21no—
112C22⋊#168—21no—
113C22⋊#168—21no—
114C22⋊#168—21no—
115C22⋊#168—21no—
116C22⋊#168C2×C411yescharacteristic
117C22⋊#168C2×C411yescharacteristic
118C22⋊#168D411yescharacteristic
119C22⋊#168D411yescharacteristic
120#3952—21no—
121#3952—21no—
122#3946—21no—
123#3946—21no—
124C8×Dic5—21no—
125C8×Dic5—21no—
126#3942C2×C411yescharacteristic
127#3942C2×C411yescharacteristic
128#3941C2×C411yescharacteristic
129#3941C2×C411yescharacteristic
130#3940C2×C411yescharacteristic
131#3940C2×C411yescharacteristic
132#3939C2×C411yescharacteristic
133#3939C2×C411yescharacteristic
134C4⋊#168C2×C411yescharacteristic
135C4⋊#168C2×C411yescharacteristic
136C4⋊#168D411yescharacteristic
137C4⋊#168D411yescharacteristic
138C4⋊#168C2311yescharacteristic
139C4⋊#168C2311yescharacteristic
140#3935—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3106—51no—
146#2988—51no—
147#2981—51no—
148#1588—51no—
149#1586—51no—
150#1583—51no—
151#1581—51no—
152#1580—51no—
153SD16⋊C8—51no—
154C8×SD16—51no—
155C8×D8—51no—
156#1573—51no—
157#1488—51no—
158#1480D511yescharacteristic, complemented
159#1454—51no—
160C5×#41—81no—
161C5×#41—81no—
162C2×C5×Q8—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4C22×C411yescharacteristic
168C2×C5×D4C22×C411yescharacteristic
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5C22×C411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C2×C22⋊D5—21no—
175#709—22no—
176#709—22no—
177C2×D20C22×C411yescharacteristic
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×Dic10C22×C411yescharacteristic
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—81no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4C22×C411yescharacteristic
189C5×C4⋊C4C22×C411yescharacteristic
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C42×C5C22×C411yescharacteristic
195C42×C5C2×D411yescharacteristic
196C42×C5#4111yescharacteristic
197C42×C5C2411yescharacteristic
198C22⋊Dic5—21no—
199#687—22no—
200#687—22no—
201#686—22no—
202#686—22no—
203#685—21no—
204#685—21no—
205C4⋊Dic5C22×C411yescharacteristic
206C4⋊Dic5C22×C411yescharacteristic
207#683—21no—
208#683—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212#681—81no—
213#681—81no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—81no—
217C2×#168—81no—
218C2×#168C22×C411yescharacteristic
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C22×C411yescharacteristic
222C2×#168C2×D411yescharacteristic
223C2×#168C2×D411yescharacteristic
224C2×#168C2×D411yescharacteristic
225C2×#168C2×D411yescharacteristic
226C8×D5—81no—
227C8×D5—81no—
228#532C2×D511yescharacteristic
229C4×#41—51no—
230#482—51no—
231#482—51no—
232#477—51no—
233#476—51no—
234#460—51no—
235#459—51no—
236#449—51no—
237#449—51no—
238C8×Q8—51no—
239C8×Q8—51no—
240C4×SD16—51no—
241C4×SD16—51no—
242C4×D8—51no—
243C4×D8—51no—
244#436—51no—
245#436—51no—
246#435—101no—
247#435—101no—
248C8×D4—51no—
249C8×D4—51no—
250C8×D4—51no—
251C8×D4—51no—
252C8×D4—101no—
253C8×D4—101no—
254#432—51no—
255#431—51no—
256#431—51no—
257#431—101no—
258#431C2×D511yescharacteristic
259C2×C4⋊C8—101no—
260C2×C4⋊C8C2×D511yescharacteristic
261#408—101no—
262#408—101no—
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⋊C8C2×D511yescharacteristic
272D4⋊C8C2×D511yescharacteristic
273D4⋊C8C2×D511yescharacteristic
274D4⋊C8C2×D511yescharacteristic
275#322—51no—
276#322—51no—
277#322—51no—
278C82—51no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5C4×D411yescharacteristic
282C22×D5—21no—
283C5×Q8—81no—
284C5×D4—21no—
285C5×D4—21no—
286C5×D4—21no—
287C5×D4—21no—
288C5×D4—81no—
289C5×D4—81no—
290C5×D4—81no—
291C5×D4—81no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5C4×D411yescharacteristic
304C2×C4×C5C4×D411yescharacteristic
305C2×C4×C5C4×D411yescharacteristic
306C2×C4×C5C23×C411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C22⋊D5—24no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313D20—21no—
314D20#13112yes—
315C4×D5—24no—
316C4×D5—41no—
317C4×D5—41no—
318C4×D5—81no—
319Dic10—21no—
320Dic10#13112yes—
321C5×C8—41no—
322C5×C8—41no—
323C5×C8—41no—
324C5×C8—41no—
325#168—21no—
326#168—21no—
327#168—21no—
328#168—21no—
329#168—21no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—41no—
334#168—41no—
335C2×#41—21no—
336C2×#41—51no—
337C2×SD16—51no—
338C2×SD16—51no—
339C2×D8—51no—
340C2×D8—51no—
341C2×M16—101no—
342C2×M16—101no—
343C22×C8—21no—
344C22×C8—101no—
345C22×C8—101no—
346C22×C8—101no—
347C22×C8—101no—
348C4⋊Q8C4×D511yescharacteristic
349#127C4×D511yescharacteristic
350#124—21no—
351#121—21no—
352#121C4×D511yescharacteristic
353#121C4×D511yescharacteristic
354C4×Q8—51no—
355C4×Q8—51no—
356C4×D4—21no—
357C4×D4—51no—
358C4×D4—51no—
359C4×D4—101no—
360C4×D4—101no—
361C4×D4C22×D511yescharacteristic
362C4×D4C22×D511yescharacteristic
363#117—51no—
364#117—101no—
365C2×C42—101no—
366C2×C42C22×D511yescharacteristic
367#107—51no—
368#107—51no—
369#106—51no—
370#106—51no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—51no—
374C4⋊C8—51no—
375C4⋊C8—51no—
376C4⋊C8—51no—
377C4⋊C8—51no—
378C4⋊C8—51no—
379C4⋊C8—101no—
380C4⋊C8—101no—
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—51no—
393C22⋊C8—51no—
394C22⋊C8—51no—
395C22⋊C8—51no—
396C22⋊C8—101no—
397C22⋊C8—101no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8—101no—
402C22⋊C8—101no—
403#97—101no—
404C4×C8—51no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—101no—
409C4×C8—101no—
410C4×C8C22×D511yescharacteristic
411C4×C8C22×D511yescharacteristic
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—41no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5C2×C4×D411yescharacteristic
422C2×D5—22no—
423C2×D5—41no—
424C2×D5—41no—
425C4×C5—21no—
426C4×C5—21no—
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—41no—
430C4×C5—41no—
431C4×C5C2×#13111yescharacteristic
432C4×C5C2×#13111yescharacteristic
433C4×C5#57611yescharacteristic
434C4×C5#57711yescharacteristic
435Dic5—22no—
436Dic5—41no—
437Dic5—41no—
438#41—81no—
439#41—81no—
440#41—102no—
441#41—102no—
442C2×Q8—21no—
443C2×Q8—51no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—51no—
449C2×D4—101no—
450C2×D4C2×C4×D511yescharacteristic
451C2×D4C2×C4×D511yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4C2×C4×D511yescharacteristic
458C22×C4D4×D511yescharacteristic
459C22×C4#71111yescharacteristic
460SD16—102no—
461SD16—102no—
462D8—102no—
463D8—102no—
464M16—401no—
465M16—401no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—51no—
475C2×C8—51no—
476C2×C8—51no—
477C2×C8—51no—
478C2×C8—81no—
479C2×C8—101no—
480C2×C8—101no—
481C2×C8—401no—
482C2×C8—401no—
483C2×C8—401no—
484C2×C8—401no—
485C4⋊C4—21no—
486C4⋊C4—51no—
487C4⋊C4—51no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4C2×C4×D511yescharacteristic
491C4⋊C4C2×C4×D511yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—101no—
497C22⋊C4—101no—
498C22⋊C4—101no—
499C42—101no—
500C42—101no—
501C42—101no—
502C42C2×C4×D511yescharacteristic
503C42D4×D511yescharacteristic
504C42#71111yescharacteristic
505C42C23×D511yescharacteristic
506C2×C5—41no—
507C2×C5—81no—
508C2×C5—81no—
509C2×C5#292911yescharacteristic
510C2×C5#294611yescharacteristic
511C2×C5#295711yescharacteristic
512D5—42no—
513C23—21no—
514C23—21no—
515C23—101no—
516C23#402711yescharacteristic
517Q8—52no—
518Q8—81no—
519Q8—101no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—52no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—104no—
530D4—101no—
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—104no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—401no—
549C2×C4#402711yescharacteristic
550C2×C4#402711yescharacteristic
551C2×C4#402711yescharacteristic
552C2×C4C22×C4×D511yescharacteristic
553C2×C4C2×D4×D511yescharacteristic
554C2×C4C2×#71111yescharacteristic
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—101no—
560C8—101no—
561C8—101no—
562C8—101no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—201no—
568C8—201no—
569C5#1792011yescharacteristic, complemented, Sylow
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—102no—
580C22—201no—
581C22—201no—
582C22C2×#402711yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—102no—
590C4—201no—
591C4—201no—
592C4D5×#13111yescharacteristic
593C4D5×#13111yescharacteristic
594C4#6609111yescharacteristic
595C4#6609611yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—202no—
600C2#1061038611yescharacteristic
601C2#1061045711yescharacteristic
602C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1480C2
socleC22×C5C2×C4×D4
prime radical#10615030C2
cosocleC42×C5C24
hypercenter#1480D5
hypocenterC5#17920
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #10615011C2semidirect
3. #10610744C2semidirect
4. C5×#1480C2semidirect
5. #10601556C2semidirect
6. #10601537C2semidirect
7. #10601216C2semidirect
8. #10598952C2semidirect
9. #10598951C2semidirect
10. #10598948C2semidirect
11. #10598946C2semidirect
12. #10598944C2semidirect
13. #10598943C2semidirect
14. #10598942C2semidirect
15. #10598941C2semidirect
158. #1480D5semidirect
569. C5#17920semidirect

Maximal subgroups

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

subgroupindex
#106150302
#106150112
#106107442
C5×#14802
#106015562
#106015372
#106012162
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