Finite Group Databasebeta

← #12070532

Subgroups — #12070532

Order 1280.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3105C211yesmaximal, characteristic
2#10614863C211yesmaximal, characteristic, complemented
3#10614034C211yesmaximal, characteristic, complemented
4#10602545C211yesmaximal, characteristic, complemented
5C2×D4⋊#168C211yesmaximal, characteristic, complemented
6#10601693C211yesmaximal, characteristic, complemented
7#10601689C211yesmaximal, characteristic, complemented
8#10601688C211yesmaximal, characteristic, complemented
9SD16⋊#168C211yesmaximal, characteristic, complemented
10#10601675C211yesmaximal, characteristic, complemented
11#10601672C211yesmaximal, characteristic, complemented
12#10601672C211yesmaximal, characteristic, complemented
13#10601671C211yesmaximal, characteristic, complemented
14#10601545C211yesmaximal, characteristic, complemented
15#10601535C211yesmaximal, characteristic, complemented
16C5×#529C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C5×#484C411yescharacteristic
19C5×#481C411yescharacteristic
20C5×#478C411yescharacteristic
21C5×#478C411yescharacteristic
22C5×#463C411yescharacteristic
23C5×#463C411yescharacteristic
24C5×#450C411yescharacteristic
25C5×#447C411yescharacteristic
26C4×C5×SD16C2211yescharacteristic
27C4×C5×SD16C2211yescharacteristic
28C4×C5×D8C2211yescharacteristic
29C4×C5×D8C2211yescharacteristic
30C5×#431C2211yescharacteristic
31#65496—21no—
32C2×C22⋊#168—21no—
33#65313C2211yescharacteristic, complemented
34Q8×#168C2211yescharacteristic, complemented
35#65301C2211yescharacteristic
36#65301C2211yescharacteristic
37#65301C2211yescharacteristic, complemented
38#65300—21no—
39#65300—21no—
40#65300—21no—
41D4×#168—21no—
42D4×#168C2211yescharacteristic
43D4×#168C2211yescharacteristic
44D4×#168C2211yescharacteristic, complemented
45#65289—21no—
46#65288—21no—
47#65215C2211yescharacteristic
48#65214C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50C2×C4×#168C2211yescharacteristic
51Q8⋊#168C2211yescharacteristic, complemented
52Q8⋊#168C2211yescharacteristic, complemented
53D4⋊#168C2211yescharacteristic
54D4⋊#168C2211yescharacteristic
55D4⋊#168C2211yescharacteristic
56D4⋊#168C2211yescharacteristic
57D4⋊#168C2211yescharacteristic, complemented
58D4⋊#168C2211yescharacteristic, complemented
59#64678C2211yescharacteristic, complemented
60#64678C2211yescharacteristic, complemented
61#64677C2211yescharacteristic, complemented
62#64677C2211yescharacteristic, complemented
63#64675C2211yescharacteristic, complemented
64#64675C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18020—51nomaximal, Sylow
68C22×C5×D4C2×C411yescharacteristic
69C23×C4×C5—21no—
70C2×C5×SD16C2×C411yescharacteristic
71C2×C5×SD16C2×C411yescharacteristic
72C2×C5×D8C2×C411yescharacteristic
73C2×C5×D8C2×C411yescharacteristic
74C5×#126—21no—
75C5×#125C2×C411yescharacteristic
76C5×#124C2×C411yescharacteristic
77C5×#123—21no—
78C5×C22⋊Q8C2×C411yescharacteristic
79C5×#121C2×C411yescharacteristic
80C4×C5×Q8C2311yescharacteristic
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C4×C5×D4—21no—
84C4×C5×D4C2×C411yescharacteristic
85C4×C5×D4C2×C411yescharacteristic
86C4×C5×D4C2311yescharacteristic
87C4×C5×D4C2311yescharacteristic
88C4×C5×D4C2311yescharacteristic
89C5×#117—21no—
90C2×C5×C4⋊C4C2×C411yescharacteristic
91C2×C5×C22⋊C4—21no—
92C2×C42×C5C2311yescharacteristic
93C2×#681—21no—
94C2×#681—21no—
95C2×#681—21no—
96C22×#168—21no—
97C22×#168—21no—
98C22×#168—21no—
99C22×#168—21no—
100C22×#168—21no—
101C5×#107C2×C411yescharacteristic
102C5×#107C2×C411yescharacteristic
103C5×#106C2×C411yescharacteristic
104C5×#106C2×C411yescharacteristic
105C5×C4⋊C8C2×C411yescharacteristic
106C5×C4⋊C8C2×C411yescharacteristic
107C5×#103C2×C411yescharacteristic
108C5×#103C2×C411yescharacteristic
109C5×#102C2×C411yescharacteristic
110C5×#102C2×C411yescharacteristic
111C5×#102C2×C411yescharacteristic
112C5×#102C2×C411yescharacteristic
113C5×#102C2×C411yescharacteristic
114C5×#102C2×C411yescharacteristic
115C5×C22⋊C8C2×C411yescharacteristic
116C5×C22⋊C8C2×C411yescharacteristic
117C4×C5×C8C2311yescharacteristic
118C4×C5×C8C2311yescharacteristic
119C22⋊#168—21no—
120C22⋊#168—21no—
121C22⋊#168—21no—
122C22⋊#168—21no—
123C22⋊#168—21no—
124C22⋊#168—21no—
125C22⋊#168—21no—
126C22⋊#168D411yescharacteristic
127C22⋊#168D411yescharacteristic
128C4⋊#168—21no—
129C4⋊#168—21no—
130C4⋊#168—21no—
131C4⋊#168D411yescharacteristic
132C4⋊#168D411yescharacteristic
133C4⋊#168C2311yescharacteristic
134C4⋊#168C2311yescharacteristic
135C4⋊#168C2311yescharacteristic
136C4⋊#168C2311yescharacteristic
137#3935—21no—
138#3935—21no—
139C4×#168—21no—
140C4×#168—21no—
141C4×#168C2311yescharacteristic
142C4×#168C2311yescharacteristic
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145#3105D511yescharacteristic
146#2994—51no—
147#2974—51no—
148#1594—51no—
149#1592—51no—
150#1583—51no—
151#1582—51no—
152#1581—51no—
153#1581—51no—
154#1580—51no—
155SD16⋊C8—51no—
156#1573—51no—
157#1494—51no—
158C2×D4⋊C8—51no—
159#1452—51no—
160C24×C5—21no—
161C2×C5×Q8C22×C411yescharacteristic
162C2×C5×D4—22no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—41no—
166C2×C5×D4C22×C411yescharacteristic
167C2×C5×D4C22×C411yescharacteristic
168C2×C5×D4C22×C411yescharacteristic
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—81no—
176C22×C4×C5—81no—
177C22×C4×C5C22×C411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5#4111yescharacteristic
180C5×SD16—22no—
181C5×SD16—41no—
182C5×D8—22no—
183C5×D8—41no—
184C2×C5×C8C22×C411yescharacteristic
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C22×C411yescharacteristic
187C2×C5×C8C22×C411yescharacteristic
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4C22×C411yescharacteristic
194C5×C4⋊C4C22×C411yescharacteristic
195C5×C4⋊C4C22×C411yescharacteristic
196C5×C4⋊C4C22×C411yescharacteristic
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—21no—
203C5×C22⋊C4—21no—
204C5×C22⋊C4—21no—
205C5×C22⋊C4—21no—
206C42×C5—21no—
207C42×C5C22×C411yescharacteristic
208C42×C5C2×D411yescharacteristic
209C42×C5#4111yescharacteristic
210C42×C5C2411yescharacteristic
211#681—81no—
212#681—81no—
213#681—81no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—42no—
221C2×#168—81no—
222C2×#168—81no—
223C2×#168—81no—
224C2×#168—81no—
225C2×#168C2×D411yescharacteristic
226C2×#168C2×D411yescharacteristic
227C2×#168C2×D411yescharacteristic
228C2×#168C2×D411yescharacteristic
229#529C2×D511yescharacteristic
230C2×C4×D4C2×D511yescharacteristic
231#484Dic511yescharacteristic
232#481Dic511yescharacteristic
233#478Dic511yescharacteristic
234#478Dic511yescharacteristic
235#463Dic511yescharacteristic
236#463Dic511yescharacteristic
237#450Dic511yescharacteristic
238#447Dic511yescharacteristic
239#446—51no—
240C8×Q8—51no—
241C4×SD16C2×D511yescharacteristic
242C4×SD16C2×D511yescharacteristic
243C4×D8C2×D511yescharacteristic
244C4×D8C2×D511yescharacteristic
245#436—51no—
246#436—51no—
247#436—51no—
248#435—101no—
249#435—101no—
250#435—101no—
251C8×D4—51no—
252C8×D4—51no—
253C8×D4—51no—
254C8×D4—101no—
255#433—101no—
256#432—51no—
257#431—51no—
258#431C2×D511yescharacteristic
259#424—101no—
260C2×C4⋊C8—51no—
261#407—101no—
262C2×C22⋊C8—101no—
263C2×C4×C8—51no—
264#335—51no—
265#335—51no—
266#334—51no—
267#334—51no—
268Q8⋊C8—51no—
269Q8⋊C8—51no—
270D4⋊C8—51no—
271D4⋊C8—51no—
272D4⋊C8—51no—
273D4⋊C8—51no—
274D4⋊C8—51no—
275D4⋊C8—51no—
276#322—51no—
277#322—51no—
278#322—51no—
279#322—51no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—42no—
284C23×C5—42no—
285C23×C5—81no—
286C23×C5C4×D411yescharacteristic
287C5×Q8—21no—
288C5×Q8—21no—
289C5×D4—21no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—21no—
293C5×D4—21no—
294C5×D4—42no—
295C5×D4—42no—
296C5×D4#13112yes—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—81no—
314C2×C4×C5—81no—
315C2×C4×C5—81no—
316C2×C4×C5C4×D411yescharacteristic
317C2×C4×C5C4×D411yescharacteristic
318C2×C4×C5C4×D411yescharacteristic
319C2×C4×C5C23×C411yescharacteristic
320C2×C4×C5C22×D411yescharacteristic
321C2×C4×C5C2×#4111yescharacteristic
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—21no—
326#168—21no—
327#168—21no—
328#168—21no—
329#168—21no—
330#168—41no—
331#168—41no—
332#168—41no—
333#168—41no—
334#168—41no—
335#168—41no—
336C22×D4C2×Dic511yescharacteristic
337C23×C4—21no—
338C2×SD16C2×Dic511yescharacteristic
339C2×SD16C2×Dic511yescharacteristic
340C2×D8C2×Dic511yescharacteristic
341C2×D8C2×Dic511yescharacteristic
342C2×M16—101no—
343C2×M16—101no—
344C2×M16—101no—
345C22×C8—101no—
346C22×C8—101no—
347C22×C8—101no—
348C22×C8—101no—
349C22×C8—101no—
350#126—21no—
351#125C2×Dic511yescharacteristic
352#124C2×Dic511yescharacteristic
353#123—21no—
354C22⋊Q8C2×Dic511yescharacteristic
355#121C2×Dic511yescharacteristic
356C4×Q8C22×D511yescharacteristic
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4C2×Dic511yescharacteristic
361C4×D4C2×Dic511yescharacteristic
362C4×D4C22×D511yescharacteristic
363C4×D4C22×D511yescharacteristic
364C4×D4C22×D511yescharacteristic
365#117—21no—
366C2×C4⋊C4C2×Dic511yescharacteristic
367C2×C22⋊C4—21no—
368C2×C42C22×D511yescharacteristic
369#107C2×Dic511yescharacteristic
370#107C2×Dic511yescharacteristic
371#106C2×Dic511yescharacteristic
372#106C2×Dic511yescharacteristic
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⋊C8—101no—
382C4⋊C8C2×Dic511yescharacteristic
383C4⋊C8C2×Dic511yescharacteristic
384#103C2×Dic511yescharacteristic
385#103C2×Dic511yescharacteristic
386#102C2×Dic511yescharacteristic
387#102C2×Dic511yescharacteristic
388#102C2×Dic511yescharacteristic
389#102C2×Dic511yescharacteristic
390#102C2×Dic511yescharacteristic
391#102C2×Dic511yescharacteristic
392C22⋊C8—51no—
393C22⋊C8—51no—
394C22⋊C8—101no—
395C22⋊C8—101no—
396C22⋊C8—101no—
397C22⋊C8—101no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401C22⋊C8C2×Dic511yescharacteristic
402C22⋊C8C2×Dic511yescharacteristic
403#97—101no—
404#97—101no—
405C4×C8—51no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—101no—
410C4×C8—101no—
411C4×C8C22×D511yescharacteristic
412C4×C8C22×D511yescharacteristic
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—22no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—84no—
425C22×C5#44412yes—
426C22×C5C2×C4×D411yescharacteristic
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5—41no—
436C4×C5C2×#13111yescharacteristic
437C4×C5#56811yescharacteristic
438C4×C5#57611yescharacteristic
439C4×C5#57711yescharacteristic
440C24—21no—
441C2×Q8C22×Dic511yescharacteristic
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C22×Dic511yescharacteristic
447C2×D4C22×Dic511yescharacteristic
448C2×D4C22×Dic511yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4D4×D511yescharacteristic
458C22×C4#71111yescharacteristic
459C22×C4C22×Dic511yescharacteristic
460SD16—22no—
461SD16—41no—
462D8—22no—
463D8—41no—
464M16—401no—
465M16—401no—
466M16—401no—
467C2×C8—51no—
468C2×C8—51no—
469C2×C8—51no—
470C2×C8—51no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—202no—
478C2×C8—401no—
479C2×C8—401no—
480C2×C8—401no—
481C2×C8—401no—
482C2×C8C22×Dic511yescharacteristic
483C2×C8C22×Dic511yescharacteristic
484C2×C8C22×Dic511yescharacteristic
485C2×C8C22×Dic511yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4C22×Dic511yescharacteristic
492C4⋊C4C22×Dic511yescharacteristic
493C4⋊C4C22×Dic511yescharacteristic
494C4⋊C4C22×Dic511yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C42—21no—
505C42D4×D511yescharacteristic
506C42#71111yescharacteristic
507C42C22×Dic511yescharacteristic
508C42C23×D511yescharacteristic
509C2×C5—22no—
510C2×C5—42no—
511C2×C5—81no—
512C2×C5—81no—
513C2×C5#293311yescharacteristic
514C2×C5#294611yescharacteristic
515C2×C5C2×#44411yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23D4×Dic511yescharacteristic
523Q8—21no—
524Q8—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—42no—
531D4—42no—
532D4#409412yes—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4D4×Dic511yescharacteristic
553C2×C4D4×Dic511yescharacteristic
554C2×C4D4×Dic511yescharacteristic
555C2×C4C2×D4×D511yescharacteristic
556C2×C4C2×#71111yescharacteristic
557C2×C4C23×Dic511yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—101no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—201no—
567C8—201no—
568C8—201no—
569C8—201no—
570C8—201no—
571C8—201no—
572C5#1802011yescharacteristic, complemented, Sylow
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—84no—
585C22#6548612yes—
586C22C2×D4×Dic511yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4#6610811yescharacteristic
597C4#6610911yescharacteristic
598C4C2×#409411yescharacteristic
599C4#6615311yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—81no—
604C2#1061464911yescharacteristic
605C2C2×#6548611yescharacteristic
606C2#1061566111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#3105C2
socleC22×C5C2×C4×D4
prime radicalC5×#447C4
cosocleC42×C5C24
hypercenter#3105D5
hypocenterC5#18020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
2. #10614863C2semidirect
3. #10614034C2semidirect
4. #10602545C2semidirect
5. C2×D4⋊#168C2semidirect
6. #10601693C2semidirect
7. #10601689C2semidirect
8. #10601688C2semidirect
9. SD16⋊#168C2semidirect
10. #10601675C2semidirect
11. #10601672C2semidirect
12. #10601672C2semidirect
13. #10601671C2semidirect
14. #10601545C2semidirect
15. #10601535C2semidirect
33. #65313C22semidirect
34. Q8×#168C22semidirect
37. #65301C22semidirect
44. D4×#168C22semidirect
51. Q8⋊#168C22semidirect
52. Q8⋊#168C22semidirect
57. D4⋊#168C22semidirect
58. D4⋊#168C22semidirect
59. #64678C22semidirect
60. #64678C22semidirect
61. #64677C22semidirect
62. #64677C22semidirect
63. #64675C22semidirect
64. #64675C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
572. C5#18020semidirect

Maximal subgroups

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

subgroupindex
C5×#31052
#106148632
#106140342
#106025452
C2×D4⋊#1682
#106016932
#106016892
#106016882
SD16⋊#1682
#106016752
#106016722
#106016712
#106015452
#106015352
#180205