Finite Group Databasebeta

← #12066821

Subgroups — #12066821

Order 1280.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617691C211yesmaximal, characteristic
2C5×#2318C211yesmaximal, characteristic, complemented
3#10614034C211yesmaximal, characteristic, complemented
4#10600358C211yesmaximal, characteristic, complemented
5#10600357C211yesmaximal, characteristic, complemented
6#10600338C211yesmaximal, characteristic, complemented
7#10600337C211yesmaximal, characteristic, complemented
8#10600325C211yesmaximal, characteristic, complemented
9#10600324C211yesmaximal, characteristic, complemented
10#10600302C211yesmaximal, characteristic, complemented
11#10600301C211yesmaximal, characteristic, complemented
12#10600237C211yesmaximal, characteristic, complemented
13#10600236C211yesmaximal, characteristic, complemented
14#10600191C211yesmaximal, characteristic, complemented
15C2×#64671C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17D4×C22⋊D5—21no—
18#66125C2211yescharacteristic
19#66125C2211yescharacteristic
20C2×#4076C2211yescharacteristic
21C2×#4076C2211yescharacteristic
22#65899C411yescharacteristic, complemented
23#65899C411yescharacteristic, complemented
24#65897C411yescharacteristic, complemented
25#65896—21no—
26#65894—21no—
27#65894—21no—
28#65887C411yescharacteristic, complemented
29#65884C411yescharacteristic, complemented
30#65884C411yescharacteristic, complemented
31D4×D20C411yescharacteristic, complemented
32#65879—21no—
33#65877C411yescharacteristic, complemented
34#65848—21no—
35#65824—21no—
36#65824—21no—
37#65813C2211yescharacteristic
38#65811C2211yescharacteristic
39C5×#388—21no—
40C5×#387—21no—
41C5×#386—21no—
42C5×#385—21no—
43C5×#383C2211yescharacteristic, complemented
44C5×#382C2211yescharacteristic, complemented
45C5×#381C2211yescharacteristic, complemented
46C5×#380C2211yescharacteristic, complemented
47C4×C5×C22⋊C4C2211yescharacteristic, complemented
48C2×C5×#95C2211yescharacteristic, complemented
49#65496C2211yescharacteristic, complemented
50#65496C2211yescharacteristic, complemented
51C2×C22⋊#168C2211yescharacteristic, complemented
52C2×C22⋊#168C2211yescharacteristic, complemented
53#65301—21no—
54#65300—21no—
55#65300—21no—
56D4×#168—21no—
57#65215C2211yescharacteristic, complemented
58#65214C2211yescharacteristic, complemented
59#64672C2211yescharacteristic, complemented
60#64672C2211yescharacteristic, complemented
61#64672C2211yescharacteristic, complemented
62#64672C2211yescharacteristic, complemented
63#64671C2211yescharacteristic
64#64671C2211yescharacteristic
65#64671C2211yescharacteristic
66#64671C2211yescharacteristic
67#64671C2211yescharacteristic, complemented
68#64671C2211yescharacteristic, complemented
69#64671C2211yescharacteristic, complemented
70#64671C2211yescharacteristic, complemented
71#64671C2211yescharacteristic, complemented
72#64671C2211yescharacteristic, complemented
73#64671C2211yescharacteristic, complemented
74#64671C2211yescharacteristic, complemented
75#17597—51nomaximal, Sylow
76C22×C5×D4D411yescharacteristic
77C23×C4×C5—21no—
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—21no—
81C22×C22⋊D5—21no—
82C2×D4×D5—21no—
83C2×#709—21no—
84C2×#709C2×C411yescharacteristic
85C2×#709C2×C411yescharacteristic, complemented
86C22×D20C2×C411yescharacteristic
87C22×D20C2×C411yescharacteristic, complemented
88C4×C5×D4C2×C411yescharacteristic
89C4×C5×D4C2×C411yescharacteristic
90C4×C5×D4C2×C411yescharacteristic
91C4×C5×D4C2×C411yescharacteristic
92C4×C5×D4D411yescharacteristic
93C4×C5×D4D411yescharacteristic
94C4×C5×D4D411yescharacteristic
95C4×C5×D4D411yescharacteristic
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4D411yescharacteristic
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4D411yescharacteristic
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106#4099—21no—
107#4099—21no—
108#4086—21no—
109#4085—21no—
110#4085—21no—
111#4084—21no—
112#4083—21no—
113#4083—21no—
114D4×Dic5—21no—
115#4076—21no—
116#4076—21no—
117#4076—21no—
118#4076—21no—
119#4076—21no—
120#4076C2×C411yescharacteristic
121#4076C2×C411yescharacteristic
122#4076C2×C411yescharacteristic
123#4076C2×C411yescharacteristic, complemented
124#4076C2×C411yescharacteristic, complemented
125#4076C2×C411yescharacteristic, complemented
126#4076C2311yescharacteristic
127#4076C2311yescharacteristic
128#4076C2311yescharacteristic
129#4075—21no—
130#4075—21no—
131#4075—21no—
132C4×C22⋊D5—21no—
133C4×C22⋊D5—21no—
134C4×C22⋊D5—21no—
135C4×C22⋊D5—21no—
136C4×C22⋊D5—21no—
137C2×#685—21no—
138C2×#685—21no—
139#4072C2×C411yescharacteristic
140#4072C2×C411yescharacteristic, complemented
141C2×C4⋊Dic5C2×C411yescharacteristic
142C2×C4⋊Dic5C2×C411yescharacteristic, complemented
143#4070C2×C411yescharacteristic
144#4070C2×C411yescharacteristic, complemented
145#4070C2311yescharacteristic
146C2×#681—21no—
147C2×#681—21no—
148C22×#168—21no—
149C22×#168—21no—
150#4044—21no—
151#4044—21no—
152#4041—21no—
153#4040—21no—
154#4040—21no—
155#4039—21no—
156#4038—21no—
157#4036—21no—
158#4031—21no—
159#4031—21no—
160#4030—21no—
161#4030—21no—
162#4030—21no—
163#4030—21no—
164#4029—21no—
165#4029—21no—
166#4028—21no—
167#4028—21no—
168#4027—21no—
169#4027—21no—
170D5×C22⋊C4—21no—
171D5×C22⋊C4—21no—
172#4024—21no—
173#4024—21no—
174#4022—21no—
175#4021—21no—
176#4021C2×C411yescharacteristic, complemented
177#4020C2×C411yescharacteristic, complemented
178C4×D20—21no—
179C4×D20C2×C411yescharacteristic, complemented
180C4×D20C2×C411yescharacteristic, complemented
181C4×D20C2×C411yescharacteristic, complemented
182#4018—21no—
183#4016C2×C411yescharacteristic, complemented
184#4015C2×C411yescharacteristic, complemented
185C4×Dic10C2×C411yescharacteristic, complemented
186C5×#95—21no—
187C5×#95—21no—
188C5×#95—21no—
189C5×#95—21no—
190C5×#95—21no—
191C5×#95C2311yescharacteristic
192C5×#95C2311yescharacteristic
193C5×#95C2311yescharacteristic
194C5×#95C2311yescharacteristic
195C22⋊#168—21no—
196C22⋊#168—21no—
197C22⋊#168—21no—
198C22⋊#168—21no—
199C22⋊#168C2311yescharacteristic
200C22⋊#168C2311yescharacteristic
201C22⋊#168C2311yescharacteristic
202C22⋊#168C2311yescharacteristic
203C4⋊#168—21no—
204C4⋊#168—21no—
205#3935—21no—
206C4×#168—21no—
207#3519—51no—
208#2974—51no—
209#2318D511yescharacteristic, complemented
210#1521—51no—
211#1519—51no—
212#1517—51no—
213#1516—51no—
214#1514—51no—
215#1513—51no—
216#1512—51no—
217#1510—51no—
218#1507—51no—
219#1504—51no—
220#1501—51no—
221C2×#327—51no—
222C24×C5C2×D411yescharacteristic
223C24×C5C2×D411yescharacteristic
224C23×D5—21no—
225C23×D5—21no—
226C2×C5×D4—42no—
227C2×C5×D4C22⋊C411yescharacteristic
228C2×C5×D4C22⋊C411yescharacteristic
229C2×C5×D4C22⋊C411yescharacteristic
230C2×C5×D4C22⋊C411yescharacteristic
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—42no—
236C22×C4×C5—81no—
237C22×C4×C5—81no—
238C22×C4×C5—81no—
239C22×C4×C5—81no—
240C22×C4×C5C22×C411yescharacteristic
241C22×C4×C5C22×C411yescharacteristic
242C22×C4×C5C22×C411yescharacteristic
243C22×C4×C5C22×C411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D411yescharacteristic
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2411yescharacteristic
253C2×C22⋊D5—21no—
254C2×C22⋊D5—21no—
255C2×C22⋊D5—21no—
256C2×C22⋊D5—21no—
257C2×C22⋊D5—21no—
258C2×C22⋊D5—21no—
259C2×C22⋊D5—21no—
260C2×C22⋊D5—21no—
261C2×C22⋊D5—21no—
262C2×C22⋊D5—21no—
263C2×C22⋊D5—21no—
264C2×C22⋊D5—81no—
265C2×C22⋊D5—81no—
266C2×C22⋊D5—81no—
267C2×C22⋊D5—81no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270D4×D5—44no—
271#709—81no—
272#709—81no—
273#709—81no—
274#709—81no—
275C2×D20—21no—
276C2×D20—21no—
277C2×D20—21no—
278C2×D20—21no—
279C2×D20—81no—
280C2×D20—81no—
281C2×D20C22×C411yescharacteristic
282C2×D20C22×C411yescharacteristic
283C2×D20C22×C411yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×C4×D5—21no—
288C2×C4×D5—21no—
289C2×Dic10—21no—
290C2×Dic10C22×C411yescharacteristic
291C5×C4⋊C4—81no—
292C5×C4⋊C4—81no—
293C5×C4⋊C4C22⋊C411yescharacteristic
294C5×C4⋊C4C22⋊C411yescharacteristic
295C5×C4⋊C4C22⋊C411yescharacteristic
296C5×C4⋊C4C22⋊C411yescharacteristic
297C5×C22⋊C4—42no—
298C5×C22⋊C4—81no—
299C5×C22⋊C4—81no—
300C5×C22⋊C4C22⋊C411yescharacteristic
301C5×C22⋊C4C22⋊C411yescharacteristic
302C5×C22⋊C4C22⋊C411yescharacteristic
303C5×C22⋊C4C22⋊C411yescharacteristic
304C5×C22⋊C4C22⋊C411yescharacteristic
305C5×C22⋊C4C22⋊C411yescharacteristic
306C5×C22⋊C4C22⋊C411yescharacteristic
307C5×C22⋊C4C22⋊C411yescharacteristic
308C42×C5—81no—
309C42×C5C22×C411yescharacteristic
310C42×C5C22×C411yescharacteristic
311C42×C5C2×D411yescharacteristic
312C42×C5C2×D411yescharacteristic
313C22⋊Dic5—21no—
314C22⋊Dic5—21no—
315C22⋊Dic5—21no—
316C22⋊Dic5—21no—
317C22⋊Dic5—21no—
318#685—21no—
319#685—21no—
320#685—21no—
321#685—21no—
322#685—21no—
323#685—21no—
324#685—21no—
325#685—21no—
326#685—21no—
327#685—21no—
328#685—21no—
329#685—21no—
330#685—21no—
331#685—21no—
332C4⋊Dic5—21no—
333C4⋊Dic5—21no—
334C4⋊Dic5—21no—
335C4⋊Dic5C22×C411yescharacteristic
336C4⋊Dic5C22×C411yescharacteristic
337C4⋊Dic5C22×C411yescharacteristic
338C4⋊Dic5C22×C411yescharacteristic
339#683—21no—
340#683—21no—
341#683—21no—
342#683—21no—
343#683—21no—
344#683—21no—
345C4×Dic5—21no—
346C4×Dic5—21no—
347C4×Dic5—21no—
348#681—81no—
349#681—81no—
350C2×#168—21no—
351C2×#168—21no—
352C2×#168—21no—
353C2×#168—21no—
354C2×#168—81no—
355C2×#168—81no—
356#555—51no—
357#554—51no—
358#553—51no—
359#553—51no—
360#553—101no—
361#550—51no—
362#546—51no—
363#546—51no—
364#546—101no—
365#546—101no—
366D42—51no—
367D42—101no—
368#540—101no—
369#538—101no—
370#538—101no—
371#532—51no—
372#529—51no—
373#525—51no—
374#525—51no—
375C2×#121—51no—
376C2×#121—51no—
377#518—101no—
378C2×C4×D4C2×D511yescharacteristic
379#436—101no—
380#435—101no—
381#435—101no—
382C8×D4—101no—
383#432—51no—
384#431—51no—
385#407—51no—
386#407—51no—
387C2×C22⋊C8—51no—
388C2×C22⋊C8—51no—
389#388—21no—
390#387—21no—
391#386—21no—
392#385—21no—
393#383C2×D511yescharacteristic, complemented
394#382C2×D511yescharacteristic, complemented
395#381C2×D511yescharacteristic, complemented
396#380C2×D511yescharacteristic, complemented
397C4×C22⋊C4C2×D511yescharacteristic, complemented
398C2×#95C2×D511yescharacteristic, complemented
399#328—51no—
400#328—51no—
401#328—51no—
402#328—51no—
403#327—51no—
404#327—51no—
405#327—51no—
406#327—51no—
407#327—51no—
408#327—51no—
409#327—51no—
410#327—51no—
411#327—51no—
412#327—51no—
413#327—51no—
414#327—51no—
415C23×C5—21no—
416C23×C5—21no—
417C23×C5—22no—
418C23×C5—21no—
419C23×C5—21no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5C2×C22⋊C411yescharacteristic
424C23×C5C2×C22⋊C411yescharacteristic
425C23×C5C2×C22⋊C411yescharacteristic
426C23×C5C2×C22⋊C411yescharacteristic
427C23×C5C22×D411yescharacteristic
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—42no—
432C22×D5—42no—
433C22×D5—81no—
434C22×D5—81no—
435C22×D5—81no—
436C22×D5—81no—
437C5×D4—22no—
438C5×D4—22no—
439C5×D4—41no—
440C5×D4—41no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C2×C4×C5—41no—
463C2×C4×C5—41no—
464C2×C4×C5—41no—
465C2×C4×C5—41no—
466C2×C4×C5—41no—
467C2×C4×C5—84no—
468C2×C4×C5C2×C22⋊C411yescharacteristic
469C2×C4×C5C2×C22⋊C411yescharacteristic
470C2×C4×C5C2×C22⋊C411yescharacteristic
471C2×C4×C5C2×C22⋊C411yescharacteristic
472C2×C4×C5C2×C22⋊C411yescharacteristic
473C2×C4×C5C2×C22⋊C411yescharacteristic
474C2×C4×C5C2×C22⋊C411yescharacteristic
475C2×C4×C5C2×C22⋊C411yescharacteristic
476C2×C4×C5C23×C411yescharacteristic
477C2×C4×C5C22×D411yescharacteristic
478C22⋊D5—42no—
479C22⋊D5—41no—
480C22⋊D5—41no—
481C22⋊D5—41no—
482C22⋊D5—41no—
483C22⋊D5—41no—
484C22⋊D5—41no—
485C22⋊D5—42no—
486C22⋊D5—81no—
487C22⋊D5—81no—
488C22⋊D5—81no—
489C22⋊D5—81no—
490C22⋊D5—81no—
491C22⋊D5—81no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—81no—
498C2×Dic5—81no—
499D20—41no—
500D20—41no—
501D20—41no—
502D20—42no—
503D20—81no—
504D20—81no—
505D20—81no—
506C4×D5—42no—
507C4×D5—81no—
508C4×D5—81no—
509C4×D5—81no—
510C4×D5—81no—
511Dic10—41no—
512Dic10—81no—
513#168—41no—
514#168—41no—
515#168—41no—
516#168—41no—
517C2×#41—51no—
518C2×#41—51no—
519C2×#41—101no—
520C22×D4—51no—
521C22×D4—51no—
522C22×D4—101no—
523C22×D4—101no—
524C22×D4—101no—
525C22×D4C22⋊D511yescharacteristic
526C23×C4—21no—
527C23×C4C22×D511yescharacteristic
528C23×C4C22×D511yescharacteristic
529C2×M16—101no—
530C2×M16—101no—
531C22×C8—101no—
532C22×C8—101no—
533C4⋊Q8—51no—
534#127—51no—
535#127—101no—
536#126—101no—
537#126—101no—
538#126—101no—
539#125—51no—
540#125—101no—
541#124—51no—
542#124—101no—
543#124—101no—
544#124—101no—
545#123—101no—
546#123—101no—
547#123—101no—
548#123—101no—
549#123—101no—
550#123—101no—
551#123—101no—
552C22⋊Q8—51no—
553C22⋊Q8—51no—
554C22⋊Q8—51no—
555C22⋊Q8—101no—
556C22⋊Q8—101no—
557#121—51no—
558#121—51no—
559#121—51no—
560#121—51no—
561#121—51no—
562#121—51no—
563#121—51no—
564#121—51no—
565#121—51no—
566#121—101no—
567#121—101no—
568#121—101no—
569#121—101no—
570#121—101no—
571#121—101no—
572#121—101no—
573#121—101no—
574#121—101no—
575#121—101no—
576#121—101no—
577#121—101no—
578#121—101no—
579#120—101no—
580#120—101no—
581#120—101no—
582#120—101no—
583#120—101no—
584#120—101no—
585C4×Q8—51no—
586C4×D4—51no—
587C4×D4—51no—
588C4×D4—51no—
589C4×D4—101no—
590C4×D4—101no—
591C4×D4—101no—
592C4×D4—101no—
593C4×D4—101no—
594C4×D4—101no—
595C4×D4—101no—
596C4×D4—101no—
597C4×D4—101no—
598C4×D4—101no—
599C4×D4C4×D511yescharacteristic
600C4×D4C4×D511yescharacteristic
601C4×D4C4×D511yescharacteristic
602C4×D4C4×D511yescharacteristic
603C4×D4D2011yescharacteristic
604C4×D4D2011yescharacteristic
605C4×D4D2011yescharacteristic
606C4×D4D2011yescharacteristic
607#117—51no—
608#117—51no—
609#117—101no—
610#117—101no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—51no—
614C2×C4⋊C4—51no—
615C2×C4⋊C4C22⋊D511yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—101no—
620C2×C22⋊C4—101no—
621C2×C22⋊C4—101no—
622C2×C22⋊C4—101no—
623C2×C22⋊C4C22⋊D511yescharacteristic
624C2×C22⋊C4C22⋊D511yescharacteristic
625C2×C42—21no—
626C2×C42C22×D511yescharacteristic
627C4⋊C8—101no—
628C4⋊C8—101no—
629C22⋊C8—51no—
630C22⋊C8—51no—
631C22⋊C8—51no—
632C22⋊C8—51no—
633C22⋊C8—101no—
634C22⋊C8—101no—
635C22⋊C8—101no—
636C22⋊C8—101no—
637#97—101no—
638C4×C8—101no—
639#95—21no—
640#95—21no—
641#95—21no—
642#95—21no—
643#95—21no—
644#95C22×D511yescharacteristic
645#95C22×D511yescharacteristic
646#95C22×D511yescharacteristic
647#95C22×D511yescharacteristic
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5—21no—
654C22×C5—21no—
655C22×C5—21no—
656C22×C5—21no—
657C22×C5—21no—
658C22×C5—21no—
659C22×C5—21no—
660C22×C5—21no—
661C22×C5—42no—
662C22×C5—42no—
663C22×C5—81no—
664C22×C5—81no—
665C22×C5#42112yes—
666C22×C5C22×C22⋊C411yescharacteristic
667C22×C5#57611yescharacteristic
668C22×C5#57711yescharacteristic
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—41no—
673C2×D5—41no—
674C2×D5—41no—
675C2×D5—41no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—162no—
679C2×D5—162no—
680C4×C5—21no—
681C4×C5—21no—
682C4×C5—21no—
683C4×C5—21no—
684C4×C5—21no—
685C4×C5—21no—
686C4×C5—21no—
687C4×C5—21no—
688C4×C5—21no—
689C4×C5—21no—
690C4×C5—81no—
691C4×C5—81no—
692C4×C5—81no—
693C4×C5—81no—
694Dic5—41no—
695Dic5—41no—
696Dic5—41no—
697Dic5—41no—
698Dic5—41no—
699C24—101no—
700C24—101no—
701C24C2×C22⋊D511yescharacteristic
702C24C2×C22⋊D511yescharacteristic
703#41—401no—
704#41—401no—
705#41—401no—
706#41—401no—
707C2×Q8—51no—
708C2×Q8—101no—
709C2×D4—42no—
710C2×D4—51no—
711C2×D4—51no—
712C2×D4—51no—
713C2×D4—101no—
714C2×D4—101no—
715C2×D4—101no—
716C2×D4—101no—
717C2×D4—101no—
718C2×D4—101no—
719C2×D4—101no—
720C2×D4—101no—
721C2×D4—101no—
722C2×D4—101no—
723C2×D4—101no—
724C2×D4—101no—
725C2×D4—101no—
726C2×D4—101no—
727C2×D4—101no—
728C2×D4—204no—
729C2×D4—401no—
730C2×D4—401no—
731C2×D4—401no—
732C2×D4—401no—
733C2×D4—401no—
734C2×D4—401no—
735C2×D4#68511yescharacteristic
736C2×D4#68511yescharacteristic
737C2×D4#68511yescharacteristic
738C2×D4#68511yescharacteristic
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—42no—
744C22×C4—81no—
745C22×C4—81no—
746C22×C4—81no—
747C22×C4—81no—
748C22×C4—101no—
749C22×C4—101no—
750C22×C4—101no—
751C22×C4—101no—
752C22×C4—101no—
753C22×C4—101no—
754C22×C4—101no—
755C22×C4C2×C4×D511yescharacteristic
756C22×C4C2×C4×D511yescharacteristic
757C22×C4C2×C4×D511yescharacteristic
758C22×C4C2×C4×D511yescharacteristic
759C22×C4C2×D2011yescharacteristic
760C22×C4C2×D2011yescharacteristic
761C22×C4C2×D2011yescharacteristic
762C22×C4C2×D2011yescharacteristic
763C22×C4C2×C22⋊D511yescharacteristic
764C22×C4C2×C22⋊D511yescharacteristic
765C22×C4C2×C22⋊D511yescharacteristic
766C22×C4C2×C22⋊D511yescharacteristic
767C22×C4C23×D511yescharacteristic
768M16—401no—
769M16—401no—
770C2×C8—101no—
771C2×C8—101no—
772C2×C8—101no—
773C2×C8—101no—
774C2×C8—401no—
775C2×C8—401no—
776C4⋊C4—51no—
777C4⋊C4—51no—
778C4⋊C4—51no—
779C4⋊C4—51no—
780C4⋊C4—81no—
781C4⋊C4—81no—
782C4⋊C4—101no—
783C4⋊C4—101no—
784C4⋊C4—101no—
785C4⋊C4—101no—
786C4⋊C4—101no—
787C4⋊C4—101no—
788C4⋊C4—101no—
789C4⋊C4—101no—
790C4⋊C4—101no—
791C4⋊C4#68511yescharacteristic
792C4⋊C4#68511yescharacteristic
793C4⋊C4#68511yescharacteristic
794C4⋊C4#68511yescharacteristic
795C22⋊C4—42no—
796C22⋊C4—81no—
797C22⋊C4—81no—
798C22⋊C4—101no—
799C22⋊C4—101no—
800C22⋊C4—101no—
801C22⋊C4—101no—
802C22⋊C4—101no—
803C22⋊C4—101no—
804C22⋊C4—101no—
805C22⋊C4—101no—
806C22⋊C4—101no—
807C22⋊C4—101no—
808C22⋊C4—101no—
809C22⋊C4—101no—
810C22⋊C4—101no—
811C22⋊C4—101no—
812C22⋊C4—101no—
813C22⋊C4—101no—
814C22⋊C4—101no—
815C22⋊C4—101no—
816C22⋊C4—101no—
817C22⋊C4#68511yescharacteristic
818C22⋊C4#68511yescharacteristic
819C22⋊C4#68511yescharacteristic
820C22⋊C4#68511yescharacteristic
821C22⋊C4#68511yescharacteristic
822C22⋊C4#68511yescharacteristic
823C22⋊C4#68511yescharacteristic
824C22⋊C4#68511yescharacteristic
825C42—81no—
826C42—101no—
827C42—101no—
828C42—101no—
829C42C2×C4×D511yescharacteristic
830C42C2×C4×D511yescharacteristic
831C42C2×D2011yescharacteristic
832C42C2×D2011yescharacteristic
833C2×C5—21no—
834C2×C5—21no—
835C2×C5—22no—
836C2×C5—41no—
837C2×C5—41no—
838C2×C5—41no—
839C2×C5#288311yescharacteristic
840C2×C5#289711yescharacteristic
841C2×C5C2×#42111yescharacteristic
842D5—81no—
843D5—81no—
844D5—81no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—101no—
854C23—101no—
855C23—101no—
856C23—202no—
857C23—202no—
858C23—401no—
859C23—401no—
860C23—401no—
861C23—401no—
862C23C2×#68511yescharacteristic
863C23C2×#68511yescharacteristic
864C23C2×#68511yescharacteristic
865C23C2×#68511yescharacteristic
866C23C22×C22⋊D511yescharacteristic
867Q8—201no—
868Q8—401no—
869D4—22no—
870D4—22no—
871D4—41no—
872D4—41no—
873D4—201no—
874D4—201no—
875D4—201no—
876D4—202no—
877D4—202no—
878D4—202no—
879D4—201no—
880D4—201no—
881D4—201no—
882D4—201no—
883D4—201no—
884D4—201no—
885D4—401no—
886D4—401no—
887D4—401no—
888D4—401no—
889D4—401no—
890D4—401no—
891D4—401no—
892D4—401no—
893D4—401no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—84no—
921C2×C4—101no—
922C2×C4—101no—
923C2×C4—101no—
924C2×C4—101no—
925C2×C4—101no—
926C2×C4—202no—
927C2×C4—401no—
928C2×C4—401no—
929C2×C4—401no—
930C2×C4—401no—
931C2×C4—401no—
932C2×C4—401no—
933C2×C4C2×#68511yescharacteristic
934C2×C4C2×#68511yescharacteristic
935C2×C4C2×#68511yescharacteristic
936C2×C4C2×#68511yescharacteristic
937C2×C4C2×#68511yescharacteristic
938C2×C4C2×#68511yescharacteristic
939C2×C4C2×#68511yescharacteristic
940C2×C4C2×#68511yescharacteristic
941C2×C4C22×C4×D511yescharacteristic
942C2×C4C22×D2011yescharacteristic
943C8—201no—
944C8—201no—
945C8—201no—
946C8—201no—
947C5#1759711yescharacteristic, complemented, Sylow
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—201no—
966C22—201no—
967C22—201no—
968C22—201no—
969C22—201no—
970C22—201no—
971C22—201no—
972C22—201no—
973C22—201no—
974C22—802no—
975C22—802no—
976C22#6529412yes—
977C22C22×#68511yescharacteristic
978C22#6616911yescharacteristic
979C22#6617111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—201no—
995C4—201no—
996C4—201no—
997C4—201no—
998C4—201no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—401no—
1006C2—401no—
1007C2—401no—
1008C2C2×#6529411yescharacteristic
1009C2#1061427711yescharacteristic
1010C2#1061429411yescharacteristic
subgroupG/H
centerC22C22×#685
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2318C2
socleC22×C5C22×C22⋊C4
prime radical#10617691C2
cosocleC22×C4×C5C24
hypercenter#2318D5
hypocenterC5#17597
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. C5×#2318C2semidirect
3. #10614034C2semidirect
4. #10600358C2semidirect
5. #10600357C2semidirect
6. #10600338C2semidirect
7. #10600337C2semidirect
8. #10600325C2semidirect
9. #10600324C2semidirect
10. #10600302C2semidirect
11. #10600301C2semidirect
12. #10600237C2semidirect
13. #10600236C2semidirect
14. #10600191C2semidirect
15. C2×#64671C2semidirect
22. #65899C4semidirect
23. #65899C4semidirect
24. #65897C4semidirect
28. #65887C4semidirect
29. #65884C4semidirect
30. #65884C4semidirect
31. D4×D20C4semidirect
33. #65877C4semidirect
43. C5×#383C22semidirect
44. C5×#382C22semidirect
45. C5×#381C22semidirect
46. C5×#380C22semidirect
47. C4×C5×C22⋊C4C22semidirect
48. C2×C5×#95C22semidirect
49. #65496C22semidirect
50. #65496C22semidirect
51. C2×C22⋊#168C22semidirect
52. C2×C22⋊#168C22semidirect
57. #65215C22semidirect
58. #65214C22semidirect
59. #64672C22semidirect
60. #64672C22semidirect
61. #64672C22semidirect
62. #64672C22semidirect
67. #64671C22semidirect
68. #64671C22semidirect
69. #64671C22semidirect
70. #64671C22semidirect
71. #64671C22semidirect
72. #64671C22semidirect
73. #64671C22semidirect
74. #64671C22semidirect
85. C2×#709C2×C4semidirect
87. C22×D20C2×C4semidirect
123. #4076C2×C4semidirect
124. #4076C2×C4semidirect
125. #4076C2×C4semidirect
140. #4072C2×C4semidirect
142. C2×C4⋊Dic5C2×C4semidirect
144. #4070C2×C4semidirect
176. #4021C2×C4semidirect
177. #4020C2×C4semidirect
179. C4×D20C2×C4semidirect
180. C4×D20C2×C4semidirect
181. C4×D20C2×C4semidirect
183. #4016C2×C4semidirect
184. #4015C2×C4semidirect
185. C4×Dic10C2×C4semidirect
209. #2318D5semidirect
393. #383C2×D5semidirect
394. #382C2×D5semidirect
395. #381C2×D5semidirect
396. #380C2×D5semidirect
397. C4×C22⋊C4C2×D5semidirect
398. C2×#95C2×D5semidirect
947. C5#17597semidirect

Maximal subgroups

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

subgroupindex
#106176912
C5×#23182
#106140342
#106003582
#106003572
#106003382
#106003372
#106003252
#106003242
#106003022
#106003012
#106002372
#106002362
#106001912
C2×#646712
#175975