Finite Group Databasebeta

← C59×#19013 #28431122

Subgroups — C59×#19013 #28431122

Order 15104.

810 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3531C211yesmaximal, characteristic
2C59×#3240C211yesmaximal, characteristic, complemented
3C59×#3237C211yesmaximal, characteristic, complemented
4C59×#3181C211yesmaximal, characteristic, complemented
5C59×#1664C211yesmaximal, characteristic, complemented
6C59×#1664C211yesmaximal, characteristic, complemented
7C59×#1664C211yesmaximal, characteristic, complemented
8C59×#1663C211yesmaximal, characteristic, complemented
9C59×#1663C211yesmaximal, characteristic, complemented
10C59×#1662C211yesmaximal, characteristic, complemented
11C59×#1661C211yesmaximal, characteristic, complemented
12C59×#1660C211yesmaximal, characteristic, complemented
13C59×#1535C211yesmaximal, characteristic, complemented
14C59×#1532C211yesmaximal, characteristic, complemented
15C59×#1531C211yesmaximal, characteristic, complemented
16C59×#564C2211yescharacteristic
17C59×#563—21no—
18C59×#563—21no—
19C59×#563—21no—
20C59×#563—21no—
21C59×#563C2211yescharacteristic
22C59×#563C2211yescharacteristic
23C59×#562—21no—
24C59×#562—21no—
25C59×#562C2211yescharacteristic
26C59×#533—21no—
27C59×#533—21no—
28C59×#533C2211yescharacteristic
29C59×#533C2211yescharacteristic
30C59×#529—21no—
31C59×#529—21no—
32C59×#529—21no—
33C59×#529—21no—
34C59×#529C2211yescharacteristic
35C59×#529C2211yescharacteristic
36C59×#501C2211yescharacteristic
37C59×#501C2211yescharacteristic
38C59×#501C2211yescharacteristic
39C59×#501C2211yescharacteristic
40C59×#501C2211yescharacteristic
41C59×#497C2211yescharacteristic
42C59×#491C2211yescharacteristic
43C59×#491C2211yescharacteristic
44C59×#491C2211yescharacteristic
45C59×#489C2211yescharacteristic
46C59×#489C2211yescharacteristic
47C59×#489C2211yescharacteristic
48C59×#485—21no—
49C59×#485—21no—
50C59×#485—21no—
51C59×#482—21no—
52C59×#479—21no—
53C59×#478—21no—
54C59×#477—21no—
55C59×#475—21no—
56C59×#467—21no—
57C59×#465—21no—
58C59×#441—21no—
59C59×#440—21no—
60C59×#432C2211yescharacteristic
61C59×#432C2211yescharacteristic
62C2×#97×C59C2211yescharacteristic
63C59×#330C2211yescharacteristic
64C59×#330C2211yescharacteristic
65C59×#330C2211yescharacteristic
66C59×#330C2211yescharacteristic
67C59×#330C2211yescharacteristic
68C59×#330C2211yescharacteristic
69C59×#330C2211yescharacteristic
70C59×#330C2211yescharacteristic
71C59×#329C2211yescharacteristic
72C59×#329C2211yescharacteristic
73C59×#329C2211yescharacteristic
74C59×#329C2211yescharacteristic
75C2×Q16×C59—21no—
76C2×SD16×C59—21no—
77C22×C8×C59—21no—
78C4⋊Q8×C59—21no—
79C4⋊Q8×C59—21no—
80C4⋊Q8×C59—21no—
81C4⋊Q8×C59—21no—
82C4⋊Q8×C59D411yescharacteristic
83C4⋊Q8×C59D411yescharacteristic
84C4⋊Q8×C59C2311yescharacteristic
85C4⋊Q8×C59C2311yescharacteristic
86#126×C59—21no—
87#126×C59—21no—
88#126×C59—21no—
89#126×C59—21no—
90#126×C59—21no—
91#126×C59—21no—
92#126×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#126×C59—21no—
96#125×C59—21no—
97#125×C59—21no—
98#125×C59—21no—
99#125×C59—21no—
100#125×C59—21no—
101#125×C59—21no—
102#125×C59—21no—
103#125×C59—21no—
104#125×C59—21no—
105#125×C59C2311yescharacteristic
106#125×C59C2311yescharacteristic
107#125×C59C2311yescharacteristic
108#125×C59C2311yescharacteristic
109#124×C59—21no—
110#124×C59—21no—
111#124×C59—21no—
112#124×C59—21no—
113#124×C59C2311yescharacteristic
114#124×C59C2311yescharacteristic
115#123×C59—21no—
116#123×C59—21no—
117#123×C59—21no—
118#123×C59—21no—
119#123×C59—21no—
120#123×C59—21no—
121#123×C59—21no—
122#123×C59—21no—
123#123×C59—21no—
124#123×C59—21no—
125C22⋊Q8×C59—21no—
126C22⋊Q8×C59—21no—
127C22⋊Q8×C59—21no—
128C22⋊Q8×C59—21no—
129C22⋊Q8×C59—21no—
130C22⋊Q8×C59—21no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59—21no—
136C22⋊Q8×C59—21no—
137C22⋊Q8×C59—21no—
138C22⋊Q8×C59—21no—
139C22⋊Q8×C59—21no—
140C22⋊Q8×C59—21no—
141C22⋊Q8×C59D411yescharacteristic
142C22⋊Q8×C59D411yescharacteristic
143#121×C59—21no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59D411yescharacteristic
148#121×C59D411yescharacteristic
149C4×Q8×C59—21no—
150C4×Q8×C59—21no—
151C4×Q8×C59—21no—
152C4×Q8×C59—21no—
153C4×Q8×C59—21no—
154C4×Q8×C59—21no—
155C4×Q8×C59D411yescharacteristic
156C4×Q8×C59D411yescharacteristic
157C4×D4×C59—21no—
158C4×D4×C59—21no—
159C4×D4×C59—21no—
160C4×D4×C59—21no—
161C4×D4×C59D411yescharacteristic
162C4×D4×C59D411yescharacteristic
163#117×C59—21no—
164#117×C59—21no—
165#117×C59—21no—
166#117×C59—21no—
167#117×C59—21no—
168#117×C59D411yescharacteristic
169#117×C59D411yescharacteristic
170C2×C42×C59—21no—
171C2×C42×C59—21no—
172C2×C42×C59C2311yescharacteristic
173#107×C59—21no—
174#107×C59—21no—
175#107×C59—21no—
176#107×C59—21no—
177#107×C59—21no—
178#106×C59—21no—
179#106×C59—21no—
180#106×C59—21no—
181#106×C59—21no—
182#106×C59—21no—
183C4⋊C8×C59—21no—
184C4⋊C8×C59—21no—
185#103×C59—21no—
186#103×C59—21no—
187#103×C59—21no—
188#103×C59—21no—
189#103×C59—21no—
190#103×C59—21no—
191#103×C59—21no—
192#103×C59—21no—
193#103×C59—21no—
194#102×C59—21no—
195#102×C59—21no—
196#102×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199#97×C59—21no—
200#97×C59C2311yescharacteristic
201#97×C59C2311yescharacteristic
202#97×C59C2311yescharacteristic
203#97×C59C2311yescharacteristic
204#97×C59C2311yescharacteristic
205#97×C59C2311yescharacteristic
206C2×Q8×C59—21no—
207C2×Q8×C59—21no—
208C2×Q8×C59—21no—
209C2×Q8×C59—21no—
210C2×Q8×C59—21no—
211C2×Q8×C59—21no—
212C2×Q8×C59C2×D411yescharacteristic
213C2×Q8×C59C2×D411yescharacteristic
214C2×D4×C59—21no—
215C2×D4×C59—21no—
216C2×D4×C59—21no—
217C2×D4×C59—21no—
218C2×D4×C59C2×D411yescharacteristic
219C2×D4×C59C2×D411yescharacteristic
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229Q16×C59—42no—
230SD16×C59—42no—
231C2×C8×C59—21no—
232C2×C8×C59—21no—
233C2×C8×C59—21no—
234C2×C8×C59—21no—
235C2×C8×C59—21no—
236C2×C8×C59—21no—
237C2×C8×C59—42no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—41no—
269C4⋊C4×C59—41no—
270C4⋊C4×C59C2×D411yescharacteristic
271C4⋊C4×C59C2×D411yescharacteristic
272C4⋊C4×C59C2×D411yescharacteristic
273C4⋊C4×C59C2×D411yescharacteristic
274C4⋊C4×C59C2×D411yescharacteristic
275C4⋊C4×C59C2×D411yescharacteristic
276C4⋊C4×C59C2×D411yescharacteristic
277C4⋊C4×C59C2×D411yescharacteristic
278C22⋊C4×C59—21no—
279C22⋊C4×C59—21no—
280C22⋊C4×C59—21no—
281C22⋊C4×C59—21no—
282C22⋊C4×C59—21no—
283C22⋊C4×C59—21no—
284C22⋊C4×C59—21no—
285C22⋊C4×C59—21no—
286C22⋊C4×C59—21no—
287C22⋊C4×C59—21no—
288C22⋊C4×C59—21no—
289C22⋊C4×C59—21no—
290C22⋊C4×C59—21no—
291C22⋊C4×C59—21no—
292C22⋊C4×C59—21no—
293C22⋊C4×C59—21no—
294C22⋊C4×C59—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—41no—
299C42×C59—21no—
300C42×C59—21no—
301C42×C59—21no—
302C42×C59—21no—
303C42×C59—21no—
304C42×C59—21no—
305C42×C59—21no—
306C42×C59—21no—
307C42×C59—41no—
308C42×C59C2×D411yescharacteristic
309C42×C59C2×D411yescharacteristic
310C42×C59C2×D411yescharacteristic
311C42×C59C2411yescharacteristic
312C23×C59—21no—
313C23×C59—21no—
314C23×C59#12011yescharacteristic
315Q8×C59—41no—
316Q8×C59—41no—
317Q8×C59—41no—
318Q8×C59—41no—
319Q8×C59—42no—
320Q8×C59—81no—
321Q8×C59—81no—
322Q8×C59—81no—
323Q8×C59—81no—
324D4×C59—41no—
325D4×C59—41no—
326D4×C59—81no—
327D4×C59—81no—
328D4×C59—81no—
329D4×C59—81no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—42no—
344C2×C4×C59—42no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—81no—
348C2×C4×C59—81no—
349C2×C4×C59—81no—
350C2×C4×C59—81no—
351C2×C4×C59#12011yescharacteristic
352C2×C4×C59#12011yescharacteristic
353C2×C4×C59#12011yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59C22×D411yescharacteristic
357C8×C59—22no—
358C8×C59—41no—
359C8×C59—41no—
360C8×C59—41no—
361C8×C59—41no—
362C8×C59—41no—
363#19013C5911yesmaximal, characteristic, direct product factor, Sylow
364C22×C59—21no—
365C22×C59—21no—
366C22×C59—21no—
367C22×C59—41no—
368C22×C59—41no—
369C22×C59—41no—
370C22×C59—41no—
371C22×C59—41no—
372C22×C59—41no—
373C22×C59C2×#12011yescharacteristic
374C4×C59—21no—
375C4×C59—21no—
376C4×C59—21no—
377C4×C59—21no—
378C4×C59—21no—
379C4×C59—21no—
380C4×C59—41no—
381C4×C59—41no—
382C4×C59—41no—
383C4×C59—41no—
384C4×C59—41no—
385C4×C59—41no—
386C4×C59—41no—
387C4×C59—41no—
388C4×C59—41no—
389C4×C59—41no—
390C4×C59—81no—
391C4×C59—81no—
392#3531C2×C5911yescharacteristic
393#3240C2×C5911yescharacteristic, complemented
394#3237C2×C5911yescharacteristic, complemented
395#3181C2×C5911yescharacteristic, complemented
396#1664C2×C5911yescharacteristic, complemented
397#1664C2×C5911yescharacteristic, complemented
398#1664C2×C5911yescharacteristic, complemented
399#1663C2×C5911yescharacteristic, complemented
400#1663C2×C5911yescharacteristic, complemented
401#1662C2×C5911yescharacteristic, complemented
402#1661C2×C5911yescharacteristic, complemented
403#1660C2×C5911yescharacteristic, complemented
404#1535C2×C5911yescharacteristic, complemented
405#1532C2×C5911yescharacteristic, complemented
406#1531C2×C5911yescharacteristic, complemented
407C2×C59—41no—
408C2×C59—81no—
409C2×C59—81no—
410C2×C59#301811yescharacteristic
411C2×C59#302011yescharacteristic
412C2×C59#302211yescharacteristic
413#564C22×C5911yescharacteristic
414#563—21no—
415#563—21no—
416#563—21no—
417#563—21no—
418#563C22×C5911yescharacteristic
419#563C22×C5911yescharacteristic
420#562—21no—
421#562—21no—
422#562C22×C5911yescharacteristic
423#533—21no—
424#533—21no—
425#533C22×C5911yescharacteristic
426#533C22×C5911yescharacteristic
427#529—21no—
428#529—21no—
429#529—21no—
430#529—21no—
431#529C22×C5911yescharacteristic
432#529C22×C5911yescharacteristic
433#501C22×C5911yescharacteristic
434#501C22×C5911yescharacteristic
435#501C22×C5911yescharacteristic
436#501C22×C5911yescharacteristic
437#501C22×C5911yescharacteristic
438#497C22×C5911yescharacteristic
439#491C22×C5911yescharacteristic
440#491C22×C5911yescharacteristic
441#491C22×C5911yescharacteristic
442#489C22×C5911yescharacteristic
443#489C22×C5911yescharacteristic
444#489C22×C5911yescharacteristic
445#485—21no—
446#485—21no—
447#485—21no—
448#482—21no—
449#479—21no—
450#478—21no—
451#477—21no—
452#475—21no—
453#467—21no—
454#465—21no—
455#441—21no—
456#440—21no—
457#432C22×C5911yescharacteristic
458#432C22×C5911yescharacteristic
459C2×#97C22×C5911yescharacteristic
460#330C22×C5911yescharacteristic
461#330C22×C5911yescharacteristic
462#330C22×C5911yescharacteristic
463#330C22×C5911yescharacteristic
464#330C22×C5911yescharacteristic
465#330C22×C5911yescharacteristic
466#330C22×C5911yescharacteristic
467#330C22×C5911yescharacteristic
468#329C22×C5911yescharacteristic
469#329C22×C5911yescharacteristic
470#329C22×C5911yescharacteristic
471#329C22×C5911yescharacteristic
472C59#1901311yescharacteristic, direct product factor, Sylow
473C2×Q16—21no—
474C2×SD16—21no—
475C22×C8—21no—
476C4⋊Q8—21no—
477C4⋊Q8—21no—
478C4⋊Q8—21no—
479C4⋊Q8—21no—
480C4⋊Q8D4×C5911yescharacteristic
481C4⋊Q8D4×C5911yescharacteristic
482C4⋊Q8C23×C5911yescharacteristic
483C4⋊Q8C23×C5911yescharacteristic
484#126—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#126—21no—
491#126—21no—
492#126—21no—
493#126—21no—
494#125—21no—
495#125—21no—
496#125—21no—
497#125—21no—
498#125—21no—
499#125—21no—
500#125—21no—
501#125—21no—
502#125—21no—
503#125C23×C5911yescharacteristic
504#125C23×C5911yescharacteristic
505#125C23×C5911yescharacteristic
506#125C23×C5911yescharacteristic
507#124—21no—
508#124—21no—
509#124—21no—
510#124—21no—
511#124C23×C5911yescharacteristic
512#124C23×C5911yescharacteristic
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8D4×C5911yescharacteristic
540C22⋊Q8D4×C5911yescharacteristic
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121D4×C5911yescharacteristic
546#121D4×C5911yescharacteristic
547C4×Q8—21no—
548C4×Q8—21no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8D4×C5911yescharacteristic
554C4×Q8D4×C5911yescharacteristic
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4D4×C5911yescharacteristic
560C4×D4D4×C5911yescharacteristic
561#117—21no—
562#117—21no—
563#117—21no—
564#117—21no—
565#117—21no—
566#117D4×C5911yescharacteristic
567#117D4×C5911yescharacteristic
568C2×C42—21no—
569C2×C42—21no—
570C2×C42C23×C5911yescharacteristic
571#107—21no—
572#107—21no—
573#107—21no—
574#107—21no—
575#107—21no—
576#106—21no—
577#106—21no—
578#106—21no—
579#106—21no—
580#106—21no—
581C4⋊C8—21no—
582C4⋊C8—21no—
583#103—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597#97—21no—
598#97C23×C5911yescharacteristic
599#97C23×C5911yescharacteristic
600#97C23×C5911yescharacteristic
601#97C23×C5911yescharacteristic
602#97C23×C5911yescharacteristic
603#97C23×C5911yescharacteristic
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C5911yescharacteristic
611C2×Q8C2×D4×C5911yescharacteristic
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4C2×D4×C5911yescharacteristic
617C2×D4C2×D4×C5911yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4C2×D4×C5911yescharacteristic
625C22×C4C2×D4×C5911yescharacteristic
626C22×C4C2×D4×C5911yescharacteristic
627Q16—42no—
628SD16—42no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—42no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4C2×D4×C5911yescharacteristic
669C4⋊C4C2×D4×C5911yescharacteristic
670C4⋊C4C2×D4×C5911yescharacteristic
671C4⋊C4C2×D4×C5911yescharacteristic
672C4⋊C4C2×D4×C5911yescharacteristic
673C4⋊C4C2×D4×C5911yescharacteristic
674C4⋊C4C2×D4×C5911yescharacteristic
675C4⋊C4C2×D4×C5911yescharacteristic
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—41no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42C2×D4×C5911yescharacteristic
707C42C2×D4×C5911yescharacteristic
708C42C2×D4×C5911yescharacteristic
709C42C24×C5911yescharacteristic
710C23—21no—
711C23—21no—
712C23#120×C5911yescharacteristic
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—42no—
718Q8—81no—
719Q8—81no—
720Q8—81no—
721Q8—81no—
722D4—41no—
723D4—41no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4#120×C5911yescharacteristic
750C2×C4#120×C5911yescharacteristic
751C2×C4#120×C5911yescharacteristic
752C2×C4C22×D4×C5911yescharacteristic
753C2×C4C22×D4×C5911yescharacteristic
754C2×C4C22×D4×C5911yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22C2×#120×C5911yescharacteristic
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C2—41no—
790C2—81no—
791C2—81no—
792C2C59×#301811yescharacteristic
793C2C59×#302011yescharacteristic
794C2C59×#302211yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC42C24×C59
prime radicalC59×#3531C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3240C2semidirect
3. C59×#3237C2semidirect
4. C59×#3181C2semidirect
5. C59×#1664C2semidirect
6. C59×#1664C2semidirect
7. C59×#1664C2semidirect
8. C59×#1663C2semidirect
9. C59×#1663C2semidirect
10. C59×#1662C2semidirect
11. C59×#1661C2semidirect
12. C59×#1660C2semidirect
13. C59×#1535C2semidirect
14. C59×#1532C2semidirect
15. C59×#1531C2semidirect
363. #19013C59direct (N × H)
393. #3240C2×C59semidirect
394. #3237C2×C59semidirect
395. #3181C2×C59semidirect
396. #1664C2×C59semidirect
397. #1664C2×C59semidirect
398. #1664C2×C59semidirect
399. #1663C2×C59semidirect
400. #1663C2×C59semidirect
401. #1662C2×C59semidirect
402. #1661C2×C59semidirect
403. #1660C2×C59semidirect
404. #1535C2×C59semidirect
405. #1532C2×C59semidirect
406. #1531C2×C59semidirect
472. C59#19013direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35312
C59×#32402
C59×#32372
C59×#31812
C59×#16642
C59×#16632
C59×#16622
C59×#16612
C59×#16602
C59×#15352
C59×#15322
C59×#15312
#1901359