Finite Group Databasebeta

← C59×#18231 #28430340

Subgroups — C59×#18231 #28430340

Order 15104.

1200 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3536C211yesmaximal, characteristic, complemented
2C59×#3006C211yesmaximal, characteristic, complemented
3C59×#3002C211yesmaximal, characteristic, complemented
4C59×#2616C211yesmaximal, characteristic, complemented
5C59×#1604C212yesmaximal, complemented
6C59×#1603C212yesmaximal, complemented
7C59×#1598C212yesmaximal, complemented
8C59×#1597C212yesmaximal, complemented
9C59×#1519C211yesmaximal, characteristic, complemented
10C59×#1513C211yesmaximal, characteristic, complemented
11C59×#1472C211yesmaximal, characteristic, complemented
12C22×#41×C59C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C59—21no—
14C2×#135×C59—21no—
15C59×#562—22no—
16C59×#554—21no—
17C59×#548—21no—
18C59×#547—21no—
19C59×#546—21no—
20C59×#546—22no—
21C59×#543—21no—
22C59×#542—21no—
23C59×#539C2212yes—
24C59×#538—21no—
25C59×#537—21no—
26C59×#537C2212yes—
27C59×#525C2211yescharacteristic
28C2×C22⋊Q8×C59—21no—
29C2×C22⋊Q8×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C59×#452—21no—
32C59×#451C2211yescharacteristic, complemented
33C59×#450C2211yescharacteristic, complemented
34C59×#449—21no—
35C59×#449—22no—
36C59×#448C2212yes—
37C59×#448C2211yescharacteristic, complemented
38C59×#447C2212yes—
39C59×#447C2211yescharacteristic, complemented
40C59×#417—21no—
41C59×#416—21no—
42C59×#407C2211yescharacteristic
43C2×C22⋊C8×C59C2211yescharacteristic
44C59×#395C2212yescomplemented
45C59×#394—22no—
46C59×#394C2212yescomplemented
47C59×#380—21no—
48C59×#380C2211yescharacteristic
49C59×#328C2212yescomplemented
50C59×#327C2212yes—
51C59×#327C2212yes—
52C59×#327C2212yescomplemented
53C59×#324C2212yescomplemented
54C59×#324C2212yescomplemented
55C2×#41×C59—21no—
56C2×#41×C59—22no—
57C2×#41×C59—21no—
58C2×#41×C59—21no—
59C2×#41×C59—21no—
60C2×#41×C59—21no—
61C2×#41×C59—44no—
62C2×#41×C59D411yescharacteristic
63C22×Q8×C59D411yescharacteristic
64C22×Q8×C59C2311yescharacteristic
65C22×D4×C59—21no—
66C22×D4×C59—21no—
67C22×D4×C59D411yescharacteristic
68C22×D4×C59C2311yescharacteristic
69C23×C4×C59—21no—
70C23×C4×C59C2311yescharacteristic
71AGL(1,ℤ/8)×C59—44no—
72#135×C59—44no—
73C2×Q16×C59—21no—
74C2×SD16×C59—21no—
75C2×SD16×C59—22no—
76C2×SD16×C59—21no—
77C2×D8×C59—22no—
78C2×D8×C59—21no—
79C2×M16×C59—21no—
80C22×C8×C59—21no—
81C4⋊Q8×C59—21no—
82#126×C59—22no—
83#125×C59—22no—
84#124×C59—22no—
85#124×C59—21no—
86#124×C59—22no—
87#123×C59—22no—
88#123×C59—22no—
89#123×C59—22no—
90#123×C59—21no—
91#123×C59—22no—
92C22⋊Q8×C59—21no—
93C22⋊Q8×C59—22no—
94C22⋊Q8×C59—22no—
95C22⋊Q8×C59—22no—
96C22⋊Q8×C59—22no—
97C22⋊Q8×C59—21no—
98C22⋊Q8×C59—21no—
99C22⋊Q8×C59—21no—
100C22⋊Q8×C59—21no—
101C22⋊Q8×C59—22no—
102C22⋊Q8×C59—22no—
103C22⋊Q8×C59—44no—
104C22⋊Q8×C59D411yescharacteristic
105C22⋊Q8×C59C2311yescharacteristic
106#121×C59—21no—
107#121×C59—22no—
108#121×C59—22no—
109#121×C59—22no—
110#121×C59—22no—
111#121×C59—21no—
112#121×C59—21no—
113#121×C59—22no—
114#121×C59D412yes—
115#121×C59D411yescharacteristic
116#121×C59C2312yes—
117#121×C59C2311yescharacteristic
118#120×C59—22no—
119#120×C59—21no—
120C4×Q8×C59—21no—
121C4×D4×C59—22no—
122C4×D4×C59—21no—
123C4×D4×C59—21no—
124C4×D4×C59—21no—
125C4×D4×C59—22no—
126#117×C59D411yescharacteristic
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59—22no—
130C2×C4⋊C4×C59D411yescharacteristic
131C2×C4⋊C4×C59D411yescharacteristic
132C2×C4⋊C4×C59C2312yes—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59D412yes—
139#103×C59—21no—
140#103×C59—21no—
141#103×C59—22no—
142#102×C59—21no—
143#102×C59—21no—
144#102×C59—22no—
145C22⋊C8×C59—21no—
146C22⋊C8×C59—21no—
147C22⋊C8×C59C2311yescharacteristic
148C22⋊C8×C59C2311yescharacteristic
149C22⋊C8×C59C2312yes—
150#95×C59—22no—
151#95×C59C2312yes—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59C2×D411yescharacteristic
155#41×C59—24no—
156#41×C59—24no—
157#41×C59—42no—
158#41×C59—42no—
159#41×C59—42no—
160#41×C59—42no—
161#41×C59—42no—
162#41×C59—42no—
163#41×C59—42no—
164#41×C59—82no—
165#41×C59—82no—
166#41×C59—82no—
167C2×Q8×C59—22no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—21no—
171C2×Q8×C59—21no—
172C2×Q8×C59—42no—
173C2×Q8×C59—42no—
174C2×Q8×C59C2×D411yescharacteristic
175C2×D4×C59—21no—
176C2×D4×C59—21no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—22no—
180C2×D4×C59—21no—
181C2×D4×C59—22no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—42no—
186C2×D4×C59—42no—
187C2×D4×C59—42no—
188C2×D4×C59—42no—
189C2×D4×C59—41no—
190C2×D4×C59—41no—
191C2×D4×C59—81no—
192C2×D4×C59—81no—
193C2×D4×C59C2×D411yescharacteristic
194C2×D4×C59C2×D412yes—
195C22×C4×C59—24no—
196C22×C4×C59—21no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—22no—
203C22×C4×C59—42no—
204C22×C4×C59—42no—
205C22×C4×C59—41no—
206C22×C4×C59—41no—
207C22×C4×C59C2×D412yes—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2411yescharacteristic
215Q16×C59—42no—
216SD16×C59—42no—
217SD16×C59—42no—
218SD16×C59—44no—
219D8×C59—42no—
220D8×C59—44no—
221M16×C59—42no—
222C2×C8×C59—21no—
223C2×C8×C59—21no—
224C2×C8×C59—22no—
225C2×C8×C59—42no—
226C4⋊C4×C59—22no—
227C4⋊C4×C59—22no—
228C4⋊C4×C59—22no—
229C4⋊C4×C59—22no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—22no—
235C4⋊C4×C59—22no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—42no—
238C4⋊C4×C59—44no—
239C4⋊C4×C59C2×D412yes—
240C4⋊C4×C59C2×D411yescharacteristic
241C4⋊C4×C59C2×D411yescharacteristic
242C22⋊C4×C59—22no—
243C22⋊C4×C59—22no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—22no—
246C22⋊C4×C59—22no—
247C22⋊C4×C59—21no—
248C22⋊C4×C59—22no—
249C22⋊C4×C59—22no—
250C22⋊C4×C59—21no—
251C22⋊C4×C59—21no—
252C22⋊C4×C59—22no—
253C22⋊C4×C59—21no—
254C22⋊C4×C59—22no—
255C22⋊C4×C59—21no—
256C22⋊C4×C59—44no—
257C22⋊C4×C59—82no—
258C22⋊C4×C59—81no—
259C42×C59—22no—
260C42×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—21no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—42no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—81no—
276C23×C59—81no—
277C23×C59#12011yescharacteristic
278C23×C59#12011yescharacteristic
279C23×C59C22×D411yescharacteristic
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—41no—
283Q8×C59—41no—
284Q8×C59—41no—
285Q8×C59—42no—
286Q8×C59—81no—
287Q8×C59—82no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—42no—
291D4×C59—41no—
292D4×C59—41no—
293D4×C59—41no—
294D4×C59—42no—
295D4×C59—44no—
296D4×C59—44no—
297D4×C59—42no—
298D4×C59—41no—
299D4×C59—42no—
300D4×C59—41no—
301D4×C59—42no—
302D4×C59—82no—
303D4×C59—81no—
304D4×C59—82no—
305D4×C59—82no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—21no—
311C2×C4×C59—22no—
312C2×C4×C59—21no—
313C2×C4×C59—22no—
314C2×C4×C59—21no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—44no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—44no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—81no—
331C2×C4×C59—82no—
332C2×C4×C59—82no—
333C2×C4×C59—82no—
334C2×C4×C59#12011yescharacteristic
335C2×C4×C59#12011yescharacteristic
336C2×C4×C59C22×D411yescharacteristic
337C2×C4×C59C22×D411yescharacteristic
338C8×C59—41no—
339C8×C59—41no—
340C8×C59—42no—
341#18231C5911yesmaximal, characteristic, direct product factor, Sylow
342C22×C59—21no—
343C22×C59—21no—
344C22×C59—21no—
345C22×C59—21no—
346C22×C59—21no—
347C22×C59—21no—
348C22×C59—21no—
349C22×C59—21no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—41no—
353C22×C59—42no—
354C22×C59—41no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—41no—
358C22×C59—42no—
359C22×C59—81no—
360C22×C59—81no—
361C22×C59—81no—
362C22×C59—81no—
363C22×C59—81no—
364C22×C59—81no—
365C22×C59—162no—
366C22×C59C2×#12011yescharacteristic
367C22×C59#57611yescharacteristic
368C22×C59#57711yescharacteristic
369C4×C59—21no—
370C4×C59—21no—
371C4×C59—21no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59—41no—
375C4×C59—41no—
376C4×C59—42no—
377C4×C59—41no—
378C4×C59—42no—
379C4×C59—82no—
380C4×C59B(4,𝔽2)12yes—
381#3536C2×C5911yescharacteristic, complemented
382#3006C2×C5911yescharacteristic, complemented
383#3002C2×C5911yescharacteristic, complemented
384#2616C2×C5911yescharacteristic, complemented
385#1604C2×C5912yescomplemented
386#1603C2×C5912yescomplemented
387#1598C2×C5912yescomplemented
388#1597C2×C5912yescomplemented
389#1519C2×C5911yescharacteristic, complemented
390#1513C2×C5911yescharacteristic, complemented
391#1472C2×C5911yescharacteristic, complemented
392C2×C59—21no—
393C2×C59—21no—
394C2×C59—41no—
395C2×C59—41no—
396C2×C59—81no—
397C2×C59—82no—
398C2×C59—82no—
399C2×C59#301211yescharacteristic
400C2×C59#302011yescharacteristic
401C2×C59C2×B(4,𝔽2)11yescharacteristic
402C22×#41C22×C5911yescharacteristic
403C2×AGL(1,ℤ/8)—21no—
404C2×#135—21no—
405#562—22no—
406#554—21no—
407#548—21no—
408#547—21no—
409#546—21no—
410#546—22no—
411#543—21no—
412#542—21no—
413#539C22×C5912yes—
414#538—21no—
415#537—21no—
416#537C22×C5912yes—
417#525C22×C5911yescharacteristic
418C2×C22⋊Q8—21no—
419C2×C22⋊Q8C22×C5911yescharacteristic
420C2×#121C22×C5911yescharacteristic
421#452—21no—
422#451C22×C5911yescharacteristic, complemented
423#450C22×C5911yescharacteristic, complemented
424#449—21no—
425#449—22no—
426#448C22×C5912yes—
427#448C22×C5911yescharacteristic, complemented
428#447C22×C5912yes—
429#447C22×C5911yescharacteristic, complemented
430#417—21no—
431#416—21no—
432#407C22×C5911yescharacteristic
433C2×C22⋊C8C22×C5911yescharacteristic
434#395C22×C5912yescomplemented
435#394—22no—
436#394C22×C5912yescomplemented
437#380—21no—
438#380C22×C5911yescharacteristic
439#328C22×C5912yescomplemented
440#327C22×C5912yes—
441#327C22×C5912yes—
442#327C22×C5912yescomplemented
443#324C22×C5912yescomplemented
444#324C22×C5912yescomplemented
445C59#1823111yescharacteristic, direct product factor, Sylow
446C2×#41—21no—
447C2×#41—22no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—44no—
453C2×#41D4×C5911yescharacteristic
454C22×Q8D4×C5911yescharacteristic
455C22×Q8C23×C5911yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4D4×C5911yescharacteristic
459C22×D4C23×C5911yescharacteristic
460C23×C4—21no—
461C23×C4C23×C5911yescharacteristic
462AGL(1,ℤ/8)—44no—
463#135—44no—
464C2×Q16—21no—
465C2×SD16—21no—
466C2×SD16—21no—
467C2×SD16—22no—
468C2×D8—21no—
469C2×D8—22no—
470C2×M16—21no—
471C22×C8—21no—
472C4⋊Q8—21no—
473#126—22no—
474#125—22no—
475#124—22no—
476#124—21no—
477#124—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—21no—
482#123—22no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—44no—
495C22⋊Q8D4×C5911yescharacteristic
496C22⋊Q8C23×C5911yescharacteristic
497#121—21no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—21no—
503#121—21no—
504#121—22no—
505#121D4×C5912yes—
506#121D4×C5911yescharacteristic
507#121C23×C5912yes—
508#121C23×C5911yescharacteristic
509#120—22no—
510#120—21no—
511C4×Q8—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—22no—
517#117D4×C5911yescharacteristic
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4D4×C5911yescharacteristic
522C2×C4⋊C4D4×C5911yescharacteristic
523C2×C4⋊C4C23×C5912yes—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4D4×C5912yes—
530#103—21no—
531#103—21no—
532#103—22no—
533#102—21no—
534#102—21no—
535#102—22no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8C23×C5911yescharacteristic
539C22⋊C8C23×C5911yescharacteristic
540C22⋊C8C23×C5912yes—
541#95—22no—
542#95C23×C5912yes—
543C24—21no—
544C24—21no—
545C24C2×D4×C5911yescharacteristic
546#41—24no—
547#41—24no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—82no—
556#41—82no—
557#41—82no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8C2×D4×C5911yescharacteristic
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4C2×D4×C5911yescharacteristic
585C2×D4C2×D4×C5912yes—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4C2×D4×C5912yes—
599C22×C4C2×D4×C5911yescharacteristic
600C22×C4C2×D4×C5911yescharacteristic
601C22×C4C2×D4×C5911yescharacteristic
602C22×C4C2×D4×C5912yes—
603C22×C4C2×D4×C5911yescharacteristic
604C22×C4C2×D4×C5911yescharacteristic
605C22×C4C24×C5911yescharacteristic
606Q16—42no—
607SD16—42no—
608SD16—42no—
609SD16—44no—
610D8—42no—
611D8—44no—
612M16—42no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—42no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4C2×D4×C5912yes—
631C4⋊C4C2×D4×C5911yescharacteristic
632C4⋊C4C2×D4×C5911yescharacteristic
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—44no—
648C22⋊C4—82no—
649C22⋊C4—81no—
650C42—22no—
651C42—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—81no—
667C23—81no—
668C23#120×C5911yescharacteristic
669C23#120×C5911yescharacteristic
670C23C22×D4×C5911yescharacteristic
671Q8—22no—
672Q8—22no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—42no—
677Q8—81no—
678Q8—82no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—44no—
687D4—44no—
688D4—42no—
689D4—41no—
690D4—42no—
691D4—41no—
692D4—42no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C5911yescharacteristic
726C2×C4#120×C5911yescharacteristic
727C2×C4C22×D4×C5911yescharacteristic
728C2×C4C22×D4×C5911yescharacteristic
729C8—41no—
730C8—41no—
731C8—42no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—162no—
756C22C2×#120×C5911yescharacteristic
757C22C59×#57611yescharacteristic
758C22C59×#57711yescharacteristic
759C4—21no—
760C4—21no—
761C4—21no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—82no—
770C4C59×B(4,𝔽2)12yes—
771C2—21no—
772C2—21no—
773C2—41no—
774C2—41no—
775C2—82no—
776C2—82no—
777C2—81no—
778C2C59×#301211yescharacteristic
779C2C59×#302011yescharacteristic
780C2C2×C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3536C2semidirect
2. C59×#3006C2semidirect
3. C59×#3002C2semidirect
4. C59×#2616C2semidirect
5. C59×#1604C2semidirect
6. C59×#1603C2semidirect
7. C59×#1598C2semidirect
8. C59×#1597C2semidirect
9. C59×#1519C2semidirect
10. C59×#1513C2semidirect
11. C59×#1472C2semidirect
32. C59×#451C22semidirect
33. C59×#450C22semidirect
37. C59×#448C22semidirect
39. C59×#447C22semidirect
44. C59×#395C22semidirect
46. C59×#394C22semidirect
49. C59×#328C22semidirect
52. C59×#327C22semidirect
53. C59×#324C22semidirect
54. C59×#324C22semidirect
341. #18231C59direct (N × H)
381. #3536C2×C59semidirect
382. #3006C2×C59semidirect
383. #3002C2×C59semidirect
384. #2616C2×C59semidirect
385. #1604C2×C59semidirect
386. #1603C2×C59semidirect
387. #1598C2×C59semidirect
388. #1597C2×C59semidirect
389. #1519C2×C59semidirect
390. #1513C2×C59semidirect
391. #1472C2×C59semidirect
422. #451C22×C59semidirect
423. #450C22×C59semidirect
427. #448C22×C59semidirect
429. #447C22×C59semidirect
434. #395C22×C59semidirect
436. #394C22×C59semidirect
439. #328C22×C59semidirect
442. #327C22×C59semidirect
443. #324C22×C59semidirect
444. #324C22×C59semidirect
445. C59#18231direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35362
C59×#30062
C59×#30022
C59×#26162
C59×#16042
C59×#16032
C59×#15982
C59×#15972
C59×#15192
C59×#15132
C59×#14722
#1823159