Finite Group Databasebeta

← C59×#18228 #28430337

Subgroups — C59×#18228 #28430337

Order 15104.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3537C211yesmaximal, characteristic, complemented
2C59×#3006C211yesmaximal, characteristic, complemented
3C59×#3002C211yesmaximal, characteristic, complemented
4C59×#2615C211yesmaximal, characteristic, complemented
5C59×#1606C212yesmaximal, complemented
6C59×#1601C212yesmaximal, complemented
7C59×#1600C212yesmaximal, complemented
8C59×#1595C212yesmaximal, complemented
9C59×#1519C211yesmaximal, characteristic, complemented
10C59×#1513C211yesmaximal, characteristic, complemented
11C59×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C59C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C59—21no—
14C2×#135×C59—21no—
15C59×#560—22no—
16C59×#553—21no—
17C59×#553—21no—
18D42×C59—22no—
19D42×C59—21no—
20D42×C59—21no—
21C59×#540—21no—
22C59×#538—21no—
23C59×#538C2212yes—
24C59×#535—21no—
25C59×#534—21no—
26C59×#534C2212yes—
27C59×#525C2211yescharacteristic
28C2×#121×C59—21no—
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C59×#452—21no—
32C59×#451C2211yescharacteristic, complemented
33C59×#450C2211yescharacteristic, complemented
34C59×#449—21no—
35C59×#449—22no—
36C59×#448C2211yescharacteristic, complemented
37C59×#448C2212yescomplemented
38C59×#447C2211yescharacteristic, complemented
39C59×#447C2212yescomplemented
40C59×#417—21no—
41C59×#416—21no—
42C59×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C59C2211yescharacteristic, complemented
44C59×#393C2212yescomplemented
45C59×#392—22no—
46C59×#392C2212yescomplemented
47C59×#380—21no—
48C59×#380C2211yescharacteristic, complemented
49C59×#328C2212yescomplemented
50C59×#327C2212yescomplemented
51C59×#327C2212yescomplemented
52C59×#327C2212yescomplemented
53C59×#323C2212yescomplemented
54C59×#323C2212yescomplemented
55C2×#41×C59—21no—
56C2×#41×C59—21no—
57C2×#41×C59—21no—
58C2×#41×C59—21no—
59C2×#41×C59—44no—
60C2×#41×C59D411yescharacteristic, complemented
61C22×Q8×C59C2311yescharacteristic
62C22×D4×C59—22no—
63C22×D4×C59—21no—
64C22×D4×C59—21no—
65C22×D4×C59—22no—
66C22×D4×C59—21no—
67C22×D4×C59—22no—
68C22×D4×C59D411yescharacteristic
69C22×D4×C59D412yes—
70C22×D4×C59D411yescharacteristic, complemented
71C22×D4×C59C2311yescharacteristic
72C23×C4×C59—21no—
73C23×C4×C59C2311yescharacteristic
74AGL(1,ℤ/8)×C59—44no—
75#135×C59—44no—
76C2×Q16×C59—21no—
77C2×SD16×C59—21no—
78C2×SD16×C59—21no—
79C2×SD16×C59—22no—
80C2×D8×C59—21no—
81C2×D8×C59—22no—
82C2×M16×C59—21no—
83C22×C8×C59—21no—
84#127×C59—22no—
85#127×C59—21no—
86#126×C59—22no—
87#126×C59—22no—
88#125×C59—21no—
89#124×C59—22no—
90#123×C59—22no—
91#123×C59—21no—
92#123×C59—22no—
93#123×C59—22no—
94#123×C59—22no—
95C22⋊Q8×C59D411yescharacteristic, complemented
96C22⋊Q8×C59C2311yescharacteristic
97#121×C59—22no—
98#121×C59—21no—
99#121×C59—21no—
100#121×C59—22no—
101#121×C59—22no—
102#121×C59—22no—
103#121×C59—22no—
104#121×C59—21no—
105#121×C59—21no—
106#121×C59—21no—
107#121×C59—21no—
108#121×C59—21no—
109#121×C59—21no—
110#121×C59—22no—
111#121×C59—44no—
112#121×C59D412yescomplemented
113#121×C59D411yescharacteristic, complemented
114#121×C59C2312yes—
115#121×C59C2311yescharacteristic
116#120×C59—22no—
117#120×C59—22no—
118#120×C59—22no—
119#120×C59—21no—
120#120×C59—22no—
121#120×C59—22no—
122#120×C59—22no—
123C4×D4×C59—22no—
124C4×D4×C59—21no—
125C4×D4×C59—21no—
126C4×D4×C59—21no—
127C4×D4×C59—21no—
128C4×D4×C59—22no—
129#117×C59—21no—
130#117×C59D411yescharacteristic, complemented
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59D411yescharacteristic
133C2×C4⋊C4×C59D411yescharacteristic, complemented
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59C2312yes—
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—22no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59C2×D412yes—
156C24×C59C2×D411yescharacteristic
157#41×C59—24no—
158#41×C59—24no—
159#41×C59—42no—
160#41×C59—42no—
161#41×C59—42no—
162#41×C59—42no—
163#41×C59—42no—
164#41×C59—42no—
165#41×C59—42no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—42no—
169C2×Q8×C59C2×D411yescharacteristic
170C2×D4×C59—22no—
171C2×D4×C59—21no—
172C2×D4×C59—21no—
173C2×D4×C59—22no—
174C2×D4×C59—22no—
175C2×D4×C59—22no—
176C2×D4×C59—22no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—21no—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—42no—
188C2×D4×C59—42no—
189C2×D4×C59—42no—
190C2×D4×C59—42no—
191C2×D4×C59—42no—
192C2×D4×C59—41no—
193C2×D4×C59—41no—
194C2×D4×C59—44no—
195C2×D4×C59—82no—
196C2×D4×C59—82no—
197C2×D4×C59—82no—
198C2×D4×C59—82no—
199C2×D4×C59—81no—
200C2×D4×C59—81no—
201C2×D4×C59—82no—
202C2×D4×C59—82no—
203C2×D4×C59—84no—
204C2×D4×C59C2×D411yescharacteristic
205C2×D4×C59C2×D412yes—
206C22×C4×C59—24no—
207C22×C4×C59—21no—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—22no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59—41no—
216C22×C4×C59—41no—
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2411yescharacteristic
224Q16×C59—42no—
225SD16×C59—42no—
226SD16×C59—42no—
227SD16×C59—44no—
228D8×C59—42no—
229D8×C59—44no—
230M16×C59—42no—
231C2×C8×C59—21no—
232C2×C8×C59—21no—
233C2×C8×C59—22no—
234C2×C8×C59—42no—
235C4⋊C4×C59—22no—
236C4⋊C4×C59—22no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—42no—
243C4⋊C4×C59C2×D412yes—
244C4⋊C4×C59C2×D411yescharacteristic
245C4⋊C4×C59C2×D411yescharacteristic
246C22⋊C4×C59—22no—
247C22⋊C4×C59—22no—
248C22⋊C4×C59—22no—
249C22⋊C4×C59—22no—
250C22⋊C4×C59—22no—
251C22⋊C4×C59—21no—
252C22⋊C4×C59—21no—
253C22⋊C4×C59—21no—
254C22⋊C4×C59—22no—
255C22⋊C4×C59—21no—
256C22⋊C4×C59—22no—
257C22⋊C4×C59—22no—
258C22⋊C4×C59—22no—
259C22⋊C4×C59—21no—
260C22⋊C4×C59—44no—
261C22⋊C4×C59—81no—
262C22⋊C4×C59—82no—
263C42×C59—22no—
264C42×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—21no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—81no—
285C23×C59—81no—
286C23×C59—82no—
287C23×C59—82no—
288C23×C59—82no—
289C23×C59#12011yescharacteristic
290C23×C59#12011yescharacteristic
291C23×C59C22×D411yescharacteristic
292Q8×C59—22no—
293Q8×C59—22no—
294Q8×C59—41no—
295Q8×C59—41no—
296Q8×C59—41no—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—42no—
300D4×C59—41no—
301D4×C59—41no—
302D4×C59—41no—
303D4×C59—44no—
304D4×C59—42no—
305D4×C59—44no—
306D4×C59—44no—
307D4×C59—42no—
308D4×C59—41no—
309D4×C59—42no—
310D4×C59—41no—
311D4×C59—42no—
312D4×C59—42no—
313D4×C59—81no—
314D4×C59—82no—
315D4×C59—82no—
316D4×C59—81no—
317D4×C59—82no—
318D4×C59—82no—
319D4×C59—82no—
320D4×C59—82no—
321D4×C59—82no—
322D4×C59—88no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—21no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—44no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—44no—
339C2×C4×C59—42no—
340C2×C4×C59—42no—
341C2×C4×C59—42no—
342C2×C4×C59—42no—
343C2×C4×C59—42no—
344C2×C4×C59—81no—
345C2×C4×C59—82no—
346C2×C4×C59—82no—
347C2×C4×C59#12011yescharacteristic
348C2×C4×C59#12011yescharacteristic
349C2×C4×C59C22×D411yescharacteristic
350C2×C4×C59C22×D411yescharacteristic
351C8×C59—41no—
352C8×C59—41no—
353C8×C59—42no—
354#18228C5911yesmaximal, characteristic, direct product factor, Sylow
355C22×C59—21no—
356C22×C59—21no—
357C22×C59—21no—
358C22×C59—21no—
359C22×C59—21no—
360C22×C59—21no—
361C22×C59—21no—
362C22×C59—21no—
363C22×C59—42no—
364C22×C59—42no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—41no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59—41no—
371C22×C59—42no—
372C22×C59—41no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—81no—
376C22×C59—81no—
377C22×C59—82no—
378C22×C59—82no—
379C22×C59—81no—
380C22×C59—81no—
381C22×C59—81no—
382C22×C59—81no—
383C22×C59—162no—
384C22×C59—164no—
385C22×C59C2×#12011yescharacteristic
386C22×C59#57611yescharacteristic
387C22×C59#57711yescharacteristic
388C4×C59—21no—
389C4×C59—21no—
390C4×C59—21no—
391C4×C59—42no—
392C4×C59—41no—
393C4×C59—42no—
394C4×C59—41no—
395C4×C59—42no—
396C4×C59—41no—
397C4×C59—82no—
398C4×C59B(4,𝔽2)12yes—
399#3537C2×C5911yescharacteristic, complemented
400#3006C2×C5911yescharacteristic, complemented
401#3002C2×C5911yescharacteristic, complemented
402#2615C2×C5911yescharacteristic, complemented
403#1606C2×C5912yescomplemented
404#1601C2×C5912yescomplemented
405#1600C2×C5912yescomplemented
406#1595C2×C5912yescomplemented
407#1519C2×C5911yescharacteristic, complemented
408#1513C2×C5911yescharacteristic, complemented
409#1471C2×C5911yescharacteristic, complemented
410C2×C59—21no—
411C2×C59—21no—
412C2×C59—41no—
413C2×C59—41no—
414C2×C59—82no—
415C2×C59—82no—
416C2×C59—82no—
417C2×C59—81no—
418C2×C59#301211yescharacteristic
419C2×C59#301911yescharacteristic
420C2×C59C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C5911yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C5912yes—
433#535—21no—
434#534—21no—
435#534C22×C5912yes—
436#525C22×C5911yescharacteristic
437C2×#121—21no—
438C2×#121C22×C5911yescharacteristic
439C2×#121C22×C5911yescharacteristic
440#452—21no—
441#451C22×C5911yescharacteristic, complemented
442#450C22×C5911yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C5911yescharacteristic, complemented
446#448C22×C5912yescomplemented
447#447C22×C5911yescharacteristic, complemented
448#447C22×C5912yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C5911yescharacteristic, complemented
452C2×C22⋊C8C22×C5911yescharacteristic, complemented
453#393C22×C5912yescomplemented
454#392—22no—
455#392C22×C5912yescomplemented
456#380—21no—
457#380C22×C5911yescharacteristic, complemented
458#328C22×C5912yescomplemented
459#327C22×C5912yescomplemented
460#327C22×C5912yescomplemented
461#327C22×C5912yescomplemented
462#323C22×C5912yescomplemented
463#323C22×C5912yescomplemented
464C59#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C5911yescharacteristic, complemented
471C22×Q8C23×C5911yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C5911yescharacteristic
479C22×D4D4×C5912yes—
480C22×D4D4×C5911yescharacteristic, complemented
481C22×D4C23×C5911yescharacteristic
482C23×C4—21no—
483C23×C4C23×C5911yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C5911yescharacteristic, complemented
506C22⋊Q8C23×C5911yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C5912yescomplemented
523#121D4×C5911yescharacteristic, complemented
524#121C23×C5912yes—
525#121C23×C5911yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C5911yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C5911yescharacteristic
543C2×C4⋊C4D4×C5911yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C5912yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C5911yescharacteristic
558C22⋊C8C23×C5911yescharacteristic
559C22⋊C8C23×C5912yes—
560#95—22no—
561#95C23×C5912yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C5912yes—
566C24C2×D4×C5911yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C5911yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C5911yescharacteristic
615C2×D4C2×D4×C5912yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C5911yescharacteristic
628C22×C4C2×D4×C5911yescharacteristic
629C22×C4C2×D4×C5911yescharacteristic
630C22×C4C2×D4×C5912yes—
631C22×C4C2×D4×C5911yescharacteristic
632C22×C4C2×D4×C5911yescharacteristic
633C22×C4C24×C5911yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C5912yes—
654C4⋊C4C2×D4×C5911yescharacteristic
655C4⋊C4C2×D4×C5911yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C5911yescharacteristic
700C23#120×C5911yescharacteristic
701C23C22×D4×C5911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C5911yescharacteristic
758C2×C4#120×C5911yescharacteristic
759C2×C4C22×D4×C5911yescharacteristic
760C2×C4C22×D4×C5911yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C5911yescharacteristic
795C22C59×#57611yescharacteristic
796C22C59×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C59×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C59×#301211yescharacteristic
817C2C59×#301911yescharacteristic
818C2C2×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×#3537C2semidirect
2. C59×#3006C2semidirect
3. C59×#3002C2semidirect
4. C59×#2615C2semidirect
5. C59×#1606C2semidirect
6. C59×#1601C2semidirect
7. C59×#1600C2semidirect
8. C59×#1595C2semidirect
9. C59×#1519C2semidirect
10. C59×#1513C2semidirect
11. C59×#1471C2semidirect
12. C22×#41×C59C22semidirect
32. C59×#451C22semidirect
33. C59×#450C22semidirect
36. C59×#448C22semidirect
37. C59×#448C22semidirect
38. C59×#447C22semidirect
39. C59×#447C22semidirect
42. C59×#407C22semidirect
43. C2×C22⋊C8×C59C22semidirect
44. C59×#393C22semidirect
46. C59×#392C22semidirect
48. C59×#380C22semidirect
49. C59×#328C22semidirect
50. C59×#327C22semidirect
51. C59×#327C22semidirect
52. C59×#327C22semidirect
53. C59×#323C22semidirect
54. C59×#323C22semidirect
60. C2×#41×C59D4semidirect
70. C22×D4×C59D4semidirect
95. C22⋊Q8×C59D4semidirect
112. #121×C59D4semidirect
113. #121×C59D4semidirect
130. #117×C59D4semidirect
133. C2×C4⋊C4×C59D4semidirect
354. #18228C59direct (N × H)
399. #3537C2×C59semidirect
400. #3006C2×C59semidirect
401. #3002C2×C59semidirect
402. #2615C2×C59semidirect
403. #1606C2×C59semidirect
404. #1601C2×C59semidirect
405. #1600C2×C59semidirect
406. #1595C2×C59semidirect
407. #1519C2×C59semidirect
408. #1513C2×C59semidirect
409. #1471C2×C59semidirect
421. C22×#41C22×C59semidirect
441. #451C22×C59semidirect
442. #450C22×C59semidirect
445. #448C22×C59semidirect
446. #448C22×C59semidirect
447. #447C22×C59semidirect
448. #447C22×C59semidirect
451. #407C22×C59semidirect
452. C2×C22⋊C8C22×C59semidirect
453. #393C22×C59semidirect
455. #392C22×C59semidirect
457. #380C22×C59semidirect
458. #328C22×C59semidirect
459. #327C22×C59semidirect
460. #327C22×C59semidirect
461. #327C22×C59semidirect
462. #323C22×C59semidirect
463. #323C22×C59semidirect
464. C59#18228direct (N × H)
470. C2×#41D4×C59semidirect
480. C22×D4D4×C59semidirect
505. C22⋊Q8D4×C59semidirect
522. #121D4×C59semidirect
523. #121D4×C59semidirect
540. #117D4×C59semidirect
543. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35372
C59×#30062
C59×#30022
C59×#26152
C59×#16062
C59×#16012
C59×#16002
C59×#15952
C59×#15192
C59×#15132
C59×#14712
#1822859