Finite Group Databasebeta

← C59×#18450 #28430559

Subgroups — C59×#18450 #28430559

Order 15104.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3537C211yesmaximal, characteristic, complemented
2C59×#3194C211yesmaximal, characteristic, complemented
3C59×#3186C211yesmaximal, characteristic, complemented
4C59×#2815C211yesmaximal, characteristic, complemented
5C59×#1612C212yesmaximal, complemented
6C59×#1607C212yesmaximal, complemented
7C59×#1600C212yesmaximal, complemented
8C59×#1595C212yesmaximal, complemented
9C59×#1516C211yesmaximal, characteristic, complemented
10C59×#1510C211yesmaximal, characteristic, complemented
11C59×#1471C211yesmaximal, characteristic, complemented
12C59×#560—22no—
13C59×#553—21no—
14C59×#553—21no—
15D42×C59—22no—
16D42×C59—21no—
17D42×C59—21no—
18C59×#540—21no—
19C59×#538—21no—
20C59×#538C2212yes—
21C59×#535—21no—
22C59×#534—21no—
23C59×#534C2212yes—
24C59×#525C2211yescharacteristic
25C2×#121×C59C2211yescharacteristic
26C2×#121×C59C2211yescharacteristic
27C2×#121×C59C2211yescharacteristic, complemented
28C59×#483C2211yescharacteristic, complemented
29C59×#482—21no—
30C59×#480—21no—
31C59×#480C2211yescharacteristic, complemented
32C59×#480C2212yescomplemented
33C59×#469—21no—
34C59×#468—21no—
35C59×#466—22no—
36C59×#450C2211yescharacteristic, complemented
37C59×#449—21no—
38C59×#447—21no—
39C59×#447C2211yescharacteristic, complemented
40C59×#447C2212yescomplemented
41C59×#407C2211yescharacteristic, complemented
42C2×C22⋊C8×C59C2211yescharacteristic, complemented
43C59×#397—21no—
44C59×#397C2212yescomplemented
45C59×#392—21no—
46C59×#392—22no—
47C59×#392C2212yescomplemented
48C59×#381C2211yescharacteristic, complemented
49C59×#328C2212yescomplemented
50C59×#327C2212yescomplemented
51C59×#327C2212yescomplemented
52C59×#327C2212yescomplemented
53C59×#323C2212yescomplemented
54C59×#323C2212yescomplemented
55C2×#41×C59D411yescharacteristic, complemented
56C22×D4×C59—22no—
57C22×D4×C59—21no—
58C22×D4×C59—21no—
59C22×D4×C59—22no—
60C22×D4×C59—21no—
61C22×D4×C59—22no—
62C22×D4×C59D412yes—
63C22×D4×C59D411yescharacteristic
64C22×D4×C59D411yescharacteristic, complemented
65C22×D4×C59C2311yescharacteristic
66C23×C4×C59C2311yescharacteristic
67C2×SD16×C59—21no—
68C2×D8×C59—22no—
69C2×D8×C59—21no—
70C2×M16×C59—21no—
71C22×C8×C59—21no—
72#127×C59—22no—
73#127×C59—21no—
74#126×C59—22no—
75#126×C59—22no—
76#125×C59—21no—
77#124×C59—22no—
78#123×C59—22no—
79#123×C59—21no—
80#123×C59—22no—
81#123×C59—22no—
82#123×C59—22no—
83C22⋊Q8×C59D411yescharacteristic, complemented
84C22⋊Q8×C59C2311yescharacteristic
85#121×C59—22no—
86#121×C59—21no—
87#121×C59—21no—
88#121×C59—22no—
89#121×C59—22no—
90#121×C59—22no—
91#121×C59—22no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59—21no—
95#121×C59—21no—
96#121×C59—21no—
97#121×C59—21no—
98#121×C59—22no—
99#121×C59—21no—
100#121×C59—21no—
101#121×C59—21no—
102#121×C59—21no—
103#121×C59D412yescomplemented
104#121×C59D411yescharacteristic, complemented
105#121×C59C2312yes—
106#121×C59C2311yescharacteristic
107#120×C59—22no—
108#120×C59—22no—
109#120×C59—22no—
110#120×C59—21no—
111#120×C59—22no—
112#120×C59—22no—
113#120×C59—22no—
114C4×D4×C59—22no—
115C4×D4×C59—21no—
116C4×D4×C59—21no—
117C4×D4×C59—21no—
118C4×D4×C59—21no—
119C4×D4×C59—22no—
120#117×C59—21no—
121#117×C59D411yescharacteristic, complemented
122C2×C4⋊C4×C59D411yescharacteristic
123C2×C4⋊C4×C59D411yescharacteristic, complemented
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—22no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59C2312yes—
131#107×C59—22no—
132#107×C59—21no—
133#106×C59—21no—
134#103×C59—21no—
135#102×C59—22no—
136#102×C59—21no—
137#102×C59—22no—
138#102×C59—21no—
139#102×C59—21no—
140C22⋊C8×C59—21no—
141C22⋊C8×C59—21no—
142C22⋊C8×C59C2312yes—
143C22⋊C8×C59C2311yescharacteristic
144C22⋊C8×C59C2311yescharacteristic
145#95×C59—21no—
146#95×C59—22no—
147#95×C59C2312yes—
148C24×C59—22no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59C2×D412yes—
152C24×C59C2×D411yescharacteristic
153#41×C59—81no—
154C2×Q8×C59C2×D411yescharacteristic
155C2×D4×C59—22no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—21no—
165C2×D4×C59—22no—
166C2×D4×C59—22no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—21no—
172C2×D4×C59—41no—
173C2×D4×C59—41no—
174C2×D4×C59—81no—
175C2×D4×C59—81no—
176C2×D4×C59—82no—
177C2×D4×C59—81no—
178C2×D4×C59—82no—
179C2×D4×C59—82no—
180C2×D4×C59—82no—
181C2×D4×C59—82no—
182C2×D4×C59—82no—
183C2×D4×C59—82no—
184C2×D4×C59—82no—
185C2×D4×C59—82no—
186C2×D4×C59—84no—
187C2×D4×C59C2×D411yescharacteristic
188C2×D4×C59C2×D412yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—22no—
194C22×C4×C59—21no—
195C22×C4×C59—81no—
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2411yescharacteristic
203SD16×C59—81no—
204D8×C59—82no—
205D8×C59—81no—
206M16×C59—81no—
207C2×C8×C59—22no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—81no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59C2×D411yescharacteristic
221C4⋊C4×C59C2×D412yes—
222C4⋊C4×C59C2×D411yescharacteristic
223C22⋊C4×C59—22no—
224C22⋊C4×C59—22no—
225C22⋊C4×C59—22no—
226C22⋊C4×C59—22no—
227C22⋊C4×C59—22no—
228C22⋊C4×C59—21no—
229C22⋊C4×C59—21no—
230C22⋊C4×C59—21no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—21no—
233C22⋊C4×C59—22no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—21no—
237C22⋊C4×C59—41no—
238C22⋊C4×C59—41no—
239C22⋊C4×C59—82no—
240C22⋊C4×C59—82no—
241C22⋊C4×C59—81no—
242C42×C59—22no—
243C42×C59—21no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—42no—
253C23×C59—42no—
254C23×C59—42no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—42no—
258C23×C59—41no—
259C23×C59—42no—
260C23×C59—81no—
261C23×C59—81no—
262C23×C59—82no—
263C23×C59—82no—
264C23×C59—82no—
265C23×C59#12011yescharacteristic
266C23×C59#12011yescharacteristic
267C23×C59C22×D411yescharacteristic
268Q8×C59—41no—
269D4×C59—42no—
270D4×C59—41no—
271D4×C59—42no—
272D4×C59—42no—
273D4×C59—42no—
274D4×C59—41no—
275D4×C59—41no—
276D4×C59—44no—
277D4×C59—42no—
278D4×C59—42no—
279D4×C59—42no—
280D4×C59—42no—
281D4×C59—81no—
282D4×C59—82no—
283D4×C59—82no—
284D4×C59—81no—
285D4×C59—82no—
286D4×C59—82no—
287D4×C59—82no—
288D4×C59—82no—
289D4×C59—82no—
290D4×C59—82no—
291D4×C59—82no—
292D4×C59—88no—
293C2×C4×C59—21no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—41no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—81no—
312C2×C4×C59—82no—
313C2×C4×C59—82no—
314C2×C4×C59#12011yescharacteristic
315C2×C4×C59#12011yescharacteristic
316C2×C4×C59C22×D411yescharacteristic
317C2×C4×C59C22×D411yescharacteristic
318C8×C59—42no—
319C8×C59—41no—
320C8×C59—41no—
321#18450C5911yesmaximal, characteristic, direct product factor, Sylow
322C22×C59—21no—
323C22×C59—21no—
324C22×C59—21no—
325C22×C59—21no—
326C22×C59—21no—
327C22×C59—21no—
328C22×C59—21no—
329C22×C59—21no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—41no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—82no—
340C22×C59—82no—
341C22×C59—82no—
342C22×C59—82no—
343C22×C59—82no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59—162no—
348C22×C59—164no—
349C22×C59C2×#12011yescharacteristic
350C22×C59#57612yes—
351C4×C59—21no—
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—42no—
356C4×C59—41no—
357C4×C59—42no—
358C4×C59—41no—
359C4×C59—41no—
360C4×C59—82no—
361C4×C59—81no—
362#3537C2×C5911yescharacteristic, complemented
363#3194C2×C5911yescharacteristic, complemented
364#3186C2×C5911yescharacteristic, complemented
365#2815C2×C5911yescharacteristic, complemented
366#1612C2×C5912yescomplemented
367#1607C2×C5912yescomplemented
368#1600C2×C5912yescomplemented
369#1595C2×C5912yescomplemented
370#1516C2×C5911yescharacteristic, complemented
371#1510C2×C5911yescharacteristic, complemented
372#1471C2×C5911yescharacteristic, complemented
373C2×C59—22no—
374C2×C59—41no—
375C2×C59—41no—
376C2×C59—82no—
377C2×C59—82no—
378C2×C59—81no—
379C2×C59—161no—
380C2×C59#300811yescharacteristic
381C2×C59#301911yescharacteristic
382C2×C59#302611yescharacteristic
383#560—22no—
384#553—21no—
385#553—21no—
386D42—22no—
387D42—21no—
388D42—21no—
389#540—21no—
390#538—21no—
391#538C22×C5912yes—
392#535—21no—
393#534—21no—
394#534C22×C5912yes—
395#525C22×C5911yescharacteristic
396C2×#121C22×C5911yescharacteristic
397C2×#121C22×C5911yescharacteristic
398C2×#121C22×C5911yescharacteristic, complemented
399#483C22×C5911yescharacteristic, complemented
400#482—21no—
401#480—21no—
402#480C22×C5911yescharacteristic, complemented
403#480C22×C5912yescomplemented
404#469—21no—
405#468—21no—
406#466—22no—
407#450C22×C5911yescharacteristic, complemented
408#449—21no—
409#447—21no—
410#447C22×C5911yescharacteristic, complemented
411#447C22×C5912yescomplemented
412#407C22×C5911yescharacteristic, complemented
413C2×C22⋊C8C22×C5911yescharacteristic, complemented
414#397—21no—
415#397C22×C5912yescomplemented
416#392—21no—
417#392—22no—
418#392C22×C5912yescomplemented
419#381C22×C5911yescharacteristic, complemented
420#328C22×C5912yescomplemented
421#327C22×C5912yescomplemented
422#327C22×C5912yescomplemented
423#327C22×C5912yescomplemented
424#323C22×C5912yescomplemented
425#323C22×C5912yescomplemented
426C59#1845011yescharacteristic, direct product factor, Sylow
427C2×#41D4×C5911yescharacteristic, complemented
428C22×D4—22no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4D4×C5912yes—
435C22×D4D4×C5911yescharacteristic
436C22×D4D4×C5911yescharacteristic, complemented
437C22×D4C23×C5911yescharacteristic
438C23×C4C23×C5911yescharacteristic
439C2×SD16—21no—
440C2×D8—22no—
441C2×D8—21no—
442C2×M16—21no—
443C22×C8—21no—
444#127—22no—
445#127—21no—
446#126—22no—
447#126—22no—
448#125—21no—
449#124—22no—
450#123—22no—
451#123—21no—
452#123—22no—
453#123—22no—
454#123—22no—
455C22⋊Q8D4×C5911yescharacteristic, complemented
456C22⋊Q8C23×C5911yescharacteristic
457#121—22no—
458#121—21no—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121D4×C5912yescomplemented
476#121D4×C5911yescharacteristic, complemented
477#121C23×C5912yes—
478#121C23×C5911yescharacteristic
479#120—22no—
480#120—22no—
481#120—22no—
482#120—21no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—22no—
492#117—21no—
493#117D4×C5911yescharacteristic, complemented
494C2×C4⋊C4D4×C5911yescharacteristic
495C2×C4⋊C4D4×C5911yescharacteristic, complemented
496C2×C4⋊C4C23×C5911yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4C23×C5912yes—
503#107—22no—
504#107—21no—
505#106—21no—
506#103—21no—
507#102—22no—
508#102—21no—
509#102—22no—
510#102—21no—
511#102—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8C23×C5911yescharacteristic
515C22⋊C8C23×C5911yescharacteristic
516C22⋊C8C23×C5912yes—
517#95—21no—
518#95—22no—
519#95C23×C5912yes—
520C24—22no—
521C24—21no—
522C24—21no—
523C24C2×D4×C5912yes—
524C24C2×D4×C5911yescharacteristic
525#41—81no—
526C2×Q8C2×D4×C5911yescharacteristic
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—84no—
559C2×D4C2×D4×C5911yescharacteristic
560C2×D4C2×D4×C5912yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—81no—
568C22×C4C2×D4×C5912yes—
569C22×C4C2×D4×C5911yescharacteristic
570C22×C4C2×D4×C5911yescharacteristic
571C22×C4C2×D4×C5911yescharacteristic
572C22×C4C2×D4×C5911yescharacteristic
573C22×C4C2×D4×C5911yescharacteristic
574C22×C4C24×C5911yescharacteristic
575SD16—81no—
576D8—82no—
577D8—81no—
578M16—81no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C5911yescharacteristic
593C4⋊C4C2×D4×C5912yes—
594C4⋊C4C2×D4×C5911yescharacteristic
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—81no—
614C42—22no—
615C42—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23#120×C5911yescharacteristic
638C23#120×C5911yescharacteristic
639C23C22×D4×C5911yescharacteristic
640Q8—41no—
641D4—42no—
642D4—41no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—81no—
654D4—82no—
655D4—82no—
656D4—81no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664D4—88no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C5911yescharacteristic
687C2×C4#120×C5911yescharacteristic
688C2×C4C22×D4×C5911yescharacteristic
689C2×C4C22×D4×C5911yescharacteristic
690C8—42no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×#120×C5911yescharacteristic
721C22C59×#57612yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C59×#300811yescharacteristic
741C2C59×#301911yescharacteristic
742C2C59×#302611yescharacteristic
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×#3194C2semidirect
3. C59×#3186C2semidirect
4. C59×#2815C2semidirect
5. C59×#1612C2semidirect
6. C59×#1607C2semidirect
7. C59×#1600C2semidirect
8. C59×#1595C2semidirect
9. C59×#1516C2semidirect
10. C59×#1510C2semidirect
11. C59×#1471C2semidirect
27. C2×#121×C59C22semidirect
28. C59×#483C22semidirect
31. C59×#480C22semidirect
32. C59×#480C22semidirect
36. C59×#450C22semidirect
39. C59×#447C22semidirect
40. C59×#447C22semidirect
41. C59×#407C22semidirect
42. C2×C22⋊C8×C59C22semidirect
44. C59×#397C22semidirect
47. C59×#392C22semidirect
48. C59×#381C22semidirect
49. C59×#328C22semidirect
50. C59×#327C22semidirect
51. C59×#327C22semidirect
52. C59×#327C22semidirect
53. C59×#323C22semidirect
54. C59×#323C22semidirect
55. C2×#41×C59D4semidirect
64. C22×D4×C59D4semidirect
83. C22⋊Q8×C59D4semidirect
103. #121×C59D4semidirect
104. #121×C59D4semidirect
121. #117×C59D4semidirect
123. C2×C4⋊C4×C59D4semidirect
321. #18450C59direct (N × H)
362. #3537C2×C59semidirect
363. #3194C2×C59semidirect
364. #3186C2×C59semidirect
365. #2815C2×C59semidirect
366. #1612C2×C59semidirect
367. #1607C2×C59semidirect
368. #1600C2×C59semidirect
369. #1595C2×C59semidirect
370. #1516C2×C59semidirect
371. #1510C2×C59semidirect
372. #1471C2×C59semidirect
398. C2×#121C22×C59semidirect
399. #483C22×C59semidirect
402. #480C22×C59semidirect
403. #480C22×C59semidirect
407. #450C22×C59semidirect
410. #447C22×C59semidirect
411. #447C22×C59semidirect
412. #407C22×C59semidirect
413. C2×C22⋊C8C22×C59semidirect
415. #397C22×C59semidirect
418. #392C22×C59semidirect
419. #381C22×C59semidirect
420. #328C22×C59semidirect
421. #327C22×C59semidirect
422. #327C22×C59semidirect
423. #327C22×C59semidirect
424. #323C22×C59semidirect
425. #323C22×C59semidirect
426. C59#18450direct (N × H)
427. C2×#41D4×C59semidirect
436. C22×D4D4×C59semidirect
455. C22⋊Q8D4×C59semidirect
475. #121D4×C59semidirect
476. #121D4×C59semidirect
493. #117D4×C59semidirect
495. 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×#31942
C59×#31862
C59×#28152
C59×#16122
C59×#16072
C59×#16002
C59×#15952
C59×#15162
C59×#15102
C59×#14712
#1845059