Finite Group Databasebeta

← C59×#18385 #28430494

Subgroups — C59×#18385 #28430494

Order 15104.

1012 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic
2C59×#3189C211yesmaximal, characteristic, complemented
3C59×#3187C211yesmaximal, characteristic, complemented
4C59×#2564C211yesmaximal, characteristic, complemented
5C59×#1618C212yesmaximal, complemented
6C59×#1615C212yesmaximal, complemented
7C59×#1606C212yesmaximal, complemented
8C59×#1603C212yesmaximal, complemented
9C2×C59×#328C211yesmaximal, characteristic, complemented
10C2×C59×#327C211yesmaximal, characteristic, complemented
11C59×#1459C211yesmaximal, characteristic, complemented
12C59×#553—22no—
13C59×#553—21no—
14C59×#552—21no—
15C59×#551—22no—
16C59×#548—21no—
17C59×#546—21no—
18C59×#539C2212yes—
19C59×#538C2212yes—
20C59×#534—21no—
21C59×#529—21no—
22C59×#525—21no—
23C2×C22⋊Q8×C59C2211yescharacteristic
24C2×C22⋊Q8×C59C2211yescharacteristic
25C2×#121×C59C2211yescharacteristic
26C59×#518—21no—
27C2×C4×D4×C59C2211yescharacteristic
28C59×#484—21no—
29C59×#484C2212yescomplemented
30C59×#483—21no—
31C59×#481C2212yes—
32C59×#467—22no—
33C59×#465—22no—
34C59×#451—21no—
35C59×#451C2212yescomplemented
36C59×#450—21no—
37C59×#448C2212yes—
38C2×C22⋊C8×C59C2211yescharacteristic
39C2×C22⋊C8×C59C2211yescharacteristic
40C59×#400C2211yescharacteristic, complemented
41C59×#399C2211yescharacteristic, complemented
42C59×#395C2211yescharacteristic, complemented
43C59×#393C2211yescharacteristic, complemented
44C59×#387—21no—
45C59×#386—21no—
46C59×#385—21no—
47C59×#380—21no—
48C2×#95×C59C2211yescharacteristic
49C59×#328C2212yescomplemented
50C59×#328C2212yescomplemented
51C59×#327C2212yes—
52C59×#327C2212yes—
53C59×#324C2212yescomplemented
54C59×#323C2212yescomplemented
55C2×#41×C59—21no—
56C22×Q8×C59D411yescharacteristic
57C22×Q8×C59C2311yescharacteristic
58C22×D4×C59—21no—
59C22×D4×C59D411yescharacteristic
60C22×D4×C59D411yescharacteristic
61C23×C4×C59—21no—
62C23×C4×C59D411yescharacteristic
63C23×C4×C59C2311yescharacteristic
64C2×Q16×C59—22no—
65C2×SD16×C59—22no—
66C22×C8×C59—21no—
67C22×C8×C59—21no—
68#126×C59—22no—
69#126×C59—22no—
70#126×C59—22no—
71#125×C59—21no—
72#125×C59—22no—
73#124×C59—21no—
74#124×C59—22no—
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78#123×C59—22no—
79#123×C59—22no—
80C22⋊Q8×C59—21no—
81C22⋊Q8×C59—22no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59—21no—
84C22⋊Q8×C59—21no—
85C22⋊Q8×C59—21no—
86C22⋊Q8×C59—21no—
87C22⋊Q8×C59—21no—
88C22⋊Q8×C59D412yes—
89C22⋊Q8×C59C2312yes—
90#121×C59—21no—
91#121×C59—22no—
92#121×C59—22no—
93#121×C59—22no—
94#121×C59—21no—
95#121×C59—21no—
96#121×C59D412yes—
97#121×C59C2312yes—
98#120×C59—22no—
99#120×C59—22no—
100C4×Q8×C59—21no—
101C4×D4×C59—22no—
102C4×D4×C59—22no—
103C4×D4×C59—22no—
104C4×D4×C59—21no—
105C4×D4×C59—21no—
106C4×D4×C59—21no—
107C4×D4×C59—21no—
108C4×D4×C59—21no—
109C4×D4×C59—22no—
110C4×D4×C59—22no—
111#117×C59—22no—
112#117×C59—21no—
113#117×C59—22no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59D411yescharacteristic
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C22⋊C4×C59C2311yescharacteristic
130C2×C42×C59D411yescharacteristic
131#107×C59—22no—
132#106×C59—22no—
133#103×C59—22no—
134#103×C59—22no—
135#103×C59—22no—
136#102×C59—22no—
137C22⋊C8×C59—21no—
138C22⋊C8×C59—21no—
139C22⋊C8×C59C2312yes—
140C22⋊C8×C59C2312yes—
141#95×C59—21no—
142#95×C59—21no—
143#95×C59—21no—
144#95×C59—21no—
145#95×C59—21no—
146#95×C59C2311yescharacteristic
147#95×C59C2311yescharacteristic
148C24×C59—21no—
149C24×C59C2×D411yescharacteristic
150C24×C59C2×D411yescharacteristic
151#41×C59—82no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—81no—
156C2×Q8×C59—81no—
157C2×Q8×C59C2×D412yes—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—21no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59—81no—
170C2×D4×C59C2×D412yes—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59—81no—
185C22×C4×C59—81no—
186C22×C4×C59—81no—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2411yescharacteristic
196Q16×C59—82no—
197SD16×C59—82no—
198C2×C8×C59—22no—
199C2×C8×C59—22no—
200C2×C8×C59—81no—
201C2×C8×C59—81no—
202C4⋊C4×C59—22no—
203C4⋊C4×C59—22no—
204C4⋊C4×C59—22no—
205C4⋊C4×C59—22no—
206C4⋊C4×C59—22no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—21no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—21no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—42no—
215C4⋊C4×C59—41no—
216C4⋊C4×C59—41no—
217C4⋊C4×C59—81no—
218C4⋊C4×C59C2×D412yes—
219C4⋊C4×C59C2×D412yes—
220C22⋊C4×C59—22no—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—22no—
223C22⋊C4×C59—22no—
224C22⋊C4×C59—22no—
225C22⋊C4×C59—22no—
226C22⋊C4×C59—21no—
227C22⋊C4×C59—22no—
228C22⋊C4×C59—21no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—21no—
233C22⋊C4×C59—21no—
234C22⋊C4×C59—42no—
235C22⋊C4×C59—41no—
236C22⋊C4×C59—41no—
237C22⋊C4×C59—81no—
238C42×C59—22no—
239C42×C59—22no—
240C42×C59—21no—
241C42×C59—21no—
242C23×C59—21no—
243C23×C59—22no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—42no—
251C23×C59—81no—
252C23×C59—81no—
253C23×C59#12011yescharacteristic
254C23×C59#12011yescharacteristic
255C23×C59#13512yes—
256C23×C59#13712yes—
257C23×C59C22×D411yescharacteristic
258Q8×C59—42no—
259Q8×C59—42no—
260Q8×C59—42no—
261Q8×C59—42no—
262D4×C59—42no—
263D4×C59—42no—
264D4×C59—42no—
265D4×C59—42no—
266D4×C59—42no—
267D4×C59—42no—
268D4×C59—44no—
269D4×C59—82no—
270D4×C59—82no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—42no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—42no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—81no—
302C2×C4×C59—81no—
303C2×C4×C59—81no—
304C2×C4×C59—82no—
305C2×C4×C59—82no—
306C2×C4×C59—84no—
307C2×C4×C59#12011yescharacteristic
308C2×C4×C59#12011yescharacteristic
309C2×C4×C59C22×D411yescharacteristic
310C2×C4×C59C22×D411yescharacteristic
311C8×C59—42no—
312C8×C59—42no—
313#18385C5911yesmaximal, characteristic, direct product factor, Sylow
314C22×C59—21no—
315C22×C59—21no—
316C22×C59—21no—
317C22×C59—21no—
318C22×C59—21no—
319C22×C59—21no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—41no—
324C22×C59—42no—
325C22×C59—42no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—42no—
329C22×C59—81no—
330C22×C59—162no—
331C22×C59#45212yes—
332C22×C59#45212yes—
333C22×C59C2×#12011yescharacteristic
334C22×C59C2×#13511yescharacteristic
335C22×C59C2×#13711yescharacteristic
336C4×C59—21no—
337C4×C59—21no—
338C4×C59—21no—
339C4×C59—21no—
340C4×C59—42no—
341C4×C59—41no—
342C4×C59—42no—
343C4×C59—41no—
344C4×C59—42no—
345C4×C59—41no—
346C4×C59—42no—
347C4×C59—81no—
348C4×C59—81no—
349C4×C59—81no—
350#3505C2×C5911yescharacteristic
351#3189C2×C5911yescharacteristic, complemented
352#3187C2×C5911yescharacteristic, complemented
353#2564C2×C5911yescharacteristic, complemented
354#1618C2×C5912yescomplemented
355#1615C2×C5912yescomplemented
356#1606C2×C5912yescomplemented
357#1603C2×C5912yescomplemented
358C2×#328C2×C5911yescharacteristic, complemented
359C2×#327C2×C5911yescharacteristic, complemented
360#1459C2×C5911yescharacteristic, complemented
361C2×C59—21no—
362C2×C59—21no—
363C2×C59—22no—
364C2×C59—22no—
365C2×C59—81no—
366C2×C59—82no—
367C2×C59C2×#45211yescharacteristic
368C2×C59#301811yescharacteristic
369C2×C59#302611yescharacteristic
370#553—22no—
371#553—21no—
372#552—21no—
373#551—22no—
374#548—21no—
375#546—21no—
376#539C22×C5912yes—
377#538C22×C5912yes—
378#534—21no—
379#529—21no—
380#525—21no—
381C2×C22⋊Q8C22×C5911yescharacteristic
382C2×C22⋊Q8C22×C5911yescharacteristic
383C2×#121C22×C5911yescharacteristic
384#518—21no—
385C2×C4×D4C22×C5911yescharacteristic
386#484—21no—
387#484C22×C5912yescomplemented
388#483—21no—
389#481C22×C5912yes—
390#467—22no—
391#465—22no—
392#451—21no—
393#451C22×C5912yescomplemented
394#450—21no—
395#448C22×C5912yes—
396C2×C22⋊C8C22×C5911yescharacteristic
397C2×C22⋊C8C22×C5911yescharacteristic
398#400C22×C5911yescharacteristic, complemented
399#399C22×C5911yescharacteristic, complemented
400#395C22×C5911yescharacteristic, complemented
401#393C22×C5911yescharacteristic, complemented
402#387—21no—
403#386—21no—
404#385—21no—
405#380—21no—
406C2×#95C22×C5911yescharacteristic
407#328C22×C5912yescomplemented
408#328C22×C5912yescomplemented
409#327C22×C5912yes—
410#327C22×C5912yes—
411#324C22×C5912yescomplemented
412#323C22×C5912yescomplemented
413C59#1838511yescharacteristic, direct product factor, Sylow
414C2×#41—21no—
415C22×Q8D4×C5911yescharacteristic
416C22×Q8C23×C5911yescharacteristic
417C22×D4—21no—
418C22×D4D4×C5911yescharacteristic
419C22×D4D4×C5911yescharacteristic
420C23×C4—21no—
421C23×C4D4×C5911yescharacteristic
422C23×C4C23×C5911yescharacteristic
423C2×Q16—22no—
424C2×SD16—22no—
425C22×C8—21no—
426C22×C8—21no—
427#126—22no—
428#126—22no—
429#126—22no—
430#125—21no—
431#125—22no—
432#124—21no—
433#124—22no—
434#123—22no—
435#123—22no—
436#123—22no—
437#123—22no—
438#123—22no—
439C22⋊Q8—21no—
440C22⋊Q8—22no—
441C22⋊Q8—21no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8D4×C5912yes—
448C22⋊Q8C23×C5912yes—
449#121—21no—
450#121—22no—
451#121—22no—
452#121—22no—
453#121—21no—
454#121—21no—
455#121D4×C5912yes—
456#121C23×C5912yes—
457#120—22no—
458#120—22no—
459C4×Q8—21no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4—21no—
468C4×D4—22no—
469C4×D4—22no—
470#117—22no—
471#117—21no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4D4×C5911yescharacteristic
478C2×C4⋊C4D4×C5911yescharacteristic
479C2×C4⋊C4C23×C5911yescharacteristic
480C2×C4⋊C4C23×C5911yescharacteristic
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4D4×C5911yescharacteristic
488C2×C22⋊C4C23×C5911yescharacteristic
489C2×C42D4×C5911yescharacteristic
490#107—22no—
491#106—22no—
492#103—22no—
493#103—22no—
494#103—22no—
495#102—22no—
496C22⋊C8—21no—
497C22⋊C8—21no—
498C22⋊C8C23×C5912yes—
499C22⋊C8C23×C5912yes—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95C23×C5911yescharacteristic
506#95C23×C5911yescharacteristic
507C24—21no—
508C24C2×D4×C5911yescharacteristic
509C24C2×D4×C5911yescharacteristic
510#41—82no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—81no—
515C2×Q8—81no—
516C2×Q8C2×D4×C5912yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4C2×D4×C5912yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C5911yescharacteristic
547C22×C4C2×D4×C5911yescharacteristic
548C22×C4C2×D4×C5911yescharacteristic
549C22×C4C2×D4×C5911yescharacteristic
550C22×C4C2×D4×C5911yescharacteristic
551C22×C4C2×D4×C5911yescharacteristic
552C22×C4C2×D4×C5911yescharacteristic
553C22×C4C2×D4×C5911yescharacteristic
554C22×C4C24×C5911yescharacteristic
555Q16—82no—
556SD16—82no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—81no—
560C2×C8—81no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—81no—
577C4⋊C4C2×D4×C5912yes—
578C4⋊C4C2×D4×C5912yes—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—21no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—42no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—81no—
597C42—22no—
598C42—22no—
599C42—21no—
600C42—21no—
601C23—21no—
602C23—22no—
603C23—21no—
604C23—21no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—81no—
611C23—81no—
612C23#120×C5911yescharacteristic
613C23#120×C5911yescharacteristic
614C23#135×C5912yes—
615C23#137×C5912yes—
616C23C22×D4×C5911yescharacteristic
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8—42no—
621D4—42no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—44no—
626D4—42no—
627D4—42no—
628D4—82no—
629D4—82no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—84no—
666C2×C4#120×C5911yescharacteristic
667C2×C4#120×C5911yescharacteristic
668C2×C4C22×D4×C5911yescharacteristic
669C2×C4C22×D4×C5911yescharacteristic
670C8—42no—
671C8—42no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—81no—
688C22—162no—
689C22C59×#45212yes—
690C22C59×#45212yes—
691C22C2×#120×C5911yescharacteristic
692C22C2×#135×C5911yescharacteristic
693C22C2×#137×C5911yescharacteristic
694C4—21no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C2—21no—
709C2—21no—
710C2—22no—
711C2—22no—
712C2—81no—
713C2—82no—
714C2C2×C59×#45211yescharacteristic
715C2C59×#301811yescharacteristic
716C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3505C2
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
2. C59×#3189C2semidirect
3. C59×#3187C2semidirect
4. C59×#2564C2semidirect
5. C59×#1618C2semidirect
6. C59×#1615C2semidirect
7. C59×#1606C2semidirect
8. C59×#1603C2semidirect
9. C2×C59×#328C2semidirect
10. C2×C59×#327C2semidirect
11. C59×#1459C2semidirect
29. C59×#484C22semidirect
35. C59×#451C22semidirect
40. C59×#400C22semidirect
41. C59×#399C22semidirect
42. C59×#395C22semidirect
43. C59×#393C22semidirect
49. C59×#328C22semidirect
50. C59×#328C22semidirect
53. C59×#324C22semidirect
54. C59×#323C22semidirect
313. #18385C59direct (N × H)
351. #3189C2×C59semidirect
352. #3187C2×C59semidirect
353. #2564C2×C59semidirect
354. #1618C2×C59semidirect
355. #1615C2×C59semidirect
356. #1606C2×C59semidirect
357. #1603C2×C59semidirect
358. C2×#328C2×C59semidirect
359. C2×#327C2×C59semidirect
360. #1459C2×C59semidirect
387. #484C22×C59semidirect
393. #451C22×C59semidirect
398. #400C22×C59semidirect
399. #399C22×C59semidirect
400. #395C22×C59semidirect
401. #393C22×C59semidirect
407. #328C22×C59semidirect
408. #328C22×C59semidirect
411. #324C22×C59semidirect
412. #323C22×C59semidirect
413. C59#18385direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35052
C59×#31892
C59×#31872
C59×#25642
C59×#16182
C59×#16152
C59×#16062
C59×#16032
C2×C59×#3282
C2×C59×#3272
C59×#14592
#1838559