Finite Group Databasebeta

← C59×#24056 #28436165

Subgroups — C59×#24056 #28436165

Order 15104.

1820 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×#3484C211yesmaximal, characteristic
2C59×#2849C212yesmaximal, complemented
3C2×C59×#386C211yesmaximal, characteristic, complemented
4C59×#2044C214yesmaximal, complemented
5C59×#1898C212yesmaximal, complemented
6C59×#1867C212yesmaximal, complemented
7C59×#1790C212yesmaximal, complemented
8C59×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C59C2211yescharacteristic
10C23×D4×C59C2211yescharacteristic
11C24×C4×C59C2211yescharacteristic, complemented
12C59×#546—22no—
13C59×#546—22no—
14D42×C59—22no—
15D42×C59—22no—
16C59×#535—21no—
17C59×#534—21no—
18C59×#534C2212yes—
19C59×#525—21no—
20C2×#123×C59—22no—
21C2×#120×C59—21no—
22C2×#120×C59C2212yes—
23C59×#518C2211yescharacteristic
24C22×C22⋊C4×C59—21no—
25C22×C22⋊C4×C59C2211yescharacteristic, complemented
26C2×#99×C59C2212yes—
27C2×#99×C59C2212yescomplemented
28C2×#99×C59C2214yescomplemented
29C59×#386—21no—
30C59×#386—21no—
31C59×#386—22no—
32C59×#386C2212yes—
33C59×#386C2212yescomplemented
34C59×#386C2214yescomplemented
35C59×#385—22no—
36C59×#385C2214yescomplemented
37C59×#381—22no—
38C59×#379C2212yescomplemented
39C2×#95×C59—21no—
40C59×#342C2214yescomplemented
41C25×C59D411yescharacteristic
42C25×C59C2311yescharacteristic
43H(5,𝔽2)×C59—24no—
44H(5,𝔽2)×C59—42no—
45C2×#41×C59—21no—
46C2×#41×C59—22no—
47C22×D4×C59—21no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—22no—
51C22×D4×C59—21no—
52C22×D4×C59—21no—
53C22×D4×C59—24no—
54C22×D4×C59—42no—
55C22×D4×C59D411yescharacteristic
56C22×D4×C59D411yescharacteristic
57C22×D4×C59D412yes—
58C22×D4×C59D412yes—
59C22×D4×C59C2312yes—
60C22×D4×C59C2311yescharacteristic
61C22×D4×C59C2311yescharacteristic
62C23×C4×C59—21no—
63C23×C4×C59—22no—
64C23×C4×C59—21no—
65C23×C4×C59—22no—
66C23×C4×C59—21no—
67C23×C4×C59—44no—
68C23×C4×C59D411yescharacteristic
69C23×C4×C59C2312yes—
70#127×C59—22no—
71#124×C59—22no—
72#123×C59—22no—
73#123×C59—22no—
74#123×C59—22no—
75#123×C59—48no—
76C22⋊Q8×C59—21no—
77C22⋊Q8×C59—21no—
78#121×C59—21no—
79#121×C59—21no—
80#121×C59—22no—
81#121×C59—22no—
82#121×C59—22no—
83#121×C59—22no—
84#121×C59—22no—
85#121×C59—22no—
86#120×C59—22no—
87#120×C59—22no—
88#120×C59—22no—
89#120×C59—22no—
90#120×C59—22no—
91#120×C59—22no—
92#120×C59—22no—
93#120×C59—22no—
94#120×C59—22no—
95C4×D4×C59—22no—
96C4×D4×C59—22no—
97C4×D4×C59—22no—
98C4×D4×C59—22no—
99#117×C59—21no—
100C2×C4⋊C4×C59—24no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—22no—
105C2×C22⋊C4×C59—22no—
106C2×C22⋊C4×C59—21no—
107C2×C22⋊C4×C59—22no—
108C2×C22⋊C4×C59—22no—
109C2×C22⋊C4×C59—24no—
110C2×C22⋊C4×C59—42no—
111C2×C22⋊C4×C59—44no—
112C2×C22⋊C4×C59D412yes—
113C2×C22⋊C4×C59D412yes—
114C2×C22⋊C4×C59C2312yes—
115C2×C22⋊C4×C59C2314yes—
116C2×C22⋊C4×C59C2312yes—
117#99×C59—24no—
118#99×C59—42no—
119#99×C59—44no—
120#95×C59—22no—
121#95×C59—22no—
122#95×C59—24no—
123#95×C59—24no—
124C24×C59—22no—
125C24×C59—22no—
126C24×C59—21no—
127C24×C59—22no—
128C24×C59—21no—
129C24×C59—21no—
130C24×C59—42no—
131C24×C59—42no—
132C24×C59—41no—
133C24×C59—42no—
134C24×C59—42no—
135C24×C59C2×D411yescharacteristic
136C24×C59C2×D412yes—
137C24×C59C2×D412yes—
138C24×C59C2×D411yescharacteristic
139C24×C59C2×D412yes—
140C24×C59C2×D411yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2411yescharacteristic
143#41×C59—48no—
144#41×C59—42no—
145#41×C59—42no—
146C2×Q8×C59—21no—
147C2×D4×C59—22no—
148C2×D4×C59—22no—
149C2×D4×C59—22no—
150C2×D4×C59—21no—
151C2×D4×C59—22no—
152C2×D4×C59—22no—
153C2×D4×C59—22no—
154C2×D4×C59—22no—
155C2×D4×C59—22no—
156C2×D4×C59—22no—
157C2×D4×C59—22no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—24no—
161C2×D4×C59—22no—
162C2×D4×C59—24no—
163C2×D4×C59—22no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—22no—
167C2×D4×C59—22no—
168C2×D4×C59—41no—
169C2×D4×C59—41no—
170C2×D4×C59—48no—
171C2×D4×C59—48no—
172C2×D4×C59—48no—
173C2×D4×C59—42no—
174C2×D4×C59—42no—
175C2×D4×C59—44no—
176C2×D4×C59—44no—
177C2×D4×C59—82no—
178C2×D4×C59—82no—
179C2×D4×C59#4114yes—
180C22×C4×C59—21no—
181C22×C4×C59—24no—
182C22×C4×C59—22no—
183C22×C4×C59—28no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—22no—
187C22×C4×C59—24no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—22no—
191C22×C4×C59—24no—
192C22×C4×C59—22no—
193C22×C4×C59—44no—
194C22×C4×C59—41no—
195C22×C4×C59—44no—
196C22×C4×C59—48no—
197C22×C4×C59—42no—
198C22×C4×C59—44no—
199C22×C4×C59—42no—
200C22×C4×C59—41no—
201C22×C4×C59—41no—
202C22×C4×C59—42no—
203C22×C4×C59—42no—
204C22×C4×C59—42no—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2×D412yes—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—48no—
215C22⋊C4×C59—22no—
216C22⋊C4×C59—22no—
217C22⋊C4×C59—22no—
218C22⋊C4×C59—22no—
219C22⋊C4×C59—22no—
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—24no—
227C22⋊C4×C59—24no—
228C22⋊C4×C59—24no—
229C22⋊C4×C59—44no—
230C22⋊C4×C59—44no—
231C22⋊C4×C59—48no—
232C22⋊C4×C59—44no—
233C22⋊C4×C59—42no—
234C22⋊C4×C59—44no—
235C42×C59—22no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—24no—
244C23×C59—24no—
245C23×C59—24no—
246C23×C59—24no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—22no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—24no—
253C23×C59—42no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—42no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—42no—
260C23×C59—42no—
261C23×C59—48no—
262C23×C59—48no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—48no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59—81no—
274C23×C59—81no—
275C23×C59—84no—
276C23×C59—81no—
277C23×C59—81no—
278C23×C59#12012yes—
279C23×C59#12011yescharacteristic
280C23×C59#12011yescharacteristic
281C23×C59#12312yescomplemented
282C23×C59C22×D411yescharacteristic
283C23×C59C22×D412yes—
284C23×C59C2×#4112yes—
285C23×C59H(5,𝔽2)12yes—
286Q8×C59—42no—
287D4×C59—28no—
288D4×C59—44no—
289D4×C59—42no—
290D4×C59—44no—
291D4×C59—44no—
292D4×C59—42no—
293D4×C59—42no—
294D4×C59—44no—
295D4×C59—44no—
296D4×C59—44no—
297D4×C59—44no—
298D4×C59—82no—
299D4×C59—82no—
300D4×C59—82no—
301D4×C59—82no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—24no—
305C2×C4×C59—28no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—24no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—44no—
316C2×C4×C59—44no—
317C2×C4×C59—42no—
318C2×C4×C59—44no—
319C2×C4×C59—48no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59—44no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—44no—
326C2×C4×C59—42no—
327C2×C4×C59—44no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—44no—
331C2×C4×C59—81no—
332C2×C4×C59—81no—
333C2×C4×C59—84no—
334C2×C4×C59#12312yescomplemented
335#24056C5911yesmaximal, characteristic, direct product factor, Sylow
336C22×C59—24no—
337C22×C59—24no—
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—22no—
341C22×C59—21no—
342C22×C59—21no—
343C22×C59—22no—
344C22×C59—21no—
345C22×C59—21no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—48no—
353C22×C59—48no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—42no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—42no—
361C22×C59—41no—
362C22×C59—42no—
363C22×C59—41no—
364C22×C59—42no—
365C22×C59—41no—
366C22×C59—81no—
367C22×C59—84no—
368C22×C59—84no—
369C22×C59—84no—
370C22×C59—81no—
371C22×C59—162no—
372C22×C59B(4,𝔽2)12yes—
373C22×C59#45812yes—
374C22×C59C2×#12011yescharacteristic
375C22×C59C2×#12311yescharacteristic
376C22×C59#53411yescharacteristic
377C22×C59#54614yes—
378C4×C59—22no—
379C4×C59—41no—
380C4×C59—42no—
381C4×C59—44no—
382C4×C59—42no—
383C4×C59—42no—
384C4×C59—84no—
385C4×C59—82no—
386#3484C2×C5911yescharacteristic
387#2849C2×C5912yescomplemented
388C2×#386C2×C5911yescharacteristic, complemented
389#2044C2×C5914yescomplemented
390#1898C2×C5912yescomplemented
391#1867C2×C5912yescomplemented
392#1790C2×C5912yescomplemented
393#1781C2×C5911yescharacteristic, complemented
394C2×C59—21no—
395C2×C59—24no—
396C2×C59—21no—
397C2×C59—22no—
398C2×C59—22no—
399C2×C59—42no—
400C2×C59—42no—
401C2×C59—81no—
402C2×C59—82no—
403C2×C59#240511yescharacteristic
404C2×C59C2×B(4,𝔽2)11yescharacteristic
405C2×C59C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C5911yescharacteristic
407C23×D4C22×C5911yescharacteristic
408C24×C4C22×C5911yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C5912yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C5912yes—
420#518C22×C5911yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C5911yescharacteristic, complemented
423C2×#99C22×C5912yes—
424C2×#99C22×C5914yescomplemented
425C2×#99C22×C5912yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C5912yes—
430#386C22×C5914yescomplemented
431#386C22×C5912yescomplemented
432#385—22no—
433#385C22×C5914yescomplemented
434#381—22no—
435#379C22×C5912yescomplemented
436C2×#95—21no—
437#342C22×C5914yescomplemented
438C59#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C5911yescharacteristic
440C25C23×C5911yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C5911yescharacteristic
454C22×D4D4×C5911yescharacteristic
455C22×D4D4×C5912yes—
456C22×D4D4×C5912yes—
457C22×D4C23×C5912yes—
458C22×D4C23×C5911yescharacteristic
459C22×D4C23×C5911yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C5911yescharacteristic
467C23×C4C23×C5912yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C5912yes—
511C2×C22⋊C4D4×C5912yes—
512C2×C22⋊C4C23×C5912yes—
513C2×C22⋊C4C23×C5914yes—
514C2×C22⋊C4C23×C5912yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C5911yescharacteristic
534C24C2×D4×C5912yes—
535C24C2×D4×C5912yes—
536C24C2×D4×C5911yescharacteristic
537C24C2×D4×C5912yes—
538C24C2×D4×C5911yescharacteristic
539C24C2×D4×C5911yescharacteristic
540C24C24×C5911yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C5914yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C5912yes—
604C22×C4C2×D4×C5911yescharacteristic
605C22×C4C2×D4×C5911yescharacteristic
606C22×C4C2×D4×C5912yes—
607C22×C4C2×D4×C5912yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C5912yes—
677C23#120×C5911yescharacteristic
678C23#120×C5911yescharacteristic
679C23#123×C5912yescomplemented
680C23C22×D4×C5911yescharacteristic
681C23C22×D4×C5912yes—
682C23C2×#41×C5912yes—
683C23H(5,𝔽2)×C5912yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C5912yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C59×B(4,𝔽2)12yes—
770C22C59×#45812yes—
771C22C2×#120×C5911yescharacteristic
772C22C2×#123×C5911yescharacteristic
773C22C59×#53411yescharacteristic
774C22C59×#54614yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C59×#240511yescharacteristic
793C2C2×C59×B(4,𝔽2)11yescharacteristic
794C2C2×C59×#45811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
prime radicalC59×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C25×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2849C2semidirect
3. C2×C59×#386C2semidirect
4. C59×#2044C2semidirect
5. C59×#1898C2semidirect
6. C59×#1867C2semidirect
7. C59×#1790C2semidirect
8. C59×#1781C2semidirect
11. C24×C4×C59C22semidirect
25. C22×C22⋊C4×C59C22semidirect
27. C2×#99×C59C22semidirect
28. C2×#99×C59C22semidirect
33. C59×#386C22semidirect
34. C59×#386C22semidirect
36. C59×#385C22semidirect
38. C59×#379C22semidirect
40. C59×#342C22semidirect
281. C23×C59#123semidirect
334. C2×C4×C59#123semidirect
335. #24056C59direct (N × H)
387. #2849C2×C59semidirect
388. C2×#386C2×C59semidirect
389. #2044C2×C59semidirect
390. #1898C2×C59semidirect
391. #1867C2×C59semidirect
392. #1790C2×C59semidirect
393. #1781C2×C59semidirect
408. C24×C4C22×C59semidirect
422. C22×C22⋊C4C22×C59semidirect
424. C2×#99C22×C59semidirect
425. C2×#99C22×C59semidirect
430. #386C22×C59semidirect
431. #386C22×C59semidirect
433. #385C22×C59semidirect
435. #379C22×C59semidirect
437. #342C22×C59semidirect
438. C59#24056direct (N × H)
679. C23#123×C59semidirect
732. C2×C4#123×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34842
C59×#28492
C2×C59×#3862
C59×#20442
C59×#18982
C59×#18672
C59×#17902
C59×#17812
#2405659