Finite Group Databasebeta

← C59×#24404 #28436513

Subgroups — C59×#24404 #28436513

Order 15104.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3484C211yesmaximal, characteristic, complemented
2C2×C59×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C59C211yesmaximal, characteristic, complemented
4C59×#2410C212yesmaximal, complemented
5C59×#2403C211yesmaximal, characteristic, complemented
6C59×#2044C212yesmaximal, complemented
7C59×#2021C212yesmaximal, complemented
8C59×#1898C212yesmaximal, complemented
9C59×#1889C211yesmaximal, characteristic, complemented
10C59×#1867C211yesmaximal, characteristic, complemented
11C59×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C23×D4×C59C2211yescharacteristic, complemented
15C59×#546—22no—
16C59×#546—22no—
17D42×C59—22no—
18D42×C59—22no—
19C59×#535—21no—
20C59×#534—21no—
21C59×#534C2212yes—
22C59×#525—21no—
23C2×#121×C59—22no—
24C2×#120×C59—21no—
25C2×#120×C59—21no—
26C2×#120×C59C2211yescharacteristic
27C2×#120×C59C2212yes—
28C2×#120×C59C2212yescomplemented
29C2×#120×C59C2211yescharacteristic, complemented
30C59×#518C2211yescharacteristic
31C22×C22⋊C4×C59C2212yescomplemented
32C59×B(4,𝔽2)—24no—
33C2×#99×C59—24no—
34C2×#99×C59C2211yescharacteristic
35C2×#99×C59C2211yescharacteristic
36C2×#99×C59C2212yescomplemented
37C2×#99×C59C2212yescomplemented
38C2×#99×C59C2212yescomplemented
39C59×#394—22no—
40C59×#392—21no—
41C59×#392—21no—
42C59×#392—22no—
43C59×#386—21no—
44C59×#386—22no—
45C59×#386C2211yescharacteristic
46C59×#386C2211yescharacteristic, complemented
47C59×#386C2212yescomplemented
48C59×#385C2212yescomplemented
49C59×#379C2212yescomplemented
50C59×#379C2211yescharacteristic, complemented
51C59×#342C2212yescomplemented
52C59×#342C2212yescomplemented
53C25×C59D411yescharacteristic, complemented
54C25×C59C2311yescharacteristic
55C25×C59C2311yescharacteristic
56H(5,𝔽2)×C59—22no—
57H(5,𝔽2)×C59—22no—
58H(5,𝔽2)×C59—42no—
59C2×#41×C59—21no—
60C2×#41×C59—22no—
61C22×D4×C59—21no—
62C22×D4×C59—22no—
63C22×D4×C59—21no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—22no—
67C22×D4×C59—21no—
68C22×D4×C59—21no—
69C22×D4×C59—22no—
70C22×D4×C59—22no—
71C22×D4×C59—21no—
72C22×D4×C59—22no—
73C22×D4×C59—21no—
74C22×D4×C59—21no—
75C22×D4×C59—22no—
76C22×D4×C59—44no—
77C22×D4×C59—42no—
78C22×D4×C59D411yescharacteristic, complemented
79C22×D4×C59D411yescharacteristic, complemented
80C22×D4×C59D412yescomplemented
81C22×D4×C59D412yescomplemented
82C22×D4×C59C2312yes—
83C22×D4×C59C2311yescharacteristic
84C22×D4×C59C2311yescharacteristic
85C23×C4×C59—22no—
86C23×C4×C59D411yescharacteristic, complemented
87C23×C4×C59C2311yescharacteristic
88#127×C59—22no—
89#124×C59—22no—
90#123×C59—22no—
91#123×C59—22no—
92#123×C59—22no—
93C22⋊Q8×C59—21no—
94C22⋊Q8×C59—21no—
95#121×C59—21no—
96#121×C59—21no—
97#121×C59—22no—
98#121×C59—22no—
99#121×C59—22no—
100#121×C59—22no—
101#121×C59—22no—
102#121×C59—22no—
103#121×C59—48no—
104#120×C59—22no—
105#120×C59—22no—
106#120×C59—22no—
107#120×C59—22no—
108#120×C59—22no—
109#120×C59—22no—
110#120×C59—22no—
111#120×C59—22no—
112#120×C59—22no—
113#120×C59—22no—
114#120×C59—22no—
115#120×C59—24no—
116#120×C59—42no—
117#120×C59—42no—
118#120×C59—44no—
119C4×D4×C59—22no—
120C4×D4×C59—22no—
121C4×D4×C59—22no—
122C4×D4×C59—22no—
123#117×C59—21no—
124C2×C4⋊C4×C59—22no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—24no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—22no—
140C2×C22⋊C4×C59—42no—
141C2×C22⋊C4×C59D412yescomplemented
142C2×C22⋊C4×C59D412yescomplemented
143C2×C22⋊C4×C59C2311yescharacteristic
144C2×C22⋊C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59C2312yes—
146C2×C22⋊C4×C59C2312yes—
147C2×C22⋊C4×C59C2312yes—
148#99×C59—22no—
149#99×C59—24no—
150#99×C59—24no—
151#99×C59—42no—
152#99×C59D414yescomplemented
153#95×C59—22no—
154#95×C59—21no—
155#95×C59—21no—
156#95×C59—22no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—22no—
160C24×C59—21no—
161C24×C59—22no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—22no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—22no—
169C24×C59—41no—
170C24×C59—42no—
171C24×C59—42no—
172C24×C59—42no—
173C24×C59—81no—
174C24×C59—81no—
175C24×C59—81no—
176C24×C59C2×D411yescharacteristic
177C24×C59C2×D412yes—
178C24×C59C2×D411yescharacteristic
179C24×C59C2×D412yes—
180C24×C59C2×D412yes—
181C24×C59C2×D411yescharacteristic
182C24×C59C2×D411yescharacteristic
183C24×C59C2411yescharacteristic
184#41×C59—44no—
185#41×C59—44no—
186#41×C59—42no—
187#41×C59—42no—
188C2×Q8×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—24no—
193C2×D4×C59—21no—
194C2×D4×C59—28no—
195C2×D4×C59—22no—
196C2×D4×C59—22no—
197C2×D4×C59—22no—
198C2×D4×C59—22no—
199C2×D4×C59—22no—
200C2×D4×C59—21no—
201C2×D4×C59—22no—
202C2×D4×C59—22no—
203C2×D4×C59—22no—
204C2×D4×C59—22no—
205C2×D4×C59—21no—
206C2×D4×C59—22no—
207C2×D4×C59—22no—
208C2×D4×C59—22no—
209C2×D4×C59—22no—
210C2×D4×C59—22no—
211C2×D4×C59—22no—
212C2×D4×C59—22no—
213C2×D4×C59—22no—
214C2×D4×C59—22no—
215C2×D4×C59—41no—
216C2×D4×C59—41no—
217C2×D4×C59—42no—
218C2×D4×C59—44no—
219C2×D4×C59—44no—
220C2×D4×C59—44no—
221C2×D4×C59—44no—
222C2×D4×C59—44no—
223C2×D4×C59—44no—
224C2×D4×C59—44no—
225C2×D4×C59—44no—
226C2×D4×C59—44no—
227C2×D4×C59—42no—
228C2×D4×C59—42no—
229C2×D4×C59—44no—
230C2×D4×C59—42no—
231C2×D4×C59—41no—
232C2×D4×C59—42no—
233C2×D4×C59—41no—
234C2×D4×C59—42no—
235C2×D4×C59—44no—
236C2×D4×C59—42no—
237C2×D4×C59—42no—
238C2×D4×C59—42no—
239C2×D4×C59—44no—
240C2×D4×C59—42no—
241C2×D4×C59—82no—
242C2×D4×C59—82no—
243C2×D4×C59—81no—
244C2×D4×C59—81no—
245C2×D4×C59—82no—
246C2×D4×C59—82no—
247C2×D4×C59C2×D412yes—
248C2×D4×C59#4112yes—
249C22×C4×C59—21no—
250C22×C4×C59—22no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—22no—
255C22×C4×C59—22no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—22no—
259C22×C4×C59—22no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—42no—
263C22×C4×C59—41no—
264C22×C4×C59—44no—
265C22×C4×C59—44no—
266C22×C4×C59—82no—
267C22×C4×C59C2×D412yes—
268C22×C4×C59C2×D411yescharacteristic
269C22×C4×C59C2×D411yescharacteristic
270C22×C4×C59C2×D412yes—
271C22×C4×C59C2×D412yes—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—22no—
275C4⋊C4×C59—22no—
276C4⋊C4×C59—44no—
277C22⋊C4×C59—22no—
278C22⋊C4×C59—22no—
279C22⋊C4×C59—22no—
280C22⋊C4×C59—22no—
281C22⋊C4×C59—22no—
282C22⋊C4×C59—22no—
283C22⋊C4×C59—22no—
284C22⋊C4×C59—22no—
285C22⋊C4×C59—22no—
286C22⋊C4×C59—22no—
287C22⋊C4×C59—22no—
288C22⋊C4×C59—22no—
289C22⋊C4×C59—22no—
290C22⋊C4×C59—21no—
291C22⋊C4×C59—21no—
292C22⋊C4×C59—22no—
293C22⋊C4×C59—22no—
294C22⋊C4×C59—44no—
295C22⋊C4×C59—44no—
296C22⋊C4×C59—42no—
297C22⋊C4×C59—42no—
298C22⋊C4×C59—42no—
299C22⋊C4×C59—44no—
300C22⋊C4×C59—42no—
301C22⋊C4×C59—44no—
302C22⋊C4×C59—42no—
303C22⋊C4×C59—82no—
304C22⋊C4×C59—81no—
305C22⋊C4×C59C2×D414yescomplemented
306C42×C59—22no—
307C23×C59—21no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—24no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—24no—
320C23×C59—22no—
321C23×C59—21no—
322C23×C59—22no—
323C23×C59—21no—
324C23×C59—21no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—41no—
328C23×C59—42no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—42no—
333C23×C59—41no—
334C23×C59—42no—
335C23×C59—42no—
336C23×C59—42no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—42no—
342C23×C59—42no—
343C23×C59—41no—
344C23×C59—42no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—42no—
348C23×C59—42no—
349C23×C59—42no—
350C23×C59—42no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—42no—
355C23×C59—42no—
356C23×C59—42no—
357C23×C59—81no—
358C23×C59—81no—
359C23×C59—82no—
360C23×C59—82no—
361C23×C59—82no—
362C23×C59—82no—
363C23×C59—84no—
364C23×C59—84no—
365C23×C59—81no—
366C23×C59—81no—
367C23×C59—84no—
368C23×C59—84no—
369C23×C59#12011yescharacteristic
370C23×C59#12012yes—
371C23×C59#12011yescharacteristic
372C23×C59#12112yescomplemented
373C23×C59C22×D411yescharacteristic
374C23×C59C22×D412yes—
375C23×C59C22×D411yescharacteristic
376C23×C59C2×#4111yescharacteristic
377C23×C59H(5,𝔽2)12yes—
378Q8×C59—42no—
379D4×C59—24no—
380D4×C59—24no—
381D4×C59—44no—
382D4×C59—42no—
383D4×C59—44no—
384D4×C59—48no—
385D4×C59—44no—
386D4×C59—44no—
387D4×C59—44no—
388D4×C59—42no—
389D4×C59—42no—
390D4×C59—42no—
391D4×C59—42no—
392D4×C59—42no—
393D4×C59—42no—
394D4×C59—44no—
395D4×C59—44no—
396D4×C59—82no—
397D4×C59—82no—
398D4×C59—82no—
399D4×C59—82no—
400D4×C59—88no—
401D4×C59—84no—
402D4×C59—84no—
403C2×C4×C59—21no—
404C2×C4×C59—21no—
405C2×C4×C59—22no—
406C2×C4×C59—24no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—21no—
411C2×C4×C59—21no—
412C2×C4×C59—21no—
413C2×C4×C59—24no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—42no—
417C2×C4×C59—42no—
418C2×C4×C59—44no—
419C2×C4×C59—42no—
420C2×C4×C59—42no—
421C2×C4×C59—41no—
422C2×C4×C59—42no—
423C2×C4×C59—42no—
424C2×C4×C59—41no—
425C2×C4×C59—42no—
426C2×C4×C59—42no—
427C2×C4×C59—42no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—42no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—42no—
436C2×C4×C59—81no—
437C2×C4×C59—81no—
438C2×C4×C59—88no—
439C2×C4×C59#12112yescomplemented
440#24404C5911yesmaximal, characteristic, direct product factor, Sylow
441C22×C59—21no—
442C22×C59—22no—
443C22×C59—21no—
444C22×C59—22no—
445C22×C59—21no—
446C22×C59—21no—
447C22×C59—21no—
448C22×C59—22no—
449C22×C59—22no—
450C22×C59—22no—
451C22×C59—21no—
452C22×C59—21no—
453C22×C59—22no—
454C22×C59—41no—
455C22×C59—41no—
456C22×C59—42no—
457C22×C59—44no—
458C22×C59—44no—
459C22×C59—42no—
460C22×C59—42no—
461C22×C59—42no—
462C22×C59—44no—
463C22×C59—42no—
464C22×C59—42no—
465C22×C59—42no—
466C22×C59—44no—
467C22×C59—41no—
468C22×C59—41no—
469C22×C59—42no—
470C22×C59—41no—
471C22×C59—42no—
472C22×C59—42no—
473C22×C59—41no—
474C22×C59—42no—
475C22×C59—41no—
476C22×C59—82no—
477C22×C59—81no—
478C22×C59—81no—
479C22×C59—81no—
480C22×C59—82no—
481C22×C59—84no—
482C22×C59—82no—
483C22×C59—82no—
484C22×C59—81no—
485C22×C59—82no—
486C22×C59—81no—
487C22×C59—81no—
488C22×C59—82no—
489C22×C59—84no—
490C22×C59—81no—
491C22×C59—81no—
492C22×C59—162no—
493C22×C59B(4,𝔽2)12yescomplemented
494C22×C59C2×#12011yescharacteristic
495C22×C59C2×#12111yescharacteristic
496C22×C59#53411yescharacteristic
497C22×C59D4212yes—
498C22×C59#54612yes—
499C4×C59—22no—
500C4×C59—44no—
501C4×C59—41no—
502C4×C59—42no—
503C4×C59—42no—
504C4×C59—42no—
505C4×C59—42no—
506C4×C59—82no—
507C4×C59—81no—
508C4×C59—81no—
509#3484C2×C5911yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C5911yescharacteristic, complemented
511C22×#99C2×C5911yescharacteristic, complemented
512#2410C2×C5912yescomplemented
513#2403C2×C5911yescharacteristic, complemented
514#2044C2×C5912yescomplemented
515#2021C2×C5912yescomplemented
516#1898C2×C5912yescomplemented
517#1889C2×C5911yescharacteristic, complemented
518#1867C2×C5911yescharacteristic, complemented
519#1790C2×C5911yescharacteristic, complemented
520C2×C59—22no—
521C2×C59—21no—
522C2×C59—21no—
523C2×C59—22no—
524C2×C59—22no—
525C2×C59—42no—
526C2×C59—41no—
527C2×C59—42no—
528C2×C59—82no—
529C2×C59—81no—
530C2×C59—82no—
531C2×C59#241011yescharacteristic
532C2×C59C2×B(4,𝔽2)11yescharacteristic
533C2×C59#302611yescharacteristic
534C2×H(5,𝔽2)C22×C5911yescharacteristic
535C23×D4C22×C5911yescharacteristic
536C23×D4C22×C5911yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C5912yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C5911yescharacteristic
549C2×#120C22×C5912yes—
550C2×#120C22×C5912yescomplemented
551C2×#120C22×C5911yescharacteristic, complemented
552#518C22×C5911yescharacteristic
553C22×C22⋊C4C22×C5912yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C5911yescharacteristic
557C2×#99C22×C5911yescharacteristic
558C2×#99C22×C5912yescomplemented
559C2×#99C22×C5912yescomplemented
560C2×#99C22×C5912yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C5911yescharacteristic
568#386C22×C5911yescharacteristic, complemented
569#386C22×C5912yescomplemented
570#385C22×C5912yescomplemented
571#379C22×C5912yescomplemented
572#379C22×C5911yescharacteristic, complemented
573#342C22×C5912yescomplemented
574#342C22×C5912yescomplemented
575C59#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C5911yescharacteristic, complemented
577C25C23×C5911yescharacteristic
578C25C23×C5911yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C5911yescharacteristic, complemented
602C22×D4D4×C5911yescharacteristic, complemented
603C22×D4D4×C5912yescomplemented
604C22×D4D4×C5912yescomplemented
605C22×D4C23×C5912yes—
606C22×D4C23×C5911yescharacteristic
607C22×D4C23×C5911yescharacteristic
608C23×C4—22no—
609C23×C4D4×C5911yescharacteristic, complemented
610C23×C4C23×C5911yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C5912yescomplemented
665C2×C22⋊C4D4×C5912yescomplemented
666C2×C22⋊C4C23×C5912yes—
667C2×C22⋊C4C23×C5911yescharacteristic
668C2×C22⋊C4C23×C5911yescharacteristic
669C2×C22⋊C4C23×C5912yes—
670C2×C22⋊C4C23×C5912yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C5914yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C5911yescharacteristic
700C24C2×D4×C5912yes—
701C24C2×D4×C5911yescharacteristic
702C24C2×D4×C5912yes—
703C24C2×D4×C5912yes—
704C24C2×D4×C5911yescharacteristic
705C24C2×D4×C5911yescharacteristic
706C24C24×C5911yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C5912yes—
771C2×D4#41×C5912yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C5912yes—
791C22×C4C2×D4×C5911yescharacteristic
792C22×C4C2×D4×C5911yescharacteristic
793C22×C4C2×D4×C5912yes—
794C22×C4C2×D4×C5912yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C5914yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C5911yescharacteristic
893C23#120×C5912yes—
894C23#120×C5911yescharacteristic
895C23#121×C5912yescomplemented
896C23C22×D4×C5911yescharacteristic
897C23C22×D4×C5912yes—
898C23C22×D4×C5911yescharacteristic
899C23C2×#41×C5911yescharacteristic
900C23H(5,𝔽2)×C5912yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C5912yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C59×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C5911yescharacteristic
1017C22C2×#121×C5911yescharacteristic
1018C22C59×#53411yescharacteristic
1019C22D42×C5912yes—
1020C22C59×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C59×#241011yescharacteristic
1043C2C2×C59×B(4,𝔽2)11yescharacteristic
1044C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C25×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3484C2semidirect
2. C2×C59×B(4,𝔽2)C2semidirect
3. C22×#99×C59C2semidirect
4. C59×#2410C2semidirect
5. C59×#2403C2semidirect
6. C59×#2044C2semidirect
7. C59×#2021C2semidirect
8. C59×#1898C2semidirect
9. C59×#1889C2semidirect
10. C59×#1867C2semidirect
11. C59×#1790C2semidirect
14. C23×D4×C59C22semidirect
28. C2×#120×C59C22semidirect
29. C2×#120×C59C22semidirect
31. C22×C22⋊C4×C59C22semidirect
36. C2×#99×C59C22semidirect
37. C2×#99×C59C22semidirect
38. C2×#99×C59C22semidirect
46. C59×#386C22semidirect
47. C59×#386C22semidirect
48. C59×#385C22semidirect
49. C59×#379C22semidirect
50. C59×#379C22semidirect
51. C59×#342C22semidirect
52. C59×#342C22semidirect
53. C25×C59D4semidirect
78. C22×D4×C59D4semidirect
79. C22×D4×C59D4semidirect
80. C22×D4×C59D4semidirect
81. C22×D4×C59D4semidirect
86. C23×C4×C59D4semidirect
141. C2×C22⋊C4×C59D4semidirect
142. C2×C22⋊C4×C59D4semidirect
152. #99×C59D4semidirect
305. C22⋊C4×C59C2×D4semidirect
372. C23×C59#121semidirect
439. C2×C4×C59#121semidirect
440. #24404C59direct (N × H)
493. C22×C59B(4,𝔽2)semidirect
509. #3484C2×C59semidirect
510. C2×B(4,𝔽2)C2×C59semidirect
511. C22×#99C2×C59semidirect
512. #2410C2×C59semidirect
513. #2403C2×C59semidirect
514. #2044C2×C59semidirect
515. #2021C2×C59semidirect
516. #1898C2×C59semidirect
517. #1889C2×C59semidirect
518. #1867C2×C59semidirect
519. #1790C2×C59semidirect
536. C23×D4C22×C59semidirect
550. C2×#120C22×C59semidirect
551. C2×#120C22×C59semidirect
553. C22×C22⋊C4C22×C59semidirect
558. C2×#99C22×C59semidirect
559. C2×#99C22×C59semidirect
560. C2×#99C22×C59semidirect
568. #386C22×C59semidirect
569. #386C22×C59semidirect
570. #385C22×C59semidirect
571. #379C22×C59semidirect
572. #379C22×C59semidirect
573. #342C22×C59semidirect
574. #342C22×C59semidirect
575. C59#24404direct (N × H)
576. C25D4×C59semidirect
601. C22×D4D4×C59semidirect
602. C22×D4D4×C59semidirect
603. C22×D4D4×C59semidirect
604. C22×D4D4×C59semidirect
609. C23×C4D4×C59semidirect
664. C2×C22⋊C4D4×C59semidirect
665. C2×C22⋊C4D4×C59semidirect
675. #99D4×C59semidirect
828. C22⋊C4C2×D4×C59semidirect
895. C23#121×C59semidirect
962. C2×C4#121×C59semidirect
1015. C22C59×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C59×#34842
C2×C59×B(4,𝔽2)2
C22×#99×C592
C59×#24102
C59×#24032
C59×#20442
C59×#20212
C59×#18982
C59×#18892
C59×#18672
C59×#17902
#2440459