Finite Group Databasebeta

← C59×#23412 #28435521

Subgroups — C59×#23412 #28435521

Order 15104.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#575C211yesmaximal, characteristic, complemented
2C2×C59×#575C211yesmaximal, characteristic, complemented
3C59×#3449C211yesmaximal, characteristic, complemented
4C2×C59×#421C211yesmaximal, characteristic, complemented
5C59×#2896C211yesmaximal, characteristic, complemented
6C2×C59×#410C211yesmaximal, characteristic, complemented
7C59×#2009C214yesmaximal, complemented
8C59×#2008C214yesmaximal, complemented
9C2×C59×#344C211yesmaximal, characteristic, complemented
10C22×#41×C59C2211yescharacteristic
11C22×#41×C59C2211yescharacteristic
12C22×#41×C59C2211yescharacteristic
13C59×#575—22no—
14C59×#575—22no—
15C59×#575—22no—
16C59×#575—22no—
17C59×#575—22no—
18C59×#575—22no—
19C59×#575—22no—
20C59×#575C2214yes—
21C2×#137×C59—21no—
22C2×#137×C59—21no—
23C2×#137×C59—21no—
24C2×#137×C59C2212yescomplemented
25C2×AGL(1,ℤ/8)×C59—21no—
26C2×AGL(1,ℤ/8)×C59—21no—
27C2×AGL(1,ℤ/8)×C59—21no—
28C2×AGL(1,ℤ/8)×C59C2212yescomplemented
29C2×#135×C59—22no—
30C2×#135×C59—22no—
31C22×M16×C59C2211yescharacteristic
32C22×M16×C59C2211yescharacteristic
33C59×#537—22no—
34C59×#536—21no—
35C59×#536C2212yescomplemented
36C59×#535—21no—
37C59×#535C2212yescomplemented
38C59×#534—22no—
39C59×#532—22no—
40C59×#525—22no—
41C59×#525—22no—
42C2×#117×C59C2211yescharacteristic
43C2×#117×C59C2211yescharacteristic
44C59×#421—22no—
45C59×#421C2214yescomplemented
46C2×#104×C59—22no—
47C59×#419C2212yescomplemented
48C59×#418C2212yescomplemented
49C59×#417—22no—
50C59×#416—22no—
51C59×#410—22no—
52C59×#410C2214yescomplemented
53C2×#99×C59—22no—
54C59×#344C2214yescomplemented
55C2×#41×C59—21no—
56C2×#41×C59—21no—
57C2×#41×C59—21no—
58C2×#41×C59—21no—
59C2×#41×C59—21no—
60C2×#41×C59—21no—
61C2×#41×C59—21no—
62C2×#41×C59—21no—
63C2×#41×C59—21no—
64C2×#41×C59—21no—
65C2×#41×C59—21no—
66C2×#41×C59—21no—
67C2×#41×C59—21no—
68C2×#41×C59—21no—
69C2×#41×C59—21no—
70C2×#41×C59—21no—
71C2×#41×C59—21no—
72C2×#41×C59—21no—
73C2×#41×C59—21no—
74C2×#41×C59—21no—
75C2×#41×C59—21no—
76C2×#41×C59—21no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—21no—
81C2×#41×C59—21no—
82C2×#41×C59—21no—
83C2×#41×C59—21no—
84C2×#41×C59—21no—
85C2×#41×C59D412yes—
86C2×#41×C59D412yes—
87C2×#41×C59D412yes—
88C2×#41×C59D412yescomplemented
89C2×#41×C59C2312yes—
90C2×#41×C59C2312yes—
91C22×Q8×C59D411yescharacteristic
92C22×Q8×C59D411yescharacteristic, complemented
93C22×Q8×C59C2311yescharacteristic
94C22×D4×C59—21no—
95C22×D4×C59—21no—
96C22×D4×C59—21no—
97C22×D4×C59D411yescharacteristic
98C22×D4×C59D411yescharacteristic, complemented
99C22×D4×C59C2311yescharacteristic
100C23×C4×C59—21no—
101C23×C4×C59—21no—
102C23×C4×C59—21no—
103C23×C4×C59C2311yescharacteristic
104#137×C59—24no—
105#137×C59—24no—
106#137×C59—24no—
107#137×C59—24no—
108#137×C59—24no—
109#137×C59—24no—
110#137×C59—24no—
111#137×C59—24no—
112AGL(1,ℤ/8)×C59—24no—
113AGL(1,ℤ/8)×C59—24no—
114AGL(1,ℤ/8)×C59—24no—
115AGL(1,ℤ/8)×C59—24no—
116AGL(1,ℤ/8)×C59—24no—
117AGL(1,ℤ/8)×C59—24no—
118AGL(1,ℤ/8)×C59—24no—
119AGL(1,ℤ/8)×C59—24no—
120#135×C59—28no—
121#135×C59—28no—
122#135×C59—28no—
123#135×C59—28no—
124C2×Q16×C59—22no—
125C2×Q16×C59—22no—
126C2×SD16×C59—22no—
127C2×SD16×C59—22no—
128C2×SD16×C59—22no—
129C2×SD16×C59—22no—
130C2×D8×C59—22no—
131C2×D8×C59—22no—
132C2×M16×C59—21no—
133C2×M16×C59—21no—
134C2×M16×C59—21no—
135C2×M16×C59—21no—
136C2×M16×C59—21no—
137C2×M16×C59—21no—
138C2×M16×C59—21no—
139C2×M16×C59D412yescomplemented
140C2×M16×C59D412yescomplemented
141C2×M16×C59D412yescomplemented
142C2×M16×C59C2312yes—
143C2×M16×C59C2312yes—
144C22×C8×C59—21no—
145C22×C8×C59D412yescomplemented
146C4⋊Q8×C59—22no—
147#127×C59—22no—
148#124×C59—22no—
149#124×C59—22no—
150#123×C59—24no—
151#123×C59—24no—
152C22⋊Q8×C59—24no—
153C22⋊Q8×C59—24no—
154#121×C59—24no—
155#121×C59—28no—
156#121×C59—24no—
157#120×C59—24no—
158#120×C59—24no—
159C4×D4×C59—28no—
160#117×C59—21no—
161#117×C59—21no—
162#117×C59—21no—
163#117×C59—21no—
164#117×C59—21no—
165#117×C59D412yes—
166#117×C59C2312yes—
167#117×C59C2312yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59D412yes—
172C2×C42×C59—21no—
173C2×C42×C59—21no—
174#104×C59—28no—
175#103×C59—24no—
176#102×C59—24no—
177#99×C59—28no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59C2×D411yescharacteristic
182#41×C59—22no—
183#41×C59—22no—
184#41×C59—22no—
185#41×C59—22no—
186#41×C59—22no—
187#41×C59—22no—
188#41×C59—22no—
189#41×C59—22no—
190#41×C59—22no—
191#41×C59—22no—
192#41×C59—22no—
193#41×C59—22no—
194#41×C59—22no—
195#41×C59—22no—
196#41×C59—22no—
197#41×C59—22no—
198#41×C59—22no—
199#41×C59—22no—
200#41×C59—22no—
201#41×C59—22no—
202#41×C59—22no—
203#41×C59—22no—
204#41×C59—22no—
205#41×C59—22no—
206#41×C59—41no—
207#41×C59—41no—
208#41×C59—41no—
209#41×C59—41no—
210#41×C59—41no—
211#41×C59—41no—
212#41×C59—41no—
213#41×C59—41no—
214#41×C59—41no—
215#41×C59—41no—
216#41×C59—41no—
217#41×C59—41no—
218#41×C59—41no—
219#41×C59—41no—
220#41×C59—41no—
221#41×C59—41no—
222#41×C59—41no—
223#41×C59—41no—
224#41×C59—41no—
225#41×C59—41no—
226#41×C59—41no—
227#41×C59—41no—
228#41×C59—41no—
229#41×C59—41no—
230C2×Q8×C59—21no—
231C2×Q8×C59—21no—
232C2×Q8×C59—21no—
233C2×Q8×C59—21no—
234C2×Q8×C59—21no—
235C2×Q8×C59—21no—
236C2×Q8×C59—21no—
237C2×Q8×C59—21no—
238C2×Q8×C59—21no—
239C2×Q8×C59—21no—
240C2×Q8×C59—21no—
241C2×Q8×C59—21no—
242C2×Q8×C59—21no—
243C2×Q8×C59—21no—
244C2×Q8×C59—21no—
245C2×Q8×C59C2×D412yes—
246C2×Q8×C59C2×D412yes—
247C2×Q8×C59C2×D412yes—
248C2×D4×C59—22no—
249C2×D4×C59—22no—
250C2×D4×C59—22no—
251C2×D4×C59—22no—
252C2×D4×C59—22no—
253C2×D4×C59—22no—
254C2×D4×C59—28no—
255C2×D4×C59—21no—
256C2×D4×C59—21no—
257C2×D4×C59—21no—
258C2×D4×C59—21no—
259C2×D4×C59—21no—
260C2×D4×C59—21no—
261C2×D4×C59—21no—
262C2×D4×C59—21no—
263C2×D4×C59—21no—
264C2×D4×C59—21no—
265C2×D4×C59—21no—
266C2×D4×C59—21no—
267C2×D4×C59—21no—
268C2×D4×C59—21no—
269C2×D4×C59—21no—
270C2×D4×C59—41no—
271C2×D4×C59—41no—
272C2×D4×C59—41no—
273C2×D4×C59—41no—
274C2×D4×C59—41no—
275C2×D4×C59—41no—
276C2×D4×C59—41no—
277C2×D4×C59—41no—
278C2×D4×C59—41no—
279C2×D4×C59—41no—
280C2×D4×C59—41no—
281C2×D4×C59—41no—
282C2×D4×C59C2×D412yes—
283C2×D4×C59C2×D412yes—
284C2×D4×C59C2×D412yes—
285C22×C4×C59—21no—
286C22×C4×C59—21no—
287C22×C4×C59—21no—
288C22×C4×C59—22no—
289C22×C4×C59—22no—
290C22×C4×C59—22no—
291C22×C4×C59—22no—
292C22×C4×C59—22no—
293C22×C4×C59—22no—
294C22×C4×C59—22no—
295C22×C4×C59—41no—
296C22×C4×C59—41no—
297C22×C4×C59—41no—
298C22×C4×C59—41no—
299C22×C4×C59—41no—
300C22×C4×C59—41no—
301C22×C4×C59—41no—
302C22×C4×C59—41no—
303C22×C4×C59—41no—
304C22×C4×C59—41no—
305C22×C4×C59—41no—
306C22×C4×C59—41no—
307C22×C4×C59—41no—
308C22×C4×C59C2×D411yescharacteristic
309C22×C4×C59C2×D411yescharacteristic
310C22×C4×C59C2×D411yescharacteristic
311C22×C4×C59C2×D411yescharacteristic
312C22×C4×C59C2×D411yescharacteristic
313C22×C4×C59C2×D411yescharacteristic
314C22×C4×C59C2×D411yescharacteristic
315C22×C4×C59C2×D411yescharacteristic
316C22×C4×C59C2×D411yescharacteristic
317C22×C4×C59C2×D411yescharacteristic
318C22×C4×C59C2×D411yescharacteristic
319C22×C4×C59#4111yescharacteristic
320C22×C4×C59#4111yescharacteristic
321C22×C4×C59C2411yescharacteristic
322Q16×C59—28no—
323Q16×C59—28no—
324SD16×C59—28no—
325SD16×C59—28no—
326SD16×C59—28no—
327SD16×C59—28no—
328D8×C59—28no—
329D8×C59—28no—
330M16×C59—22no—
331M16×C59—22no—
332M16×C59—22no—
333M16×C59—22no—
334M16×C59—22no—
335M16×C59—22no—
336M16×C59—22no—
337M16×C59C2×D414yes—
338C2×C8×C59—22no—
339C2×C8×C59—22no—
340C2×C8×C59—22no—
341C2×C8×C59—22no—
342C2×C8×C59—22no—
343C2×C8×C59C2×D414yes—
344C4⋊C4×C59—28no—
345C4⋊C4×C59—22no—
346C4⋊C4×C59—22no—
347C4⋊C4×C59—22no—
348C4⋊C4×C59—41no—
349C22⋊C4×C59—28no—
350C22⋊C4×C59—28no—
351C22⋊C4×C59—22no—
352C22⋊C4×C59—22no—
353C22⋊C4×C59—41no—
354C22⋊C4×C59C2×D414yes—
355C42×C59—22no—
356C42×C59—22no—
357C42×C59—22no—
358C42×C59—41no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—81no—
369C23×C59—82no—
370C23×C59—82no—
371C23×C59—82no—
372C23×C59#12011yescharacteristic
373C23×C59#12011yescharacteristic
374C23×C59#12111yescharacteristic
375C23×C59#12111yescharacteristic
376C23×C59#12711yescharacteristic
377C23×C59#12711yescharacteristic
378C23×C59C22×D411yescharacteristic
379Q8×C59—22no—
380Q8×C59—22no—
381Q8×C59—22no—
382Q8×C59—22no—
383Q8×C59—22no—
384Q8×C59—22no—
385Q8×C59—41no—
386Q8×C59—41no—
387Q8×C59—41no—
388Q8×C59—41no—
389Q8×C59—41no—
390Q8×C59—41no—
391D4×C59—22no—
392D4×C59—22no—
393D4×C59—22no—
394D4×C59—22no—
395D4×C59—22no—
396D4×C59—22no—
397D4×C59—42no—
398D4×C59—42no—
399D4×C59—42no—
400D4×C59—42no—
401D4×C59—42no—
402D4×C59—42no—
403D4×C59—42no—
404D4×C59—42no—
405D4×C59—42no—
406D4×C59—42no—
407D4×C59—42no—
408D4×C59—42no—
409D4×C59—41no—
410D4×C59—41no—
411D4×C59—41no—
412D4×C59—41no—
413D4×C59—41no—
414D4×C59—41no—
415D4×C59—88no—
416C2×C4×C59—24no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—42no—
427C2×C4×C59—42no—
428C2×C4×C59—42no—
429C2×C4×C59—42no—
430C2×C4×C59—42no—
431C2×C4×C59—42no—
432C2×C4×C59—42no—
433C2×C4×C59—42no—
434C2×C4×C59—42no—
435C2×C4×C59—42no—
436C2×C4×C59—42no—
437C2×C4×C59—42no—
438C2×C4×C59—42no—
439C2×C4×C59—82no—
440C2×C4×C59—82no—
441C2×C4×C59#12011yescharacteristic
442C2×C4×C59#12011yescharacteristic
443C2×C4×C59#12011yescharacteristic
444C2×C4×C59#12011yescharacteristic
445C2×C4×C59#12011yescharacteristic
446C2×C4×C59#12011yescharacteristic
447C2×C4×C59#12011yescharacteristic
448C2×C4×C59#12011yescharacteristic
449C2×C4×C59#12011yescharacteristic
450C2×C4×C59#12011yescharacteristic
451C2×C4×C59#12111yescharacteristic
452C2×C4×C59#12111yescharacteristic
453C2×C4×C59#12111yescharacteristic
454C2×C4×C59#12111yescharacteristic
455C2×C4×C59#12111yescharacteristic
456C2×C4×C59#12111yescharacteristic
457C2×C4×C59#12111yescharacteristic
458C2×C4×C59#12111yescharacteristic
459C2×C4×C59#12111yescharacteristic
460C2×C4×C59#12111yescharacteristic
461C2×C4×C59#12711yescharacteristic
462C2×C4×C59#12711yescharacteristic
463C2×C4×C59C22×D411yescharacteristic
464C2×C4×C59C22×D411yescharacteristic
465C2×C4×C59C22×D411yescharacteristic
466C2×C4×C59C22×D411yescharacteristic
467C2×C4×C59C22×D411yescharacteristic
468C2×C4×C59C2×#4111yescharacteristic
469C8×C59—24no—
470C8×C59—24no—
471#23412C5911yesmaximal, characteristic, direct product factor, Sylow
472C22×C59—41no—
473C22×C59—41no—
474C22×C59—41no—
475C22×C59—41no—
476C22×C59—41no—
477C22×C59—41no—
478C22×C59—41no—
479C22×C59—44no—
480C22×C59—44no—
481C22×C59—42no—
482C22×C59—42no—
483C22×C59—42no—
484C22×C59—82no—
485C22×C59—82no—
486C22×C59—82no—
487C22×C59—82no—
488C22×C59—82no—
489C22×C59—82no—
490C22×C59—82no—
491C22×C59#39211yescharacteristic
492C22×C59#39211yescharacteristic
493C22×C59#39211yescharacteristic
494C22×C59#39211yescharacteristic
495C22×C59C2×#12011yescharacteristic
496C22×C59C2×#12111yescharacteristic
497C22×C59C2×#12711yescharacteristic
498C4×C59—44no—
499C4×C59—42no—
500C4×C59—42no—
501C4×C59—42no—
502C4×C59—82no—
503C4×C59#39211yescharacteristic
504C4×C59#39211yescharacteristic
505C4×C59#39211yescharacteristic
506C4×C59#39211yescharacteristic
507C4×C59C2×#12011yescharacteristic
508C4×C59C2×#12011yescharacteristic
509C4×C59C2×#12111yescharacteristic
510C4×C59C2×#12111yescharacteristic
511C2×#575C2×C5911yescharacteristic, complemented
512C2×#575C2×C5911yescharacteristic, complemented
513#3449C2×C5911yescharacteristic, complemented
514C2×#421C2×C5911yescharacteristic, complemented
515#2896C2×C5911yescharacteristic, complemented
516C2×#410C2×C5911yescharacteristic, complemented
517#2009C2×C5914yescomplemented
518#2008C2×C5914yescomplemented
519C2×#344C2×C5911yescharacteristic, complemented
520C2×C59—21no—
521C2×C59—21no—
522C2×C59—21no—
523C2×C59—21no—
524C2×C59—21no—
525C2×C59—21no—
526C2×C59—21no—
527C2×C59—82no—
528C2×C59—82no—
529C2×C59—82no—
530C2×C59C2×#39211yescharacteristic
531C22×#41C22×C5911yescharacteristic
532C22×#41C22×C5911yescharacteristic
533C22×#41C22×C5911yescharacteristic
534#575—22no—
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575C22×C5914yes—
542C2×#137—21no—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137C22×C5912yescomplemented
546C2×AGL(1,ℤ/8)—21no—
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)C22×C5912yescomplemented
550C2×#135—22no—
551C2×#135—22no—
552C22×M16C22×C5911yescharacteristic
553C22×M16C22×C5911yescharacteristic
554#537—22no—
555#536—21no—
556#536C22×C5912yescomplemented
557#535—21no—
558#535C22×C5912yescomplemented
559#534—22no—
560#532—22no—
561#525—22no—
562#525—22no—
563C2×#117C22×C5911yescharacteristic
564C2×#117C22×C5911yescharacteristic
565#421—22no—
566#421C22×C5914yescomplemented
567C2×#104—22no—
568#419C22×C5912yescomplemented
569#418C22×C5912yescomplemented
570#417—22no—
571#416—22no—
572#410—22no—
573#410C22×C5914yescomplemented
574C2×#99—22no—
575#344C22×C5914yescomplemented
576C59#2341211yescharacteristic, direct product factor, Sylow
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C5912yes—
608C2×#41D4×C5912yes—
609C2×#41D4×C5912yes—
610C2×#41D4×C5912yescomplemented
611C2×#41C23×C5912yes—
612C2×#41C23×C5912yes—
613C22×Q8D4×C5911yescharacteristic
614C22×Q8D4×C5911yescharacteristic, complemented
615C22×Q8C23×C5911yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C5911yescharacteristic
620C22×D4D4×C5911yescharacteristic, complemented
621C22×D4C23×C5911yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C5911yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C5912yescomplemented
662C2×M16D4×C5912yescomplemented
663C2×M16D4×C5912yescomplemented
664C2×M16C23×C5912yes—
665C2×M16C23×C5912yes—
666C22×C8—21no—
667C22×C8D4×C5912yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C5912yes—
688#117C23×C5912yes—
689#117C23×C5912yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C5912yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C5911yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C5912yes—
768C2×Q8C2×D4×C5912yes—
769C2×Q8C2×D4×C5912yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C5912yes—
805C2×D4C2×D4×C5912yes—
806C2×D4C2×D4×C5912yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C5911yescharacteristic
831C22×C4C2×D4×C5911yescharacteristic
832C22×C4C2×D4×C5911yescharacteristic
833C22×C4C2×D4×C5911yescharacteristic
834C22×C4C2×D4×C5911yescharacteristic
835C22×C4C2×D4×C5911yescharacteristic
836C22×C4C2×D4×C5911yescharacteristic
837C22×C4C2×D4×C5911yescharacteristic
838C22×C4C2×D4×C5911yescharacteristic
839C22×C4C2×D4×C5911yescharacteristic
840C22×C4C2×D4×C5911yescharacteristic
841C22×C4#41×C5911yescharacteristic
842C22×C4#41×C5911yescharacteristic
843C22×C4C24×C5911yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C5914yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C5914yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C5914yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C5911yescharacteristic
895C23#120×C5911yescharacteristic
896C23#121×C5911yescharacteristic
897C23#121×C5911yescharacteristic
898C23#127×C5911yescharacteristic
899C23#127×C5911yescharacteristic
900C23C22×D4×C5911yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C5911yescharacteristic
964C2×C4#120×C5911yescharacteristic
965C2×C4#120×C5911yescharacteristic
966C2×C4#120×C5911yescharacteristic
967C2×C4#120×C5911yescharacteristic
968C2×C4#120×C5911yescharacteristic
969C2×C4#120×C5911yescharacteristic
970C2×C4#120×C5911yescharacteristic
971C2×C4#120×C5911yescharacteristic
972C2×C4#120×C5911yescharacteristic
973C2×C4#121×C5911yescharacteristic
974C2×C4#121×C5911yescharacteristic
975C2×C4#121×C5911yescharacteristic
976C2×C4#121×C5911yescharacteristic
977C2×C4#121×C5911yescharacteristic
978C2×C4#121×C5911yescharacteristic
979C2×C4#121×C5911yescharacteristic
980C2×C4#121×C5911yescharacteristic
981C2×C4#121×C5911yescharacteristic
982C2×C4#121×C5911yescharacteristic
983C2×C4#127×C5911yescharacteristic
984C2×C4#127×C5911yescharacteristic
985C2×C4C22×D4×C5911yescharacteristic
986C2×C4C22×D4×C5911yescharacteristic
987C2×C4C22×D4×C5911yescharacteristic
988C2×C4C22×D4×C5911yescharacteristic
989C2×C4C22×D4×C5911yescharacteristic
990C2×C4C2×#41×C5911yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22C59×#39211yescharacteristic
1013C22C59×#39211yescharacteristic
1014C22C59×#39211yescharacteristic
1015C22C59×#39211yescharacteristic
1016C22C2×#120×C5911yescharacteristic
1017C22C2×#121×C5911yescharacteristic
1018C22C2×#127×C5911yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4C59×#39211yescharacteristic
1025C4C59×#39211yescharacteristic
1026C4C59×#39211yescharacteristic
1027C4C59×#39211yescharacteristic
1028C4C2×#120×C5911yescharacteristic
1029C4C2×#120×C5911yescharacteristic
1030C4C2×#121×C5911yescharacteristic
1031C4C2×#121×C5911yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×C59×#39211yescharacteristic
subgroupG/H
centerC4×C59#392
commutator, Frattini, cosocleC22×C4C24×C59
socleC2×C59C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#575C2semidirect
2. C2×C59×#575C2semidirect
3. C59×#3449C2semidirect
4. C2×C59×#421C2semidirect
5. C59×#2896C2semidirect
6. C2×C59×#410C2semidirect
7. C59×#2009C2semidirect
8. C59×#2008C2semidirect
9. C2×C59×#344C2semidirect
24. C2×#137×C59C22semidirect
28. C2×AGL(1,ℤ/8)×C59C22semidirect
35. C59×#536C22semidirect
37. C59×#535C22semidirect
45. C59×#421C22semidirect
47. C59×#419C22semidirect
48. C59×#418C22semidirect
52. C59×#410C22semidirect
54. C59×#344C22semidirect
88. C2×#41×C59D4semidirect
92. C22×Q8×C59D4semidirect
98. C22×D4×C59D4semidirect
139. C2×M16×C59D4semidirect
140. C2×M16×C59D4semidirect
141. C2×M16×C59D4semidirect
145. C22×C8×C59D4semidirect
471. #23412C59direct (N × H)
511. C2×#575C2×C59semidirect
512. C2×#575C2×C59semidirect
513. #3449C2×C59semidirect
514. C2×#421C2×C59semidirect
515. #2896C2×C59semidirect
516. C2×#410C2×C59semidirect
517. #2009C2×C59semidirect
518. #2008C2×C59semidirect
519. C2×#344C2×C59semidirect
545. C2×#137C22×C59semidirect
549. C2×AGL(1,ℤ/8)C22×C59semidirect
556. #536C22×C59semidirect
558. #535C22×C59semidirect
566. #421C22×C59semidirect
568. #419C22×C59semidirect
569. #418C22×C59semidirect
573. #410C22×C59semidirect
575. #344C22×C59semidirect
576. C59#23412direct (N × H)
610. C2×#41D4×C59semidirect
614. C22×Q8D4×C59semidirect
620. C22×D4D4×C59semidirect
661. C2×M16D4×C59semidirect
662. C2×M16D4×C59semidirect
663. C2×M16D4×C59semidirect
667. C22×C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5752
C59×#34492
C2×C59×#4212
C59×#28962
C2×C59×#4102
C59×#20092
C59×#20082
C2×C59×#3442
#2341259