Finite Group Databasebeta

← C59×#18224 #28430333

Subgroups — C59×#18224 #28430333

Order 15104.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic, complemented
2C59×#3003C211yesmaximal, characteristic, complemented
3C2×C59×#447C211yesmaximal, characteristic, complemented
4C59×#2613C211yesmaximal, characteristic, complemented
5C59×#1600C212yesmaximal, complemented
6C59×#1598C212yesmaximal, complemented
7C59×#1597C212yesmaximal, complemented
8C59×#1595C212yesmaximal, complemented
9C59×#1516C211yesmaximal, characteristic, complemented
10C59×#1510C211yesmaximal, characteristic, complemented
11C59×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C59C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C59—21no—
14C22×D8×C59—21no—
15C59×#562—21no—
16C59×#560—21no—
17C59×#553—21no—
18C59×#551—21no—
19C59×#546—21no—
20C59×#546—21no—
21C59×#546—21no—
22D42×C59—21no—
23C59×#540—21no—
24C59×#539—21no—
25C59×#539C2211yescharacteristic, complemented
26C59×#538—21no—
27C59×#538C2211yescharacteristic, complemented
28C59×#537C2211yescharacteristic, complemented
29C59×#534—21no—
30C59×#534C2211yescharacteristic, complemented
31C59×#525C2211yescharacteristic
32C2×#123×C59C2211yescharacteristic
33C2×#121×C59C2211yescharacteristic
34C2×#120×C59—21no—
35C59×#450—21no—
36C59×#450C2212yescomplemented
37C59×#447—21no—
38C59×#447—21no—
39C59×#447—21no—
40C59×#447C2212yes—
41C59×#447C2212yescomplemented
42C59×#447C2212yescomplemented
43C59×#418—21no—
44C2×#102×C59—21no—
45C59×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C59C2211yescharacteristic, complemented
47C59×#394—21no—
48C59×#394C2212yescomplemented
49C59×#392—21no—
50C59×#392C2212yescomplemented
51C59×#381C2211yescharacteristic, complemented
52C59×#379—21no—
53C59×#328C2212yescomplemented
54C59×#327C2212yescomplemented
55C59×#327C2212yescomplemented
56C59×#327C2212yescomplemented
57C59×#324C2212yescomplemented
58C59×#323C2212yescomplemented
59C25×C59—21no—
60C2×#41×C59—21no—
61C2×#41×C59D411yescharacteristic, complemented
62C22×D4×C59—21no—
63C22×D4×C59—21no—
64C22×D4×C59—21no—
65C22×D4×C59—22no—
66C22×D4×C59—21no—
67C22×D4×C59—21no—
68C22×D4×C59—21no—
69C22×D4×C59—21no—
70C22×D4×C59—21no—
71C22×D4×C59—44no—
72C22×D4×C59D411yescharacteristic
73C22×D4×C59D411yescharacteristic, complemented
74C22×D4×C59C2312yes—
75C23×C4×C59C2311yescharacteristic
76AGL(1,ℤ/8)×C59—44no—
77C2×SD16×C59—22no—
78C2×D8×C59—22no—
79C2×D8×C59—22no—
80C2×D8×C59—22no—
81C2×D8×C59—44no—
82C2×M16×C59—21no—
83C22×C8×C59—21no—
84#127×C59—21no—
85#126×C59—21no—
86#126×C59—21no—
87#126×C59—21no—
88#126×C59—21no—
89#125×C59—21no—
90#125×C59—21no—
91#124×C59—21no—
92#124×C59—21no—
93#124×C59—21no—
94#123×C59—21no—
95#123×C59—21no—
96#123×C59—21no—
97#123×C59—21no—
98#123×C59—21no—
99#123×C59—21no—
100#123×C59—21no—
101#123×C59—21no—
102#123×C59—21no—
103#123×C59—21no—
104#123×C59—21no—
105#123×C59—21no—
106#123×C59—21no—
107#123×C59—21no—
108C22⋊Q8×C59—21no—
109C22⋊Q8×C59—21no—
110C22⋊Q8×C59—21no—
111C22⋊Q8×C59—21no—
112C22⋊Q8×C59—21no—
113C22⋊Q8×C59D411yescharacteristic, complemented
114C22⋊Q8×C59C2311yescharacteristic
115#121×C59—21no—
116#121×C59—21no—
117#121×C59—21no—
118#121×C59—21no—
119#121×C59—21no—
120#121×C59—21no—
121#121×C59—21no—
122#121×C59—21no—
123#121×C59—21no—
124#121×C59—21no—
125#121×C59—21no—
126#121×C59—21no—
127#121×C59—21no—
128#121×C59—21no—
129#121×C59—21no—
130#121×C59D411yescharacteristic, complemented
131#121×C59D411yescharacteristic, complemented
132#121×C59D411yescharacteristic, complemented
133#121×C59C2311yescharacteristic
134#121×C59C2311yescharacteristic
135#121×C59C2311yescharacteristic
136#120×C59—21no—
137#120×C59—21no—
138#120×C59—21no—
139#120×C59—21no—
140#120×C59—21no—
141#120×C59—21no—
142#120×C59—21no—
143#120×C59—21no—
144#120×C59—44no—
145C4×D4×C59—21no—
146C4×D4×C59—21no—
147C4×D4×C59—21no—
148C4×D4×C59—21no—
149C4×D4×C59—21no—
150C4×D4×C59—21no—
151C4×D4×C59—21no—
152C4×D4×C59—21no—
153#117×C59—21no—
154#117×C59D411yescharacteristic, complemented
155C2×C4⋊C4×C59D411yescharacteristic
156C2×C4⋊C4×C59D411yescharacteristic, complemented
157C2×C4⋊C4×C59C2311yescharacteristic
158C2×C22⋊C4×C59—21no—
159C2×C22⋊C4×C59—21no—
160C2×C22⋊C4×C59—21no—
161C2×C22⋊C4×C59—21no—
162C2×C22⋊C4×C59—22no—
163C2×C22⋊C4×C59—22no—
164C2×C22⋊C4×C59—22no—
165C2×C22⋊C4×C59D411yescharacteristic
166C2×C22⋊C4×C59D411yescharacteristic
167C2×C22⋊C4×C59C2311yescharacteristic
168#102×C59—22no—
169#102×C59—22no—
170#102×C59—22no—
171#102×C59—22no—
172C22⋊C8×C59—21no—
173C22⋊C8×C59—21no—
174C22⋊C8×C59C2312yes—
175C22⋊C8×C59C2312yes—
176#95×C59—21no—
177#95×C59C2312yes—
178C24×C59—24no—
179C24×C59—21no—
180C24×C59—22no—
181C24×C59—21no—
182C24×C59—42no—
183C24×C59—41no—
184C24×C59—41no—
185C24×C59—82no—
186C24×C59—82no—
187C24×C59C2×D411yescharacteristic
188C24×C59C2×D411yescharacteristic
189#41×C59—42no—
190#41×C59—82no—
191C2×Q8×C59—21no—
192C2×Q8×C59C2×D411yescharacteristic
193C2×D4×C59—24no—
194C2×D4×C59—24no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—21no—
198C2×D4×C59—21no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—21no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—22no—
213C2×D4×C59—22no—
214C2×D4×C59—42no—
215C2×D4×C59—42no—
216C2×D4×C59—42no—
217C2×D4×C59—44no—
218C2×D4×C59—44no—
219C2×D4×C59—44no—
220C2×D4×C59—44no—
221C2×D4×C59—42no—
222C2×D4×C59—44no—
223C2×D4×C59—41no—
224C2×D4×C59—41no—
225C2×D4×C59—82no—
226C2×D4×C59—82no—
227C2×D4×C59—82no—
228C2×D4×C59—82no—
229C2×D4×C59—82no—
230C2×D4×C59C2×D411yescharacteristic
231C2×D4×C59C2×D411yescharacteristic
232C2×D4×C59C2×D411yescharacteristic
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—22no—
241C22×C4×C59—42no—
242C22×C4×C59C2×D411yescharacteristic
243C22×C4×C59C2×D411yescharacteristic
244C22×C4×C59C2×D411yescharacteristic
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D411yescharacteristic
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2411yescharacteristic
251SD16×C59—44no—
252D8×C59—44no—
253D8×C59—44no—
254D8×C59—44no—
255M16×C59—42no—
256C2×C8×C59—22no—
257C2×C8×C59—22no—
258C2×C8×C59—42no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59C2×D411yescharacteristic
273C4⋊C4×C59C2×D411yescharacteristic
274C4⋊C4×C59C2×D411yescharacteristic
275C4⋊C4×C59C2×D411yescharacteristic
276C22⋊C4×C59—21no—
277C22⋊C4×C59—21no—
278C22⋊C4×C59—21no—
279C22⋊C4×C59—21no—
280C22⋊C4×C59—21no—
281C22⋊C4×C59—21no—
282C22⋊C4×C59—21no—
283C22⋊C4×C59—21no—
284C22⋊C4×C59—21no—
285C22⋊C4×C59—21no—
286C22⋊C4×C59—21no—
287C22⋊C4×C59—21no—
288C22⋊C4×C59—21no—
289C22⋊C4×C59—21no—
290C22⋊C4×C59—21no—
291C22⋊C4×C59—21no—
292C22⋊C4×C59—21no—
293C22⋊C4×C59—21no—
294C22⋊C4×C59—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—44no—
302C22⋊C4×C59—42no—
303C22⋊C4×C59—82no—
304C22⋊C4×C59—82no—
305C42×C59—21no—
306C42×C59—21no—
307C42×C59—21no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—24no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—21no—
314C23×C59—21no—
315C23×C59—22no—
316C23×C59—41no—
317C23×C59—42no—
318C23×C59—42no—
319C23×C59—44no—
320C23×C59—42no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—42no—
324C23×C59—42no—
325C23×C59—42no—
326C23×C59—44no—
327C23×C59—42no—
328C23×C59—81no—
329C23×C59—81no—
330C23×C59—82no—
331C23×C59—82no—
332C23×C59—82no—
333C23×C59—82no—
334C23×C59—88no—
335C23×C59—81no—
336C23×C59—81no—
337C23×C59—81no—
338C23×C59—88no—
339C23×C59#12011yescharacteristic
340C23×C59#12011yescharacteristic
341C23×C59C22×D411yescharacteristic
342Q8×C59—41no—
343Q8×C59—81no—
344D4×C59—24no—
345D4×C59—24no—
346D4×C59—41no—
347D4×C59—41no—
348D4×C59—41no—
349D4×C59—42no—
350D4×C59—42no—
351D4×C59—44no—
352D4×C59—44no—
353D4×C59—42no—
354D4×C59—42no—
355D4×C59—42no—
356D4×C59—42no—
357D4×C59—42no—
358D4×C59—81no—
359D4×C59—81no—
360D4×C59—81no—
361D4×C59—81no—
362D4×C59—81no—
363D4×C59—81no—
364D4×C59—81no—
365D4×C59—81no—
366D4×C59—81no—
367D4×C59—81no—
368D4×C59—81no—
369D4×C59—81no—
370D4×C59—88no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—21no—
376C2×C4×C59—21no—
377C2×C4×C59—21no—
378C2×C4×C59—21no—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—22no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—42no—
389C2×C4×C59—42no—
390C2×C4×C59—42no—
391C2×C4×C59—81no—
392C2×C4×C59—81no—
393C2×C4×C59—81no—
394C2×C4×C59—81no—
395C2×C4×C59—81no—
396C2×C4×C59—81no—
397C2×C4×C59—81no—
398C2×C4×C59#12011yescharacteristic
399C2×C4×C59#12011yescharacteristic
400C2×C4×C59C22×D411yescharacteristic
401C2×C4×C59C22×D411yescharacteristic
402C8×C59—42no—
403C8×C59—42no—
404#18224C5911yesmaximal, characteristic, direct product factor, Sylow
405C22×C59—21no—
406C22×C59—21no—
407C22×C59—21no—
408C22×C59—21no—
409C22×C59—21no—
410C22×C59—21no—
411C22×C59—21no—
412C22×C59—44no—
413C22×C59—44no—
414C22×C59—44no—
415C22×C59—41no—
416C22×C59—41no—
417C22×C59—41no—
418C22×C59—41no—
419C22×C59—41no—
420C22×C59—41no—
421C22×C59—41no—
422C22×C59—41no—
423C22×C59—41no—
424C22×C59—41no—
425C22×C59—44no—
426C22×C59—41no—
427C22×C59—41no—
428C22×C59—82no—
429C22×C59—82no—
430C22×C59—82no—
431C22×C59—88no—
432C22×C59—88no—
433C22×C59—82no—
434C22×C59—82no—
435C22×C59—162no—
436C22×C59—162no—
437C22×C59B(4,𝔽2)12yes—
438C22×C59C2×#12011yescharacteristic
439C22×C59#57612yes—
440C4×C59—21no—
441C4×C59—21no—
442C4×C59—21no—
443C4×C59—21no—
444C4×C59—41no—
445C4×C59—41no—
446C4×C59—41no—
447C4×C59—41no—
448C4×C59—41no—
449C4×C59—41no—
450C4×C59—41no—
451C4×C59—41no—
452C4×C59—82no—
453#3534C2×C5911yescharacteristic, complemented
454#3003C2×C5911yescharacteristic, complemented
455C2×#447C2×C5911yescharacteristic, complemented
456#2613C2×C5911yescharacteristic, complemented
457#1600C2×C5912yescomplemented
458#1598C2×C5912yescomplemented
459#1597C2×C5912yescomplemented
460#1595C2×C5912yescomplemented
461#1516C2×C5911yescharacteristic, complemented
462#1510C2×C5911yescharacteristic, complemented
463#1468C2×C5911yescharacteristic, complemented
464C2×C59—22no—
465C2×C59—22no—
466C2×C59—41no—
467C2×C59—84no—
468C2×C59—81no—
469C2×C59—81no—
470C2×C59—81no—
471C2×C59—81no—
472C2×C59#300811yescharacteristic
473C2×C59#302111yescharacteristic
474C2×C59C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C5911yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C5911yescharacteristic, complemented
489#538—21no—
490#538C22×C5911yescharacteristic, complemented
491#537C22×C5911yescharacteristic, complemented
492#534—21no—
493#534C22×C5911yescharacteristic, complemented
494#525C22×C5911yescharacteristic
495C2×#123C22×C5911yescharacteristic
496C2×#121C22×C5911yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C5912yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C5912yes—
504#447C22×C5912yescomplemented
505#447C22×C5912yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C5911yescharacteristic, complemented
509C2×C22⋊C8C22×C5911yescharacteristic, complemented
510#394—21no—
511#394C22×C5912yescomplemented
512#392—21no—
513#392C22×C5912yescomplemented
514#381C22×C5911yescharacteristic, complemented
515#379—21no—
516#328C22×C5912yescomplemented
517#327C22×C5912yescomplemented
518#327C22×C5912yescomplemented
519#327C22×C5912yescomplemented
520#324C22×C5912yescomplemented
521#323C22×C5912yescomplemented
522C59#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C5911yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C5911yescharacteristic
537C22×D4D4×C5911yescharacteristic, complemented
538C22×D4C23×C5912yes—
539C23×C4C23×C5911yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C5911yescharacteristic, complemented
578C22⋊Q8C23×C5911yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C5911yescharacteristic, complemented
595#121D4×C5911yescharacteristic, complemented
596#121D4×C5911yescharacteristic, complemented
597#121C23×C5911yescharacteristic
598#121C23×C5911yescharacteristic
599#121C23×C5911yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C5911yescharacteristic, complemented
619C2×C4⋊C4D4×C5911yescharacteristic
620C2×C4⋊C4D4×C5911yescharacteristic, complemented
621C2×C4⋊C4C23×C5911yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C5911yescharacteristic
630C2×C22⋊C4D4×C5911yescharacteristic
631C2×C22⋊C4C23×C5911yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C5912yes—
639C22⋊C8C23×C5912yes—
640#95—21no—
641#95C23×C5912yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C5911yescharacteristic
652C24C2×D4×C5911yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C5911yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C5911yescharacteristic
695C2×D4C2×D4×C5911yescharacteristic
696C2×D4C2×D4×C5911yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C5911yescharacteristic
707C22×C4C2×D4×C5911yescharacteristic
708C22×C4C2×D4×C5911yescharacteristic
709C22×C4C2×D4×C5911yescharacteristic
710C22×C4C2×D4×C5911yescharacteristic
711C22×C4C2×D4×C5911yescharacteristic
712C22×C4C2×D4×C5911yescharacteristic
713C22×C4C2×D4×C5911yescharacteristic
714C22×C4C24×C5911yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C5911yescharacteristic
737C4⋊C4C2×D4×C5911yescharacteristic
738C4⋊C4C2×D4×C5911yescharacteristic
739C4⋊C4C2×D4×C5911yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C5911yescharacteristic
804C23#120×C5911yescharacteristic
805C23C22×D4×C5911yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C5911yescharacteristic
863C2×C4#120×C5911yescharacteristic
864C2×C4C22×D4×C5911yescharacteristic
865C2×C4C22×D4×C5911yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C59×B(4,𝔽2)12yes—
901C22C2×#120×C5911yescharacteristic
902C22C59×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C59×#300811yescharacteristic
925C2C59×#302111yescharacteristic
926C2C2×C59×B(4,𝔽2)11yescharacteristic
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×#3534C2semidirect
2. C59×#3003C2semidirect
3. C2×C59×#447C2semidirect
4. C59×#2613C2semidirect
5. C59×#1600C2semidirect
6. C59×#1598C2semidirect
7. C59×#1597C2semidirect
8. C59×#1595C2semidirect
9. C59×#1516C2semidirect
10. C59×#1510C2semidirect
11. C59×#1468C2semidirect
12. C23×D4×C59C22semidirect
25. C59×#539C22semidirect
27. C59×#538C22semidirect
28. C59×#537C22semidirect
30. C59×#534C22semidirect
36. C59×#450C22semidirect
41. C59×#447C22semidirect
42. C59×#447C22semidirect
45. C59×#407C22semidirect
46. C2×C22⋊C8×C59C22semidirect
48. C59×#394C22semidirect
50. C59×#392C22semidirect
51. C59×#381C22semidirect
53. C59×#328C22semidirect
54. C59×#327C22semidirect
55. C59×#327C22semidirect
56. C59×#327C22semidirect
57. C59×#324C22semidirect
58. C59×#323C22semidirect
61. C2×#41×C59D4semidirect
73. C22×D4×C59D4semidirect
113. C22⋊Q8×C59D4semidirect
130. #121×C59D4semidirect
131. #121×C59D4semidirect
132. #121×C59D4semidirect
154. #117×C59D4semidirect
156. C2×C4⋊C4×C59D4semidirect
404. #18224C59direct (N × H)
453. #3534C2×C59semidirect
454. #3003C2×C59semidirect
455. C2×#447C2×C59semidirect
456. #2613C2×C59semidirect
457. #1600C2×C59semidirect
458. #1598C2×C59semidirect
459. #1597C2×C59semidirect
460. #1595C2×C59semidirect
461. #1516C2×C59semidirect
462. #1510C2×C59semidirect
463. #1468C2×C59semidirect
475. C23×D4C22×C59semidirect
488. #539C22×C59semidirect
490. #538C22×C59semidirect
491. #537C22×C59semidirect
493. #534C22×C59semidirect
499. #450C22×C59semidirect
504. #447C22×C59semidirect
505. #447C22×C59semidirect
508. #407C22×C59semidirect
509. C2×C22⋊C8C22×C59semidirect
511. #394C22×C59semidirect
513. #392C22×C59semidirect
514. #381C22×C59semidirect
516. #328C22×C59semidirect
517. #327C22×C59semidirect
518. #327C22×C59semidirect
519. #327C22×C59semidirect
520. #324C22×C59semidirect
521. #323C22×C59semidirect
522. C59#18224direct (N × H)
525. C2×#41D4×C59semidirect
537. C22×D4D4×C59semidirect
577. C22⋊Q8D4×C59semidirect
594. #121D4×C59semidirect
595. #121D4×C59semidirect
596. #121D4×C59semidirect
618. #117D4×C59semidirect
620. 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×#35342
C59×#30032
C2×C59×#4472
C59×#26132
C59×#16002
C59×#15982
C59×#15972
C59×#15952
C59×#15162
C59×#15102
C59×#14682
#1822459