Finite Group Databasebeta

← C59×#18233 #28430342

Subgroups — C59×#18233 #28430342

Order 15104.

1002 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic
2C59×#3092C211yesmaximal, characteristic, complemented
3C2×C59×#481C211yesmaximal, characteristic, complemented
4C59×#2623C211yesmaximal, characteristic, complemented
5C59×#1618C212yesmaximal, complemented
6C59×#1616C212yesmaximal, complemented
7C59×#1615C212yesmaximal, complemented
8C59×#1613C212yesmaximal, complemented
9C59×#1516C211yesmaximal, characteristic, complemented
10C59×#1510C211yesmaximal, characteristic, complemented
11C59×#1468C211yesmaximal, characteristic, complemented
12C59×#562—21no—
13C59×#560—21no—
14C59×#553—21no—
15C59×#551—21no—
16C59×#546—21no—
17C59×#546—21no—
18C59×#546—21no—
19D42×C59—21no—
20C59×#540—21no—
21C59×#539—21no—
22C59×#539C2211yescharacteristic
23C59×#538—21no—
24C59×#538C2211yescharacteristic
25C59×#537C2211yescharacteristic
26C59×#534—21no—
27C59×#534C2211yescharacteristic
28C59×#525C2211yescharacteristic
29C2×#123×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C22×C4⋊C4×C59C2211yescharacteristic, complemented
32C59×#484C2212yescomplemented
33C59×#483—21no—
34C59×#481—21no—
35C59×#481—21no—
36C59×#481C2212yes—
37C59×#481C2212yescomplemented
38C59×#481C2212yescomplemented
39C59×#480—21no—
40C59×#428—21no—
41C2×#106×C59—21no—
42C59×#417—21no—
43C2×#102×C59—21no—
44C59×#407C2211yescharacteristic, complemented
45C2×C22⋊C8×C59C2211yescharacteristic, complemented
46C59×#400C2212yescomplemented
47C59×#399C2212yescomplemented
48C59×#398—21no—
49C59×#397—21no—
50C59×#386—21no—
51C59×#385—21no—
52C59×#381C2211yescharacteristic, complemented
53C59×#328C2212yescomplemented
54C59×#327C2212yes—
55C59×#327C2212yescomplemented
56C59×#327C2212yescomplemented
57C59×#324C2212yescomplemented
58C59×#323C2212yescomplemented
59C2×#41×C59—21no—
60C2×#41×C59D411yescharacteristic
61C22×D4×C59—21no—
62C22×D4×C59—21no—
63C22×D4×C59—21no—
64C22×D4×C59D411yescharacteristic
65C22×D4×C59D411yescharacteristic
66C23×C4×C59—21no—
67C23×C4×C59C2311yescharacteristic
68C2×M16×C59—21no—
69C22×C8×C59—21no—
70#127×C59—21no—
71#126×C59—21no—
72#126×C59—21no—
73#126×C59—21no—
74#126×C59—21no—
75#125×C59—21no—
76#125×C59—21no—
77#124×C59—21no—
78#124×C59—21no—
79#124×C59—21no—
80#123×C59—21no—
81#123×C59—21no—
82#123×C59—21no—
83#123×C59—21no—
84#123×C59—21no—
85#123×C59—21no—
86#123×C59—21no—
87#123×C59—21no—
88#123×C59—21no—
89#123×C59—21no—
90#123×C59—21no—
91#123×C59—21no—
92#123×C59—21no—
93#123×C59—21no—
94C22⋊Q8×C59—21no—
95C22⋊Q8×C59—21no—
96C22⋊Q8×C59—21no—
97C22⋊Q8×C59—21no—
98C22⋊Q8×C59—21no—
99C22⋊Q8×C59D411yescharacteristic
100C22⋊Q8×C59C2311yescharacteristic
101#121×C59—21no—
102#121×C59—21no—
103#121×C59—21no—
104#121×C59—21no—
105#121×C59—21no—
106#121×C59—21no—
107#121×C59—21no—
108#121×C59—21no—
109#121×C59—21no—
110#121×C59—21no—
111#121×C59—21no—
112#121×C59—21no—
113#121×C59—21no—
114#121×C59—21no—
115#121×C59—21no—
116#121×C59D411yescharacteristic
117#121×C59D411yescharacteristic
118#121×C59D411yescharacteristic
119#121×C59C2311yescharacteristic
120#121×C59C2311yescharacteristic
121#121×C59C2311yescharacteristic
122#120×C59—21no—
123#120×C59—21no—
124#120×C59—21no—
125#120×C59—21no—
126#120×C59—21no—
127#120×C59—21no—
128#120×C59—21no—
129#120×C59—21no—
130C4×D4×C59—21no—
131C4×D4×C59—21no—
132C4×D4×C59—21no—
133C4×D4×C59—21no—
134C4×D4×C59—21no—
135C4×D4×C59—21no—
136C4×D4×C59—21no—
137C4×D4×C59—21no—
138#117×C59—21no—
139#117×C59D411yescharacteristic
140C2×C4⋊C4×C59—21no—
141C2×C4⋊C4×C59—21no—
142C2×C4⋊C4×C59—21no—
143C2×C4⋊C4×C59—21no—
144C2×C4⋊C4×C59—21no—
145C2×C4⋊C4×C59—22no—
146C2×C4⋊C4×C59D411yescharacteristic
147C2×C4⋊C4×C59D411yescharacteristic
148C2×C4⋊C4×C59C2312yes—
149C2×C4⋊C4×C59C2311yescharacteristic
150C2×C22⋊C4×C59—21no—
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59D411yescharacteristic
156C2×C22⋊C4×C59D411yescharacteristic
157C2×C22⋊C4×C59C2311yescharacteristic
158#107×C59—22no—
159#106×C59—22no—
160#106×C59—22no—
161#106×C59—22no—
162#103×C59—22no—
163#102×C59—22no—
164#102×C59—22no—
165#102×C59—22no—
166C22⋊C8×C59—21no—
167C22⋊C8×C59—21no—
168C22⋊C8×C59C2312yes—
169C22⋊C8×C59C2312yes—
170#95×C59—21no—
171#95×C59—22no—
172#95×C59—22no—
173#95×C59C2312yes—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59C2×D411yescharacteristic
177C24×C59C2×D411yescharacteristic
178#41×C59—42no—
179#41×C59—82no—
180C2×Q8×C59—21no—
181C2×Q8×C59C2×D411yescharacteristic
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—21no—
198C2×D4×C59—21no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—82no—
202C2×D4×C59—82no—
203C2×D4×C59—82no—
204C2×D4×C59C2×D411yescharacteristic
205C2×D4×C59C2×D411yescharacteristic
206C2×D4×C59C2×D411yescharacteristic
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—22no—
215C22×C4×C59—22no—
216C22×C4×C59—42no—
217C22×C4×C59—41no—
218C22×C4×C59—41no—
219C22×C4×C59—82no—
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2411yescharacteristic
229M16×C59—42no—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59—42no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—22no—
247C4⋊C4×C59—22no—
248C4⋊C4×C59—41no—
249C4⋊C4×C59—41no—
250C4⋊C4×C59—82no—
251C4⋊C4×C59C2×D411yescharacteristic
252C4⋊C4×C59C2×D411yescharacteristic
253C4⋊C4×C59C2×D411yescharacteristic
254C4⋊C4×C59C2×D411yescharacteristic
255C22⋊C4×C59—21no—
256C22⋊C4×C59—21no—
257C22⋊C4×C59—21no—
258C22⋊C4×C59—21no—
259C22⋊C4×C59—21no—
260C22⋊C4×C59—21no—
261C22⋊C4×C59—21no—
262C22⋊C4×C59—21no—
263C22⋊C4×C59—21no—
264C22⋊C4×C59—21no—
265C22⋊C4×C59—21no—
266C22⋊C4×C59—21no—
267C22⋊C4×C59—21no—
268C22⋊C4×C59—21no—
269C22⋊C4×C59—21no—
270C22⋊C4×C59—21no—
271C22⋊C4×C59—21no—
272C22⋊C4×C59—21no—
273C22⋊C4×C59—21no—
274C22⋊C4×C59—21no—
275C22⋊C4×C59—21no—
276C22⋊C4×C59—21no—
277C22⋊C4×C59—21no—
278C22⋊C4×C59—21no—
279C22⋊C4×C59—21no—
280C22⋊C4×C59—42no—
281C22⋊C4×C59—82no—
282C42×C59—21no—
283C42×C59—21no—
284C42×C59—21no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—22no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59—41no—
295C23×C59—42no—
296C23×C59—81no—
297C23×C59—81no—
298C23×C59—81no—
299C23×C59—81no—
300C23×C59—81no—
301C23×C59#12011yescharacteristic
302C23×C59#12011yescharacteristic
303C23×C59C22×D411yescharacteristic
304Q8×C59—41no—
305Q8×C59—81no—
306D4×C59—41no—
307D4×C59—41no—
308D4×C59—41no—
309D4×C59—42no—
310D4×C59—42no—
311D4×C59—42no—
312D4×C59—42no—
313D4×C59—42no—
314D4×C59—81no—
315D4×C59—81no—
316D4×C59—81no—
317D4×C59—81no—
318D4×C59—81no—
319D4×C59—81no—
320D4×C59—81no—
321D4×C59—81no—
322D4×C59—81no—
323D4×C59—81no—
324D4×C59—81no—
325D4×C59—81no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—22no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—42no—
344C2×C4×C59—42no—
345C2×C4×C59—42no—
346C2×C4×C59—42no—
347C2×C4×C59—42no—
348C2×C4×C59—42no—
349C2×C4×C59—81no—
350C2×C4×C59—81no—
351C2×C4×C59—81no—
352C2×C4×C59—81no—
353C2×C4×C59—81no—
354C2×C4×C59—81no—
355C2×C4×C59—81no—
356C2×C4×C59—82no—
357C2×C4×C59—82no—
358C2×C4×C59#12011yescharacteristic
359C2×C4×C59#12011yescharacteristic
360C2×C4×C59C22×D411yescharacteristic
361C2×C4×C59C22×D411yescharacteristic
362C8×C59—42no—
363C8×C59—42no—
364#18233C5911yesmaximal, characteristic, direct product factor, Sylow
365C22×C59—21no—
366C22×C59—21no—
367C22×C59—21no—
368C22×C59—21no—
369C22×C59—21no—
370C22×C59—21no—
371C22×C59—21no—
372C22×C59—44no—
373C22×C59—41no—
374C22×C59—41no—
375C22×C59—41no—
376C22×C59—41no—
377C22×C59—41no—
378C22×C59—41no—
379C22×C59—41no—
380C22×C59—41no—
381C22×C59—41no—
382C22×C59—41no—
383C22×C59—41no—
384C22×C59—41no—
385C22×C59—82no—
386C22×C59—162no—
387C22×C59—162no—
388C22×C59#45812yes—
389C22×C59C2×#12011yescharacteristic
390C22×C59#57712yes—
391C4×C59—21no—
392C4×C59—21no—
393C4×C59—21no—
394C4×C59—21no—
395C4×C59—41no—
396C4×C59—41no—
397C4×C59—41no—
398C4×C59—41no—
399C4×C59—41no—
400C4×C59—41no—
401C4×C59—41no—
402C4×C59—41no—
403C4×C59—82no—
404C4×C59—82no—
405#3534C2×C5911yescharacteristic
406#3092C2×C5911yescharacteristic, complemented
407C2×#481C2×C5911yescharacteristic, complemented
408#2623C2×C5911yescharacteristic, complemented
409#1618C2×C5912yescomplemented
410#1616C2×C5912yescomplemented
411#1615C2×C5912yescomplemented
412#1613C2×C5912yescomplemented
413#1516C2×C5911yescharacteristic, complemented
414#1510C2×C5911yescharacteristic, complemented
415#1468C2×C5911yescharacteristic, complemented
416C2×C59—22no—
417C2×C59—22no—
418C2×C59—41no—
419C2×C59—81no—
420C2×C59—81no—
421C2×C59—81no—
422C2×C59—81no—
423C2×C59#300911yescharacteristic
424C2×C59#302111yescharacteristic
425C2×C59C2×#45811yescharacteristic
426#562—21no—
427#560—21no—
428#553—21no—
429#551—21no—
430#546—21no—
431#546—21no—
432#546—21no—
433D42—21no—
434#540—21no—
435#539—21no—
436#539C22×C5911yescharacteristic
437#538—21no—
438#538C22×C5911yescharacteristic
439#537C22×C5911yescharacteristic
440#534—21no—
441#534C22×C5911yescharacteristic
442#525C22×C5911yescharacteristic
443C2×#123C22×C5911yescharacteristic
444C2×#121C22×C5911yescharacteristic
445C22×C4⋊C4C22×C5911yescharacteristic, complemented
446#484C22×C5912yescomplemented
447#483—21no—
448#481—21no—
449#481—21no—
450#481C22×C5912yes—
451#481C22×C5912yescomplemented
452#481C22×C5912yescomplemented
453#480—21no—
454#428—21no—
455C2×#106—21no—
456#417—21no—
457C2×#102—21no—
458#407C22×C5911yescharacteristic, complemented
459C2×C22⋊C8C22×C5911yescharacteristic, complemented
460#400C22×C5912yescomplemented
461#399C22×C5912yescomplemented
462#398—21no—
463#397—21no—
464#386—21no—
465#385—21no—
466#381C22×C5911yescharacteristic, complemented
467#328C22×C5912yescomplemented
468#327C22×C5912yes—
469#327C22×C5912yescomplemented
470#327C22×C5912yescomplemented
471#324C22×C5912yescomplemented
472#323C22×C5912yescomplemented
473C59#1823311yescharacteristic, direct product factor, Sylow
474C2×#41—21no—
475C2×#41D4×C5911yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4D4×C5911yescharacteristic
480C22×D4D4×C5911yescharacteristic
481C23×C4—21no—
482C23×C4C23×C5911yescharacteristic
483C2×M16—21no—
484C22×C8—21no—
485#127—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#125—21no—
491#125—21no—
492#124—21no—
493#124—21no—
494#124—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123—21no—
499#123—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506#123—21no—
507#123—21no—
508#123—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8D4×C5911yescharacteristic
515C22⋊Q8C23×C5911yescharacteristic
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C5911yescharacteristic
532#121D4×C5911yescharacteristic
533#121D4×C5911yescharacteristic
534#121C23×C5911yescharacteristic
535#121C23×C5911yescharacteristic
536#121C23×C5911yescharacteristic
537#120—21no—
538#120—21no—
539#120—21no—
540#120—21no—
541#120—21no—
542#120—21no—
543#120—21no—
544#120—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553#117—21no—
554#117D4×C5911yescharacteristic
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4D4×C5911yescharacteristic
562C2×C4⋊C4D4×C5911yescharacteristic
563C2×C4⋊C4C23×C5912yes—
564C2×C4⋊C4C23×C5911yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4D4×C5911yescharacteristic
571C2×C22⋊C4D4×C5911yescharacteristic
572C2×C22⋊C4C23×C5911yescharacteristic
573#107—22no—
574#106—22no—
575#106—22no—
576#106—22no—
577#103—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C23×C5912yes—
584C22⋊C8C23×C5912yes—
585#95—21no—
586#95—22no—
587#95—22no—
588#95C23×C5912yes—
589C24—21no—
590C24—21no—
591C24C2×D4×C5911yescharacteristic
592C24C2×D4×C5911yescharacteristic
593#41—42no—
594#41—82no—
595C2×Q8—21no—
596C2×Q8C2×D4×C5911yescharacteristic
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4C2×D4×C5911yescharacteristic
620C2×D4C2×D4×C5911yescharacteristic
621C2×D4C2×D4×C5911yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—82no—
635C22×C4C2×D4×C5911yescharacteristic
636C22×C4C2×D4×C5911yescharacteristic
637C22×C4C2×D4×C5911yescharacteristic
638C22×C4C2×D4×C5911yescharacteristic
639C22×C4C2×D4×C5911yescharacteristic
640C22×C4C2×D4×C5911yescharacteristic
641C22×C4C2×D4×C5911yescharacteristic
642C22×C4C2×D4×C5911yescharacteristic
643C22×C4C24×C5911yescharacteristic
644M16—42no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—42no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—82no—
666C4⋊C4C2×D4×C5911yescharacteristic
667C4⋊C4C2×D4×C5911yescharacteristic
668C4⋊C4C2×D4×C5911yescharacteristic
669C4⋊C4C2×D4×C5911yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—42no—
696C22⋊C4—82no—
697C42—21no—
698C42—21no—
699C42—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23#120×C5911yescharacteristic
717C23#120×C5911yescharacteristic
718C23C22×D4×C5911yescharacteristic
719Q8—41no—
720Q8—81no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4#120×C5911yescharacteristic
774C2×C4#120×C5911yescharacteristic
775C2×C4C22×D4×C5911yescharacteristic
776C2×C4C22×D4×C5911yescharacteristic
777C8—42no—
778C8—42no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—44no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—82no—
800C22—162no—
801C22—162no—
802C22C59×#45812yes—
803C22C2×#120×C5911yescharacteristic
804C22C59×#57712yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—82no—
818C4—82no—
819C2—22no—
820C2—22no—
821C2—41no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—81no—
826C2C59×#300911yescharacteristic
827C2C59×#302111yescharacteristic
828C2C2×C59×#45811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3534C2
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×#3092C2semidirect
3. C2×C59×#481C2semidirect
4. C59×#2623C2semidirect
5. C59×#1618C2semidirect
6. C59×#1616C2semidirect
7. C59×#1615C2semidirect
8. C59×#1613C2semidirect
9. C59×#1516C2semidirect
10. C59×#1510C2semidirect
11. C59×#1468C2semidirect
31. C22×C4⋊C4×C59C22semidirect
32. C59×#484C22semidirect
37. C59×#481C22semidirect
38. C59×#481C22semidirect
44. C59×#407C22semidirect
45. C2×C22⋊C8×C59C22semidirect
46. C59×#400C22semidirect
47. C59×#399C22semidirect
52. C59×#381C22semidirect
53. C59×#328C22semidirect
55. C59×#327C22semidirect
56. C59×#327C22semidirect
57. C59×#324C22semidirect
58. C59×#323C22semidirect
364. #18233C59direct (N × H)
406. #3092C2×C59semidirect
407. C2×#481C2×C59semidirect
408. #2623C2×C59semidirect
409. #1618C2×C59semidirect
410. #1616C2×C59semidirect
411. #1615C2×C59semidirect
412. #1613C2×C59semidirect
413. #1516C2×C59semidirect
414. #1510C2×C59semidirect
415. #1468C2×C59semidirect
445. C22×C4⋊C4C22×C59semidirect
446. #484C22×C59semidirect
451. #481C22×C59semidirect
452. #481C22×C59semidirect
458. #407C22×C59semidirect
459. C2×C22⋊C8C22×C59semidirect
460. #400C22×C59semidirect
461. #399C22×C59semidirect
466. #381C22×C59semidirect
467. #328C22×C59semidirect
469. #327C22×C59semidirect
470. #327C22×C59semidirect
471. #324C22×C59semidirect
472. #323C22×C59semidirect
473. C59#18233direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35342
C59×#30922
C2×C59×#4812
C59×#26232
C59×#16182
C59×#16162
C59×#16152
C59×#16132
C59×#15162
C59×#15102
C59×#14682
#1823359