Finite Group Databasebeta

← C59×#25563 #28437672

Subgroups — C59×#25563 #28437672

Order 15104.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3490C211yesmaximal, characteristic, complemented
2C59×#2410C212yesmaximal, complemented
3C59×#2405C211yesmaximal, characteristic, complemented
4C59×#2062C211yesmaximal, characteristic, complemented
5C59×#2044C211yesmaximal, characteristic, complemented
6C59×#2029C211yesmaximal, characteristic, complemented
7C59×#2021C211yesmaximal, characteristic, complemented
8C59×#1898C212yesmaximal, complemented
9C59×#1889C212yesmaximal, complemented
10C59×#1867C212yesmaximal, complemented
11C2×C59×#342C211yesmaximal, characteristic, complemented
12C23×D4×C59C2211yescharacteristic
13C59×#551—22no—
14C59×#551—22no—
15C59×#546—22no—
16C59×#546—22no—
17C59×#543C2211yescharacteristic
18C59×#538—21no—
19C59×#538—21no—
20C59×#534C2211yescharacteristic
21C59×#525—21no—
22C59×#525—21no—
23C2×#123×C59—21no—
24C2×#121×C59—22no—
25C2×#120×C59C2212yes—
26C2×#120×C59C2212yes—
27C59×#518C2212yes—
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2212yes—
30C2×#99×C59C2212yes—
31C2×#99×C59C2212yes—
32C59×#394—21no—
33C59×#394—21no—
34C59×#394—22no—
35C59×#392—22no—
36C59×#386—21no—
37C59×#386—22no—
38C59×#386C2212yes—
39C59×#385C2211yescharacteristic
40C59×#385C2212yes—
41C59×#385C2211yescharacteristic
42C59×#379C2211yescharacteristic
43C59×#379C2212yes—
44C59×#379C2211yescharacteristic
45C59×#379C2211yescharacteristic
46C59×#342C2211yescharacteristic
47C59×#342C2211yescharacteristic
48C59×#342C2212yes—
49C59×#342C2212yes—
50C59×#342C2212yes—
51C25×C59C2311yescharacteristic
52C25×C59C2311yescharacteristic
53C2×#41×C59—21no—
54C2×#41×C59—21no—
55C22×D4×C59—22no—
56C22×D4×C59—21no—
57C22×D4×C59—22no—
58C22×D4×C59—21no—
59C22×D4×C59—22no—
60C22×D4×C59—44no—
61C22×D4×C59D412yescomplemented
62C22×D4×C59D412yescomplemented
63C22×D4×C59C2312yes—
64C23×C4×C59—22no—
65C23×C4×C59D411yescharacteristic, complemented
66C23×C4×C59D411yescharacteristic, complemented
67C23×C4×C59C2311yescharacteristic
68#126×C59—22no—
69#126×C59—22no—
70#124×C59—22no—
71#124×C59—22no—
72#123×C59—22no—
73#123×C59—22no—
74#123×C59—22no—
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—44no—
78C22⋊Q8×C59—21no—
79C22⋊Q8×C59—21no—
80C22⋊Q8×C59—21no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—22no—
83C22⋊Q8×C59—22no—
84#121×C59—21no—
85#121×C59—21no—
86#121×C59—22no—
87#121×C59—22no—
88#121×C59—21no—
89#121×C59—21no—
90#121×C59—48no—
91#120×C59—22no—
92#120×C59—22no—
93#120×C59—22no—
94#120×C59—22no—
95#120×C59—22no—
96#120×C59—24no—
97#120×C59—42no—
98C4×D4×C59—22no—
99C4×D4×C59—22no—
100C4×D4×C59—22no—
101C4×D4×C59—22no—
102C4×D4×C59—22no—
103C4×D4×C59—22no—
104#117×C59—21no—
105#117×C59—21no—
106#117×C59—22no—
107C2×C4⋊C4×C59—22no—
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59—21no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—24no—
114C2×C22⋊C4×C59—21no—
115C2×C22⋊C4×C59—22no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—22no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—42no—
126C2×C22⋊C4×C59D412yescomplemented
127C2×C22⋊C4×C59D411yescharacteristic, complemented
128C2×C22⋊C4×C59D411yescharacteristic, complemented
129C2×C22⋊C4×C59D412yescomplemented
130C2×C22⋊C4×C59C2312yes—
131C2×C22⋊C4×C59C2311yescharacteristic
132C2×C22⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59C2311yescharacteristic
134C2×C22⋊C4×C59C2311yescharacteristic
135C2×C22⋊C4×C59C2312yes—
136C2×C22⋊C4×C59C2312yes—
137#99×C59—24no—
138#99×C59—42no—
139#95×C59—22no—
140#95×C59—21no—
141#95×C59—21no—
142#95×C59—22no—
143C24×C59—22no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—42no—
152C24×C59—42no—
153C24×C59—81no—
154C24×C59—81no—
155C24×C59C2×D412yes—
156C24×C59C2×D411yescharacteristic
157C24×C59C2×D412yes—
158C24×C59C2×D412yes—
159C24×C59C2×D411yescharacteristic
160C24×C59C2411yescharacteristic
161#41×C59—82no—
162#41×C59—82no—
163C2×Q8×C59—21no—
164C2×Q8×C59—21no—
165C2×D4×C59—28no—
166C2×D4×C59—24no—
167C2×D4×C59—22no—
168C2×D4×C59—22no—
169C2×D4×C59—22no—
170C2×D4×C59—22no—
171C2×D4×C59—22no—
172C2×D4×C59—22no—
173C2×D4×C59—22no—
174C2×D4×C59—22no—
175C2×D4×C59—21no—
176C2×D4×C59—21no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—44no—
180C2×D4×C59—42no—
181C2×D4×C59—44no—
182C2×D4×C59—42no—
183C2×D4×C59—44no—
184C2×D4×C59—42no—
185C2×D4×C59—44no—
186C2×D4×C59—42no—
187C2×D4×C59—41no—
188C2×D4×C59—41no—
189C2×D4×C59—44no—
190C2×D4×C59—44no—
191C2×D4×C59—82no—
192C2×D4×C59—82no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—22no—
205C22×C4×C59—42no—
206C22×C4×C59—44no—
207C22×C4×C59—42no—
208C22×C4×C59—44no—
209C22×C4×C59—81no—
210C22×C4×C59—82no—
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D412yes—
217C22×C4×C59C2×D411yescharacteristic
218C4⋊C4×C59—22no—
219C4⋊C4×C59—22no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—22no—
225C4⋊C4×C59—22no—
226C4⋊C4×C59—44no—
227C4⋊C4×C59—42no—
228C4⋊C4×C59—42no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—22no—
233C22⋊C4×C59—22no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—22no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—22no—
240C22⋊C4×C59—22no—
241C22⋊C4×C59—22no—
242C22⋊C4×C59—22no—
243C22⋊C4×C59—22no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—22no—
246C22⋊C4×C59—21no—
247C22⋊C4×C59—22no—
248C22⋊C4×C59—21no—
249C22⋊C4×C59—44no—
250C22⋊C4×C59—44no—
251C22⋊C4×C59—44no—
252C22⋊C4×C59—44no—
253C22⋊C4×C59—42no—
254C22⋊C4×C59—42no—
255C22⋊C4×C59—42no—
256C22⋊C4×C59—81no—
257C22⋊C4×C59—81no—
258C22⋊C4×C59—82no—
259C22⋊C4×C59—81no—
260C22⋊C4×C59#4114yescomplemented
261C42×C59—22no—
262C42×C59—22no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—24no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—24no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—42no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—42no—
289C23×C59—41no—
290C23×C59—42no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59—84no—
300C23×C59—84no—
301C23×C59—82no—
302C23×C59—82no—
303C23×C59—82no—
304C23×C59—82no—
305C23×C59#12012yes—
306C23×C59#12011yescharacteristic
307C23×C59#12011yescharacteristic
308C23×C59C22×D411yescharacteristic
309C23×C59C22×D412yes—
310C23×C59C2×#4112yes—
311C23×C59H(5,𝔽2)11yescharacteristic
312C23×C592−1+411yescharacteristic
313Q8×C59—81no—
314Q8×C59—81no—
315D4×C59—44no—
316D4×C59—48no—
317D4×C59—44no—
318D4×C59—42no—
319D4×C59—42no—
320D4×C59—42no—
321D4×C59—42no—
322D4×C59—44no—
323D4×C59—44no—
324D4×C59—82no—
325D4×C59—82no—
326D4×C59—81no—
327D4×C59—81no—
328D4×C59—88no—
329C2×C4×C59—24no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—24no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—42no—
342C2×C4×C59—41no—
343C2×C4×C59—42no—
344C2×C4×C59—42no—
345C2×C4×C59—42no—
346C2×C4×C59—41no—
347C2×C4×C59—42no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—42no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—42no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—42no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—42no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—42no—
363C2×C4×C59—81no—
364C2×C4×C59—81no—
365C2×C4×C59—82no—
366C2×C4×C59—82no—
367C2×C4×C59—88no—
368#25563C5911yesmaximal, characteristic, direct product factor, Sylow
369C22×C59—21no—
370C22×C59—21no—
371C22×C59—22no—
372C22×C59—21no—
373C22×C59—22no—
374C22×C59—21no—
375C22×C59—21no—
376C22×C59—22no—
377C22×C59—21no—
378C22×C59—22no—
379C22×C59—21no—
380C22×C59—22no—
381C22×C59—42no—
382C22×C59—41no—
383C22×C59—41no—
384C22×C59—44no—
385C22×C59—42no—
386C22×C59—42no—
387C22×C59—44no—
388C22×C59—44no—
389C22×C59—42no—
390C22×C59—42no—
391C22×C59—44no—
392C22×C59—42no—
393C22×C59—42no—
394C22×C59—42no—
395C22×C59—42no—
396C22×C59—82no—
397C22×C59—81no—
398C22×C59—81no—
399C22×C59—82no—
400C22×C59—82no—
401C22×C59—82no—
402C22×C59—82no—
403C22×C59—81no—
404C22×C59—81no—
405C22×C59—82no—
406C22×C59—81no—
407C22×C59—81no—
408C22×C59B(4,𝔽2)12yes—
409C22×C59C2×#12011yescharacteristic
410C22×C59#53211yescharacteristic
411C22×C59#53711yescharacteristic
412C22×C59#54612yes—
413C22×C59#54712yes—
414C4×C59—44no—
415C4×C59—42no—
416C4×C59—42no—
417C4×C59—41no—
418C4×C59—41no—
419C4×C59—42no—
420C4×C59—41no—
421C4×C59—41no—
422C4×C59—42no—
423C4×C59—81no—
424C4×C59—81no—
425C4×C59—82no—
426#3490C2×C5911yescharacteristic, complemented
427#2410C2×C5912yescomplemented
428#2405C2×C5911yescharacteristic, complemented
429#2062C2×C5911yescharacteristic, complemented
430#2044C2×C5911yescharacteristic, complemented
431#2029C2×C5911yescharacteristic, complemented
432#2021C2×C5911yescharacteristic, complemented
433#1898C2×C5912yescomplemented
434#1889C2×C5912yescomplemented
435#1867C2×C5912yescomplemented
436C2×#342C2×C5911yescharacteristic, complemented
437C2×C59—22no—
438C2×C59—21no—
439C2×C59—21no—
440C2×C59—22no—
441C2×C59—22no—
442C2×C59—41no—
443C2×C59—42no—
444C2×C59—82no—
445C2×C59—82no—
446C2×C59#243011yescharacteristic
447C2×C59C2×B(4,𝔽2)11yescharacteristic
448C2×C59#302611yescharacteristic
449C23×D4C22×C5911yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C5911yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C5911yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C5912yes—
463C2×#120C22×C5912yes—
464#518C22×C5912yes—
465C22×C22⋊C4C22×C5911yescharacteristic
466C22×C22⋊C4C22×C5912yes—
467C2×#99C22×C5912yes—
468C2×#99C22×C5912yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C5912yes—
476#385C22×C5912yes—
477#385C22×C5911yescharacteristic
478#385C22×C5911yescharacteristic
479#379C22×C5911yescharacteristic
480#379C22×C5912yes—
481#379C22×C5911yescharacteristic
482#379C22×C5911yescharacteristic
483#342C22×C5912yes—
484#342C22×C5911yescharacteristic
485#342C22×C5912yes—
486#342C22×C5912yes—
487#342C22×C5911yescharacteristic
488C59#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C5911yescharacteristic
490C25C23×C5911yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C5912yescomplemented
500C22×D4D4×C5912yescomplemented
501C22×D4C23×C5912yes—
502C23×C4—22no—
503C23×C4D4×C5911yescharacteristic, complemented
504C23×C4D4×C5911yescharacteristic, complemented
505C23×C4C23×C5911yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C5911yescharacteristic, complemented
565C2×C22⋊C4D4×C5911yescharacteristic, complemented
566C2×C22⋊C4D4×C5912yescomplemented
567C2×C22⋊C4D4×C5912yescomplemented
568C2×C22⋊C4C23×C5912yes—
569C2×C22⋊C4C23×C5911yescharacteristic
570C2×C22⋊C4C23×C5911yescharacteristic
571C2×C22⋊C4C23×C5911yescharacteristic
572C2×C22⋊C4C23×C5911yescharacteristic
573C2×C22⋊C4C23×C5912yes—
574C2×C22⋊C4C23×C5912yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C5912yes—
594C24C2×D4×C5911yescharacteristic
595C24C2×D4×C5912yes—
596C24C2×D4×C5912yes—
597C24C2×D4×C5911yescharacteristic
598C24C24×C5911yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C5912yes—
650C22×C4C2×D4×C5911yescharacteristic
651C22×C4C2×D4×C5912yes—
652C22×C4C2×D4×C5911yescharacteristic
653C22×C4C2×D4×C5911yescharacteristic
654C22×C4C2×D4×C5912yes—
655C22×C4C2×D4×C5911yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C5914yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C5912yes—
744C23#120×C5911yescharacteristic
745C23#120×C5911yescharacteristic
746C23C22×D4×C5911yescharacteristic
747C23C22×D4×C5912yes—
748C23C2×#41×C5912yes—
749C23H(5,𝔽2)×C5911yescharacteristic
750C232−1+4×C5911yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C59×B(4,𝔽2)12yes—
846C22C2×#120×C5911yescharacteristic
847C22C59×#53211yescharacteristic
848C22C59×#53711yescharacteristic
849C22C59×#54612yes—
850C22C59×#54712yes—
851C4—44no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C59×#243011yescharacteristic
873C2C2×C59×B(4,𝔽2)11yescharacteristic
874C2C59×#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×#3490C2semidirect
2. C59×#2410C2semidirect
3. C59×#2405C2semidirect
4. C59×#2062C2semidirect
5. C59×#2044C2semidirect
6. C59×#2029C2semidirect
7. C59×#2021C2semidirect
8. C59×#1898C2semidirect
9. C59×#1889C2semidirect
10. C59×#1867C2semidirect
11. C2×C59×#342C2semidirect
61. C22×D4×C59D4semidirect
62. C22×D4×C59D4semidirect
65. C23×C4×C59D4semidirect
66. C23×C4×C59D4semidirect
126. C2×C22⋊C4×C59D4semidirect
127. C2×C22⋊C4×C59D4semidirect
128. C2×C22⋊C4×C59D4semidirect
129. C2×C22⋊C4×C59D4semidirect
260. C22⋊C4×C59#41semidirect
368. #25563C59direct (N × H)
426. #3490C2×C59semidirect
427. #2410C2×C59semidirect
428. #2405C2×C59semidirect
429. #2062C2×C59semidirect
430. #2044C2×C59semidirect
431. #2029C2×C59semidirect
432. #2021C2×C59semidirect
433. #1898C2×C59semidirect
434. #1889C2×C59semidirect
435. #1867C2×C59semidirect
436. C2×#342C2×C59semidirect
488. C59#25563direct (N × H)
499. C22×D4D4×C59semidirect
500. C22×D4D4×C59semidirect
503. C23×C4D4×C59semidirect
504. C23×C4D4×C59semidirect
564. C2×C22⋊C4D4×C59semidirect
565. C2×C22⋊C4D4×C59semidirect
566. C2×C22⋊C4D4×C59semidirect
567. C2×C22⋊C4D4×C59semidirect
698. C22⋊C4#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#34902
C59×#24102
C59×#24052
C59×#20622
C59×#20442
C59×#20292
C59×#20212
C59×#18982
C59×#18892
C59×#18672
C2×C59×#3422
#2556359