Finite Group Databasebeta

← C59×#25586 #28437695

Subgroups — C59×#25586 #28437695

Order 15104.

1196 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic
2C59×#2503C211yesmaximal, characteristic, complemented
3C59×#2501C211yesmaximal, characteristic, complemented
4C59×#2486C211yesmaximal, characteristic, complemented
5C59×#2022C214yesmaximal, complemented
6C59×#1996C211yesmaximal, characteristic, complemented
7C59×#1964C211yesmaximal, characteristic, complemented
8C59×#1890C214yesmaximal, complemented
9C4×#99×C59C211yesmaximal, characteristic, complemented
10C59×#553—21no—
11C59×#553—22no—
12C59×#552—21no—
13C59×#551—22no—
14C59×#548—21no—
15C59×#546—21no—
16C59×#539—21no—
17C59×#538—21no—
18C59×#534C2212yes—
19C59×#529—21no—
20C59×#525—21no—
21C2×#123×C59C2214yes—
22C2×#123×C59C2212yes—
23C2×C22⋊Q8×C59C2211yescharacteristic
24C2×#121×C59C2211yescharacteristic
25C59×#518C2212yes—
26C2×C4×D4×C59C2211yescharacteristic
27C22×C4⋊C4×C59C2211yescharacteristic
28C2×#99×C59C2212yes—
29C2×#99×C59C2214yes—
30C59×#400—22no—
31C59×#399—22no—
32C59×#398—21no—
33C59×#397—21no—
34C59×#391—21no—
35C59×#390—21no—
36C59×#389—21no—
37C59×#384—21no—
38C59×#382—21no—
39C59×#381C2212yes—
40C59×#381C2214yes—
41C59×#380—21no—
42C59×#380C2211yescharacteristic
43C4×C22⋊C4×C59C2211yescharacteristic
44C4×C22⋊C4×C59C2211yescharacteristic
45C59×#342C2214yes—
46C59×#342C2212yes—
47C2×#41×C59—21no—
48C22×Q8×C59D411yescharacteristic
49C22×D4×C59D411yescharacteristic
50C22×D4×C59C2311yescharacteristic
51C22×D4×C59C2312yes—
52C23×C4×C59D411yescharacteristic
53C23×C4×C59C2312yes—
54C23×C4×C59C2311yescharacteristic
55#126×C59—22no—
56#126×C59—22no—
57#126×C59—22no—
58#125×C59—21no—
59#125×C59—22no—
60#124×C59—21no—
61#124×C59—22no—
62#123×C59—22no—
63#123×C59—22no—
64#123×C59—22no—
65#123×C59—22no—
66#123×C59—22no—
67#123×C59—28no—
68#123×C59—44no—
69#123×C59—44no—
70C22⋊Q8×C59—21no—
71C22⋊Q8×C59—22no—
72C22⋊Q8×C59—21no—
73C22⋊Q8×C59—21no—
74C22⋊Q8×C59—21no—
75C22⋊Q8×C59—21no—
76#121×C59—21no—
77#121×C59—22no—
78#121×C59—21no—
79#121×C59—21no—
80#121×C59—21no—
81#121×C59—21no—
82#121×C59—22no—
83#121×C59—22no—
84#120×C59—22no—
85#120×C59—22no—
86C4×Q8×C59—21no—
87C4×D4×C59—22no—
88C4×D4×C59—21no—
89C4×D4×C59—21no—
90C4×D4×C59—21no—
91C4×D4×C59—21no—
92C4×D4×C59—21no—
93C4×D4×C59—22no—
94C4×D4×C59—22no—
95C4×D4×C59—22no—
96C4×D4×C59—22no—
97#117×C59—21no—
98#117×C59—22no—
99#117×C59—22no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59—21no—
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59—21no—
104C2×C4⋊C4×C59—24no—
105C2×C4⋊C4×C59—22no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59D411yescharacteristic
110C2×C4⋊C4×C59D411yescharacteristic
111C2×C4⋊C4×C59D411yescharacteristic
112C2×C4⋊C4×C59D412yes—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59—22no—
115C2×C22⋊C4×C59—24no—
116C2×C22⋊C4×C59D411yescharacteristic
117C2×C22⋊C4×C59D412yes—
118C2×C22⋊C4×C59C2312yes—
119C2×C22⋊C4×C59C2312yes—
120C2×C22⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59C2312yes—
122C2×C22⋊C4×C59C2312yes—
123C2×C42×C59—21no—
124C2×C42×C59—21no—
125C2×C42×C59D411yescharacteristic
126#99×C59—24no—
127#99×C59—44no—
128#95×C59—21no—
129#95×C59—21no—
130#95×C59—22no—
131#95×C59—21no—
132#95×C59—24no—
133#95×C59—22no—
134#95×C59—24no—
135C24×C59C2×D412yes—
136C24×C59C2×D411yescharacteristic
137C24×C59C2411yescharacteristic
138#41×C59—82no—
139C2×Q8×C59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—42no—
142C2×D4×C59—21no—
143C2×D4×C59—22no—
144C2×D4×C59—21no—
145C2×D4×C59—22no—
146C2×D4×C59—22no—
147C2×D4×C59—24no—
148C2×D4×C59—24no—
149C2×D4×C59—22no—
150C2×D4×C59—22no—
151C2×D4×C59—22no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—42no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—24no—
166C22×C4×C59—24no—
167C22×C4×C59—42no—
168C22×C4×C59—42no—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D412yes—
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D412yes—
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D412yes—
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C4⋊C4×C59—22no—
182C4⋊C4×C59—22no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59—22no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—22no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—22no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—48no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—44no—
196C4⋊C4×C59—41no—
197C4⋊C4×C59—41no—
198C4⋊C4×C59—41no—
199C4⋊C4×C59—41no—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—22no—
203C22⋊C4×C59—22no—
204C22⋊C4×C59—22no—
205C22⋊C4×C59—22no—
206C22⋊C4×C59—21no—
207C22⋊C4×C59—22no—
208C22⋊C4×C59—21no—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C22⋊C4×C59—22no—
212C22⋊C4×C59—21no—
213C22⋊C4×C59—21no—
214C22⋊C4×C59—22no—
215C22⋊C4×C59—22no—
216C22⋊C4×C59—22no—
217C22⋊C4×C59—24no—
218C22⋊C4×C59—48no—
219C22⋊C4×C59—44no—
220C22⋊C4×C59#4114yescomplemented
221C42×C59—22no—
222C42×C59—22no—
223C42×C59—21no—
224C42×C59—21no—
225C42×C59—42no—
226C42×C59—42no—
227C23×C59—21no—
228C23×C59—22no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—24no—
232C23×C59—41no—
233C23×C59—41no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59—42no—
237C23×C59—42no—
238C23×C59C22×D411yescharacteristic
239C23×C59C22×D411yescharacteristic
240C23×C59C22×D411yescharacteristic
241C23×C59C2×#4112yes—
242C23×C59H(5,𝔽2)12yes—
243Q8×C59—42no—
244Q8×C59—81no—
245D4×C59—42no—
246D4×C59—42no—
247D4×C59—42no—
248D4×C59—42no—
249D4×C59—44no—
250D4×C59—42no—
251D4×C59—81no—
252D4×C59—82no—
253D4×C59—82no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—21no—
258C2×C4×C59—22no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—24no—
266C2×C4×C59—24no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—42no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59—44no—
286C2×C4×C59—42no—
287C2×C4×C59—44no—
288C2×C4×C59—81no—
289C2×C4×C59—82no—
290C2×C4×C59—82no—
291C2×C4×C59#12011yescharacteristic
292C2×C4×C59#12011yescharacteristic
293C2×C4×C59#12011yescharacteristic
294C2×C4×C59#12011yescharacteristic
295#25586C5911yesmaximal, characteristic, direct product factor, Sylow
296C22×C59—21no—
297C22×C59—21no—
298C22×C59—21no—
299C22×C59—21no—
300C22×C59—21no—
301C22×C59—21no—
302C22×C59—42no—
303C22×C59—42no—
304C22×C59—42no—
305C22×C59—41no—
306C22×C59—42no—
307C22×C59—41no—
308C22×C59—42no—
309C22×C59—42no—
310C22×C59—41no—
311C22×C59—84no—
312C22×C59—81no—
313C22×C59C2×#12011yescharacteristic
314C22×C59#53211yescharacteristic
315C22×C59#53511yescharacteristic
316C22×C59#54612yes—
317C22×C59#55012yes—
318C4×C59—21no—
319C4×C59—21no—
320C4×C59—21no—
321C4×C59—44no—
322C4×C59—41no—
323C4×C59—42no—
324C4×C59—41no—
325C4×C59—42no—
326C4×C59—41no—
327C4×C59—42no—
328C4×C59—82no—
329C4×C59—82no—
330C4×C59—82no—
331C4×C59#45812yes—
332#3505C2×C5911yescharacteristic
333#2503C2×C5911yescharacteristic, complemented
334#2501C2×C5911yescharacteristic, complemented
335#2486C2×C5911yescharacteristic, complemented
336#2022C2×C5914yescomplemented
337#1996C2×C5911yescharacteristic, complemented
338#1964C2×C5911yescharacteristic, complemented
339#1890C2×C5914yescomplemented
340C4×#99C2×C5911yescharacteristic, complemented
341C2×C59—22no—
342C2×C59—21no—
343C2×C59—22no—
344C2×C59—21no—
345C2×C59—81no—
346C2×C59—82no—
347C2×C59#243111yescharacteristic
348C2×C59C2×#45811yescharacteristic
349C2×C59#302811yescharacteristic
350#553—21no—
351#553—22no—
352#552—21no—
353#551—22no—
354#548—21no—
355#546—21no—
356#539—21no—
357#538—21no—
358#534C22×C5912yes—
359#529—21no—
360#525—21no—
361C2×#123C22×C5914yes—
362C2×#123C22×C5912yes—
363C2×C22⋊Q8C22×C5911yescharacteristic
364C2×#121C22×C5911yescharacteristic
365#518C22×C5912yes—
366C2×C4×D4C22×C5911yescharacteristic
367C22×C4⋊C4C22×C5911yescharacteristic
368C2×#99C22×C5912yes—
369C2×#99C22×C5914yes—
370#400—22no—
371#399—22no—
372#398—21no—
373#397—21no—
374#391—21no—
375#390—21no—
376#389—21no—
377#384—21no—
378#382—21no—
379#381C22×C5912yes—
380#381C22×C5914yes—
381#380—21no—
382#380C22×C5911yescharacteristic
383C4×C22⋊C4C22×C5911yescharacteristic
384C4×C22⋊C4C22×C5911yescharacteristic
385#342C22×C5912yes—
386#342C22×C5914yes—
387C59#2558611yescharacteristic, direct product factor, Sylow
388C2×#41—21no—
389C22×Q8D4×C5911yescharacteristic
390C22×D4D4×C5911yescharacteristic
391C22×D4C23×C5911yescharacteristic
392C22×D4C23×C5912yes—
393C23×C4D4×C5911yescharacteristic
394C23×C4C23×C5912yes—
395C23×C4C23×C5911yescharacteristic
396#126—22no—
397#126—22no—
398#126—22no—
399#125—21no—
400#125—22no—
401#124—21no—
402#124—22no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—28no—
409#123—44no—
410#123—44no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417#121—21no—
418#121—22no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—22no—
424#121—22no—
425#120—22no—
426#120—22no—
427C4×Q8—21no—
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438#117—21no—
439#117—22no—
440#117—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C5911yescharacteristic
451C2×C4⋊C4D4×C5911yescharacteristic
452C2×C4⋊C4D4×C5911yescharacteristic
453C2×C4⋊C4D4×C5912yes—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4D4×C5911yescharacteristic
458C2×C22⋊C4D4×C5912yes—
459C2×C22⋊C4C23×C5912yes—
460C2×C22⋊C4C23×C5912yes—
461C2×C22⋊C4C23×C5911yescharacteristic
462C2×C22⋊C4C23×C5912yes—
463C2×C22⋊C4C23×C5912yes—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42D4×C5911yescharacteristic
467#99—24no—
468#99—44no—
469#95—21no—
470#95—21no—
471#95—22no—
472#95—21no—
473#95—24no—
474#95—22no—
475#95—24no—
476C24C2×D4×C5912yes—
477C24C2×D4×C5911yescharacteristic
478C24C24×C5911yescharacteristic
479#41—82no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×D4×C5911yescharacteristic
511C22×C4C2×D4×C5912yes—
512C22×C4C2×D4×C5911yescharacteristic
513C22×C4C2×D4×C5911yescharacteristic
514C22×C4C2×D4×C5911yescharacteristic
515C22×C4C2×D4×C5911yescharacteristic
516C22×C4C2×D4×C5912yes—
517C22×C4C2×D4×C5911yescharacteristic
518C22×C4C2×D4×C5912yes—
519C22×C4C2×D4×C5911yescharacteristic
520C22×C4C2×D4×C5911yescharacteristic
521C22×C4C2×D4×C5911yescharacteristic
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—48no—
535C4⋊C4—44no—
536C4⋊C4—42no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—48no—
560C22⋊C4—44no—
561C22⋊C4#41×C5914yescomplemented
562C42—22no—
563C42—22no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C23—21no—
569C23—22no—
570C23—21no—
571C23—21no—
572C23—24no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23C22×D4×C5911yescharacteristic
580C23C22×D4×C5911yescharacteristic
581C23C22×D4×C5911yescharacteristic
582C23C2×#41×C5912yes—
583C23H(5,𝔽2)×C5912yes—
584Q8—42no—
585Q8—81no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590D4—44no—
591D4—42no—
592D4—81no—
593D4—82no—
594D4—82no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4#120×C5911yescharacteristic
633C2×C4#120×C5911yescharacteristic
634C2×C4#120×C5911yescharacteristic
635C2×C4#120×C5911yescharacteristic
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—84no—
652C22—81no—
653C22C2×#120×C5911yescharacteristic
654C22C59×#53211yescharacteristic
655C22C59×#53511yescharacteristic
656C22C59×#54612yes—
657C22C59×#55012yes—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—44no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—82no—
669C4—82no—
670C4—82no—
671C4C59×#45812yes—
672C2—22no—
673C2—21no—
674C2—22no—
675C2—21no—
676C2—81no—
677C2—82no—
678C2C59×#243111yescharacteristic
679C2C2×C59×#45811yescharacteristic
680C2C59×#302811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
prime radicalC59×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2503C2semidirect
3. C59×#2501C2semidirect
4. C59×#2486C2semidirect
5. C59×#2022C2semidirect
6. C59×#1996C2semidirect
7. C59×#1964C2semidirect
8. C59×#1890C2semidirect
9. C4×#99×C59C2semidirect
220. C22⋊C4×C59#41semidirect
295. #25586C59direct (N × H)
333. #2503C2×C59semidirect
334. #2501C2×C59semidirect
335. #2486C2×C59semidirect
336. #2022C2×C59semidirect
337. #1996C2×C59semidirect
338. #1964C2×C59semidirect
339. #1890C2×C59semidirect
340. C4×#99C2×C59semidirect
387. C59#25586direct (N × H)
561. 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×#35052
C59×#25032
C59×#25012
C59×#24862
C59×#20222
C59×#19962
C59×#19642
C59×#18902
C4×#99×C592
#2558659