Finite Group Databasebeta

← C59×#16701 #28428810

Subgroups — C59×#16701 #28428810

Order 15104.

1338 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#397C211yesmaximal, characteristic
3C2×C59×#388C211yesmaximal, characteristic
4C2×C59×#382C211yesmaximal, characteristic, complemented
5C59×#1445C211yesmaximal, characteristic, complemented
6C59×#1445C211yesmaximal, characteristic, complemented
7C59×#1441C212yesmaximal, complemented
8C59×#1441C212yesmaximal, complemented
9C59×#1440C212yesmaximal
10C59×#1439C212yesmaximal
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2212yes—
22C22×C42×C59C2211yescharacteristic
23C59×#399—24no—
24C59×#397—24no—
25C59×#388—24no—
26C59×#382—24no—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C25×C59C2311yescharacteristic
40C23×C4×C59C2311yescharacteristic
41C23×C4×C59C2312yes—
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2312yes—
45C23×C4×C59C2311yescharacteristic
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C2×C4⋊C4×C59—22no—
51C2×C4⋊C4×C59—22no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—24no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—42no—
62C2×C4⋊C4×C59—42no—
63C2×C4⋊C4×C59—42no—
64C2×C22⋊C4×C59—22no—
65C2×C22⋊C4×C59—22no—
66C2×C22⋊C4×C59—24no—
67C2×C22⋊C4×C59—24no—
68C2×C22⋊C4×C59—22no—
69C2×C22⋊C4×C59—22no—
70C2×C22⋊C4×C59—24no—
71C2×C22⋊C4×C59—24no—
72C2×C22⋊C4×C59—42no—
73C2×C22⋊C4×C59—42no—
74C2×C22⋊C4×C59—42no—
75C2×C22⋊C4×C59—42no—
76C2×C22⋊C4×C59D414yes—
77C2×C42×C59—24no—
78C2×C42×C59D414yes—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—22no—
82#95×C59—22no—
83#95×C59—22no—
84#95×C59—24no—
85#95×C59—22no—
86#95×C59—42no—
87#95×C59—42no—
88#95×C59—42no—
89#95×C59—42no—
90#95×C59—42no—
91C24×C59—21no—
92C24×C59—21no—
93C24×C59—22no—
94C24×C59—22no—
95C24×C59—21no—
96C24×C59—21no—
97C24×C59—22no—
98C24×C59—21no—
99C24×C59—21no—
100C24×C59—22no—
101C24×C59C2×D412yes—
102C24×C59C2411yescharacteristic
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—21no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—21no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—21no—
121C22×C4×C59—22no—
122C22×C4×C59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—22no—
153C22×C4×C59C2×D412yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×D412yes—
158C22×C4×C59#4114yes—
159C22×C4×C59#4112yes—
160C22×C4×C59#4114yes—
161C4⋊C4×C59—48no—
162C4⋊C4×C59—48no—
163C4⋊C4×C59—44no—
164C4⋊C4×C59—44no—
165C4⋊C4×C59—44no—
166C22⋊C4×C59—28no—
167C22⋊C4×C59—48no—
168C22⋊C4×C59—44no—
169C22⋊C4×C59—48no—
170C22⋊C4×C59—44no—
171C42×C59—28no—
172C23×C59—22no—
173C23×C59—22no—
174C23×C59—22no—
175C23×C59—24no—
176C23×C59—24no—
177C23×C59—41no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59—41no—
181C23×C59—41no—
182C23×C59—41no—
183C23×C59—42no—
184C23×C59—42no—
185C23×C59—42no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—42no—
189C23×C59—42no—
190C23×C59—42no—
191C23×C59—42no—
192C23×C59—42no—
193C23×C59—42no—
194C23×C59—42no—
195C23×C59C22×D411yescharacteristic
196C23×C59C22×D411yescharacteristic
197C23×C59C2×#4111yescharacteristic
198C23×C59C2×#4112yes—
199C23×C59C2×#4112yes—
200C23×C59H(5,𝔽2)11yescharacteristic
201C23×C59H(5,𝔽2)11yescharacteristic
202C23×C59H(5,𝔽2)12yes—
203C23×C592−1+411yescharacteristic
204C23×C592−1+411yescharacteristic
205C23×C592−1+412yes—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—24no—
211C2×C4×C59—24no—
212C2×C4×C59—24no—
213C2×C4×C59—24no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—22no—
218C2×C4×C59—24no—
219C2×C4×C59—24no—
220C2×C4×C59—24no—
221C2×C4×C59—24no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—41no—
234C2×C4×C59—42no—
235C2×C4×C59—41no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—41no—
239C2×C4×C59—42no—
240C2×C4×C59—41no—
241C2×C4×C59—42no—
242C2×C4×C59—41no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—41no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250C2×C4×C59—42no—
251C2×C4×C59—42no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—42no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59#12114yes—
263C2×C4×C59#12314yes—
264#16701C5911yesmaximal, characteristic, direct product factor, Sylow
265C22×C59—42no—
266C22×C59—44no—
267C22×C59—44no—
268C22×C59—42no—
269C22×C59—42no—
270C22×C59—81no—
271C22×C59—81no—
272C22×C59—81no—
273C22×C59—81no—
274C22×C59—82no—
275C22×C59—82no—
276C22×C59C2×#12111yescharacteristic
277C22×C59C2×#12311yescharacteristic
278C22×C59#53211yescharacteristic
279C22×C59#53511yescharacteristic
280C22×C59#53511yescharacteristic
281C22×C59#53611yescharacteristic
282C22×C59#53611yescharacteristic
283C22×C59#53711yescharacteristic
284C22×C59#53711yescharacteristic
285C22×C59#53912yes—
286C22×C59#54012yes—
287C22×C59#54112yes—
288C22×C59#54211yescharacteristic
289C22×C59#54211yescharacteristic
290C22×C59#54212yes—
291C22×C59#54612yes—
292C22×C59#54712yes—
293C22×C59#55112yes—
294C22×C59#55212yes—
295C22×C59#55212yes—
296C22×C59#55912yes—
297C22×C59#56212yes—
298C22×C59#56312yes—
299C4×C59—24no—
300C4×C59—24no—
301C4×C59—42no—
302C4×C59—44no—
303C4×C59—42no—
304C4×C59—81no—
305C4×C59—82no—
306C4×C59—81no—
307C4×C59—82no—
308C4×C59—82no—
309C2×#399C2×C5911yescharacteristic
310C2×#397C2×C5911yescharacteristic
311C2×#388C2×C5911yescharacteristic
312C2×#382C2×C5911yescharacteristic, complemented
313#1445C2×C5911yescharacteristic, complemented
314#1445C2×C5911yescharacteristic, complemented
315#1441C2×C5912yescomplemented
316#1441C2×C5912yescomplemented
317#1440C2×C5912yes—
318#1439C2×C5912yes—
319C4⋊#95C2×C5911yescharacteristic, complemented
320C2×C59—82no—
321C2×C59#248611yescharacteristic
322C2×C59#249811yescharacteristic
323C2×C59#254411yescharacteristic
324C2×C59#262011yescharacteristic
325C2×C59#262411yescharacteristic
326C2×C59#266411yescharacteristic
327C2×C59#269812yes—
328C2×C59#270612yes—
329C2×C59#275412yes—
330C2×C59#277312yes—
331C2×C59#282011yescharacteristic
332C22×C4⋊C4C22×C5911yescharacteristic
333C22×C4⋊C4C22×C5911yescharacteristic
334C22×C4⋊C4C22×C5912yes—
335C22×C4⋊C4C22×C5912yes—
336C22×C4⋊C4C22×C5911yescharacteristic
337C22×C22⋊C4C22×C5911yescharacteristic
338C22×C22⋊C4C22×C5912yes—
339C22×C22⋊C4C22×C5911yescharacteristic
340C22×C22⋊C4C22×C5912yes—
341C22×C22⋊C4C22×C5911yescharacteristic
342C22×C42C22×C5911yescharacteristic
343#399—24no—
344#397—24no—
345#388—24no—
346#382—24no—
347C2×#95C22×C5911yescharacteristic
348C2×#95C22×C5912yes—
349C2×#95C22×C5911yescharacteristic
350C2×#95C22×C5912yes—
351C2×#95C22×C5912yes—
352C2×#95C22×C5911yescharacteristic
353C2×#95C22×C5911yescharacteristic
354C2×#95C22×C5912yes—
355C2×#95C22×C5912yes—
356C2×#95C22×C5912yes—
357C2×#95C22×C5912yes—
358C2×#95C22×C5912yes—
359C59#1670111yescharacteristic, direct product factor, Sylow
360C25C23×C5911yescharacteristic
361C23×C4C23×C5912yes—
362C23×C4C23×C5912yes—
363C23×C4C23×C5912yes—
364C23×C4C23×C5911yescharacteristic
365C23×C4C23×C5911yescharacteristic
366C23×C4C23×C5911yescharacteristic
367C23×C4C23×C5911yescharacteristic
368C23×C4C23×C5912yes—
369C23×C4C23×C5911yescharacteristic
370C23×C4C23×C5911yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4D4×C5914yes—
398C2×C42—24no—
399C2×C42D4×C5914yes—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—22no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24C2×D4×C5912yes—
423C24C24×C5911yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4C2×D4×C5912yes—
475C22×C4C2×D4×C5912yes—
476C22×C4C2×D4×C5912yes—
477C22×C4C2×D4×C5912yes—
478C22×C4C2×D4×C5912yes—
479C22×C4#41×C5914yes—
480C22×C4#41×C5912yes—
481C22×C4#41×C5914yes—
482C4⋊C4—48no—
483C4⋊C4—48no—
484C4⋊C4—44no—
485C4⋊C4—44no—
486C4⋊C4—44no—
487C22⋊C4—28no—
488C22⋊C4—48no—
489C22⋊C4—44no—
490C22⋊C4—48no—
491C22⋊C4—44no—
492C42—28no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—24no—
497C23—24no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23C22×D4×C5911yescharacteristic
517C23C22×D4×C5911yescharacteristic
518C23C2×#41×C5911yescharacteristic
519C23C2×#41×C5912yes—
520C23C2×#41×C5912yes—
521C23H(5,𝔽2)×C5911yescharacteristic
522C23H(5,𝔽2)×C5911yescharacteristic
523C23H(5,𝔽2)×C5912yes—
524C232−1+4×C5911yescharacteristic
525C232−1+4×C5911yescharacteristic
526C232−1+4×C5912yes—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4#121×C5914yes—
584C2×C4#123×C5914yes—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—44no—
589C22—44no—
590C22—81no—
591C22—82no—
592C22—82no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22C2×#121×C5911yescharacteristic
597C22C2×#123×C5911yescharacteristic
598C22C59×#53211yescharacteristic
599C22C59×#53511yescharacteristic
600C22C59×#53511yescharacteristic
601C22C59×#53611yescharacteristic
602C22C59×#53611yescharacteristic
603C22C59×#53711yescharacteristic
604C22C59×#53711yescharacteristic
605C22C59×#53912yes—
606C22C59×#54012yes—
607C22C59×#54112yes—
608C22C59×#54211yescharacteristic
609C22C59×#54212yes—
610C22C59×#54211yescharacteristic
611C22C59×#54612yes—
612C22C59×#54712yes—
613C22C59×#55112yes—
614C22C59×#55212yes—
615C22C59×#55212yes—
616C22C59×#55912yes—
617C22C59×#56212yes—
618C22C59×#56312yes—
619C4—24no—
620C4—24no—
621C4—42no—
622C4—42no—
623C4—44no—
624C4—82no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—82no—
629C2—82no—
630C2C59×#248611yescharacteristic
631C2C59×#249811yescharacteristic
632C2C59×#254411yescharacteristic
633C2C59×#262011yescharacteristic
634C2C59×#262411yescharacteristic
635C2C59×#266411yescharacteristic
636C2C59×#269812yes—
637C2C59×#270612yes—
638C2C59×#275412yes—
639C2C59×#277312yes—
640C2C59×#282011yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C59×#382C2semidirect
5. C59×#1445C2semidirect
6. C59×#1445C2semidirect
7. C59×#1441C2semidirect
8. C59×#1441C2semidirect
11. C59×C4⋊#95C2semidirect
264. #16701C59direct (N × H)
312. C2×#382C2×C59semidirect
313. #1445C2×C59semidirect
314. #1445C2×C59semidirect
315. #1441C2×C59semidirect
316. #1441C2×C59semidirect
319. C4⋊#95C2×C59semidirect
359. C59#16701direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3992
C2×C59×#3972
C2×C59×#3882
C2×C59×#3822
C59×#14452
C59×#14412
C59×#14402
C59×#14392
C59×C4⋊#952
#1670159