Finite Group Databasebeta

← C59×#13901 #28426010

Subgroups — C59×#13901 #28426010

Order 15104.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#383C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
3C22×#95×C59C211yesmaximal, characteristic
4C59×#1443C212yesmaximal, complemented
5C59×#1443C212yesmaximal, complemented
6C59×#1434C211yesmaximal, characteristic, complemented
7C59×#1434C211yesmaximal, characteristic, complemented
8C59×#1434C211yesmaximal, characteristic, complemented
9C59×C22⋊#95C211yesmaximal, characteristic
10C59×C22⋊#95C212yesmaximal
11C59×C22⋊#95C212yesmaximal
12C24×C4×C59C2212yes—
13C24×C4×C59C2211yescharacteristic
14C22×C22⋊C4×C59C2212yes—
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2211yescharacteristic
17C22×C42×C59C2211yescharacteristic
18C22×C42×C59C2211yescharacteristic
19C59×#383—24no—
20C4×C22⋊C4×C59C418yescomplemented
21C2×#95×C59—24no—
22C2×#95×C59C2211yescharacteristic
23C2×#95×C59C2212yes—
24C2×#95×C59C2211yescharacteristic
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2211yescharacteristic
37C2×#95×C59C2211yescharacteristic
38C25×C59C2311yescharacteristic
39C23×C4×C59—24no—
40C23×C4×C59—24no—
41C23×C4×C59—24no—
42C23×C4×C59—22no—
43C23×C4×C59—24no—
44C23×C4×C59—22no—
45C23×C4×C59—24no—
46C23×C4×C59—24no—
47C23×C4×C59—42no—
48C23×C4×C59—42no—
49C23×C4×C59—42no—
50C23×C4×C59C2×C414yes—
51C23×C4×C59C2312yes—
52C23×C4×C59C2312yes—
53C23×C4×C59C2311yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2311yescharacteristic
58C23×C4×C59C2312yes—
59C23×C4×C59C2312yes—
60C23×C4×C59C2311yescharacteristic
61C2×C22⋊C4×C59—22no—
62C2×C22⋊C4×C59—24no—
63C2×C22⋊C4×C59—22no—
64C2×C22⋊C4×C59—24no—
65C2×C22⋊C4×C59—24no—
66C2×C22⋊C4×C59—24no—
67C2×C22⋊C4×C59C2×C414yes—
68C2×C22⋊C4×C59C2×C414yes—
69C2×C42×C59—22no—
70C2×C42×C59—22no—
71C2×C42×C59—42no—
72C2×C42×C59C2×C414yescomplemented
73C2×C42×C59C2×C414yescomplemented
74#95×C59—24no—
75#95×C59—22no—
76#95×C59—24no—
77#95×C59—24no—
78#95×C59—22no—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—22no—
82#95×C59—42no—
83#95×C59—42no—
84#95×C59—42no—
85#95×C59—42no—
86#95×C59—42no—
87#95×C59C2×C414yescomplemented
88#95×C59C2×C414yescomplemented
89#95×C59D414yes—
90C24×C59—21no—
91C24×C59—21no—
92C24×C59—22no—
93C24×C59—22no—
94C24×C59—21no—
95C24×C59—21no—
96C24×C59C22×C412yes—
97C24×C59#4112yes—
98C24×C59#4114yes—
99C24×C59#4112yes—
100C24×C59#4114yes—
101C24×C59C2411yescharacteristic
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—216no—
105C22×C4×C59—28no—
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
117C22×C4×C59—21no—
118C22×C4×C59—21no—
119C22×C4×C59—21no—
120C22×C4×C59—22no—
121C22×C4×C59—21no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—28no—
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—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—44no—
156C22×C4×C59—48no—
157C22×C4×C59—48no—
158C22×C4×C59—48no—
159C22×C4×C59—48no—
160C22×C4×C59—48no—
161C22×C4×C59—48no—
162C22×C4×C59—48no—
163C22×C4×C59—48no—
164C22×C4×C59C22×C412yes—
165C22×C4×C59C22×C412yes—
166C22×C4×C59C22×C412yes—
167C22×C4×C59C22×C412yes—
168C22×C4×C59C22×C412yes—
169C22×C4×C59C22×C412yes—
170C22×C4×C59C2×D414yes—
171C22×C4×C59C2×D412yes—
172C22×C4×C59#4114yes—
173C22×C4×C59#4112yes—
174C22⋊C4×C59—28no—
175C22⋊C4×C59—28no—
176C22⋊C4×C59—48no—
177C42×C59—28no—
178C42×C59—44no—
179C23×C59—22no—
180C23×C59—22no—
181C23×C59—22no—
182C23×C59—22no—
183C23×C59—24no—
184C23×C59—24no—
185C23×C59—24no—
186C23×C59—24no—
187C23×C59—24no—
188C23×C59—22no—
189C23×C59—22no—
190C23×C59—24no—
191C23×C59—24no—
192C23×C59—24no—
193C23×C59—24no—
194C23×C59—22no—
195C23×C59—22no—
196C23×C59—24no—
197C23×C59#11714yes—
198C23×C59#11714yes—
199C23×C59#11714yes—
200C23×C59#12618yes—
201C23×C59#12618yes—
202C23×C59C23×C411yescharacteristic
203C23×C59C22×D411yescharacteristic
204C23×C59C2×#4112yes—
205C23×C59C2×#4112yes—
206C23×C59C2×#4111yescharacteristic
207C23×C59C2×#4111yescharacteristic
208C23×C59C2×#4111yescharacteristic
209C23×C59C2×#4112yes—
210C23×C59H(5,𝔽2)12yes—
211C23×C59H(5,𝔽2)11yescharacteristic
212C23×C592−1+411yescharacteristic
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—24no—
216C2×C4×C59—24no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
222C2×C4×C59—22no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—22no—
231C2×C4×C59—22no—
232C2×C4×C59—24no—
233C2×C4×C59—24no—
234C2×C4×C59—24no—
235C2×C4×C59—24no—
236C2×C4×C59—24no—
237C2×C4×C59—24no—
238C2×C4×C59—416no—
239C2×C4×C59—432no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—41no—
249C2×C4×C59—42no—
250C2×C4×C59—42no—
251C2×C4×C59—42no—
252C2×C4×C59—41no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—42no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59C4×D414yes—
275#13901C5911yesmaximal, characteristic, direct product factor, Sylow
276C22×C59—24no—
277C22×C59—24no—
278C22×C59—24no—
279C22×C59—24no—
280C22×C59—24no—
281C22×C59—28no—
282C22×C59—28no—
283C22×C59—28no—
284C22×C59—28no—
285C22×C59—24no—
286C22×C59#38318yescomplemented
287C22×C59C2×#11711yescharacteristic
288C22×C59C2×#11711yescharacteristic
289C22×C59C2×#11711yescharacteristic
290C22×C59C2×C4×D411yescharacteristic
291C22×C59C4×#4111yescharacteristic
292C22×C59#51811yescharacteristic
293C22×C59#52011yescharacteristic
294C22×C59#52512yes—
295C22×C59C2×#12612yes—
296C22×C59C2×#12612yes—
297C22×C59#52912yes—
298C22×C59#53812yes—
299C22×C59#53912yes—
300C22×C59#54612yes—
301C22×C59#54611yescharacteristic
302C22×C59#54811yescharacteristic
303C22×C59#55112yes—
304C22×C59#55112yes—
305C22×C59#55112yes—
306C22×C59#55212yes—
307C22×C59#55211yescharacteristic
308C22×C59#55311yescharacteristic
309C22×C59#55312yes—
310C4×C59—24no—
311C4×C59—42no—
312C4×C59—42no—
313C4×C59—42no—
314C4×C59—42no—
315C4×C59—44no—
316C4×C59—44no—
317C4×C59—42no—
318C4×C59—82no—
319C4×C59—82no—
320C2×#383C2×C5911yescharacteristic, complemented
321C2×C4×C22⋊C4C2×C5911yescharacteristic
322C22×#95C2×C5911yescharacteristic
323#1443C2×C5912yescomplemented
324#1443C2×C5912yescomplemented
325#1434C2×C5911yescharacteristic, complemented
326#1434C2×C5911yescharacteristic, complemented
327#1434C2×C5911yescharacteristic, complemented
328C22⋊#95C2×C5911yescharacteristic
329C22⋊#95C2×C5912yes—
330C22⋊#95C2×C5912yes—
331C2×C59—28no—
332C2×C59C2×#38311yescharacteristic
333C2×C59#229011yescharacteristic
334C2×C59#231811yescharacteristic
335C2×C59#234211yescharacteristic
336C2×C59#234311yescharacteristic
337C2×C59#235211yescharacteristic
338C2×C59#235311yescharacteristic
339C2×C59#248012yes—
340C2×C59#248112yes—
341C2×C59#249312yes—
342C2×C59#251012yes—
343C24×C4C22×C5912yes—
344C24×C4C22×C5911yescharacteristic
345C22×C22⋊C4C22×C5912yes—
346C22×C22⋊C4C22×C5911yescharacteristic
347C22×C22⋊C4C22×C5911yescharacteristic
348C22×C42C22×C5911yescharacteristic
349C22×C42C22×C5911yescharacteristic
350#383—24no—
351C4×C22⋊C4C4×C5918yescomplemented
352C2×#95—24no—
353C2×#95C22×C5911yescharacteristic
354C2×#95C22×C5912yes—
355C2×#95C22×C5912yes—
356C2×#95C22×C5911yescharacteristic
357C2×#95C22×C5912yes—
358C2×#95C22×C5912yes—
359C2×#95C22×C5911yescharacteristic
360C2×#95C22×C5912yes—
361C2×#95C22×C5912yes—
362C2×#95C22×C5912yes—
363C2×#95C22×C5912yes—
364C2×#95C22×C5912yes—
365C2×#95C22×C5912yes—
366C2×#95C22×C5911yescharacteristic
367C2×#95C22×C5911yescharacteristic
368C2×#95C22×C5911yescharacteristic
369C59#1390111yescharacteristic, direct product factor, Sylow
370C25C23×C5911yescharacteristic
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4C2×C4×C5914yes—
383C23×C4C23×C5912yes—
384C23×C4C23×C5912yes—
385C23×C4C23×C5911yescharacteristic
386C23×C4C23×C5911yescharacteristic
387C23×C4C23×C5911yescharacteristic
388C23×C4C23×C5911yescharacteristic
389C23×C4C23×C5911yescharacteristic
390C23×C4C23×C5912yes—
391C23×C4C23×C5912yes—
392C23×C4C23×C5911yescharacteristic
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4C2×C4×C5914yes—
400C2×C22⋊C4C2×C4×C5914yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—42no—
404C2×C42C2×C4×C5914yescomplemented
405C2×C42C2×C4×C5914yescomplemented
406#95—24no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95C2×C4×C5914yescomplemented
420#95C2×C4×C5914yescomplemented
421#95D4×C5914yes—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24C22×C4×C5912yes—
429C24#41×C5912yes—
430C24#41×C5914yes—
431C24#41×C5912yes—
432C24#41×C5914yes—
433C24C24×C5911yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4C22×C4×C5912yes—
497C22×C4C22×C4×C5912yes—
498C22×C4C22×C4×C5912yes—
499C22×C4C22×C4×C5912yes—
500C22×C4C22×C4×C5912yes—
501C22×C4C22×C4×C5912yes—
502C22×C4C2×D4×C5914yes—
503C22×C4C2×D4×C5912yes—
504C22×C4#41×C5914yes—
505C22×C4#41×C5912yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—48no—
509C42—28no—
510C42—44no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—22no—
528C23—24no—
529C23#117×C5914yes—
530C23#117×C5914yes—
531C23#117×C5914yes—
532C23#126×C5918yes—
533C23#126×C5918yes—
534C23C23×C4×C5911yescharacteristic
535C23C22×D4×C5911yescharacteristic
536C23C2×#41×C5912yes—
537C23C2×#41×C5912yes—
538C23C2×#41×C5911yescharacteristic
539C23C2×#41×C5911yescharacteristic
540C23C2×#41×C5911yescharacteristic
541C23C2×#41×C5912yes—
542C23H(5,𝔽2)×C5912yes—
543C23H(5,𝔽2)×C5911yescharacteristic
544C232−1+4×C5911yescharacteristic
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—416no—
571C2×C4—432no—
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—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4C4×D4×C5914yes—
607C22—28no—
608C22—28no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—28no—
616C22—28no—
617C22C59×#38318yescomplemented
618C22C2×#117×C5911yescharacteristic
619C22C2×#117×C5911yescharacteristic
620C22C2×#117×C5911yescharacteristic
621C22C2×C4×D4×C5911yescharacteristic
622C22C4×#41×C5911yescharacteristic
623C22C59×#51811yescharacteristic
624C22C59×#52011yescharacteristic
625C22C59×#52512yes—
626C22C2×#126×C5912yes—
627C22C2×#126×C5912yes—
628C22C59×#52912yes—
629C22C59×#53812yes—
630C22C59×#53912yes—
631C22C59×#54612yes—
632C22C59×#54611yescharacteristic
633C22C59×#54811yescharacteristic
634C22C59×#55112yes—
635C22C59×#55112yes—
636C22C59×#55112yes—
637C22C59×#55211yescharacteristic
638C22C59×#55212yes—
639C22C59×#55311yescharacteristic
640C22C59×#55312yes—
641C4—24no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—44no—
648C4—44no—
649C4—82no—
650C4—82no—
651C2—28no—
652C2C2×C59×#38311yescharacteristic
653C2C59×#229011yescharacteristic
654C2C59×#231811yescharacteristic
655C2C59×#234211yescharacteristic
656C2C59×#234311yescharacteristic
657C2C59×#235211yescharacteristic
658C2C59×#235311yescharacteristic
659C2C59×#248012yes—
660C2C59×#248112yes—
661C2C59×#249312yes—
662C2C59×#251012yes—
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#383C2semidirect
4. C59×#1443C2semidirect
5. C59×#1443C2semidirect
6. C59×#1434C2semidirect
7. C59×#1434C2semidirect
8. C59×#1434C2semidirect
20. C4×C22⋊C4×C59C4semidirect
72. C2×C42×C59C2×C4semidirect
73. C2×C42×C59C2×C4semidirect
87. #95×C59C2×C4semidirect
88. #95×C59C2×C4semidirect
275. #13901C59direct (N × H)
286. C22×C59#383semidirect
320. C2×#383C2×C59semidirect
323. #1443C2×C59semidirect
324. #1443C2×C59semidirect
325. #1434C2×C59semidirect
326. #1434C2×C59semidirect
327. #1434C2×C59semidirect
351. C4×C22⋊C4C4×C59semidirect
369. C59#13901direct (N × H)
404. C2×C42C2×C4×C59semidirect
405. C2×C42C2×C4×C59semidirect
419. #95C2×C4×C59semidirect
420. #95C2×C4×C59semidirect
617. C22C59×#383semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3832
C2×C4×C22⋊C4×C592
C22×#95×C592
C59×#14432
C59×#14342
C59×C22⋊#952
#1390159