Finite Group Databasebeta

← C59×#16321 #28428430

Subgroups — C59×#16321 #28428430

Order 15104.

1582 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#399C211yesmaximal, characteristic
2C2×C59×#398C212yesmaximal, complemented
3C2×C59×#385C211yesmaximal, characteristic
4C2×C59×#385C212yesmaximal
5C59×#1444C212yesmaximal, complemented
6C59×#1444C212yesmaximal, complemented
7C59×#1443C212yesmaximal, complemented
8C59×#1440C212yesmaximal
9C59×#1439C211yesmaximal, characteristic
10C24×C4×C59C2211yescharacteristic
11C22×C4⋊C4×C59C2212yes—
12C22×C4⋊C4×C59C2212yes—
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2211yescharacteristic
21C59×#399—24no—
22C59×#398—28no—
23C59×#385—24no—
24C59×#385—28no—
25C2×#95×C59C2212yes—
26C2×#95×C59C2212yes—
27C2×#95×C59C2212yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C25×C59C2311yescharacteristic
36C23×C4×C59—22no—
37C23×C4×C59—24no—
38C23×C4×C59—41no—
39C23×C4×C59—42no—
40C23×C4×C59—41no—
41C23×C4×C59C2312yes—
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2312yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2312yes—
49C2×C4⋊C4×C59—24no—
50C2×C4⋊C4×C59—24no—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—24no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—42no—
59C2×C4⋊C4×C59—41no—
60C2×C4⋊C4×C59—42no—
61C2×C4⋊C4×C59—42no—
62C2×C4⋊C4×C59—42no—
63C2×C4⋊C4×C59—42no—
64C2×C4⋊C4×C59—41no—
65C2×C4⋊C4×C59—41no—
66C2×C22⋊C4×C59—22no—
67C2×C22⋊C4×C59—24no—
68C2×C22⋊C4×C59—22no—
69C2×C22⋊C4×C59—24no—
70C2×C22⋊C4×C59—24no—
71C2×C22⋊C4×C59—24no—
72C2×C22⋊C4×C59—24no—
73C2×C22⋊C4×C59—41no—
74C2×C22⋊C4×C59—41no—
75C2×C22⋊C4×C59—42no—
76C2×C22⋊C4×C59D414yes—
77C2×C22⋊C4×C59Q814yes—
78#95×C59—24no—
79#95×C59—24no—
80#95×C59—24no—
81#95×C59—24no—
82#95×C59—22no—
83#95×C59—24no—
84#95×C59—24no—
85#95×C59—41no—
86#95×C59—42no—
87#95×C59D418yes—
88C24×C59—22no—
89C24×C59—22no—
90C24×C59—21no—
91C24×C59—21no—
92C24×C59—22no—
93C24×C59—21no—
94C24×C59—21no—
95C24×C59—22no—
96C24×C59C2×D412yes—
97C24×C59C2×Q812yes—
98C24×C59#4112yes—
99C24×C59C2411yescharacteristic
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
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—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—22no—
137C22×C4×C59—22no—
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—44no—
146C22×C4×C59—48no—
147C22×C4×C59—48no—
148C22×C4×C59—44no—
149C22×C4×C59—44no—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×D414yes—
152C22×C4×C59C2×D414yes—
153C22×C4×C59C2×D414yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×Q814yes—
156C22×C4×C59#4114yes—
157C4⋊C4×C59—48no—
158C4⋊C4×C59—44no—
159C4⋊C4×C59—48no—
160C4⋊C4×C59—48no—
161C4⋊C4×C59—44no—
162C4⋊C4×C59—48no—
163C22⋊C4×C59—216no—
164C22⋊C4×C59—28no—
165C22⋊C4×C59—44no—
166C22⋊C4×C59—48no—
167C23×C59—24no—
168C23×C59—22no—
169C23×C59—22no—
170C23×C59—22no—
171C23×C59—22no—
172C23×C59—24no—
173C23×C59—22no—
174C23×C59—22no—
175C23×C59—24no—
176C23×C59—24no—
177C23×C59—24no—
178C23×C59—24no—
179C23×C59—42no—
180C23×C59—42no—
181C23×C59—42no—
182C23×C59—42no—
183C23×C59—41no—
184C23×C59—42no—
185C23×C59—41no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—42no—
189C23×C59C22⋊Q814yes—
190C23×C59C22×D411yescharacteristic
191C23×C59C22×D412yes—
192C23×C59C22×Q811yescharacteristic
193C23×C59C2×#4111yescharacteristic
194C23×C59C2×#4112yes—
195C23×C59H(5,𝔽2)11yescharacteristic
196C23×C59H(5,𝔽2)11yescharacteristic
197C23×C59H(5,𝔽2)12yes—
198C23×C592−1+411yescharacteristic
199C23×C592−1+412yes—
200C23×C592−1+411yescharacteristic
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—24no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—24no—
207C2×C4×C59—24no—
208C2×C4×C59—24no—
209C2×C4×C59—24no—
210C2×C4×C59—24no—
211C2×C4×C59—24no—
212C2×C4×C59—24no—
213C2×C4×C59—24no—
214C2×C4×C59—24no—
215C2×C4×C59—24no—
216C2×C4×C59—24no—
217C2×C4×C59—24no—
218C2×C4×C59—24no—
219C2×C4×C59—24no—
220C2×C4×C59—416no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
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—42no—
234C2×C4×C59—42no—
235C2×C4×C59—41no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—41no—
243C2×C4×C59—41no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59—41no—
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—
254#16321C5911yesmaximal, characteristic, direct product factor, Sylow
255C22×C59—24no—
256C22×C59—28no—
257C22×C59—42no—
258C22×C59—44no—
259C22×C59—42no—
260C22×C59—42no—
261C22×C59—44no—
262C22×C59—42no—
263C22×C59—44no—
264C22×C59—42no—
265C22×C59—42no—
266C22×C59C2×C22⋊Q811yescharacteristic
267C22×C59#52512yes—
268C22×C59#53411yescharacteristic
269C22×C59#53512yes—
270C22×C59#53611yescharacteristic
271C22×C59#53612yes—
272C22×C59#53911yescharacteristic
273C22×C59#53912yes—
274C22×C59#53911yescharacteristic
275C22×C59#53912yes—
276C22×C59#53912yes—
277C22×C59#54411yescharacteristic
278C22×C59#54411yescharacteristic
279C22×C59D4211yescharacteristic
280C22×C59D4212yes—
281C22×C59#54712yes—
282C22×C59#54712yes—
283C22×C59D4×Q812yes—
284C22×C59#55412yes—
285C22×C59#55911yescharacteristic
286C22×C59#56011yescharacteristic
287C22×C59#56311yescharacteristic
288C22×C59#56312yes—
289C4×C59—44no—
290C4×C59—42no—
291C4×C59—44no—
292C4×C59—44no—
293C4×C59—44no—
294C4×C59—44no—
295C4×C59—42no—
296C4×C59—82no—
297C2×#399C2×C5911yescharacteristic
298C2×#398C2×C5912yescomplemented
299C2×#385C2×C5912yes—
300C2×#385C2×C5911yescharacteristic
301#1444C2×C5912yescomplemented
302#1444C2×C5912yescomplemented
303#1443C2×C5912yescomplemented
304#1440C2×C5912yes—
305#1439C2×C5911yescharacteristic
306C2×C59—44no—
307C2×C59#244912yes—
308C2×C59#245511yescharacteristic
309C2×C59#262711yescharacteristic
310C2×C59#263312yes—
311C2×C59#266911yescharacteristic
312C2×C59#267711yescharacteristic
313C2×C59#268012yes—
314C2×C59#272012yes—
315C2×C59#272411yescharacteristic
316C2×C59#280711yescharacteristic
317C2×C59#283411yescharacteristic
318C24×C4C22×C5911yescharacteristic
319C22×C4⋊C4C22×C5911yescharacteristic
320C22×C4⋊C4C22×C5912yes—
321C22×C4⋊C4C22×C5912yes—
322C22×C4⋊C4C22×C5912yes—
323C22×C4⋊C4C22×C5911yescharacteristic
324C22×C4⋊C4C22×C5912yes—
325C22×C22⋊C4C22×C5912yes—
326C22×C22⋊C4C22×C5912yes—
327C22×C22⋊C4C22×C5911yescharacteristic
328C22×C22⋊C4C22×C5911yescharacteristic
329#399—24no—
330#398—28no—
331#385—24no—
332#385—28no—
333C2×#95C22×C5912yes—
334C2×#95C22×C5912yes—
335C2×#95C22×C5911yescharacteristic
336C2×#95C22×C5912yes—
337C2×#95C22×C5912yes—
338C2×#95C22×C5912yes—
339C2×#95C22×C5912yes—
340C2×#95C22×C5911yescharacteristic
341C2×#95C22×C5912yes—
342C2×#95C22×C5912yes—
343C59#1632111yescharacteristic, direct product factor, Sylow
344C25C23×C5911yescharacteristic
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—41no—
348C23×C4—42no—
349C23×C4—41no—
350C23×C4C23×C5912yes—
351C23×C4C23×C5911yescharacteristic
352C23×C4C23×C5912yes—
353C23×C4C23×C5912yes—
354C23×C4C23×C5911yescharacteristic
355C23×C4C23×C5912yes—
356C23×C4C23×C5912yes—
357C23×C4C23×C5912yes—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4D4×C5914yes—
386C2×C22⋊C4Q8×C5914yes—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—22no—
392#95—24no—
393#95—24no—
394#95—41no—
395#95—42no—
396#95D4×C5918yes—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24C2×D4×C5912yes—
406C24C2×Q8×C5912yes—
407C24#41×C5912yes—
408C24C24×C5911yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—48no—
456C22×C4—48no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4C2×D4×C5912yes—
460C22×C4C2×D4×C5914yes—
461C22×C4C2×D4×C5914yes—
462C22×C4C2×D4×C5914yes—
463C22×C4C2×D4×C5912yes—
464C22×C4C2×Q8×C5914yes—
465C22×C4#41×C5914yes—
466C4⋊C4—48no—
467C4⋊C4—44no—
468C4⋊C4—48no—
469C4⋊C4—48no—
470C4⋊C4—44no—
471C4⋊C4—48no—
472C22⋊C4—216no—
473C22⋊C4—28no—
474C22⋊C4—44no—
475C22⋊C4—48no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23C22⋊Q8×C5914yes—
499C23C22×D4×C5911yescharacteristic
500C23C22×D4×C5912yes—
501C23C22×Q8×C5911yescharacteristic
502C23C2×#41×C5911yescharacteristic
503C23C2×#41×C5912yes—
504C23H(5,𝔽2)×C5911yescharacteristic
505C23H(5,𝔽2)×C5911yescharacteristic
506C23H(5,𝔽2)×C5912yes—
507C232−1+4×C5911yescharacteristic
508C232−1+4×C5912yes—
509C232−1+4×C5911yescharacteristic
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—416no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C22—24no—
564C22—28no—
565C22—42no—
566C22—42no—
567C22—44no—
568C22—42no—
569C22—42no—
570C22—44no—
571C22—42no—
572C22—44no—
573C22—42no—
574C22C2×C22⋊Q8×C5911yescharacteristic
575C22C59×#52512yes—
576C22C59×#53411yescharacteristic
577C22C59×#53512yes—
578C22C59×#53611yescharacteristic
579C22C59×#53612yes—
580C22C59×#53912yes—
581C22C59×#53911yescharacteristic
582C22C59×#53912yes—
583C22C59×#53911yescharacteristic
584C22C59×#53912yes—
585C22C59×#54411yescharacteristic
586C22C59×#54411yescharacteristic
587C22D42×C5911yescharacteristic
588C22D42×C5912yes—
589C22C59×#54712yes—
590C22C59×#54712yes—
591C22D4×Q8×C5912yes—
592C22C59×#55412yes—
593C22C59×#55911yescharacteristic
594C22C59×#56011yescharacteristic
595C22C59×#56311yescharacteristic
596C22C59×#56312yes—
597C4—44no—
598C4—44no—
599C4—42no—
600C4—44no—
601C4—44no—
602C4—44no—
603C4—42no—
604C4—82no—
605C2—44no—
606C2C59×#244912yes—
607C2C59×#245511yescharacteristic
608C2C59×#262711yescharacteristic
609C2C59×#263312yes—
610C2C59×#266911yescharacteristic
611C2C59×#267711yescharacteristic
612C2C59×#268012yes—
613C2C59×#272012yes—
614C2C59×#272411yescharacteristic
615C2C59×#280711yescharacteristic
616C2C59×#283411yescharacteristic
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
2. C2×C59×#398C2semidirect
5. C59×#1444C2semidirect
6. C59×#1444C2semidirect
7. C59×#1443C2semidirect
254. #16321C59direct (N × H)
298. C2×#398C2×C59semidirect
301. #1444C2×C59semidirect
302. #1444C2×C59semidirect
303. #1443C2×C59semidirect
343. C59#16321direct (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×#3982
C2×C59×#3852
C59×#14442
C59×#14432
C59×#14402
C59×#14392
#1632159