Finite Group Databasebeta

← C59×#16683 #28428792

Subgroups — C59×#16683 #28428792

Order 15104.

1338 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C59C211yesmaximal, characteristic
2C2×C59×#400C211yesmaximal, characteristic
3C2×C59×#398C211yesmaximal, characteristic
4C2×C59×#387C211yesmaximal, characteristic
5C59×#1445C211yesmaximal, characteristic
6C59×#1445C211yesmaximal, characteristic
7C59×#1444C212yesmaximal
8C59×#1442C212yesmaximal
9C59×#1442C212yesmaximal
10C59×#1441C212yesmaximal
11C59×#1434C211yesmaximal, characteristic
12C2×#125×C59—24no—
13C2×#125×C59—24no—
14C2×#125×C59—24no—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2212yes—
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C42×C59C2211yescharacteristic
23C59×#400—24no—
24C59×#398—24no—
25C59×#387—24no—
26C2×#95×C59C2211yescharacteristic
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2312yes—
50C23×C4×C59C2311yescharacteristic
51C23×C4×C59C2311yescharacteristic
52#125×C59—232no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—24no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—24no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—24no—
68C2×C4⋊C4×C59—22no—
69C2×C4⋊C4×C59—22no—
70C2×C4⋊C4×C59—24no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59D414yes—
73C2×C4⋊C4×C59D414yes—
74C2×C42×C59—22no—
75C2×C42×C59—22no—
76C2×C42×C59D414yes—
77#95×C59—22no—
78#95×C59—22no—
79#95×C59—22no—
80#95×C59—22no—
81#95×C59—22no—
82#95×C59—24no—
83#95×C59—24no—
84#95×C59—22no—
85#95×C59—24no—
86#95×C59—24no—
87#95×C59—24no—
88#95×C59—24no—
89#95×C59—24no—
90#95×C59—42no—
91#95×C59—42no—
92C24×C59C2411yescharacteristic
93C22×C4×C59—22no—
94C22×C4×C59—22no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—21no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—21no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—21no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—21no—
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—21no—
149C22×C4×C59—22no—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×D414yes—
152C22×C4×C59C2×D412yes—
153C22×C4×C59C2×D414yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59#4114yes—
158C22×C4×C59#4112yes—
159C22×C4×C59#4112yes—
160C4⋊C4×C59—28no—
161C4⋊C4×C59—216no—
162C4⋊C4×C59—216no—
163C4⋊C4×C59—28no—
164C4⋊C4×C59—28no—
165C4⋊C4×C59—48no—
166C4⋊C4×C59—44no—
167C42×C59—28no—
168C23×C59C22×D411yescharacteristic
169C23×C59C22×D411yescharacteristic
170C23×C59C22×D411yescharacteristic
171C23×C59C2×#4111yescharacteristic
172C23×C59C2×#4111yescharacteristic
173C23×C59C2×#4112yes—
174C23×C59H(5,𝔽2)11yescharacteristic
175C23×C592−1+412yes—
176C23×C592−1+412yes—
177C23×C592−1+412yes—
178C23×C592−1+411yescharacteristic
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—24no—
182C2×C4×C59—24no—
183C2×C4×C59—22no—
184C2×C4×C59—22no—
185C2×C4×C59—24no—
186C2×C4×C59—24no—
187C2×C4×C59—22no—
188C2×C4×C59—22no—
189C2×C4×C59—22no—
190C2×C4×C59—22no—
191C2×C4×C59—22no—
192C2×C4×C59—22no—
193C2×C4×C59—24no—
194C2×C4×C59—22no—
195C2×C4×C59—24no—
196C2×C4×C59—24no—
197C2×C4×C59—24no—
198C2×C4×C59—24no—
199C2×C4×C59—22no—
200C2×C4×C59—24no—
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—41no—
204C2×C4×C59—42no—
205C2×C4×C59—41no—
206C2×C4×C59—42no—
207C2×C4×C59—41no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—41no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—42no—
218C2×C4×C59—41no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—41no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—41no—
235C2×C4×C59—42no—
236C2×C4×C59—41no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59#12014yes—
246#16683C5911yesmaximal, characteristic, direct product factor, Sylow
247C22×C59C2×#12011yescharacteristic
248C22×C59#52511yescharacteristic
249C22×C59#53211yescharacteristic
250C22×C59#53611yescharacteristic
251C22×C59#53611yescharacteristic
252C22×C59#53611yescharacteristic
253C22×C59#53612yes—
254C22×C59#53612yes—
255C22×C59#53711yescharacteristic
256C22×C59#53912yes—
257C22×C59#54112yes—
258C22×C59#54112yes—
259C22×C59#54112yes—
260C22×C59#54611yescharacteristic
261C22×C59#54711yescharacteristic
262C22×C59#54712yes—
263C22×C59#54811yescharacteristic
264C22×C59#54812yes—
265C22×C59#55011yescharacteristic
266C22×C59#55212yes—
267C22×C59#55212yes—
268C22×C59#56312yes—
269C22×C59#56412yes—
270C4×C59—24no—
271C4×C59—42no—
272C4×C59—42no—
273C4×C59—44no—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—44no—
277C4×C59—44no—
278C4×C59—81no—
279C4×C59—81no—
280C4×C59—82no—
281C22×#125C2×C5911yescharacteristic
282C2×#400C2×C5911yescharacteristic
283C2×#398C2×C5911yescharacteristic
284C2×#387C2×C5911yescharacteristic
285#1445C2×C5911yescharacteristic
286#1445C2×C5911yescharacteristic
287#1444C2×C5912yes—
288#1442C2×C5912yes—
289#1442C2×C5912yes—
290#1441C2×C5912yes—
291#1434C2×C5911yescharacteristic
292C2×C59#240711yescharacteristic
293C2×C59#243211yescharacteristic
294C2×C59#261111yescharacteristic
295C2×C59#261411yescharacteristic
296C2×C59#263411yescharacteristic
297C2×C59#266411yescharacteristic
298C2×C59#269012yes—
299C2×C59#271912yes—
300C2×C59#271912yes—
301C2×C59#272112yes—
302C2×C59#282211yescharacteristic
303C2×#125—24no—
304C2×#125—24no—
305C2×#125—24no—
306C22×C4⋊C4C22×C5911yescharacteristic
307C22×C4⋊C4C22×C5912yes—
308C22×C4⋊C4C22×C5912yes—
309C22×C4⋊C4C22×C5911yescharacteristic
310C22×C4⋊C4C22×C5912yes—
311C22×C4⋊C4C22×C5911yescharacteristic
312C22×C4⋊C4C22×C5911yescharacteristic
313C22×C42C22×C5911yescharacteristic
314#400—24no—
315#398—24no—
316#387—24no—
317C2×#95C22×C5911yescharacteristic
318C2×#95C22×C5912yes—
319C2×#95C22×C5911yescharacteristic
320C2×#95C22×C5912yes—
321C2×#95C22×C5912yes—
322C2×#95C22×C5912yes—
323C2×#95C22×C5911yescharacteristic
324C2×#95C22×C5912yes—
325C2×#95C22×C5911yescharacteristic
326C2×#95C22×C5911yescharacteristic
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5911yescharacteristic
330C2×#95C22×C5912yes—
331C2×#95C22×C5912yes—
332C59#1668311yescharacteristic, direct product factor, Sylow
333C23×C4C23×C5911yescharacteristic
334C23×C4C23×C5912yes—
335C23×C4C23×C5911yescharacteristic
336C23×C4C23×C5912yes—
337C23×C4C23×C5912yes—
338C23×C4C23×C5911yescharacteristic
339C23×C4C23×C5911yescharacteristic
340C23×C4C23×C5911yescharacteristic
341C23×C4C23×C5911yescharacteristic
342C23×C4C23×C5912yes—
343C23×C4C23×C5911yescharacteristic
344#125—232no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4D4×C5914yes—
365C2×C4⋊C4D4×C5914yes—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42D4×C5914yes—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—24no—
375#95—24no—
376#95—22no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—42no—
383#95—42no—
384C24C24×C5911yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4C2×D4×C5912yes—
443C22×C4C2×D4×C5914yes—
444C22×C4C2×D4×C5912yes—
445C22×C4C2×D4×C5914yes—
446C22×C4C2×D4×C5912yes—
447C22×C4C2×D4×C5912yes—
448C22×C4C2×D4×C5912yes—
449C22×C4#41×C5914yes—
450C22×C4#41×C5912yes—
451C22×C4#41×C5912yes—
452C4⋊C4—216no—
453C4⋊C4—216no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—48no—
458C4⋊C4—44no—
459C42—28no—
460C23C22×D4×C5911yescharacteristic
461C23C22×D4×C5911yescharacteristic
462C23C22×D4×C5911yescharacteristic
463C23C2×#41×C5911yescharacteristic
464C23C2×#41×C5911yescharacteristic
465C23C2×#41×C5912yes—
466C23H(5,𝔽2)×C5911yescharacteristic
467C232−1+4×C5912yes—
468C232−1+4×C5912yes—
469C232−1+4×C5912yes—
470C232−1+4×C5911yescharacteristic
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4#120×C5914yes—
538C22C2×#120×C5911yescharacteristic
539C22C59×#52511yescharacteristic
540C22C59×#53211yescharacteristic
541C22C59×#53611yescharacteristic
542C22C59×#53611yescharacteristic
543C22C59×#53611yescharacteristic
544C22C59×#53612yes—
545C22C59×#53612yes—
546C22C59×#53711yescharacteristic
547C22C59×#53912yes—
548C22C59×#54112yes—
549C22C59×#54112yes—
550C22C59×#54112yes—
551C22C59×#54611yescharacteristic
552C22C59×#54711yescharacteristic
553C22C59×#54712yes—
554C22C59×#54811yescharacteristic
555C22C59×#54812yes—
556C22C59×#55011yescharacteristic
557C22C59×#55212yes—
558C22C59×#55212yes—
559C22C59×#56312yes—
560C22C59×#56412yes—
561C4—24no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—44no—
569C4—81no—
570C4—81no—
571C4—82no—
572C2C59×#240711yescharacteristic
573C2C59×#243211yescharacteristic
574C2C59×#261111yescharacteristic
575C2C59×#261411yescharacteristic
576C2C59×#263411yescharacteristic
577C2C59×#266411yescharacteristic
578C2C59×#269012yes—
579C2C59×#271912yes—
580C2C59×#271912yes—
581C2C59×#272112yes—
582C2C59×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C59C24
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
246. #16683C59direct (N × H)
332. C59#16683direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C592
C2×C59×#4002
C2×C59×#3982
C2×C59×#3872
C59×#14452
C59×#14442
C59×#14422
C59×#14412
C59×#14342
#1668359