Finite Group Databasebeta

← C59×#14818 #28426927

Subgroups — C59×#14818 #28426927

Order 15104.

1418 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#398C211yesmaximal, characteristic
2C2×C59×#389C211yesmaximal, characteristic
3C2×C59×#389C212yesmaximal
4C2×C59×#387C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C59C211yesmaximal, characteristic
6C59×#1445C211yesmaximal, characteristic
7C59×#1444C211yesmaximal, characteristic
8C59×#1441C211yesmaximal, characteristic
9C59×#1441C212yesmaximal
10C59×#1441C212yesmaximal
11C59×#1436C212yesmaximal
12C22×C4⋊C4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2212yes—
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2212yes—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C4⋊C4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2212yes—
20C22×C42×C59C2212yes—
21C22×C42×C59C2211yescharacteristic
22C59×#398—24no—
23C59×#389—28no—
24C59×#389—24no—
25C59×#387—24no—
26C4×C4⋊C4×C59—24no—
27C2×#95×C59C2211yescharacteristic
28C2×#95×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2212yes—
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C23×C4×C59C2311yescharacteristic
41C23×C4×C59C2311yescharacteristic
42C23×C4×C59C2312yes—
43C23×C4×C59C2311yescharacteristic
44C23×C4×C59C2311yescharacteristic
45C23×C4×C59C2312yes—
46C23×C4×C59C2312yes—
47C23×C4×C59C2311yescharacteristic
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2312yes—
51C2×C4⋊C4×C59—24no—
52C2×C4⋊C4×C59—22no—
53C2×C4⋊C4×C59—24no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—24no—
57C2×C4⋊C4×C59—24no—
58C2×C4⋊C4×C59—22no—
59C2×C4⋊C4×C59—24no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—24no—
62C2×C4⋊C4×C59—24no—
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—24no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—22no—
68C2×C4⋊C4×C59—22no—
69C2×C4⋊C4×C59—24no—
70C2×C4⋊C4×C59—22no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59D414yes—
73C2×C4⋊C4×C59Q818yes—
74C2×C42×C59—22no—
75C2×C42×C59—22no—
76C2×C42×C59—24no—
77C2×C42×C59—24no—
78C2×C42×C59—42no—
79C2×C42×C59D414yes—
80#95×C59—22no—
81#95×C59—22no—
82#95×C59—22no—
83#95×C59—22no—
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—24no—
91#95×C59—42no—
92#95×C59D414yes—
93C24×C59C2411yescharacteristic
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—22no—
97C22×C4×C59—21no—
98C22×C4×C59—21no—
99C22×C4×C59—22no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—21no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—21no—
117C22×C4×C59—21no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—21no—
125C22×C4×C59—22no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
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—21no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—21no—
145C22×C4×C59—22no—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×D412yes—
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D414yes—
153C22×C4×C59C2×D412yes—
154C22×C4×C59C2×Q814yes—
155C22×C4×C59C2×Q814yes—
156C22×C4×C59C2×Q814yes—
157C22×C4×C59#4114yes—
158C22×C4×C59#4112yes—
159C22×C4×C59#4112yes—
160C22×C4×C59#4114yes—
161C4⋊C4×C59—28no—
162C4⋊C4×C59—216no—
163C4⋊C4×C59—28no—
164C4⋊C4×C59—216no—
165C4⋊C4×C59—48no—
166C4⋊C4×C59—44no—
167C4⋊C4×C59—48no—
168C4⋊C4×C59—44no—
169C42×C59—28no—
170C42×C59—48no—
171C23×C59C22×D411yescharacteristic
172C23×C59C22×D411yescharacteristic
173C23×C59C22×D411yescharacteristic
174C23×C59C22×Q812yes—
175C23×C59C2×#4111yescharacteristic
176C23×C59C2×#4111yescharacteristic
177C23×C59C2×#4112yes—
178C23×C59C2×#4112yes—
179C23×C59H(5,𝔽2)11yescharacteristic
180C23×C592−1+412yes—
181C23×C592−1+411yescharacteristic
182C2×C4×C59—22no—
183C2×C4×C59—22no—
184C2×C4×C59—24no—
185C2×C4×C59—22no—
186C2×C4×C59—24no—
187C2×C4×C59—22no—
188C2×C4×C59—24no—
189C2×C4×C59—22no—
190C2×C4×C59—22no—
191C2×C4×C59—24no—
192C2×C4×C59—22no—
193C2×C4×C59—24no—
194C2×C4×C59—24no—
195C2×C4×C59—22no—
196C2×C4×C59—24no—
197C2×C4×C59—22no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—22no—
201C2×C4×C59—24no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—24no—
205C2×C4×C59—24no—
206C2×C4×C59—24no—
207C2×C4×C59—24no—
208C2×C4×C59—24no—
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—24no—
212C2×C4×C59—24no—
213C2×C4×C59—42no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—41no—
221C2×C4×C59—42no—
222C2×C4×C59—41no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
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—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59#12114yes—
246C2×C4×C59#12114yes—
247C2×C4×C59C22⋊Q818yes—
248C2×C4×C59C4⋊Q814yes—
249#14818C5911yesmaximal, characteristic, direct product factor, Sylow
250C22×C59C2×#12111yescharacteristic
251C22×C59C2×#12111yescharacteristic
252C22×C59C2×C22⋊Q812yes—
253C22×C59#52511yescharacteristic
254C22×C59#52512yes—
255C22×C59#52912yes—
256C22×C59C2×C4⋊Q811yescharacteristic
257C22×C59#53211yescharacteristic
258C22×C59#53312yes—
259C22×C59#53611yescharacteristic
260C22×C59#53711yescharacteristic
261C22×C59#53912yes—
262C22×C59#54112yes—
263C22×C59D4211yescharacteristic
264C22×C59#54712yes—
265C22×C59#54711yescharacteristic
266C22×C59#54811yescharacteristic
267C22×C59D4×Q812yes—
268C22×C59#55212yes—
269C22×C59#55311yescharacteristic
270C22×C59#55412yes—
271C22×C59#55712yes—
272C22×C59#55712yes—
273C4×C59—24no—
274C4×C59—24no—
275C4×C59—24no—
276C4×C59—28no—
277C4×C59—42no—
278C4×C59—44no—
279C4×C59—42no—
280C4×C59—44no—
281C4×C59—81no—
282C4×C59—81no—
283C4×C59—82no—
284C2×#398C2×C5911yescharacteristic
285C2×#389C2×C5911yescharacteristic
286C2×#389C2×C5912yes—
287C2×#387C2×C5911yescharacteristic
288C2×C4×C4⋊C4C2×C5911yescharacteristic
289#1445C2×C5911yescharacteristic
290#1444C2×C5911yescharacteristic
291#1441C2×C5911yescharacteristic
292#1441C2×C5912yes—
293#1441C2×C5912yes—
294#1436C2×C5912yes—
295C2×C59#239211yescharacteristic
296C2×C59#241311yescharacteristic
297C2×C59#241611yescharacteristic
298C2×C59#244912yes—
299C2×C59#245312yes—
300C2×C59#246212yes—
301C2×C59#254611yescharacteristic
302C2×C59#258411yescharacteristic
303C2×C59#258512yes—
304C2×C59#266411yescharacteristic
305C2×C59#285711yescharacteristic
306C22×C4⋊C4C22×C5911yescharacteristic
307C22×C4⋊C4C22×C5911yescharacteristic
308C22×C4⋊C4C22×C5912yes—
309C22×C4⋊C4C22×C5912yes—
310C22×C4⋊C4C22×C5911yescharacteristic
311C22×C4⋊C4C22×C5912yes—
312C22×C4⋊C4C22×C5911yescharacteristic
313C22×C4⋊C4C22×C5912yes—
314C22×C42C22×C5912yes—
315C22×C42C22×C5911yescharacteristic
316#398—24no—
317#389—28no—
318#389—24no—
319#387—24no—
320C4×C4⋊C4—24no—
321C2×#95C22×C5912yes—
322C2×#95C22×C5911yescharacteristic
323C2×#95C22×C5912yes—
324C2×#95C22×C5912yes—
325C2×#95C22×C5911yescharacteristic
326C2×#95C22×C5911yescharacteristic
327C2×#95C22×C5912yes—
328C2×#95C22×C5912yes—
329C2×#95C22×C5911yescharacteristic
330C2×#95C22×C5912yes—
331C2×#95C22×C5911yescharacteristic
332C2×#95C22×C5912yes—
333C2×#95C22×C5911yescharacteristic
334C59#1481811yescharacteristic, direct product factor, Sylow
335C23×C4C23×C5912yes—
336C23×C4C23×C5911yescharacteristic
337C23×C4C23×C5911yescharacteristic
338C23×C4C23×C5911yescharacteristic
339C23×C4C23×C5911yescharacteristic
340C23×C4C23×C5912yes—
341C23×C4C23×C5912yes—
342C23×C4C23×C5911yescharacteristic
343C23×C4C23×C5911yescharacteristic
344C23×C4C23×C5911yescharacteristic
345C23×C4C23×C5912yes—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4D4×C5914yes—
368C2×C4⋊C4Q8×C5918yes—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—42no—
374C2×C42D4×C5914yes—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95D4×C5914yes—
388C24C24×C5911yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4C2×D4×C5912yes—
442C22×C4C2×D4×C5912yes—
443C22×C4C2×D4×C5912yes—
444C22×C4C2×D4×C5912yes—
445C22×C4C2×D4×C5912yes—
446C22×C4C2×D4×C5912yes—
447C22×C4C2×D4×C5914yes—
448C22×C4C2×D4×C5912yes—
449C22×C4C2×Q8×C5914yes—
450C22×C4C2×Q8×C5914yes—
451C22×C4C2×Q8×C5914yes—
452C22×C4#41×C5914yes—
453C22×C4#41×C5912yes—
454C22×C4#41×C5912yes—
455C22×C4#41×C5914yes—
456C4⋊C4—28no—
457C4⋊C4—216no—
458C4⋊C4—28no—
459C4⋊C4—216no—
460C4⋊C4—48no—
461C4⋊C4—44no—
462C4⋊C4—48no—
463C4⋊C4—44no—
464C42—28no—
465C42—48no—
466C23C22×D4×C5911yescharacteristic
467C23C22×D4×C5911yescharacteristic
468C23C22×D4×C5911yescharacteristic
469C23C22×Q8×C5912yes—
470C23C2×#41×C5911yescharacteristic
471C23C2×#41×C5911yescharacteristic
472C23C2×#41×C5912yes—
473C23C2×#41×C5912yes—
474C23H(5,𝔽2)×C5911yescharacteristic
475C232−1+4×C5912yes—
476C232−1+4×C5911yescharacteristic
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
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#121×C5914yes—
541C2×C4#121×C5914yes—
542C2×C4C22⋊Q8×C5918yes—
543C2×C4C4⋊Q8×C5914yes—
544C22C2×#121×C5911yescharacteristic
545C22C2×#121×C5911yescharacteristic
546C22C2×C22⋊Q8×C5912yes—
547C22C59×#52511yescharacteristic
548C22C59×#52512yes—
549C22C59×#52912yes—
550C22C2×C4⋊Q8×C5911yescharacteristic
551C22C59×#53211yescharacteristic
552C22C59×#53312yes—
553C22C59×#53611yescharacteristic
554C22C59×#53711yescharacteristic
555C22C59×#53912yes—
556C22C59×#54112yes—
557C22D42×C5911yescharacteristic
558C22C59×#54712yes—
559C22C59×#54711yescharacteristic
560C22C59×#54811yescharacteristic
561C22D4×Q8×C5912yes—
562C22C59×#55212yes—
563C22C59×#55311yescharacteristic
564C22C59×#55412yes—
565C22C59×#55712yes—
566C22C59×#55712yes—
567C4—24no—
568C4—24no—
569C4—24no—
570C4—28no—
571C4—42no—
572C4—44no—
573C4—42no—
574C4—44no—
575C4—81no—
576C4—81no—
577C4—82no—
578C2C59×#239211yescharacteristic
579C2C59×#241311yescharacteristic
580C2C59×#241611yescharacteristic
581C2C59×#244912yes—
582C2C59×#245312yes—
583C2C59×#246212yes—
584C2C59×#254611yescharacteristic
585C2C59×#258411yescharacteristic
586C2C59×#258512yes—
587C2C59×#266411yescharacteristic
588C2C59×#285711yescharacteristic
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
249. #14818C59direct (N × H)
334. C59#14818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3982
C2×C59×#3892
C2×C59×#3872
C2×C4×C4⋊C4×C592
C59×#14452
C59×#14442
C59×#14412
C59×#14362
#1481859