Finite Group Databasebeta

← C59×#18276 #28430385

Subgroups — C59×#18276 #28430385

Order 15104.

966 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3559C211yesmaximal, characteristic, complemented
2C59×#3109C211yesmaximal, characteristic, complemented
3C59×#3105C211yesmaximal, characteristic, complemented
4C59×#2562C211yesmaximal, characteristic, complemented
5C59×#1616C212yesmaximal, complemented
6C59×#1615C212yesmaximal, complemented
7C59×#1598C212yesmaximal, complemented
8C59×#1597C212yesmaximal, complemented
9C59×#1509C211yesmaximal, characteristic, complemented
10C59×#1502C211yesmaximal, characteristic, complemented
11C59×#1470C211yesmaximal, characteristic, complemented
12C59×#563—21no—
13C59×#562—21no—
14C59×#554—21no—
15C59×#553—21no—
16C59×#553—21no—
17C59×#547—22no—
18C59×#547—21no—
19C59×#544—21no—
20C59×#540—21no—
21C59×#539—22no—
22C59×#539C2212yes—
23C59×#537C2212yes—
24C59×#532C2211yescharacteristic
25C59×#529C2211yescharacteristic
26C2×#125×C59C2211yescharacteristic
27C2×C4×D4×C59C2211yescharacteristic
28C59×#484C2211yescharacteristic
29C59×#481C2211yescharacteristic
30C59×#481C2212yes—
31C59×#478—21no—
32C59×#476—21no—
33C59×#463—21no—
34C59×#459—21no—
35C59×#450C2211yescharacteristic
36C59×#447C2211yescharacteristic
37C59×#447C2212yes—
38C59×#442—22no—
39C4×SD16×C59—21no—
40C4×D8×C59—21no—
41C59×#432C2211yescharacteristic
42C59×#431C2211yescharacteristic
43C59×#400C2212yes—
44C59×#394C2212yes—
45C59×#388—22no—
46C59×#380—21no—
47C59×#380—21no—
48C4×C4⋊C4×C59C2211yescharacteristic
49C59×#328C2212yes—
50C59×#327C2212yes—
51C59×#327C2212yes—
52C59×#327C2212yes—
53C59×#324C2212yes—
54C59×#324C2212yes—
55C2×#41×C59—21no—
56C2×#41×C59—22no—
57C22×D4×C59C2311yescharacteristic
58C23×C4×C59—21no—
59C2×SD16×C59—21no—
60C2×D8×C59—21no—
61C2×D8×C59—22no—
62C4⋊Q8×C59—21no—
63C4⋊Q8×C59—22no—
64C4⋊Q8×C59D411yescharacteristic
65#127×C59D411yescharacteristic
66#126×C59—22no—
67#126×C59—22no—
68#126×C59—21no—
69#125×C59—21no—
70#125×C59—22no—
71#125×C59—21no—
72#125×C59—21no—
73#125×C59—21no—
74#125×C59—21no—
75#125×C59D411yescharacteristic
76#124×C59—21no—
77#124×C59D411yescharacteristic
78#123×C59—22no—
79#123×C59—22no—
80#123×C59—22no—
81#123×C59—22no—
82#123×C59—22no—
83#123×C59—21no—
84#123×C59—22no—
85C22⋊Q8×C59—22no—
86C22⋊Q8×C59—22no—
87C22⋊Q8×C59—22no—
88C22⋊Q8×C59—22no—
89C22⋊Q8×C59—22no—
90C22⋊Q8×C59—22no—
91C22⋊Q8×C59C2311yescharacteristic
92#121×C59—21no—
93#121×C59—22no—
94#121×C59—21no—
95#121×C59—22no—
96#121×C59—22no—
97#121×C59—21no—
98#121×C59—22no—
99#121×C59C2311yescharacteristic
100#121×C59C2312yes—
101C4×Q8×C59D411yescharacteristic
102C4×D4×C59—22no—
103C4×D4×C59—21no—
104C4×D4×C59—21no—
105C4×D4×C59—21no—
106C4×D4×C59—22no—
107C4×D4×C59—21no—
108C4×D4×C59—21no—
109C4×D4×C59—21no—
110C4×D4×C59—21no—
111C4×D4×C59—21no—
112C4×D4×C59D411yescharacteristic
113C4×D4×C59D412yes—
114#117×C59—21no—
115#117×C59—21no—
116C2×C4⋊C4×C59—22no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59D411yescharacteristic
121C2×C4⋊C4×C59D412yes—
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2312yes—
124C2×C22⋊C4×C59—22no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—22no—
127C2×C42×C59—21no—
128C2×C42×C59C2311yescharacteristic
129#107×C59—21no—
130#106×C59—21no—
131#106×C59—22no—
132C4⋊C8×C59—21no—
133C4⋊C8×C59—21no—
134#103×C59—21no—
135#102×C59—21no—
136#102×C59—22no—
137#102×C59—21no—
138#102×C59—21no—
139#102×C59—22no—
140C22⋊C8×C59C2311yescharacteristic
141C22⋊C8×C59C2311yescharacteristic
142C22⋊C8×C59C2312yes—
143#97×C59—21no—
144C4×C8×C59—21no—
145#95×C59—22no—
146#95×C59—22no—
147#95×C59C2312yes—
148C24×C59—21no—
149#41×C59—81no—
150#41×C59—81no—
151#41×C59—82no—
152#41×C59—82no—
153C2×Q8×C59—22no—
154C2×Q8×C59—21no—
155C2×Q8×C59C2×D411yescharacteristic
156C2×D4×C59—21no—
157C2×D4×C59—22no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—42no—
165C2×D4×C59C2×D411yescharacteristic
166C2×D4×C59C2×D412yes—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—21no—
171C22×C4×C59—22no—
172C22×C4×C59—21no—
173C22×C4×C59—22no—
174C22×C4×C59—42no—
175C22×C4×C59—42no—
176C22×C4×C59—41no—
177C22×C4×C59—41no—
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D412yes—
182C22×C4×C59C2411yescharacteristic
183SD16×C59—42no—
184D8×C59—44no—
185D8×C59—42no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—22no—
189C4⋊C4×C59—22no—
190C4⋊C4×C59—22no—
191C4⋊C4×C59—22no—
192C4⋊C4×C59—22no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—22no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—22no—
204C4⋊C4×C59—22no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—42no—
209C4⋊C4×C59C2×D412yes—
210C4⋊C4×C59C2×D411yescharacteristic
211C4⋊C4×C59C2×D411yescharacteristic
212C22⋊C4×C59—22no—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—22no—
215C22⋊C4×C59—22no—
216C22⋊C4×C59—22no—
217C22⋊C4×C59—21no—
218C22⋊C4×C59—21no—
219C22⋊C4×C59—21no—
220C22⋊C4×C59—21no—
221C22⋊C4×C59—22no—
222C22⋊C4×C59—21no—
223C22⋊C4×C59—22no—
224C22⋊C4×C59—44no—
225C22⋊C4×C59—41no—
226C22⋊C4×C59—41no—
227C22⋊C4×C59—82no—
228C42×C59—22no—
229C42×C59—21no—
230C42×C59—81no—
231C42×C59C2×D411yescharacteristic
232C42×C59C2×D411yescharacteristic
233C42×C59C2×D411yescharacteristic
234C42×C59C2×D411yescharacteristic
235C23×C59—22no—
236C23×C59—21no—
237C23×C59—22no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59C22×D411yescharacteristic
245Q8×C59—41no—
246Q8×C59—81no—
247Q8×C59—82no—
248D4×C59—22no—
249D4×C59—22no—
250D4×C59—42no—
251D4×C59—41no—
252D4×C59—41no—
253D4×C59—41no—
254D4×C59—42no—
255D4×C59—41no—
256D4×C59—42no—
257D4×C59—41no—
258D4×C59—42no—
259D4×C59—81no—
260D4×C59—82no—
261D4×C59—82no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—22no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—41no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—42no—
282C2×C4×C59—82no—
283C2×C4×C59—82no—
284C2×C4×C59—82no—
285C2×C4×C59—82no—
286C2×C4×C59—82no—
287C2×C4×C59—82no—
288C2×C4×C59#12011yescharacteristic
289C2×C4×C59#12011yescharacteristic
290C2×C4×C59#12011yescharacteristic
291C2×C4×C59#12011yescharacteristic
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C22×D411yescharacteristic
294C8×C59—42no—
295C8×C59—41no—
296C8×C59—41no—
297#18276C5911yesmaximal, characteristic, direct product factor, Sylow
298C22×C59—21no—
299C22×C59—21no—
300C22×C59—42no—
301C22×C59—42no—
302C22×C59—42no—
303C22×C59—41no—
304C22×C59—41no—
305C22×C59—42no—
306C22×C59—42no—
307C22×C59—42no—
308C22×C59—41no—
309C22×C59—81no—
310C22×C59—81no—
311C22×C59—81no—
312C22×C59—81no—
313C22×C59C2×#12011yescharacteristic
314C22×C59#57611yescharacteristic
315C22×C59#57711yescharacteristic
316C4×C59—21no—
317C4×C59—21no—
318C4×C59—21no—
319C4×C59—21no—
320C4×C59—21no—
321C4×C59—42no—
322C4×C59—42no—
323C4×C59—41no—
324C4×C59—41no—
325C4×C59—42no—
326C4×C59—41no—
327C4×C59—82no—
328C4×C59—81no—
329C4×C59#45412yes—
330#3559C2×C5911yescharacteristic, complemented
331#3109C2×C5911yescharacteristic, complemented
332#3105C2×C5911yescharacteristic, complemented
333#2562C2×C5911yescharacteristic, complemented
334#1616C2×C5912yescomplemented
335#1615C2×C5912yescomplemented
336#1598C2×C5912yescomplemented
337#1597C2×C5912yescomplemented
338#1509C2×C5911yescharacteristic, complemented
339#1502C2×C5911yescharacteristic, complemented
340#1470C2×C5911yescharacteristic, complemented
341C2×C59—21no—
342C2×C59—21no—
343C2×C59—81no—
344C2×C59—82no—
345C2×C59—82no—
346C2×C59#301211yescharacteristic
347C2×C59C2×#45411yescharacteristic
348C2×C59#302511yescharacteristic
349#563—21no—
350#562—21no—
351#554—21no—
352#553—21no—
353#553—21no—
354#547—22no—
355#547—21no—
356#544—21no—
357#540—21no—
358#539—22no—
359#539C22×C5912yes—
360#537C22×C5912yes—
361#532C22×C5911yescharacteristic
362#529C22×C5911yescharacteristic
363C2×#125C22×C5911yescharacteristic
364C2×C4×D4C22×C5911yescharacteristic
365#484C22×C5911yescharacteristic
366#481C22×C5911yescharacteristic
367#481C22×C5912yes—
368#478—21no—
369#476—21no—
370#463—21no—
371#459—21no—
372#450C22×C5911yescharacteristic
373#447C22×C5911yescharacteristic
374#447C22×C5912yes—
375#442—22no—
376C4×SD16—21no—
377C4×D8—21no—
378#432C22×C5911yescharacteristic
379#431C22×C5911yescharacteristic
380#400C22×C5912yes—
381#394C22×C5912yes—
382#388—22no—
383#380—21no—
384#380—21no—
385C4×C4⋊C4C22×C5911yescharacteristic
386#328C22×C5912yes—
387#327C22×C5912yes—
388#327C22×C5912yes—
389#327C22×C5912yes—
390#324C22×C5912yes—
391#324C22×C5912yes—
392C59#1827611yescharacteristic, direct product factor, Sylow
393C2×#41—21no—
394C2×#41—22no—
395C22×D4C23×C5911yescharacteristic
396C23×C4—21no—
397C2×SD16—21no—
398C2×D8—21no—
399C2×D8—22no—
400C4⋊Q8—21no—
401C4⋊Q8—22no—
402C4⋊Q8D4×C5911yescharacteristic
403#127D4×C5911yescharacteristic
404#126—22no—
405#126—22no—
406#126—21no—
407#125—21no—
408#125—22no—
409#125—21no—
410#125—21no—
411#125—21no—
412#125—21no—
413#125D4×C5911yescharacteristic
414#124—21no—
415#124D4×C5911yescharacteristic
416#123—22no—
417#123—22no—
418#123—22no—
419#123—22no—
420#123—22no—
421#123—21no—
422#123—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8C23×C5911yescharacteristic
430#121—21no—
431#121—22no—
432#121—21no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—22no—
437#121C23×C5911yescharacteristic
438#121C23×C5912yes—
439C4×Q8D4×C5911yescharacteristic
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—22no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4D4×C5911yescharacteristic
451C4×D4D4×C5912yes—
452#117—21no—
453#117—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C5911yescharacteristic
458C2×C4⋊C4D4×C5912yes—
459C2×C4⋊C4D4×C5911yescharacteristic
460C2×C4⋊C4C23×C5911yescharacteristic
461C2×C4⋊C4C23×C5912yes—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C42—21no—
466C2×C42C23×C5911yescharacteristic
467#107—21no—
468#106—21no—
469#106—22no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472#103—21no—
473#102—21no—
474#102—22no—
475#102—21no—
476#102—21no—
477#102—22no—
478C22⋊C8C23×C5911yescharacteristic
479C22⋊C8C23×C5911yescharacteristic
480C22⋊C8C23×C5912yes—
481#97—21no—
482C4×C8—21no—
483#95—22no—
484#95—22no—
485#95C23×C5912yes—
486C24—21no—
487#41—81no—
488#41—81no—
489#41—82no—
490#41—82no—
491C2×Q8—22no—
492C2×Q8—21no—
493C2×Q8C2×D4×C5911yescharacteristic
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4C2×D4×C5911yescharacteristic
504C2×D4C2×D4×C5912yes—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4C2×D4×C5912yes—
517C22×C4C2×D4×C5911yescharacteristic
518C22×C4C2×D4×C5911yescharacteristic
519C22×C4C2×D4×C5912yes—
520C22×C4C24×C5911yescharacteristic
521SD16—42no—
522D8—44no—
523D8—42no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4C2×D4×C5912yes—
548C4⋊C4C2×D4×C5911yescharacteristic
549C4⋊C4C2×D4×C5911yescharacteristic
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—22no—
562C22⋊C4—44no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—82no—
566C42—22no—
567C42—21no—
568C42—81no—
569C42C2×D4×C5911yescharacteristic
570C42C2×D4×C5911yescharacteristic
571C42C2×D4×C5911yescharacteristic
572C42C2×D4×C5911yescharacteristic
573C23—22no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C22×D4×C5911yescharacteristic
583Q8—41no—
584Q8—81no—
585Q8—82no—
586D4—22no—
587D4—22no—
588D4—42no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—41no—
596D4—42no—
597D4—81no—
598D4—82no—
599D4—82no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4#120×C5911yescharacteristic
627C2×C4#120×C5911yescharacteristic
628C2×C4#120×C5911yescharacteristic
629C2×C4#120×C5911yescharacteristic
630C2×C4C22×D4×C5911yescharacteristic
631C2×C4C22×D4×C5911yescharacteristic
632C8—42no—
633C8—41no—
634C8—41no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—41no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C2×#120×C5911yescharacteristic
651C22C59×#57611yescharacteristic
652C22C59×#57711yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—82no—
665C4—81no—
666C4C59×#45412yes—
667C2—21no—
668C2—21no—
669C2—82no—
670C2—81no—
671C2—82no—
672C2C59×#301211yescharacteristic
673C2C2×C59×#45411yescharacteristic
674C2C59×#302511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3559C2semidirect
2. C59×#3109C2semidirect
3. C59×#3105C2semidirect
4. C59×#2562C2semidirect
5. C59×#1616C2semidirect
6. C59×#1615C2semidirect
7. C59×#1598C2semidirect
8. C59×#1597C2semidirect
9. C59×#1509C2semidirect
10. C59×#1502C2semidirect
11. C59×#1470C2semidirect
297. #18276C59direct (N × H)
330. #3559C2×C59semidirect
331. #3109C2×C59semidirect
332. #3105C2×C59semidirect
333. #2562C2×C59semidirect
334. #1616C2×C59semidirect
335. #1615C2×C59semidirect
336. #1598C2×C59semidirect
337. #1597C2×C59semidirect
338. #1509C2×C59semidirect
339. #1502C2×C59semidirect
340. #1470C2×C59semidirect
392. C59#18276direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35592
C59×#31092
C59×#31052
C59×#25622
C59×#16162
C59×#16152
C59×#15982
C59×#15972
C59×#15092
C59×#15022
C59×#14702
#1827659