Finite Group Databasebeta

← C59×#18275 #28430384

Subgroups — C59×#18275 #28430384

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3561C211yesmaximal, characteristic
2C59×#3113C211yesmaximal, characteristic, complemented
3C59×#3108C211yesmaximal, characteristic, complemented
4C59×#2592C211yesmaximal, characteristic, complemented
5C59×#1612C212yesmaximal, complemented
6C59×#1608C212yesmaximal, complemented
7C59×#1606C212yesmaximal, complemented
8C59×#1602C212yesmaximal, complemented
9C59×#1509C211yesmaximal, characteristic, complemented
10C59×#1503C211yesmaximal, characteristic, complemented
11C59×#1469C211yesmaximal, characteristic, complemented
12C59×#563—21no—
13C59×#562—21no—
14C59×#556—21no—
15C59×#551—22no—
16D4×Q8×C59—21no—
17C59×#548—21no—
18C59×#546—21no—
19C59×#543C2212yes—
20C59×#542—21no—
21C59×#542—22no—
22C59×#538C2212yes—
23C59×#536—21no—
24C59×#533C2211yescharacteristic
25C59×#529C2211yescharacteristic
26C2×#124×C59C2211yescharacteristic
27C2×C4×Q8×C59C2211yescharacteristic
28C59×#483C2211yescharacteristic
29C59×#483C2212yes—
30C59×#480C2211yescharacteristic
31C59×#479—21no—
32C59×#475—21no—
33C59×#464—21no—
34C59×#462—21no—
35C59×#451C2211yescharacteristic
36C59×#451C2212yes—
37C59×#448C2211yescharacteristic
38C59×#441—22no—
39C4×Q16×C59—21no—
40C4×SD16×C59—21no—
41C59×#432C2211yescharacteristic
42C59×#431C2211yescharacteristic
43C59×#397C2212yes—
44C59×#393C2212yes—
45C59×#391—21no—
46C59×#390—21no—
47C59×#388—22no—
48C4×C4⋊C4×C59C2211yescharacteristic
49C59×#328C2212yes—
50C59×#328C2212yes—
51C59×#328C2212yes—
52C59×#327C2212yes—
53C59×#323C2212yes—
54C59×#323C2212yes—
55C2×#41×C59—21no—
56C22×Q8×C59—21no—
57C22×Q8×C59D411yescharacteristic
58C22×Q8×C59C2311yescharacteristic
59C22×D4×C59D411yescharacteristic
60C2×Q16×C59—21no—
61C2×Q16×C59—22no—
62C2×SD16×C59—21no—
63C4⋊Q8×C59—21no—
64C4⋊Q8×C59—22no—
65C4⋊Q8×C59D411yescharacteristic
66C4⋊Q8×C59D411yescharacteristic
67#126×C59—22no—
68#126×C59—22no—
69#126×C59—22no—
70#126×C59—21no—
71#125×C59—21no—
72#125×C59D411yescharacteristic
73#124×C59—21no—
74#124×C59—22no—
75#124×C59—22no—
76#124×C59—21no—
77#124×C59—21no—
78#124×C59—21no—
79#124×C59—21no—
80#124×C59D411yescharacteristic
81#123×C59—22no—
82#123×C59—22no—
83#123×C59—22no—
84#123×C59—21no—
85#123×C59—22no—
86C22⋊Q8×C59—22no—
87C22⋊Q8×C59—21no—
88C22⋊Q8×C59—22no—
89C22⋊Q8×C59—22no—
90C22⋊Q8×C59—22no—
91C22⋊Q8×C59—21no—
92C22⋊Q8×C59—22no—
93C22⋊Q8×C59—22no—
94C22⋊Q8×C59—22no—
95C22⋊Q8×C59C2311yescharacteristic
96C22⋊Q8×C59C2312yes—
97#121×C59—21no—
98#121×C59—22no—
99#121×C59—22no—
100#121×C59C2311yescharacteristic
101#120×C59—22no—
102C4×Q8×C59—21no—
103C4×Q8×C59—21no—
104C4×Q8×C59—21no—
105C4×Q8×C59—21no—
106C4×Q8×C59—21no—
107C4×Q8×C59—21no—
108C4×Q8×C59D411yescharacteristic
109C4×Q8×C59D412yes—
110C4×D4×C59—21no—
111C4×D4×C59—22no—
112C4×D4×C59—21no—
113C4×D4×C59—22no—
114C4×D4×C59D411yescharacteristic
115#117×C59—22no—
116#117×C59—21no—
117#117×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59D412yes—
125C2×C22⋊C4×C59C2312yes—
126C2×C42×C59—21no—
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#103×C59—22no—
136#103×C59—21no—
137#103×C59—21no—
138#103×C59—22no—
139#102×C59—21no—
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×C59C2×D412yes—
149#41×C59—82no—
150C2×Q8×C59—22no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—42no—
157C2×Q8×C59—42no—
158C2×Q8×C59—82no—
159C2×Q8×C59C2×D411yescharacteristic
160C2×Q8×C59C2×D412yes—
161C2×D4×C59—21no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—42no—
167C2×D4×C59C2×D411yescharacteristic
168C22×C4×C59—21no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—21no—
173C22×C4×C59—22no—
174C22×C4×C59—21no—
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D412yes—
178C22×C4×C59C2411yescharacteristic
179Q16×C59—42no—
180Q16×C59—44no—
181SD16×C59—42no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—22no—
185C4⋊C4×C59—22no—
186C4⋊C4×C59—22no—
187C4⋊C4×C59—22no—
188C4⋊C4×C59—22no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—22no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—22no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59—41no—
202C4⋊C4×C59—41no—
203C4⋊C4×C59C2×D411yescharacteristic
204C4⋊C4×C59C2×D412yes—
205C4⋊C4×C59C2×D411yescharacteristic
206C22⋊C4×C59—22no—
207C22⋊C4×C59—22no—
208C22⋊C4×C59—22no—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C22⋊C4×C59—21no—
212C22⋊C4×C59—22no—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—22no—
215C22⋊C4×C59—21no—
216C22⋊C4×C59—21no—
217C22⋊C4×C59—21no—
218C22⋊C4×C59—22no—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—21no—
221C22⋊C4×C59—44no—
222C22⋊C4×C59—82no—
223C42×C59—22no—
224C42×C59—22no—
225C42×C59—21no—
226C42×C59—41no—
227C42×C59—41no—
228C42×C59—81no—
229C42×C59C2×D411yescharacteristic
230C42×C59C2×D411yescharacteristic
231C42×C59C2×D411yescharacteristic
232C42×C59C2×D411yescharacteristic
233C23×C59—22no—
234C23×C59—21no—
235C23×C59—22no—
236C23×C59—22no—
237C23×C59—42no—
238C23×C59—42no—
239C23×C59C22×D411yescharacteristic
240Q8×C59—22no—
241Q8×C59—22no—
242Q8×C59—41no—
243Q8×C59—42no—
244Q8×C59—41no—
245Q8×C59—41no—
246Q8×C59—42no—
247Q8×C59—42no—
248Q8×C59—81no—
249Q8×C59—82no—
250D4×C59—41no—
251D4×C59—41no—
252D4×C59—41no—
253D4×C59—42no—
254D4×C59—81no—
255D4×C59—82no—
256D4×C59—82no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—21no—
262C2×C4×C59—22no—
263C2×C4×C59—21no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—21no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—41no—
275C2×C4×C59—42no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—82no—
279C2×C4×C59—82no—
280C2×C4×C59—82no—
281C2×C4×C59#12011yescharacteristic
282C2×C4×C59#12011yescharacteristic
283C2×C4×C59#12011yescharacteristic
284C2×C4×C59#12011yescharacteristic
285C2×C4×C59C22×D411yescharacteristic
286C2×C4×C59C22×D411yescharacteristic
287C8×C59—41no—
288C8×C59—41no—
289C8×C59—42no—
290#18275C5911yesmaximal, characteristic, direct product factor, Sylow
291C22×C59—21no—
292C22×C59—21no—
293C22×C59—41no—
294C22×C59—42no—
295C22×C59—41no—
296C22×C59—42no—
297C22×C59—42no—
298C22×C59—41no—
299C22×C59—82no—
300C22×C59—82no—
301C22×C59C2×#12011yescharacteristic
302C22×C59#57711yescharacteristic
303C22×C59#57811yescharacteristic
304C4×C59—21no—
305C4×C59—21no—
306C4×C59—21no—
307C4×C59—21no—
308C4×C59—21no—
309C4×C59—41no—
310C4×C59—41no—
311C4×C59—42no—
312C4×C59—42no—
313C4×C59—42no—
314C4×C59—41no—
315C4×C59—42no—
316C4×C59—82no—
317C4×C59—81no—
318C4×C59#45512yes—
319#3561C2×C5911yescharacteristic
320#3113C2×C5911yescharacteristic, complemented
321#3108C2×C5911yescharacteristic, complemented
322#2592C2×C5911yescharacteristic, complemented
323#1612C2×C5912yescomplemented
324#1608C2×C5912yescomplemented
325#1606C2×C5912yescomplemented
326#1602C2×C5912yescomplemented
327#1509C2×C5911yescharacteristic, complemented
328#1503C2×C5911yescharacteristic, complemented
329#1469C2×C5911yescharacteristic, complemented
330C2×C59—21no—
331C2×C59—21no—
332C2×C59—81no—
333C2×C59—82no—
334C2×C59#301311yescharacteristic
335C2×C59C2×#45511yescharacteristic
336C2×C59#302511yescharacteristic
337#563—21no—
338#562—21no—
339#556—21no—
340#551—22no—
341D4×Q8—21no—
342#548—21no—
343#546—21no—
344#543C22×C5912yes—
345#542—21no—
346#542—22no—
347#538C22×C5912yes—
348#536—21no—
349#533C22×C5911yescharacteristic
350#529C22×C5911yescharacteristic
351C2×#124C22×C5911yescharacteristic
352C2×C4×Q8C22×C5911yescharacteristic
353#483C22×C5911yescharacteristic
354#483C22×C5912yes—
355#480C22×C5911yescharacteristic
356#479—21no—
357#475—21no—
358#464—21no—
359#462—21no—
360#451C22×C5911yescharacteristic
361#451C22×C5912yes—
362#448C22×C5911yescharacteristic
363#441—22no—
364C4×Q16—21no—
365C4×SD16—21no—
366#432C22×C5911yescharacteristic
367#431C22×C5911yescharacteristic
368#397C22×C5912yes—
369#393C22×C5912yes—
370#391—21no—
371#390—21no—
372#388—22no—
373C4×C4⋊C4C22×C5911yescharacteristic
374#328C22×C5912yes—
375#328C22×C5912yes—
376#328C22×C5912yes—
377#327C22×C5912yes—
378#323C22×C5912yes—
379#323C22×C5912yes—
380C59#1827511yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C22×Q8—21no—
383C22×Q8D4×C5911yescharacteristic
384C22×Q8C23×C5911yescharacteristic
385C22×D4D4×C5911yescharacteristic
386C2×Q16—21no—
387C2×Q16—22no—
388C2×SD16—21no—
389C4⋊Q8—21no—
390C4⋊Q8—22no—
391C4⋊Q8D4×C5911yescharacteristic
392C4⋊Q8D4×C5911yescharacteristic
393#126—22no—
394#126—22no—
395#126—22no—
396#126—21no—
397#125—21no—
398#125D4×C5911yescharacteristic
399#124—21no—
400#124—22no—
401#124—22no—
402#124—21no—
403#124—21no—
404#124—21no—
405#124—21no—
406#124D4×C5911yescharacteristic
407#123—22no—
408#123—22no—
409#123—22no—
410#123—21no—
411#123—22no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8C23×C5911yescharacteristic
422C22⋊Q8C23×C5912yes—
423#121—21no—
424#121—22no—
425#121—22no—
426#121C23×C5911yescharacteristic
427#120—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8D4×C5911yescharacteristic
435C4×Q8D4×C5912yes—
436C4×D4—21no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—22no—
440C4×D4D4×C5911yescharacteristic
441#117—22no—
442#117—21no—
443#117—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C5911yescharacteristic
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4D4×C5912yes—
451C2×C22⋊C4C23×C5912yes—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C5911yescharacteristic
455#107—21no—
456#106—21no—
457#106—22no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460#103—21no—
461#103—22no—
462#103—21no—
463#103—21no—
464#103—22no—
465#102—21no—
466C22⋊C8C23×C5912yes—
467C22⋊C8C23×C5911yescharacteristic
468C22⋊C8C23×C5911yescharacteristic
469#97—21no—
470C4×C8—21no—
471#95—22no—
472#95—22no—
473#95C23×C5912yes—
474C24C2×D4×C5912yes—
475#41—82no—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—82no—
485C2×Q8C2×D4×C5911yescharacteristic
486C2×Q8C2×D4×C5912yes—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4C2×D4×C5911yescharacteristic
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4C2×D4×C5911yescharacteristic
502C22×C4C2×D4×C5911yescharacteristic
503C22×C4C2×D4×C5912yes—
504C22×C4C24×C5911yescharacteristic
505Q16—42no—
506Q16—44no—
507SD16—42no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C5911yescharacteristic
530C4⋊C4C2×D4×C5912yes—
531C4⋊C4C2×D4×C5911yescharacteristic
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—44no—
548C22⋊C4—82no—
549C42—22no—
550C42—22no—
551C42—21no—
552C42—41no—
553C42—41no—
554C42—81no—
555C42C2×D4×C5911yescharacteristic
556C42C2×D4×C5911yescharacteristic
557C42C2×D4×C5911yescharacteristic
558C42C2×D4×C5911yescharacteristic
559C23—22no—
560C23—21no—
561C23—22no—
562C23—22no—
563C23—42no—
564C23—42no—
565C23C22×D4×C5911yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—42no—
570Q8—41no—
571Q8—41no—
572Q8—42no—
573Q8—42no—
574Q8—81no—
575Q8—82no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—42no—
580D4—81no—
581D4—82no—
582D4—82no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4#120×C5911yescharacteristic
608C2×C4#120×C5911yescharacteristic
609C2×C4#120×C5911yescharacteristic
610C2×C4#120×C5911yescharacteristic
611C2×C4C22×D4×C5911yescharacteristic
612C2×C4C22×D4×C5911yescharacteristic
613C8—41no—
614C8—41no—
615C8—42no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—42no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—41no—
624C22—82no—
625C22—82no—
626C22C2×#120×C5911yescharacteristic
627C22C59×#57711yescharacteristic
628C22C59×#57811yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—82no—
642C4—81no—
643C4C59×#45512yes—
644C2—21no—
645C2—21no—
646C2—82no—
647C2—81no—
648C2C59×#301311yescharacteristic
649C2C2×C59×#45511yescharacteristic
650C2C59×#302511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#3561C2
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
2. C59×#3113C2semidirect
3. C59×#3108C2semidirect
4. C59×#2592C2semidirect
5. C59×#1612C2semidirect
6. C59×#1608C2semidirect
7. C59×#1606C2semidirect
8. C59×#1602C2semidirect
9. C59×#1509C2semidirect
10. C59×#1503C2semidirect
11. C59×#1469C2semidirect
290. #18275C59direct (N × H)
320. #3113C2×C59semidirect
321. #3108C2×C59semidirect
322. #2592C2×C59semidirect
323. #1612C2×C59semidirect
324. #1608C2×C59semidirect
325. #1606C2×C59semidirect
326. #1602C2×C59semidirect
327. #1509C2×C59semidirect
328. #1503C2×C59semidirect
329. #1469C2×C59semidirect
380. C59#18275direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35612
C59×#31132
C59×#31082
C59×#25922
C59×#16122
C59×#16082
C59×#16062
C59×#16022
C59×#15092
C59×#15032
C59×#14692
#1827559