Finite Group Databasebeta

← C59×#18378 #28430487

Subgroups — C59×#18378 #28430487

Order 15104.

1006 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3492C211yesmaximal, characteristic, complemented
2C59×#3188C212yesmaximal, complemented
3C59×#2591C211yesmaximal, characteristic, complemented
4C59×#1617C211yesmaximal, characteristic, complemented
5C59×#1616C211yesmaximal, characteristic, complemented
6C59×#1615C212yesmaximal, complemented
7C59×#1599C211yesmaximal, characteristic, complemented
8C59×#1598C211yesmaximal, characteristic, complemented
9C59×#1597C212yesmaximal, complemented
10C59×#1501C212yesmaximal, complemented
11C2×C59×#324C211yesmaximal, characteristic, complemented
12C59×#554—22no—
13C59×#553—22no—
14C59×#552—22no—
15C59×#547—22no—
16C59×#544C2211yescharacteristic
17C59×#539—21no—
18C59×#539C2212yes—
19C59×#537C2211yescharacteristic
20C59×#525—21no—
21C59×#525—21no—
22C59×#525C2212yes—
23C2×#121×C59C2211yescharacteristic
24C59×#520—21no—
25C22×C4⋊C4×C59C2211yescharacteristic
26C59×#484C2212yes—
27C59×#482—22no—
28C59×#481C2212yes—
29C59×#466—22no—
30C59×#465—22no—
31C59×#450C2212yes—
32C59×#449—22no—
33C59×#447C2212yes—
34C2×C22⋊C8×C59C2212yes—
35C59×#400C2211yescharacteristic
36C59×#400C2211yescharacteristic
37C59×#394C2211yescharacteristic
38C59×#394C2211yescharacteristic
39C59×#388—21no—
40C59×#388—21no—
41C59×#386—21no—
42C59×#386—21no—
43C4×C22⋊C4×C59C2211yescharacteristic
44C59×#328C2212yes—
45C59×#328C2212yes—
46C59×#327C2212yes—
47C59×#327C2212yes—
48C59×#324C2212yes—
49C59×#324C2211yescharacteristic
50C59×#324C2211yescharacteristic
51C2×#41×C59—21no—
52C2×#41×C59—21no—
53C2×#41×C59D412yes—
54C22×D4×C59—21no—
55C22×D4×C59C2311yescharacteristic
56C23×C4×C59D411yescharacteristic
57C23×C4×C59D411yescharacteristic
58C23×C4×C59C2311yescharacteristic
59C2×SD16×C59—22no—
60C2×D8×C59—22no—
61C22×C8×C59—22no—
62C4⋊Q8×C59—22no—
63#126×C59—22no—
64#126×C59—22no—
65#125×C59—22no—
66#125×C59—22no—
67#125×C59—22no—
68#123×C59—22no—
69#123×C59—22no—
70#123×C59—22no—
71#123×C59—22no—
72#123×C59—22no—
73C22⋊Q8×C59—21no—
74C22⋊Q8×C59—21no—
75C22⋊Q8×C59—21no—
76C22⋊Q8×C59—22no—
77C22⋊Q8×C59—22no—
78C22⋊Q8×C59—21no—
79C22⋊Q8×C59—22no—
80C22⋊Q8×C59D412yes—
81C22⋊Q8×C59C2312yes—
82#121×C59—21no—
83#121×C59—21no—
84#121×C59—21no—
85#121×C59—22no—
86#121×C59—21no—
87#121×C59—22no—
88#121×C59—22no—
89#121×C59D412yes—
90#121×C59C2312yes—
91#120×C59—22no—
92C4×Q8×C59—22no—
93C4×D4×C59—22no—
94C4×D4×C59—22no—
95C4×D4×C59—22no—
96C4×D4×C59—22no—
97C4×D4×C59—22no—
98C4×D4×C59—22no—
99C4×D4×C59—22no—
100#117×C59—22no—
101#117×C59—21no—
102#117×C59—21no—
103#117×C59D412yes—
104C2×C4⋊C4×C59—22no—
105C2×C4⋊C4×C59—22no—
106C2×C4⋊C4×C59—22no—
107C2×C4⋊C4×C59D411yescharacteristic
108C2×C4⋊C4×C59D411yescharacteristic
109C2×C4⋊C4×C59C2311yescharacteristic
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C22⋊C4×C59—21no—
113C2×C22⋊C4×C59—21no—
114C2×C22⋊C4×C59—21no—
115C2×C22⋊C4×C59—21no—
116C2×C22⋊C4×C59—21no—
117C2×C22⋊C4×C59—21no—
118C2×C42×C59—21no—
119#107×C59—22no—
120#106×C59—22no—
121#103×C59—22no—
122#102×C59—22no—
123#102×C59—22no—
124#102×C59—22no—
125C22⋊C8×C59—22no—
126C22⋊C8×C59C2312yes—
127C22⋊C8×C59C2312yes—
128#95×C59—21no—
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59C2311yescharacteristic
133#95×C59C2311yescharacteristic
134C24×C59—21no—
135C24×C59C2×D411yescharacteristic
136#41×C59—42no—
137#41×C59—42no—
138#41×C59—82no—
139#41×C59—82no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59C2×D412yes—
143C2×D4×C59—21no—
144C2×D4×C59—22no—
145C2×D4×C59—22no—
146C2×D4×C59—22no—
147C2×D4×C59—21no—
148C2×D4×C59—22no—
149C2×D4×C59—42no—
150C2×D4×C59—42no—
151C2×D4×C59—41no—
152C2×D4×C59—41no—
153C2×D4×C59—81no—
154C2×D4×C59C2×D412yes—
155C22×C4×C59—22no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—22no—
160C22×C4×C59—21no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—41no—
167C22×C4×C59—81no—
168C22×C4×C59—81no—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D412yes—
175C22×C4×C59C2×D412yes—
176C22×C4×C59C2411yescharacteristic
177SD16×C59—82no—
178D8×C59—82no—
179C2×C8×C59—22no—
180C2×C8×C59—22no—
181C2×C8×C59—82no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—22no—
188C4⋊C4×C59—22no—
189C4⋊C4×C59—22no—
190C4⋊C4×C59—22no—
191C4⋊C4×C59—22no—
192C4⋊C4×C59—22no—
193C4⋊C4×C59—22no—
194C4⋊C4×C59—22no—
195C4⋊C4×C59—22no—
196C4⋊C4×C59—22no—
197C4⋊C4×C59C2×D412yes—
198C4⋊C4×C59C2×D412yes—
199C22⋊C4×C59—22no—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—22no—
203C22⋊C4×C59—22no—
204C22⋊C4×C59—22no—
205C22⋊C4×C59—22no—
206C22⋊C4×C59—22no—
207C22⋊C4×C59—22no—
208C22⋊C4×C59—42no—
209C22⋊C4×C59—42no—
210C22⋊C4×C59—42no—
211C22⋊C4×C59—42no—
212C22⋊C4×C59—81no—
213C22⋊C4×C59—81no—
214C42×C59—22no—
215C42×C59—22no—
216C42×C59—22no—
217C42×C59—81no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—22no—
221C23×C59—22no—
222C23×C59—41no—
223C23×C59—41no—
224C23×C59—41no—
225C23×C59—41no—
226C23×C59—41no—
227C23×C59—41no—
228C23×C59—41no—
229C23×C59—41no—
230C23×C59#12011yescharacteristic
231C23×C59#12011yescharacteristic
232C23×C59C22×D411yescharacteristic
233Q8×C59—42no—
234Q8×C59—42no—
235Q8×C59—81no—
236D4×C59—42no—
237D4×C59—42no—
238D4×C59—42no—
239D4×C59—42no—
240D4×C59—44no—
241D4×C59—42no—
242D4×C59—42no—
243D4×C59—44no—
244D4×C59—81no—
245D4×C59—82no—
246D4×C59—82no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—21no—
252C2×C4×C59—22no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—41no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—41no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—44no—
264C2×C4×C59—42no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—82no—
277C2×C4×C59—81no—
278C2×C4×C59—82no—
279C2×C4×C59#12012yes—
280C2×C4×C59#13512yes—
281C2×C4×C59C22×D412yes—
282C8×C59—42no—
283C8×C59—42no—
284#18378C5911yesmaximal, characteristic, direct product factor, Sylow
285C22×C59—21no—
286C22×C59—21no—
287C22×C59—21no—
288C22×C59—21no—
289C22×C59—21no—
290C22×C59—21no—
291C22×C59—21no—
292C22×C59—42no—
293C22×C59—42no—
294C22×C59—42no—
295C22×C59—42no—
296C22×C59—42no—
297C22×C59—81no—
298C22×C59—81no—
299C22×C59—81no—
300C22×C59—81no—
301C22×C59—81no—
302C22×C59—81no—
303C22×C59—81no—
304C22×C59#45412yes—
305C22×C59C2×#12011yescharacteristic
306C22×C59C2×#13511yescharacteristic
307C22×C59#57511yescharacteristic
308C4×C59—22no—
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—41no—
312C4×C59—42no—
313C4×C59—42no—
314C4×C59—41no—
315C4×C59—41no—
316C4×C59—42no—
317C4×C59—81no—
318C4×C59—81no—
319C4×C59—81no—
320#3492C2×C5911yescharacteristic, complemented
321#3188C2×C5912yescomplemented
322#2591C2×C5911yescharacteristic, complemented
323#1617C2×C5911yescharacteristic, complemented
324#1616C2×C5911yescharacteristic, complemented
325#1615C2×C5912yescomplemented
326#1599C2×C5911yescharacteristic, complemented
327#1598C2×C5911yescharacteristic, complemented
328#1597C2×C5912yescomplemented
329#1501C2×C5912yescomplemented
330C2×#324C2×C5911yescharacteristic, complemented
331C2×C59—21no—
332C2×C59—21no—
333C2×C59—22no—
334C2×C59—41no—
335C2×C59—82no—
336C2×C59—161no—
337C2×C59#300211yescharacteristic
338C2×C59C2×#45411yescharacteristic
339C2×C59#302611yescharacteristic
340#554—22no—
341#553—22no—
342#552—22no—
343#547—22no—
344#544C22×C5911yescharacteristic
345#539—21no—
346#539C22×C5912yes—
347#537C22×C5911yescharacteristic
348#525—21no—
349#525—21no—
350#525C22×C5912yes—
351C2×#121C22×C5911yescharacteristic
352#520—21no—
353C22×C4⋊C4C22×C5911yescharacteristic
354#484C22×C5912yes—
355#482—22no—
356#481C22×C5912yes—
357#466—22no—
358#465—22no—
359#450C22×C5912yes—
360#449—22no—
361#447C22×C5912yes—
362C2×C22⋊C8C22×C5912yes—
363#400C22×C5911yescharacteristic
364#400C22×C5911yescharacteristic
365#394C22×C5911yescharacteristic
366#394C22×C5911yescharacteristic
367#388—21no—
368#388—21no—
369#386—21no—
370#386—21no—
371C4×C22⋊C4C22×C5911yescharacteristic
372#328C22×C5912yes—
373#328C22×C5912yes—
374#327C22×C5912yes—
375#327C22×C5912yes—
376#324C22×C5912yes—
377#324C22×C5911yescharacteristic
378#324C22×C5911yescharacteristic
379C59#1837811yescharacteristic, direct product factor, Sylow
380C2×#41—21no—
381C2×#41—21no—
382C2×#41D4×C5912yes—
383C22×D4—21no—
384C22×D4C23×C5911yescharacteristic
385C23×C4D4×C5911yescharacteristic
386C23×C4D4×C5911yescharacteristic
387C23×C4C23×C5911yescharacteristic
388C2×SD16—22no—
389C2×D8—22no—
390C22×C8—22no—
391C4⋊Q8—22no—
392#126—22no—
393#126—22no—
394#125—22no—
395#125—22no—
396#125—22no—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—22no—
409C22⋊Q8D4×C5912yes—
410C22⋊Q8C23×C5912yes—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—22no—
415#121—21no—
416#121—22no—
417#121—22no—
418#121D4×C5912yes—
419#121C23×C5912yes—
420#120—22no—
421C4×Q8—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429#117—22no—
430#117—21no—
431#117—21no—
432#117D4×C5912yes—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4D4×C5911yescharacteristic
437C2×C4⋊C4D4×C5911yescharacteristic
438C2×C4⋊C4C23×C5911yescharacteristic
439C2×C4⋊C4C23×C5911yescharacteristic
440C2×C4⋊C4C23×C5911yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42—21no—
448#107—22no—
449#106—22no—
450#103—22no—
451#102—22no—
452#102—22no—
453#102—22no—
454C22⋊C8—22no—
455C22⋊C8C23×C5912yes—
456C22⋊C8C23×C5912yes—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95C23×C5911yescharacteristic
462#95C23×C5911yescharacteristic
463C24—21no—
464C24C2×D4×C5911yescharacteristic
465#41—42no—
466#41—42no—
467#41—82no—
468#41—82no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8C2×D4×C5912yes—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—81no—
483C2×D4C2×D4×C5912yes—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4C2×D4×C5911yescharacteristic
499C22×C4C2×D4×C5911yescharacteristic
500C22×C4C2×D4×C5911yescharacteristic
501C22×C4C2×D4×C5911yescharacteristic
502C22×C4C2×D4×C5911yescharacteristic
503C22×C4C2×D4×C5912yes—
504C22×C4C2×D4×C5912yes—
505C22×C4C24×C5911yescharacteristic
506SD16—82no—
507D8—82no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—82no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4C2×D4×C5912yes—
527C4⋊C4C2×D4×C5912yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—81no—
547C23—22no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23#120×C5911yescharacteristic
560C23#120×C5911yescharacteristic
561C23C22×D4×C5911yescharacteristic
562Q8—42no—
563Q8—42no—
564Q8—81no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—42no—
569D4—44no—
570D4—44no—
571D4—42no—
572D4—42no—
573D4—81no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—82no—
606C2×C4—81no—
607C2×C4—82no—
608C2×C4#120×C5912yes—
609C2×C4#135×C5912yes—
610C2×C4C22×D4×C5912yes—
611C8—42no—
612C8—42no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22C59×#45412yes—
633C22C2×#120×C5911yescharacteristic
634C22C2×#135×C5911yescharacteristic
635C22C59×#57511yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—81no—
648C2—21no—
649C2—21no—
650C2—22no—
651C2—41no—
652C2—82no—
653C2—161no—
654C2C59×#300211yescharacteristic
655C2C2×C59×#45411yescharacteristic
656C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3492C2semidirect
2. C59×#3188C2semidirect
3. C59×#2591C2semidirect
4. C59×#1617C2semidirect
5. C59×#1616C2semidirect
6. C59×#1615C2semidirect
7. C59×#1599C2semidirect
8. C59×#1598C2semidirect
9. C59×#1597C2semidirect
10. C59×#1501C2semidirect
11. C2×C59×#324C2semidirect
284. #18378C59direct (N × H)
320. #3492C2×C59semidirect
321. #3188C2×C59semidirect
322. #2591C2×C59semidirect
323. #1617C2×C59semidirect
324. #1616C2×C59semidirect
325. #1615C2×C59semidirect
326. #1599C2×C59semidirect
327. #1598C2×C59semidirect
328. #1597C2×C59semidirect
329. #1501C2×C59semidirect
330. C2×#324C2×C59semidirect
379. C59#18378direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#34922
C59×#31882
C59×#25912
C59×#16172
C59×#16162
C59×#16152
C59×#15992
C59×#15982
C59×#15972
C59×#15012
C2×C59×#3242
#1837859