Finite Group Databasebeta

← C59×#18279 #28430388

Subgroups — C59×#18279 #28430388

Order 15104.

878 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3563C211yesmaximal, characteristic
2C59×#3113C211yesmaximal, characteristic, complemented
3C59×#3108C211yesmaximal, characteristic
4C59×#2584C211yesmaximal, characteristic, complemented
5C59×#1611C212yesmaximal, complemented
6C59×#1609C212yesmaximal
7C59×#1605C212yesmaximal, complemented
8C59×#1603C212yesmaximal
9C59×#1509C211yesmaximal, characteristic
10C59×#1503C211yesmaximal, characteristic, complemented
11C59×#1470C211yesmaximal, characteristic, complemented
12C59×#564—21no—
13C59×#563—21no—
14C59×#557—21no—
15C59×#554—21no—
16C59×#552—21no—
17C59×#552—22no—
18C59×#552—21no—
19C59×#544—21no—
20C59×#544C2212yes—
21C59×#541—21no—
22C59×#541—22no—
23C59×#539C2212yes—
24C59×#533C2211yescharacteristic
25C59×#529C2211yescharacteristic
26C2×#125×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×#398C2212yes—
44C59×#395C2212yes—
45C59×#389—21no—
46C59×#389—22no—
47C59×#389—21no—
48C4×C4⋊C4×C59C2211yescharacteristic
49C59×#328C2212yes—
50C59×#328C2212yes—
51C59×#328C2212yes—
52C59×#327C2212yes—
53C59×#324C2212yes—
54C59×#324C2212yes—
55C22×Q8×C59C2311yescharacteristic
56C2×Q16×C59—21no—
57C2×Q16×C59—22no—
58C2×SD16×C59—21no—
59C4⋊Q8×C59—21no—
60C4⋊Q8×C59—22no—
61C4⋊Q8×C59—22no—
62C4⋊Q8×C59D411yescharacteristic
63C4⋊Q8×C59D411yescharacteristic
64#126×C59—22no—
65#126×C59—22no—
66#126×C59—22no—
67#126×C59—22no—
68#126×C59—21no—
69#125×C59—22no—
70#125×C59—22no—
71#125×C59—22no—
72#125×C59—22no—
73#125×C59—21no—
74#125×C59—22no—
75#125×C59—22no—
76#125×C59—22no—
77#125×C59—22no—
78#125×C59—21no—
79#125×C59—21no—
80#125×C59—21no—
81#125×C59—21no—
82#125×C59—21no—
83#125×C59D411yescharacteristic
84#124×C59D411yescharacteristic
85#123×C59—22no—
86#123×C59—21no—
87#123×C59—22no—
88C22⋊Q8×C59—21no—
89C22⋊Q8×C59—21no—
90C22⋊Q8×C59—22no—
91C22⋊Q8×C59—22no—
92C22⋊Q8×C59—22no—
93C22⋊Q8×C59—21no—
94C22⋊Q8×C59—22no—
95C22⋊Q8×C59C2311yescharacteristic
96C22⋊Q8×C59C2312yes—
97#121×C59C2311yescharacteristic
98C4×Q8×C59—21no—
99C4×Q8×C59—22no—
100C4×Q8×C59—21no—
101C4×Q8×C59—21no—
102C4×Q8×C59—21no—
103C4×Q8×C59—21no—
104C4×Q8×C59—21no—
105C4×Q8×C59—21no—
106C4×Q8×C59D411yescharacteristic
107C4×Q8×C59D412yes—
108C4×D4×C59—21no—
109C4×D4×C59—22no—
110C4×D4×C59D411yescharacteristic
111#117×C59—22no—
112#117×C59—21no—
113#117×C59—21no—
114#117×C59—22no—
115#117×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—22no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—22no—
121C2×C4⋊C4×C59D411yescharacteristic
122C2×C4⋊C4×C59D412yes—
123C2×C4⋊C4×C59D411yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊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—
148C2×Q8×C59—22no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—42no—
153C2×Q8×C59C2×D412yes—
154C2×Q8×C59C2×D411yescharacteristic
155C2×D4×C59—21no—
156C2×D4×C59C2×D411yescharacteristic
157C22×C4×C59—22no—
158C22×C4×C59—21no—
159C22×C4×C59—22no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D412yes—
166C22×C4×C59C2411yescharacteristic
167Q16×C59—42no—
168Q16×C59—44no—
169SD16×C59—42no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—22no—
173C4⋊C4×C59—24no—
174C4⋊C4×C59—22no—
175C4⋊C4×C59—22no—
176C4⋊C4×C59—22no—
177C4⋊C4×C59—22no—
178C4⋊C4×C59—22no—
179C4⋊C4×C59—22no—
180C4⋊C4×C59—22no—
181C4⋊C4×C59—22no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—22no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—22no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—22no—
195C4⋊C4×C59—22no—
196C4⋊C4×C59—22no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—44no—
202C4⋊C4×C59—41no—
203C4⋊C4×C59—41no—
204C4⋊C4×C59—82no—
205C4⋊C4×C59C2×D411yescharacteristic
206C4⋊C4×C59C2×D412yes—
207C4⋊C4×C59C2×D411yescharacteristic
208C22⋊C4×C59—22no—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C22⋊C4×C59—22no—
212C22⋊C4×C59—21no—
213C22⋊C4×C59—21no—
214C22⋊C4×C59—21no—
215C22⋊C4×C59—21no—
216C22⋊C4×C59—21no—
217C42×C59—22no—
218C42×C59—22no—
219C42×C59—22no—
220C42×C59—22no—
221C42×C59—21no—
222C42×C59—41no—
223C42×C59—41no—
224C42×C59—81no—
225C42×C59C2×D411yescharacteristic
226C42×C59C2×D411yescharacteristic
227C42×C59C2×D411yescharacteristic
228C42×C59C2×D411yescharacteristic
229C23×C59—21no—
230C23×C59C22×D411yescharacteristic
231Q8×C59—22no—
232Q8×C59—22no—
233Q8×C59—41no—
234Q8×C59—42no—
235Q8×C59—41no—
236Q8×C59—41no—
237Q8×C59—42no—
238Q8×C59—82no—
239D4×C59—41no—
240D4×C59—41no—
241D4×C59—41no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—22no—
245C2×C4×C59—24no—
246C2×C4×C59—22no—
247C2×C4×C59—22no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—22no—
251C2×C4×C59—21no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—41no—
257C2×C4×C59—42no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—82no—
267C2×C4×C59#12011yescharacteristic
268C2×C4×C59#12011yescharacteristic
269C2×C4×C59#12011yescharacteristic
270C2×C4×C59#12011yescharacteristic
271C2×C4×C59C22×D411yescharacteristic
272C2×C4×C59C22×D411yescharacteristic
273C8×C59—41no—
274C8×C59—41no—
275C8×C59—42no—
276#18279C5911yesmaximal, characteristic, direct product factor, Sylow
277C22×C59—21no—
278C22×C59—21no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59C2×#12011yescharacteristic
283C22×C59#57711yescharacteristic
284C22×C59#57811yescharacteristic
285C4×C59—21no—
286C4×C59—21no—
287C4×C59—21no—
288C4×C59—21no—
289C4×C59—21no—
290C4×C59—44no—
291C4×C59—42no—
292C4×C59—41no—
293C4×C59—41no—
294C4×C59—42no—
295C4×C59—42no—
296C4×C59—42no—
297C4×C59—42no—
298C4×C59—41no—
299C4×C59—81no—
300C4×C59#45612yes—
301#3563C2×C5911yescharacteristic
302#3113C2×C5911yescharacteristic, complemented
303#3108C2×C5911yescharacteristic
304#2584C2×C5911yescharacteristic, complemented
305#1611C2×C5912yescomplemented
306#1609C2×C5912yes—
307#1605C2×C5912yescomplemented
308#1603C2×C5912yes—
309#1509C2×C5911yescharacteristic
310#1503C2×C5911yescharacteristic, complemented
311#1470C2×C5911yescharacteristic, complemented
312C2×C59—21no—
313C2×C59—21no—
314C2×C59—81no—
315C2×C59#301311yescharacteristic
316C2×C59C2×#45611yescharacteristic
317C2×C59#302511yescharacteristic
318#564—21no—
319#563—21no—
320#557—21no—
321#554—21no—
322#552—21no—
323#552—22no—
324#552—21no—
325#544—21no—
326#544C22×C5912yes—
327#541—21no—
328#541—22no—
329#539C22×C5912yes—
330#533C22×C5911yescharacteristic
331#529C22×C5911yescharacteristic
332C2×#125C22×C5911yescharacteristic
333C2×C4×Q8C22×C5911yescharacteristic
334#483C22×C5911yescharacteristic
335#483C22×C5912yes—
336#480C22×C5911yescharacteristic
337#479—21no—
338#475—21no—
339#464—21no—
340#462—21no—
341#451C22×C5911yescharacteristic
342#451C22×C5912yes—
343#448C22×C5911yescharacteristic
344#441—22no—
345C4×Q16—21no—
346C4×SD16—21no—
347#432C22×C5911yescharacteristic
348#431C22×C5911yescharacteristic
349#398C22×C5912yes—
350#395C22×C5912yes—
351#389—21no—
352#389—22no—
353#389—21no—
354C4×C4⋊C4C22×C5911yescharacteristic
355#328C22×C5912yes—
356#328C22×C5912yes—
357#328C22×C5912yes—
358#327C22×C5912yes—
359#324C22×C5912yes—
360#324C22×C5912yes—
361C59#1827911yescharacteristic, direct product factor, Sylow
362C22×Q8C23×C5911yescharacteristic
363C2×Q16—21no—
364C2×Q16—22no—
365C2×SD16—21no—
366C4⋊Q8—21no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8D4×C5911yescharacteristic
370C4⋊Q8D4×C5911yescharacteristic
371#126—22no—
372#126—22no—
373#126—22no—
374#126—22no—
375#126—21no—
376#125—22no—
377#125—22no—
378#125—22no—
379#125—22no—
380#125—21no—
381#125—22no—
382#125—22no—
383#125—22no—
384#125—22no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125D4×C5911yescharacteristic
391#124D4×C5911yescharacteristic
392#123—22no—
393#123—21no—
394#123—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8C23×C5911yescharacteristic
403C22⋊Q8C23×C5912yes—
404#121C23×C5911yescharacteristic
405C4×Q8—21no—
406C4×Q8—22no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8D4×C5911yescharacteristic
414C4×Q8D4×C5912yes—
415C4×D4—21no—
416C4×D4—22no—
417C4×D4D4×C5911yescharacteristic
418#117—22no—
419#117—21no—
420#117—21no—
421#117—22no—
422#117—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4D4×C5911yescharacteristic
429C2×C4⋊C4D4×C5912yes—
430C2×C4⋊C4D4×C5911yescharacteristic
431C2×C4⋊C4C23×C5911yescharacteristic
432C2×C4⋊C4C23×C5912yes—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C5911yescharacteristic
436#107—21no—
437#106—21no—
438#106—22no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441#103—21no—
442#103—22no—
443#103—21no—
444#103—21no—
445#103—22no—
446#102—21no—
447C22⋊C8C23×C5912yes—
448C22⋊C8C23×C5911yescharacteristic
449C22⋊C8C23×C5911yescharacteristic
450#97—21no—
451C4×C8—21no—
452#95—22no—
453#95—22no—
454#95C23×C5912yes—
455C2×Q8—22no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8C2×D4×C5912yes—
461C2×Q8C2×D4×C5911yescharacteristic
462C2×D4—21no—
463C2×D4C2×D4×C5911yescharacteristic
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4C2×D4×C5912yes—
470C22×C4C2×D4×C5911yescharacteristic
471C22×C4C2×D4×C5911yescharacteristic
472C22×C4C2×D4×C5912yes—
473C22×C4C24×C5911yescharacteristic
474Q16—42no—
475Q16—44no—
476SD16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—22no—
480C4⋊C4—22no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—44no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—82no—
512C4⋊C4C2×D4×C5911yescharacteristic
513C4⋊C4C2×D4×C5912yes—
514C4⋊C4C2×D4×C5911yescharacteristic
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—21no—
529C42—41no—
530C42—41no—
531C42—81no—
532C42C2×D4×C5911yescharacteristic
533C42C2×D4×C5911yescharacteristic
534C42C2×D4×C5911yescharacteristic
535C42C2×D4×C5911yescharacteristic
536C23—21no—
537C23C22×D4×C5911yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—41no—
541Q8—42no—
542Q8—41no—
543Q8—41no—
544Q8—42no—
545Q8—82no—
546D4—41no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—82no—
574C2×C4#120×C5911yescharacteristic
575C2×C4#120×C5911yescharacteristic
576C2×C4#120×C5911yescharacteristic
577C2×C4#120×C5911yescharacteristic
578C2×C4C22×D4×C5911yescharacteristic
579C2×C4C22×D4×C5911yescharacteristic
580C8—41no—
581C8—41no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×#120×C5911yescharacteristic
589C22C59×#57711yescharacteristic
590C22C59×#57811yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—44no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—41no—
605C4—81no—
606C4C59×#45612yes—
607C2—21no—
608C2—21no—
609C2—81no—
610C2C59×#301311yescharacteristic
611C2C2×C59×#45611yescharacteristic
612C2C59×#302511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radical#121×C59C23
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
4. C59×#2584C2semidirect
5. C59×#1611C2semidirect
7. C59×#1605C2semidirect
10. C59×#1503C2semidirect
11. C59×#1470C2semidirect
276. #18279C59direct (N × H)
302. #3113C2×C59semidirect
304. #2584C2×C59semidirect
305. #1611C2×C59semidirect
307. #1605C2×C59semidirect
310. #1503C2×C59semidirect
311. #1470C2×C59semidirect
361. C59#18279direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35632
C59×#31132
C59×#31082
C59×#25842
C59×#16112
C59×#16092
C59×#16052
C59×#16032
C59×#15092
C59×#15032
C59×#14702
#1827959