Finite Group Databasebeta

← C59×#8490 #28420599

Subgroups — C59×#8490 #28420599

Order 15104.

630 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3564C211yesmaximal, characteristic
2C59×#1554C211yesmaximal, characteristic, complemented
3C59×#1535C211yesmaximal, characteristic, complemented
4C59×#1497C211yesmaximal, characteristic, complemented
5C59×#1482C211yesmaximal, characteristic, complemented
6C59×#1473C211yesmaximal, characteristic, complemented
7C59×#1473C211yesmaximal, characteristic, complemented
8C59×#563—21no—
9C59×#563—21no—
10C59×#556—21no—
11C59×#554—21no—
12C59×#552—21no—
13C59×#552—21no—
14C59×#551—21no—
15C59×#551—21no—
16C59×#544C411yescharacteristic
17C59×#543C411yescharacteristic
18C59×#542—21no—
19C59×#541—21no—
20C59×#541—21no—
21C59×#539—21no—
22C59×#539C411yescharacteristic
23C59×#538C411yescharacteristic
24C59×#533C2211yescharacteristic
25C59×#529C2211yescharacteristic
26C2×#126×C59C2211yescharacteristic
27C59×#432C2211yescharacteristic
28C59×#432C2211yescharacteristic
29C59×#431C2211yescharacteristic
30C59×#431C2211yescharacteristic
31C59×#333—21no—
32C59×#332—21no—
33C59×#330—21no—
34C59×#329—21no—
35C59×Q8⋊C8—21no—
36C59×Q8⋊C8—21no—
37C59×Q8⋊C8—21no—
38C59×D4⋊C8—21no—
39C59×#324—21no—
40C59×#324—21no—
41C59×#323—21no—
42C59×#323—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59D411yescharacteristic
47C4⋊Q8×C59D411yescharacteristic
48#126×C59—21no—
49#126×C59—21no—
50#126×C59—21no—
51#126×C59—21no—
52#126×C59—21no—
53#126×C59—21no—
54#126×C59—21no—
55#126×C59—21no—
56#126×C59—21no—
57#126×C59—21no—
58#126×C59—21no—
59#126×C59—21no—
60#126×C59—21no—
61#125×C59—21no—
62#125×C59—21no—
63#125×C59—21no—
64#125×C59—21no—
65#125×C59—21no—
66#125×C59—21no—
67#125×C59—21no—
68#125×C59—21no—
69#125×C59—21no—
70#125×C59D411yescharacteristic
71#124×C59—21no—
72#124×C59—21no—
73#124×C59—21no—
74#124×C59D411yescharacteristic
75#123×C59—21no—
76#123×C59—21no—
77#123×C59—21no—
78#123×C59—21no—
79#123×C59—21no—
80#123×C59—21no—
81#123×C59—21no—
82#123×C59—21no—
83C22⋊Q8×C59—21no—
84C22⋊Q8×C59—21no—
85C22⋊Q8×C59—21no—
86C22⋊Q8×C59—21no—
87C22⋊Q8×C59—21no—
88C22⋊Q8×C59—21no—
89C22⋊Q8×C59—21no—
90C22⋊Q8×C59—21no—
91C22⋊Q8×C59—21no—
92C22⋊Q8×C59—21no—
93C22⋊Q8×C59—21no—
94C22⋊Q8×C59—21no—
95C22⋊Q8×C59—21no—
96C22⋊Q8×C59—21no—
97C22⋊Q8×C59C2×C411yescharacteristic
98C22⋊Q8×C59C2×C411yescharacteristic
99C22⋊Q8×C59C2×C411yescharacteristic
100#121×C59—21no—
101#121×C59C2×C411yescharacteristic
102#120×C59—21no—
103C4×Q8×C59—21no—
104C4×Q8×C59—21no—
105C4×Q8×C59—21no—
106C4×Q8×C59D411yescharacteristic
107C4×Q8×C59D411yescharacteristic
108C4×Q8×C59D411yescharacteristic
109C4×D4×C59—21no—
110C4×D4×C59—21no—
111C4×D4×C59—21no—
112C4×D4×C59—21no—
113C4×D4×C59—21no—
114C4×D4×C59D411yescharacteristic
115#117×C59—21no—
116#117×C59—21no—
117#117×C59—21no—
118#117×C59—21no—
119#117×C59—21no—
120#117×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59C2×C411yescharacteristic
123C2×C4⋊C4×C59D411yescharacteristic
124C2×C4⋊C4×C59D411yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59C2×C411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C42×C59C2311yescharacteristic
130C4⋊C8×C59—21no—
131C4⋊C8×C59—21no—
132C4⋊C8×C59—21no—
133C4⋊C8×C59—21no—
134C22⋊C8×C59—21no—
135C22⋊C8×C59—21no—
136C22⋊C8×C59—21no—
137C22⋊C8×C59—21no—
138#97×C59—21no—
139#97×C59—21no—
140C4×C8×C59—21no—
141C4×C8×C59—21no—
142C24×C59C22⋊C411yescharacteristic
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59C22⋊C411yescharacteristic
147C2×Q8×C59C22⋊C411yescharacteristic
148C2×Q8×C59C22⋊C411yescharacteristic
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59C22⋊C411yescharacteristic
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59C22⋊C411yescharacteristic
159C22×C4×C59C22⋊C411yescharacteristic
160C22×C4×C59C22⋊C411yescharacteristic
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C2×C8×C59—41no—
165C2×C8×C59—41no—
166C2×C8×C59—41no—
167C2×C8×C59—41no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—21no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—21no—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
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—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59C22⋊C411yescharacteristic
198C4⋊C4×C59C22⋊C411yescharacteristic
199C4⋊C4×C59C22⋊C411yescharacteristic
200C4⋊C4×C59C22⋊C411yescharacteristic
201C22⋊C4×C59—21no—
202C22⋊C4×C59—21no—
203C22⋊C4×C59—21no—
204C22⋊C4×C59—21no—
205C22⋊C4×C59—21no—
206C22⋊C4×C59—21no—
207C22⋊C4×C59—21no—
208C22⋊C4×C59—21no—
209C22⋊C4×C59—21no—
210C22⋊C4×C59—21no—
211C22⋊C4×C59—21no—
212C22⋊C4×C59—21no—
213C22⋊C4×C59—21no—
214C22⋊C4×C59—21no—
215C22⋊C4×C59—21no—
216C22⋊C4×C59—21no—
217C22⋊C4×C59—21no—
218C22⋊C4×C59—21no—
219C22⋊C4×C59—21no—
220C22⋊C4×C59—21no—
221C22⋊C4×C59—21no—
222C42×C59—21no—
223C42×C59—21no—
224C42×C59—21no—
225C42×C59—21no—
226C42×C59—21no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59C2×D411yescharacteristic
230C42×C59C2×D411yescharacteristic
231C42×C59C2×D411yescharacteristic
232C42×C59C2×D411yescharacteristic
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59C2×C22⋊C411yescharacteristic
239Q8×C59—41no—
240Q8×C59—41no—
241Q8×C59—41no—
242Q8×C59—81no—
243Q8×C59—81no—
244Q8×C59—81no—
245D4×C59—41no—
246D4×C59—42no—
247D4×C59—81no—
248D4×C59—81no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—81no—
266C2×C4×C59—81no—
267C2×C4×C59—81no—
268C2×C4×C59—81no—
269C2×C4×C59—81no—
270C2×C4×C59C2×C22⋊C411yescharacteristic
271C2×C4×C59C2×C22⋊C411yescharacteristic
272C2×C4×C59#12011yescharacteristic
273C2×C4×C59#12011yescharacteristic
274C2×C4×C59#12011yescharacteristic
275C2×C4×C59#12011yescharacteristic
276C8×C59—81no—
277C8×C59—81no—
278C8×C59—81no—
279C8×C59—81no—
280#8490C5911yesmaximal, characteristic, direct product factor, Sylow
281C22×C59—21no—
282C22×C59—21no—
283C22×C59—21no—
284C22×C59—41no—
285C22×C59—41no—
286C22×C59—41no—
287C22×C59—41no—
288C22×C59—41no—
289C22×C59—41no—
290C22×C59—161no—
291C22×C59#37911yescharacteristic
292C4×C59—21no—
293C4×C59—21no—
294C4×C59—21no—
295C4×C59—21no—
296C4×C59—21no—
297C4×C59—21no—
298C4×C59—41no—
299C4×C59—41no—
300C4×C59—41no—
301C4×C59—41no—
302C4×C59—41no—
303C4×C59—41no—
304C4×C59—41no—
305C4×C59—41no—
306C4×C59—41no—
307C4×C59—41no—
308#3564C2×C5911yescharacteristic
309#1554C2×C5911yescharacteristic, complemented
310#1535C2×C5911yescharacteristic, complemented
311#1497C2×C5911yescharacteristic, complemented
312#1482C2×C5911yescharacteristic, complemented
313#1473C2×C5911yescharacteristic, complemented
314#1473C2×C5911yescharacteristic, complemented
315C2×C59—41no—
316C2×C59—81no—
317C2×C59—81no—
318C2×C59#179111yescharacteristic
319C2×C59#179411yescharacteristic
320C2×C59#179611yescharacteristic
321#563—21no—
322#563—21no—
323#556—21no—
324#554—21no—
325#552—21no—
326#552—21no—
327#551—21no—
328#551—21no—
329#544C4×C5911yescharacteristic
330#543C4×C5911yescharacteristic
331#542—21no—
332#541—21no—
333#541—21no—
334#539—21no—
335#539C4×C5911yescharacteristic
336#538C4×C5911yescharacteristic
337#533C22×C5911yescharacteristic
338#529C22×C5911yescharacteristic
339C2×#126C22×C5911yescharacteristic
340#432C22×C5911yescharacteristic
341#432C22×C5911yescharacteristic
342#431C22×C5911yescharacteristic
343#431C22×C5911yescharacteristic
344#333—21no—
345#332—21no—
346#330—21no—
347#329—21no—
348Q8⋊C8—21no—
349Q8⋊C8—21no—
350Q8⋊C8—21no—
351D4⋊C8—21no—
352#324—21no—
353#324—21no—
354#323—21no—
355#323—21no—
356C59#849011yescharacteristic, direct product factor, Sylow
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8D4×C5911yescharacteristic
361C4⋊Q8D4×C5911yescharacteristic
362#126—21no—
363#126—21no—
364#126—21no—
365#126—21no—
366#126—21no—
367#126—21no—
368#126—21no—
369#126—21no—
370#126—21no—
371#126—21no—
372#126—21no—
373#126—21no—
374#126—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125D4×C5911yescharacteristic
385#124—21no—
386#124—21no—
387#124—21no—
388#124D4×C5911yescharacteristic
389#123—21no—
390#123—21no—
391#123—21no—
392#123—21no—
393#123—21no—
394#123—21no—
395#123—21no—
396#123—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8C2×C4×C5911yescharacteristic
412C22⋊Q8C2×C4×C5911yescharacteristic
413C22⋊Q8C2×C4×C5911yescharacteristic
414#121—21no—
415#121C2×C4×C5911yescharacteristic
416#120—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8D4×C5911yescharacteristic
421C4×Q8D4×C5911yescharacteristic
422C4×Q8D4×C5911yescharacteristic
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4D4×C5911yescharacteristic
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C2×C4×C5911yescharacteristic
437C2×C4⋊C4D4×C5911yescharacteristic
438C2×C4⋊C4D4×C5911yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4C2×C4×C5911yescharacteristic
441C2×C22⋊C4D4×C5911yescharacteristic
442C2×C22⋊C4D4×C5911yescharacteristic
443C2×C42C23×C5911yescharacteristic
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454C4×C8—21no—
455C4×C8—21no—
456C24C22⋊C4×C5911yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C22⋊C4×C5911yescharacteristic
461C2×Q8C22⋊C4×C5911yescharacteristic
462C2×Q8C22⋊C4×C5911yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C22⋊C4×C5911yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22⋊C4×C5911yescharacteristic
473C22×C4C22⋊C4×C5911yescharacteristic
474C22×C4C22⋊C4×C5911yescharacteristic
475C22×C4C22×C4×C5911yescharacteristic
476C22×C4C2×D4×C5911yescharacteristic
477C22×C4C2×D4×C5911yescharacteristic
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4C22⋊C4×C5911yescharacteristic
512C4⋊C4C22⋊C4×C5911yescharacteristic
513C4⋊C4C22⋊C4×C5911yescharacteristic
514C4⋊C4C22⋊C4×C5911yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42C2×D4×C5911yescharacteristic
544C42C2×D4×C5911yescharacteristic
545C42C2×D4×C5911yescharacteristic
546C42C2×D4×C5911yescharacteristic
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×C22⋊C4×C5911yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—81no—
557Q8—81no—
558Q8—81no—
559D4—41no—
560D4—42no—
561D4—81no—
562D4—81no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C2×C22⋊C4×C5911yescharacteristic
585C2×C4C2×C22⋊C4×C5911yescharacteristic
586C2×C4#120×C5911yescharacteristic
587C2×C4#120×C5911yescharacteristic
588C2×C4#120×C5911yescharacteristic
589C2×C4#120×C5911yescharacteristic
590C8—81no—
591C8—81no—
592C8—81no—
593C8—81no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—161no—
604C22C59×#37911yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C2—41no—
622C2—81no—
623C2—81no—
624C2C59×#179111yescharacteristic
625C2C59×#179411yescharacteristic
626C2C59×#179611yescharacteristic
subgroupG/H
center, socleC22×C59#379
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC59×#538C4
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×#1554C2semidirect
3. C59×#1535C2semidirect
4. C59×#1497C2semidirect
5. C59×#1482C2semidirect
6. C59×#1473C2semidirect
7. C59×#1473C2semidirect
280. #8490C59direct (N × H)
309. #1554C2×C59semidirect
310. #1535C2×C59semidirect
311. #1497C2×C59semidirect
312. #1482C2×C59semidirect
313. #1473C2×C59semidirect
314. #1473C2×C59semidirect
356. C59#8490direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35642
C59×#15542
C59×#15352
C59×#14972
C59×#14822
C59×#14732
#849059