Finite Group Databasebeta

← C59×#62889 #28474998

Subgroups — C59×#62889 #28474998

Order 15104.

6186 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3564C218yesmaximal, complemented
2C59×#3563C218yesmaximal, complemented
3C59×#3563C218yesmaximal, complemented
4C59×#3557C214yesmaximal, complemented
5C59×#3556C214yesmaximal, complemented
6C59×#3555C218yesmaximal, complemented
7C59×#3555C218yesmaximal, complemented
8C59×#3509C212yesmaximal, complemented
9C59×#3507C212yesmaximal, complemented
10C59×#3504C212yesmaximal, complemented
11C59×#3502C212yesmaximal, complemented
12C59×#3495C214yesmaximal, complemented
13C59×#3458C211yesmaximal, characteristic, complemented
14C59×#3455C211yesmaximal, characteristic
15C2×C59×#541C211yesmaximal, characteristic, complemented
16C59×#564C22116yescomplemented
17C59×#563C22116yes—
18C59×#563C22116yes—
19C59×#563C22116yescomplemented
20C59×#559C2214yescomplemented
21Q82×C59C2214yescomplemented
22Q82×C59C2214yescomplemented
23C59×#557C2214yescomplemented
24C59×#557C2218yescomplemented
25C59×#557C2214yescomplemented
26C59×#557C22116yescomplemented
27C59×#557C2218yescomplemented
28C59×#557C2218yescomplemented
29C59×#557C2218yescomplemented
30C59×#557C2214yescomplemented
31C59×#556C22116yes—
32C59×#556C2218yes—
33C59×#556C2214yescomplemented
34C59×#556C2218yescomplemented
35C59×#556C2218yescomplemented
36C59×#554C2218yes—
37C59×#554C22116yes—
38C59×#554C2214yescomplemented
39C59×#554C2218yescomplemented
40C59×#552C22116yes—
41C59×#552C22116yes—
42C59×#552C2218yes—
43C59×#552C2218yes—
44C59×#552C22116yes—
45C59×#552C2218yescomplemented
46C59×#552C22116yescomplemented
47C59×#551C22116yes—
48C59×#544C2214yes—
49C59×#544C2214yes—
50C59×#544C2214yes—
51C59×#544C2218yes—
52C59×#544C2214yes—
53C59×#544C22116yescomplemented
54C59×#544C2218yescomplemented
55C59×#543C2214yes—
56C59×#542C2214yes—
57C59×#542C22116yes—
58C59×#542C2218yes—
59C59×#541C2214yes—
60C59×#541C22116yes—
61C59×#541C2218yes—
62C59×#541C2218yes—
63C59×#541C2212yes—
64C59×#541C2214yes—
65C59×#541C22116yes—
66C59×#541C2214yescomplemented
67C59×#541C2214yescomplemented
68C59×#541C22116yescomplemented
69C59×#541C22116yescomplemented
70C59×#541C22116yescomplemented
71C59×#540C2212yes—
72C59×#539C2218yes—
73C59×#539C22116yes—
74C59×#539C2214yes—
75C59×#538C2214yes—
76C59×#536C2214yes—
77C59×#533C2212yes—
78C59×#533C2212yes—
79C59×#533C2214yes—
80C59×#533C2218yes—
81C59×#533C2214yes—
82C59×#533C2218yes—
83C59×#533C2211yescharacteristic
84C59×#533C2218yescomplemented
85C59×#533C2214yescomplemented
86C59×#532C2211yescharacteristic
87C2×C4⋊Q8×C59C2211yescharacteristic
88C59×#529C2218yes—
89C59×#529C2218yes—
90C59×#529C2218yes—
91C2×#126×C59C2214yes—
92C2×#125×C59C2214yes—
93C2×#125×C59C2211yescharacteristic
94C2×#125×C59C2214yescomplemented
95C59×#525C2212yes—
96C2×C22⋊Q8×C59C2212yes—
97C59×#520C2214yes—
98C59×#519C2214yes—
99C4×#41×C59C2212yes—
100C2×C4×Q8×C59C2212yes—
101C2×#117×C59C2211yescharacteristic
102C2×#117×C59C2212yes—
103C2×#41×C59C2312yes—
104C22×Q8×C59C2312yes—
105C23×C4×C59C2311yescharacteristic
106C4⋊Q8×C59C2314yes—
107C4⋊Q8×C59C2314yes—
108C4⋊Q8×C59C2311yescharacteristic
109C4⋊Q8×C59C2314yes—
110C4⋊Q8×C59C2318yes—
111C4⋊Q8×C59C2318yes—
112C4⋊Q8×C59C2318yes—
113C4⋊Q8×C59C2312yes—
114C4⋊Q8×C59C2318yes—
115C4⋊Q8×C59C2312yes—
116C4⋊Q8×C59C2312yes—
117C4⋊Q8×C59C2318yes—
118C4⋊Q8×C59C2318yes—
119C4⋊Q8×C59C2318yes—
120C4⋊Q8×C59C23116yes—
121C4⋊Q8×C59C23116yes—
122C4⋊Q8×C59C23116yes—
123#127×C59C2311yescharacteristic
124#126×C59C23116yes—
125#126×C59C23116yes—
126#126×C59C2318yes—
127#126×C59C2318yes—
128#126×C59C23116yes—
129#126×C59C23116yes—
130#126×C59C23116yes—
131#126×C59C23116yes—
132#126×C59C23116yes—
133#126×C59C23116yes—
134#126×C59C23116yes—
135#126×C59C23116yes—
136#125×C59C2314yes—
137#125×C59C23116yes—
138#125×C59C23116yes—
139#125×C59C2314yes—
140#125×C59C2312yes—
141#125×C59C23116yes—
142#125×C59C2318yes—
143#125×C59C2318yes—
144#125×C59C2318yes—
145#125×C59C2318yes—
146#125×C59C2312yes—
147#125×C59C23116yes—
148#125×C59C2312yes—
149#125×C59C2318yes—
150#125×C59C23116yes—
151#125×C59C2314yes—
152#125×C59C2318yes—
153#125×C59C23116yes—
154#125×C59C23116yes—
155#125×C59C23116yes—
156#125×C59C23116yes—
157#125×C59C23116yes—
158#125×C59C23116yes—
159#125×C59C23116yes—
160#125×C59C23116yes—
161#125×C59C23116yes—
162#124×C59C2318yes—
163#124×C59C2318yes—
164#124×C59C2318yes—
165#124×C59C2312yes—
166#124×C59C23116yes—
167#123×C59C2314yes—
168#123×C59C23116yes—
169#123×C59C2318yes—
170#123×C59C2318yes—
171#123×C59C23116yes—
172#123×C59C23116yes—
173#123×C59C23116yes—
174C22⋊Q8×C59C2318yes—
175C22⋊Q8×C59C2318yes—
176C22⋊Q8×C59C2314yes—
177C22⋊Q8×C59C2314yes—
178C22⋊Q8×C59C2318yes—
179C22⋊Q8×C59C2314yes—
180C22⋊Q8×C59C2314yes—
181C22⋊Q8×C59C2318yes—
182C22⋊Q8×C59C2318yes—
183C22⋊Q8×C59C23116yes—
184C22⋊Q8×C59C2318yes—
185C22⋊Q8×C59C2318yes—
186C22⋊Q8×C59C2318yes—
187C22⋊Q8×C59C23116yes—
188C22⋊Q8×C59C2318yes—
189C22⋊Q8×C59C2318yes—
190C22⋊Q8×C59C23116yes—
191C22⋊Q8×C59C23116yes—
192C22⋊Q8×C59C23116yes—
193C22⋊Q8×C59C23116yes—
194C22⋊Q8×C59C23116yes—
195C22⋊Q8×C59C23116yes—
196#121×C59C2314yes—
197#121×C59C2314yes—
198#121×C59C2318yes—
199#120×C59C2314yes—
200C4×Q8×C59C2314yes—
201C4×Q8×C59C2314yes—
202C4×Q8×C59C2314yes—
203C4×Q8×C59C2314yes—
204C4×Q8×C59C2314yes—
205C4×Q8×C59C2318yes—
206C4×Q8×C59C2318yes—
207C4×Q8×C59C2318yes—
208C4×Q8×C59C2318yes—
209C4×Q8×C59C2318yes—
210C4×Q8×C59C2314yes—
211C4×Q8×C59C2318yes—
212C4×Q8×C59C2318yes—
213C4×Q8×C59C2314yes—
214C4×Q8×C59C2314yes—
215C4×Q8×C59C23116yes—
216C4×Q8×C59C2318yes—
217C4×Q8×C59C23116yes—
218C4×Q8×C59C2318yes—
219C4×Q8×C59C23116yes—
220C4×Q8×C59C23116yes—
221C4×D4×C59C2318yes—
222C4×D4×C59C2314yes—
223C4×D4×C59C23116yes—
224C4×D4×C59C2318yes—
225C4×D4×C59C2318yes—
226C4×D4×C59C2314yes—
227C4×D4×C59C2318yes—
228C4×D4×C59C23116yes—
229#117×C59C2314yes—
230#117×C59C2314yes—
231#117×C59C2312yes—
232#117×C59C2312yes—
233#117×C59C2314yes—
234#117×C59C2312yes—
235#117×C59C2314yes—
236#117×C59C2312yes—
237#117×C59C2312yes—
238#117×C59C2314yes—
239#117×C59C23116yes—
240#117×C59C2318yes—
241#117×C59C23116yes—
242#117×C59C23116yes—
243#117×C59C23116yes—
244#117×C59C23116yes—
245C2×C4⋊C4×C59C2312yes—
246C2×C4⋊C4×C59C2314yes—
247C2×C4⋊C4×C59C2312yes—
248C2×C4⋊C4×C59C2314yes—
249C2×C4⋊C4×C59C2318yes—
250C2×C4⋊C4×C59C2314yes—
251C2×C4⋊C4×C59C2314yes—
252C2×C4⋊C4×C59C2314yes—
253C2×C4⋊C4×C59C23116yes—
254C2×C22⋊C4×C59C2312yes—
255C2×C22⋊C4×C59C2314yes—
256C2×C22⋊C4×C59C2314yes—
257C2×C42×C59C2311yescharacteristic
258C2×C42×C59C2311yescharacteristic
259C2×C42×C59C2314yes—
260C2×C42×C59C2314yes—
261C2×C42×C59C2314yes—
262C24×C59C2411yescharacteristic
263#41×C59—28no—
264C2×Q8×C59—28no—
265C2×Q8×C59C2414yes—
266C2×Q8×C59C2414yes—
267C2×Q8×C59C2412yes—
268C2×Q8×C59C2418yes—
269C2×Q8×C59C2414yes—
270C2×Q8×C59C24116yes—
271C2×Q8×C59C2414yes—
272C2×Q8×C59C2414yes—
273C2×D4×C59C2414yes—
274C2×D4×C59C2412yes—
275C2×D4×C59C2418yes—
276C2×D4×C59C2414yes—
277C22×C4×C59—24no—
278C22×C4×C59C2412yes—
279C22×C4×C59C2414yes—
280C22×C4×C59C2414yes—
281C22×C4×C59C2411yescharacteristic
282C22×C4×C59C2412yes—
283C22×C4×C59C2412yes—
284C22×C4×C59C2412yes—
285C22×C4×C59C2414yes—
286C22×C4×C59C2418yes—
287C22×C4×C59C2418yes—
288C22×C4×C59C24116yes—
289C22×C4×C59C2411yescharacteristic
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C2414yes—
292C4⋊C4×C59C24116yes—
293C4⋊C4×C59C2418yes—
294C4⋊C4×C59C2414yes—
295C4⋊C4×C59C2414yes—
296C4⋊C4×C59C2418yes—
297C4⋊C4×C59C2414yes—
298C4⋊C4×C59C24116yes—
299C4⋊C4×C59C24116yes—
300C4⋊C4×C59C24116yes—
301C4⋊C4×C59C24116yes—
302C4⋊C4×C59C2414yes—
303C4⋊C4×C59C24116yes—
304C4⋊C4×C59C2418yes—
305C4⋊C4×C59C2418yes—
306C4⋊C4×C59C2418yes—
307C4⋊C4×C59C2418yes—
308C4⋊C4×C59C24116yes—
309C4⋊C4×C59C2414yes—
310C4⋊C4×C59C2418yes—
311C4⋊C4×C59C24116yes—
312C4⋊C4×C59C24116yes—
313C4⋊C4×C59C2414yes—
314C4⋊C4×C59C2414yes—
315C4⋊C4×C59C24116yes—
316C4⋊C4×C59C2418yes—
317C4⋊C4×C59C2418yes—
318C4⋊C4×C59C2418yes—
319C4⋊C4×C59C2418yes—
320C4⋊C4×C59C2414yes—
321C4⋊C4×C59C24116yes—
322C4⋊C4×C59C2414yes—
323C22⋊C4×C59C2418yes—
324C22⋊C4×C59C2414yes—
325C22⋊C4×C59C2414yes—
326C22⋊C4×C59C2414yes—
327C22⋊C4×C59C2414yes—
328C22⋊C4×C59C24116yes—
329C22⋊C4×C59C2414yes—
330C22⋊C4×C59C2418yes—
331C22⋊C4×C59C2418yes—
332C22⋊C4×C59C2418yes—
333C22⋊C4×C59C24116yes—
334C22⋊C4×C59C24116yes—
335C22⋊C4×C59C2418yes—
336C22⋊C4×C59C24116yes—
337C42×C59C2412yes—
338C42×C59C2414yes—
339C42×C59C2412yes—
340C42×C59C2414yes—
341C42×C59C2412yes—
342C42×C59C2418yes—
343C42×C59C2411yescharacteristic
344C42×C59C2411yescharacteristic
345C42×C59C2418yes—
346C42×C59C2414yes—
347C42×C59C2418yes—
348C42×C59C2418yes—
349C42×C59C24116yes—
350C42×C59C24116yes—
351C42×C59C24116yes—
352C23×C59—22no—
353C23×C59—42no—
354C23×C59C2512yes—
355C23×C59C2514yes—
356C23×C59C2511yescharacteristic
357Q8×C59—28no—
358Q8×C59—28no—
359Q8×C59—24no—
360Q8×C59—48no—
361Q8×C59—44no—
362Q8×C59—416no—
363Q8×C59—44no—
364Q8×C59—44no—
365D4×C59—28no—
366D4×C59—24no—
367D4×C59—44no—
368D4×C59—48no—
369C2×C4×C59—22no—
370C2×C4×C59—28no—
371C2×C4×C59—24no—
372C2×C4×C59—24no—
373C2×C4×C59—28no—
374C2×C4×C59—42no—
375C2×C4×C59—44no—
376C2×C4×C59—416no—
377C2×C4×C59—48no—
378C2×C4×C59—48no—
379C2×C4×C59—42no—
380C2×C4×C592−1+414yes—
381C2×C4×C59C2518yes—
382C2×C4×C59C2512yes—
383C2×C4×C59C2518yes—
384C2×C4×C59C2514yes—
385C2×C4×C59C2518yes—
386C2×C4×C59C2512yes—
387C2×C4×C59C2512yes—
388C2×C4×C59C2514yes—
389C2×C4×C59C2518yes—
390C2×C4×C59C2518yes—
391C2×C4×C59C2511yescharacteristic
392C2×C4×C59C2511yescharacteristic
393#62889C5911yesmaximal, characteristic, direct product factor, Sylow
394C22×C59—22no—
395C22×C59—22no—
396C22×C59—24no—
397C22×C59—28no—
398C22×C59—24no—
399C22×C59—82no—
400C22×C59C2×2−1+412yes—
401C22×C59C2611yescharacteristic
402C4×C59—22no—
403C4×C59—24no—
404C4×C59—28no—
405C4×C59—28no—
406C4×C59—24no—
407C4×C59—28no—
408C4×C59—22no—
409C4×C59—28no—
410C4×C59—28no—
411C4×C59—22no—
412C4×C59C2×2−1+412yes—
413C4×C59C2×2−1+412yes—
414#3564C2×C5918yescomplemented
415#3563C2×C5918yescomplemented
416#3563C2×C5918yescomplemented
417#3557C2×C5914yescomplemented
418#3556C2×C5914yescomplemented
419#3555C2×C5918yescomplemented
420#3555C2×C5918yescomplemented
421#3509C2×C5912yescomplemented
422#3507C2×C5912yescomplemented
423#3504C2×C5912yescomplemented
424#3502C2×C5912yescomplemented
425#3495C2×C5914yescomplemented
426#3458C2×C5911yescharacteristic, complemented
427#3455C2×C5911yescharacteristic
428C2×#541C2×C5911yescharacteristic, complemented
429C2×C59—22no—
430C2×C59—44no—
431C2×C59—42no—
432C2×C59C22×2−1+411yescharacteristic
433C2×C592−1+612yes—
434#564C22×C59116yescomplemented
435#563C22×C59116yes—
436#563C22×C59116yes—
437#563C22×C59116yescomplemented
438#559C22×C5914yescomplemented
439Q82C22×C5914yescomplemented
440Q82C22×C5914yescomplemented
441#557C22×C5914yescomplemented
442#557C22×C5918yescomplemented
443#557C22×C5918yescomplemented
444#557C22×C5914yescomplemented
445#557C22×C5918yescomplemented
446#557C22×C5914yescomplemented
447#557C22×C5918yescomplemented
448#557C22×C59116yescomplemented
449#556C22×C5918yes—
450#556C22×C59116yes—
451#556C22×C5914yescomplemented
452#556C22×C5918yescomplemented
453#556C22×C5918yescomplemented
454#554C22×C5918yes—
455#554C22×C59116yes—
456#554C22×C5918yescomplemented
457#554C22×C5914yescomplemented
458#552C22×C5918yes—
459#552C22×C5918yes—
460#552C22×C59116yes—
461#552C22×C59116yes—
462#552C22×C59116yes—
463#552C22×C5918yescomplemented
464#552C22×C59116yescomplemented
465#551C22×C59116yes—
466#544C22×C5914yes—
467#544C22×C5914yes—
468#544C22×C5914yes—
469#544C22×C5914yes—
470#544C22×C5918yes—
471#544C22×C5918yescomplemented
472#544C22×C59116yescomplemented
473#543C22×C5914yes—
474#542C22×C5914yes—
475#542C22×C5918yes—
476#542C22×C59116yes—
477#541C22×C5914yes—
478#541C22×C5918yes—
479#541C22×C5914yes—
480#541C22×C5912yes—
481#541C22×C5918yes—
482#541C22×C59116yes—
483#541C22×C59116yes—
484#541C22×C5914yescomplemented
485#541C22×C5914yescomplemented
486#541C22×C59116yescomplemented
487#541C22×C59116yescomplemented
488#541C22×C59116yescomplemented
489#540C22×C5912yes—
490#539C22×C5914yes—
491#539C22×C5918yes—
492#539C22×C59116yes—
493#538C22×C5914yes—
494#536C22×C5914yes—
495#533C22×C5911yescharacteristic
496#533C22×C5912yes—
497#533C22×C5912yes—
498#533C22×C5914yes—
499#533C22×C5914yes—
500#533C22×C5918yes—
501#533C22×C5918yes—
502#533C22×C5914yescomplemented
503#533C22×C5918yescomplemented
504#532C22×C5911yescharacteristic
505C2×C4⋊Q8C22×C5911yescharacteristic
506#529C22×C5918yes—
507#529C22×C5918yes—
508#529C22×C5918yes—
509C2×#126C22×C5914yes—
510C2×#125C22×C5911yescharacteristic
511C2×#125C22×C5914yes—
512C2×#125C22×C5914yescomplemented
513#525C22×C5912yes—
514C2×C22⋊Q8C22×C5912yes—
515#520C22×C5914yes—
516#519C22×C5914yes—
517C4×#41C22×C5912yes—
518C2×C4×Q8C22×C5912yes—
519C2×#117C22×C5911yescharacteristic
520C2×#117C22×C5912yes—
521C59#6288911yescharacteristic, direct product factor, Sylow
522C2×#41C23×C5912yes—
523C22×Q8C23×C5912yes—
524C23×C4C23×C5911yescharacteristic
525C4⋊Q8C23×C5914yes—
526C4⋊Q8C23×C5914yes—
527C4⋊Q8C23×C5911yescharacteristic
528C4⋊Q8C23×C5914yes—
529C4⋊Q8C23×C5918yes—
530C4⋊Q8C23×C5918yes—
531C4⋊Q8C23×C5918yes—
532C4⋊Q8C23×C5912yes—
533C4⋊Q8C23×C5918yes—
534C4⋊Q8C23×C5912yes—
535C4⋊Q8C23×C5912yes—
536C4⋊Q8C23×C5918yes—
537C4⋊Q8C23×C5918yes—
538C4⋊Q8C23×C5918yes—
539C4⋊Q8C23×C59116yes—
540C4⋊Q8C23×C59116yes—
541C4⋊Q8C23×C59116yes—
542#127C23×C5911yescharacteristic
543#126C23×C59116yes—
544#126C23×C59116yes—
545#126C23×C5918yes—
546#126C23×C5918yes—
547#126C23×C59116yes—
548#126C23×C59116yes—
549#126C23×C59116yes—
550#126C23×C59116yes—
551#126C23×C59116yes—
552#126C23×C59116yes—
553#126C23×C59116yes—
554#126C23×C59116yes—
555#125C23×C5914yes—
556#125C23×C59116yes—
557#125C23×C59116yes—
558#125C23×C5914yes—
559#125C23×C5912yes—
560#125C23×C59116yes—
561#125C23×C5918yes—
562#125C23×C5918yes—
563#125C23×C5918yes—
564#125C23×C5918yes—
565#125C23×C5912yes—
566#125C23×C59116yes—
567#125C23×C5912yes—
568#125C23×C5918yes—
569#125C23×C59116yes—
570#125C23×C5914yes—
571#125C23×C5918yes—
572#125C23×C59116yes—
573#125C23×C59116yes—
574#125C23×C59116yes—
575#125C23×C59116yes—
576#125C23×C59116yes—
577#125C23×C59116yes—
578#125C23×C59116yes—
579#125C23×C59116yes—
580#125C23×C59116yes—
581#124C23×C5918yes—
582#124C23×C5918yes—
583#124C23×C5918yes—
584#124C23×C5912yes—
585#124C23×C59116yes—
586#123C23×C5914yes—
587#123C23×C59116yes—
588#123C23×C5918yes—
589#123C23×C5918yes—
590#123C23×C59116yes—
591#123C23×C59116yes—
592#123C23×C59116yes—
593C22⋊Q8C23×C5918yes—
594C22⋊Q8C23×C5918yes—
595C22⋊Q8C23×C5914yes—
596C22⋊Q8C23×C5914yes—
597C22⋊Q8C23×C5918yes—
598C22⋊Q8C23×C5914yes—
599C22⋊Q8C23×C5914yes—
600C22⋊Q8C23×C5918yes—
601C22⋊Q8C23×C5918yes—
602C22⋊Q8C23×C59116yes—
603C22⋊Q8C23×C5918yes—
604C22⋊Q8C23×C5918yes—
605C22⋊Q8C23×C5918yes—
606C22⋊Q8C23×C59116yes—
607C22⋊Q8C23×C5918yes—
608C22⋊Q8C23×C5918yes—
609C22⋊Q8C23×C59116yes—
610C22⋊Q8C23×C59116yes—
611C22⋊Q8C23×C59116yes—
612C22⋊Q8C23×C59116yes—
613C22⋊Q8C23×C59116yes—
614C22⋊Q8C23×C59116yes—
615#121C23×C5914yes—
616#121C23×C5914yes—
617#121C23×C5918yes—
618#120C23×C5914yes—
619C4×Q8C23×C5914yes—
620C4×Q8C23×C5914yes—
621C4×Q8C23×C5914yes—
622C4×Q8C23×C5914yes—
623C4×Q8C23×C5914yes—
624C4×Q8C23×C5918yes—
625C4×Q8C23×C5918yes—
626C4×Q8C23×C5918yes—
627C4×Q8C23×C5918yes—
628C4×Q8C23×C5918yes—
629C4×Q8C23×C5914yes—
630C4×Q8C23×C5918yes—
631C4×Q8C23×C5918yes—
632C4×Q8C23×C5914yes—
633C4×Q8C23×C5914yes—
634C4×Q8C23×C59116yes—
635C4×Q8C23×C5918yes—
636C4×Q8C23×C59116yes—
637C4×Q8C23×C5918yes—
638C4×Q8C23×C59116yes—
639C4×Q8C23×C59116yes—
640C4×D4C23×C5918yes—
641C4×D4C23×C5914yes—
642C4×D4C23×C59116yes—
643C4×D4C23×C5918yes—
644C4×D4C23×C5918yes—
645C4×D4C23×C5914yes—
646C4×D4C23×C5918yes—
647C4×D4C23×C59116yes—
648#117C23×C5914yes—
649#117C23×C5914yes—
650#117C23×C5912yes—
651#117C23×C5912yes—
652#117C23×C5914yes—
653#117C23×C5912yes—
654#117C23×C5914yes—
655#117C23×C5912yes—
656#117C23×C5912yes—
657#117C23×C5914yes—
658#117C23×C59116yes—
659#117C23×C5918yes—
660#117C23×C59116yes—
661#117C23×C59116yes—
662#117C23×C59116yes—
663#117C23×C59116yes—
664C2×C4⋊C4C23×C5912yes—
665C2×C4⋊C4C23×C5914yes—
666C2×C4⋊C4C23×C5912yes—
667C2×C4⋊C4C23×C5914yes—
668C2×C4⋊C4C23×C5918yes—
669C2×C4⋊C4C23×C5914yes—
670C2×C4⋊C4C23×C5914yes—
671C2×C4⋊C4C23×C5914yes—
672C2×C4⋊C4C23×C59116yes—
673C2×C22⋊C4C23×C5912yes—
674C2×C22⋊C4C23×C5914yes—
675C2×C22⋊C4C23×C5914yes—
676C2×C42C23×C5911yescharacteristic
677C2×C42C23×C5911yescharacteristic
678C2×C42C23×C5914yes—
679C2×C42C23×C5914yes—
680C2×C42C23×C5914yes—
681C24C24×C5911yescharacteristic
682#41—28no—
683C2×Q8—28no—
684C2×Q8C24×C5914yes—
685C2×Q8C24×C5914yes—
686C2×Q8C24×C5912yes—
687C2×Q8C24×C5918yes—
688C2×Q8C24×C5914yes—
689C2×Q8C24×C59116yes—
690C2×Q8C24×C5914yes—
691C2×Q8C24×C5914yes—
692C2×D4C24×C5914yes—
693C2×D4C24×C5912yes—
694C2×D4C24×C5918yes—
695C2×D4C24×C5914yes—
696C22×C4—24no—
697C22×C4C24×C5912yes—
698C22×C4C24×C5914yes—
699C22×C4C24×C5914yes—
700C22×C4C24×C5911yescharacteristic
701C22×C4C24×C5912yes—
702C22×C4C24×C5912yes—
703C22×C4C24×C5912yes—
704C22×C4C24×C5914yes—
705C22×C4C24×C5918yes—
706C22×C4C24×C5918yes—
707C22×C4C24×C59116yes—
708C22×C4C24×C5911yescharacteristic
709C4⋊C4C24×C5914yes—
710C4⋊C4C24×C5914yes—
711C4⋊C4C24×C59116yes—
712C4⋊C4C24×C5918yes—
713C4⋊C4C24×C5914yes—
714C4⋊C4C24×C5914yes—
715C4⋊C4C24×C5918yes—
716C4⋊C4C24×C5914yes—
717C4⋊C4C24×C59116yes—
718C4⋊C4C24×C59116yes—
719C4⋊C4C24×C59116yes—
720C4⋊C4C24×C59116yes—
721C4⋊C4C24×C5914yes—
722C4⋊C4C24×C59116yes—
723C4⋊C4C24×C5918yes—
724C4⋊C4C24×C5918yes—
725C4⋊C4C24×C5918yes—
726C4⋊C4C24×C5918yes—
727C4⋊C4C24×C59116yes—
728C4⋊C4C24×C5914yes—
729C4⋊C4C24×C5918yes—
730C4⋊C4C24×C59116yes—
731C4⋊C4C24×C59116yes—
732C4⋊C4C24×C5914yes—
733C4⋊C4C24×C5914yes—
734C4⋊C4C24×C59116yes—
735C4⋊C4C24×C5918yes—
736C4⋊C4C24×C5918yes—
737C4⋊C4C24×C5918yes—
738C4⋊C4C24×C5918yes—
739C4⋊C4C24×C5914yes—
740C4⋊C4C24×C59116yes—
741C4⋊C4C24×C5914yes—
742C22⋊C4C24×C5918yes—
743C22⋊C4C24×C5914yes—
744C22⋊C4C24×C5914yes—
745C22⋊C4C24×C5914yes—
746C22⋊C4C24×C5914yes—
747C22⋊C4C24×C59116yes—
748C22⋊C4C24×C5914yes—
749C22⋊C4C24×C5918yes—
750C22⋊C4C24×C5918yes—
751C22⋊C4C24×C5918yes—
752C22⋊C4C24×C59116yes—
753C22⋊C4C24×C59116yes—
754C22⋊C4C24×C5918yes—
755C22⋊C4C24×C59116yes—
756C42C24×C5912yes—
757C42C24×C5914yes—
758C42C24×C5912yes—
759C42C24×C5914yes—
760C42C24×C5912yes—
761C42C24×C5918yes—
762C42C24×C5911yescharacteristic
763C42C24×C5911yescharacteristic
764C42C24×C5918yes—
765C42C24×C5914yes—
766C42C24×C5918yes—
767C42C24×C5918yes—
768C42C24×C59116yes—
769C42C24×C59116yes—
770C42C24×C59116yes—
771C23—22no—
772C23—42no—
773C23C25×C5912yes—
774C23C25×C5914yes—
775C23C25×C5911yescharacteristic
776Q8—28no—
777Q8—28no—
778Q8—24no—
779Q8—48no—
780Q8—44no—
781Q8—416no—
782Q8—44no—
783Q8—44no—
784D4—28no—
785D4—24no—
786D4—44no—
787D4—48no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—416no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—42no—
799C2×C42−1+4×C5914yes—
800C2×C4C25×C5918yes—
801C2×C4C25×C5912yes—
802C2×C4C25×C5918yes—
803C2×C4C25×C5914yes—
804C2×C4C25×C5918yes—
805C2×C4C25×C5912yes—
806C2×C4C25×C5912yes—
807C2×C4C25×C5914yes—
808C2×C4C25×C5918yes—
809C2×C4C25×C5918yes—
810C2×C4C25×C5911yescharacteristic
811C2×C4C25×C5911yescharacteristic
812C22—22no—
813C22—22no—
814C22—24no—
815C22—28no—
816C22—24no—
817C22—82no—
818C22C2×2−1+4×C5912yes—
819C22C26×C5911yescharacteristic
820C4—22no—
821C4—24no—
822C4—28no—
823C4—28no—
824C4—24no—
825C4—28no—
826C4—22no—
827C4—28no—
828C4—28no—
829C4—22no—
830C4C2×2−1+4×C5912yes—
831C4C2×2−1+4×C5912yes—
832C2—22no—
833C2—42no—
834C2—44no—
835C2C22×2−1+4×C5911yescharacteristic
836C2C59×2−1+612yes—
subgroupG/H
center, socleC22×C59C26
commutator, Frattini, cosocleC22C26×C59
prime radicalC59×#3455C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3564C2semidirect
2. C59×#3563C2semidirect
3. C59×#3563C2semidirect
4. C59×#3557C2semidirect
5. C59×#3556C2semidirect
6. C59×#3555C2semidirect
7. C59×#3555C2semidirect
8. C59×#3509C2semidirect
9. C59×#3507C2semidirect
10. C59×#3504C2semidirect
11. C59×#3502C2semidirect
12. C59×#3495C2semidirect
13. C59×#3458C2semidirect
15. C2×C59×#541C2semidirect
16. C59×#564C22semidirect
19. C59×#563C22semidirect
20. C59×#559C22semidirect
21. Q82×C59C22semidirect
22. Q82×C59C22semidirect
23. C59×#557C22semidirect
24. C59×#557C22semidirect
25. C59×#557C22semidirect
26. C59×#557C22semidirect
27. C59×#557C22semidirect
28. C59×#557C22semidirect
29. C59×#557C22semidirect
30. C59×#557C22semidirect
33. C59×#556C22semidirect
34. C59×#556C22semidirect
35. C59×#556C22semidirect
38. C59×#554C22semidirect
39. C59×#554C22semidirect
45. C59×#552C22semidirect
46. C59×#552C22semidirect
53. C59×#544C22semidirect
54. C59×#544C22semidirect
66. C59×#541C22semidirect
67. C59×#541C22semidirect
68. C59×#541C22semidirect
69. C59×#541C22semidirect
70. C59×#541C22semidirect
84. C59×#533C22semidirect
85. C59×#533C22semidirect
94. C2×#125×C59C22semidirect
393. #62889C59direct (N × H)
414. #3564C2×C59semidirect
415. #3563C2×C59semidirect
416. #3563C2×C59semidirect
417. #3557C2×C59semidirect
418. #3556C2×C59semidirect
419. #3555C2×C59semidirect
420. #3555C2×C59semidirect
421. #3509C2×C59semidirect
422. #3507C2×C59semidirect
423. #3504C2×C59semidirect
424. #3502C2×C59semidirect
425. #3495C2×C59semidirect
426. #3458C2×C59semidirect
428. C2×#541C2×C59semidirect
434. #564C22×C59semidirect
437. #563C22×C59semidirect
438. #559C22×C59semidirect
439. Q82C22×C59semidirect
440. Q82C22×C59semidirect
441. #557C22×C59semidirect
442. #557C22×C59semidirect
443. #557C22×C59semidirect
444. #557C22×C59semidirect
445. #557C22×C59semidirect
446. #557C22×C59semidirect
447. #557C22×C59semidirect
448. #557C22×C59semidirect
451. #556C22×C59semidirect
452. #556C22×C59semidirect
453. #556C22×C59semidirect
456. #554C22×C59semidirect
457. #554C22×C59semidirect
463. #552C22×C59semidirect
464. #552C22×C59semidirect
471. #544C22×C59semidirect
472. #544C22×C59semidirect
484. #541C22×C59semidirect
485. #541C22×C59semidirect
486. #541C22×C59semidirect
487. #541C22×C59semidirect
488. #541C22×C59semidirect
502. #533C22×C59semidirect
503. #533C22×C59semidirect
512. C2×#125C22×C59semidirect
521. C59#62889direct (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×#35632
C59×#35572
C59×#35562
C59×#35552
C59×#35092
C59×#35072
C59×#35042
C59×#35022
C59×#34952
C59×#34582
C59×#34552
C2×C59×#5412
#6288959