Finite Group Databasebeta

← C59×#25654 #28437763

Subgroups — C59×#25654 #28437763

Order 15104.

1018 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#556C211yesmaximal, characteristic
2C2×C59×#488C211yesmaximal, characteristic
3C2×C59×#479C211yesmaximal, characteristic, complemented
4C59×#2584C211yesmaximal, characteristic, complemented
5C59×#2043C211yesmaximal, characteristic, complemented
6C59×#2043C211yesmaximal, characteristic, complemented
7C59×#2042C211yesmaximal, characteristic
8C59×#2042C211yesmaximal, characteristic
9C59×#1984C211yesmaximal, characteristic, complemented
10C59×#1983C211yesmaximal, characteristic
11C59×#1865C211yesmaximal, characteristic, complemented
12C59×#1864C211yesmaximal, characteristic
13C59×#1863C211yesmaximal, characteristic, complemented
14C59×#1862C211yesmaximal, characteristic
15C4×#103×C59C211yesmaximal, characteristic, complemented
16C59×#556—24no—
17C59×#556—24no—
18C2×C4⋊Q8×C59C2211yescharacteristic
19C2×#126×C59—21no—
20C2×#126×C59—21no—
21C2×#125×C59C2211yescharacteristic
22C2×#124×C59C2211yescharacteristic
23C2×#124×C59C2211yescharacteristic
24C2×C22⋊Q8×C59—21no—
25C2×C4×Q8×C59C2211yescharacteristic
26C2×C4×Q8×C59C2211yescharacteristic
27C2×C4×Q8×C59C2211yescharacteristic
28C2×C4×D4×C59C2211yescharacteristic
29C2×#117×C59—21no—
30C59×#488—24no—
31C59×#479—24no—
32C2×#107×C59C2211yescharacteristic
33C2×#106×C59C2211yescharacteristic
34C2×C4⋊C8×C59C2211yescharacteristic
35C2×#103×C59C2211yescharacteristic
36C2×#103×C59C2211yescharacteristic
37C2×#103×C59C2211yescharacteristic
38C2×#103×C59C2211yescharacteristic
39C2×#103×C59C2211yescharacteristic
40C2×#103×C59C2211yescharacteristic
41C2×#103×C59C2211yescharacteristic
42C2×#103×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×C4×C8×C59C2211yescharacteristic
48C59×#398—21no—
49C59×#395—21no—
50C59×#389—21no—
51C59×#389—21no—
52C59×#389C2211yescharacteristic
53C59×#389C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C59×#389C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×Q8×C59D411yescharacteristic
64C22×Q8×C59C2311yescharacteristic
65C22×Q8×C59C2311yescharacteristic
66C22×D4×C59C2311yescharacteristic
67C23×C4×C59—21no—
68C22×C8×C59C2311yescharacteristic
69C22×C8×C59C2311yescharacteristic
70C22×C8×C59C2311yescharacteristic
71C22×C8×C59C2311yescharacteristic
72C4⋊Q8×C59—22no—
73C4⋊Q8×C59—22no—
74#126×C59—28no—
75#126×C59—28no—
76#125×C59—22no—
77#125×C59—22no—
78#124×C59—22no—
79#124×C59—22no—
80#124×C59—22no—
81#124×C59D414yes—
82C22⋊Q8×C59—28no—
83C4×Q8×C59—22no—
84C4×Q8×C59—22no—
85C4×Q8×C59—22no—
86C4×Q8×C59—22no—
87C4×Q8×C59—22no—
88C4×Q8×C59D414yes—
89C4×D4×C59—22no—
90C4×D4×C59—22no—
91#117×C59—28no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—21no—
95C2×C4⋊C4×C59—21no—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59—21no—
102C2×C4⋊C4×C59D411yescharacteristic
103C2×C4⋊C4×C59D411yescharacteristic
104C2×C4⋊C4×C59D411yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C4⋊C4×C59C2311yescharacteristic
107C2×C4⋊C4×C59C2311yescharacteristic
108C2×C4⋊C4×C59C2311yescharacteristic
109C2×C4⋊C4×C59C2311yescharacteristic
110C2×C22⋊C4×C59—21no—
111C2×C22⋊C4×C59—21no—
112C2×C22⋊C4×C59—21no—
113C2×C22⋊C4×C59—21no—
114C2×C22⋊C4×C59—21no—
115C2×C42×C59—21no—
116C2×C42×C59—21no—
117C2×C42×C59—21no—
118C2×C42×C59C2311yescharacteristic
119C2×C42×C59C2311yescharacteristic
120C2×C42×C59C2311yescharacteristic
121#107×C59—22no—
122#106×C59—22no—
123C4⋊C8×C59—22no—
124#103×C59—22no—
125#103×C59—22no—
126#103×C59—22no—
127#103×C59—22no—
128#103×C59—22no—
129#103×C59—22no—
130#103×C59—22no—
131#103×C59—22no—
132#102×C59—22no—
133#102×C59—22no—
134#102×C59—22no—
135#102×C59—22no—
136C4×C8×C59—22no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59—21no—
142C24×C59—21no—
143C2×Q8×C59—22no—
144C2×Q8×C59—22no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—41no—
156C2×Q8×C59C2×D412yes—
157C2×Q8×C59C2×D412yes—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59C2×D412yes—
164C22×C4×C59—24no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—42no—
173C22×C4×C59—42no—
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2411yescharacteristic
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C4⋊C4×C59—24no—
194C4⋊C4×C59—24no—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—24no—
197C4⋊C4×C59—22no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—22no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—42no—
208C4⋊C4×C59—42no—
209C4⋊C4×C59—42no—
210C4⋊C4×C59—42no—
211C4⋊C4×C59—81no—
212C4⋊C4×C59—81no—
213C4⋊C4×C59C2×D412yes—
214C4⋊C4×C59#4112yes—
215C4⋊C4×C59#4112yes—
216C22⋊C4×C59—24no—
217C22⋊C4×C59—24no—
218C22⋊C4×C59—24no—
219C22⋊C4×C59—24no—
220C22⋊C4×C59—24no—
221C42×C59—24no—
222C42×C59—24no—
223C42×C59—21no—
224C42×C59—21no—
225C42×C59—21no—
226C42×C59—21no—
227C42×C59—81no—
228C42×C59C2×D412yes—
229C42×C59C2×D412yes—
230C23×C59—22no—
231C23×C59—41no—
232C23×C59—41no—
233C23×C59—41no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59C22×D411yescharacteristic
238Q8×C59—22no—
239Q8×C59—22no—
240Q8×C59—22no—
241Q8×C59—22no—
242Q8×C59—44no—
243Q8×C59—41no—
244Q8×C59—41no—
245Q8×C59—41no—
246Q8×C59—41no—
247D4×C59—22no—
248D4×C59—22no—
249D4×C59—41no—
250D4×C59—41no—
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—22no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—48no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59#12012yes—
289C2×C4×C59#12012yes—
290C2×C4×C59#13512yes—
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C2×C4×C592−1+411yescharacteristic
296C2×C4×C592−1+411yescharacteristic
297C8×C59—41no—
298C8×C59—41no—
299C8×C59—41no—
300C8×C59—41no—
301#25654C5911yesmaximal, characteristic, direct product factor, Sylow
302C22×C59—42no—
303C22×C59—42no—
304C22×C59—42no—
305C22×C59—81no—
306C22×C59—81no—
307C22×C59—81no—
308C22×C59—81no—
309C22×C59C2×#12011yescharacteristic
310C22×C59#54811yescharacteristic
311C22×C59#54811yescharacteristic
312C22×C59C2×#13511yescharacteristic
313C22×C59#57511yescharacteristic
314C22×C59#57711yescharacteristic
315C22×C59#57811yescharacteristic
316C4×C59—22no—
317C4×C59—22no—
318C4×C59—22no—
319C4×C59—42no—
320C4×C59—42no—
321C4×C59—42no—
322C4×C59—42no—
323C4×C59—41no—
324C4×C59—42no—
325C4×C59—41no—
326C4×C59—41no—
327C4×C59—81no—
328C4×C59—81no—
329C4×C59#53211yescharacteristic
330C4×C59#53611yescharacteristic
331C4×C59#54711yescharacteristic
332C4×C59#54711yescharacteristic
333C2×#556C2×C5911yescharacteristic
334C2×#488C2×C5911yescharacteristic
335C2×#479C2×C5911yescharacteristic, complemented
336#2584C2×C5911yescharacteristic, complemented
337#2043C2×C5911yescharacteristic, complemented
338#2043C2×C5911yescharacteristic, complemented
339#2042C2×C5911yescharacteristic
340#2042C2×C5911yescharacteristic
341#1984C2×C5911yescharacteristic, complemented
342#1983C2×C5911yescharacteristic
343#1865C2×C5911yescharacteristic, complemented
344#1864C2×C5911yescharacteristic
345#1863C2×C5911yescharacteristic, complemented
346#1862C2×C5911yescharacteristic
347C4×#103C2×C5911yescharacteristic, complemented
348C2×C59—82no—
349C2×C59#243211yescharacteristic
350C2×C59#300211yescharacteristic
351C2×C59#301311yescharacteristic
352C2×C59#336011yescharacteristic
353C2×C59#336411yescharacteristic
354C2×C59#337611yescharacteristic
355C2×C59#337711yescharacteristic
356#556—24no—
357#556—24no—
358C2×C4⋊Q8C22×C5911yescharacteristic
359C2×#126—21no—
360C2×#126—21no—
361C2×#125C22×C5911yescharacteristic
362C2×#124C22×C5911yescharacteristic
363C2×#124C22×C5911yescharacteristic
364C2×C22⋊Q8—21no—
365C2×C4×Q8C22×C5911yescharacteristic
366C2×C4×Q8C22×C5911yescharacteristic
367C2×C4×Q8C22×C5911yescharacteristic
368C2×C4×D4C22×C5911yescharacteristic
369C2×#117—21no—
370#488—24no—
371#479—24no—
372C2×#107C22×C5911yescharacteristic
373C2×#106C22×C5911yescharacteristic
374C2×C4⋊C8C22×C5911yescharacteristic
375C2×#103C22×C5911yescharacteristic
376C2×#103C22×C5911yescharacteristic
377C2×#103C22×C5911yescharacteristic
378C2×#103C22×C5911yescharacteristic
379C2×#103C22×C5911yescharacteristic
380C2×#103C22×C5911yescharacteristic
381C2×#103C22×C5911yescharacteristic
382C2×#103C22×C5911yescharacteristic
383C2×#102C22×C5911yescharacteristic
384C2×#102C22×C5911yescharacteristic
385C2×#102C22×C5911yescharacteristic
386C2×#102C22×C5911yescharacteristic
387C2×C4×C8C22×C5911yescharacteristic
388#398—21no—
389#395—21no—
390#389—21no—
391#389—21no—
392#389C22×C5911yescharacteristic
393#389C22×C5911yescharacteristic
394#389C22×C5911yescharacteristic
395#389C22×C5911yescharacteristic
396C4×C4⋊C4C22×C5911yescharacteristic
397#340C22×C5911yescharacteristic
398#340C22×C5911yescharacteristic
399#336C22×C5911yescharacteristic
400#336C22×C5911yescharacteristic
401#336C22×C5911yescharacteristic
402#336C22×C5911yescharacteristic
403C59#2565411yescharacteristic, direct product factor, Sylow
404C22×Q8D4×C5911yescharacteristic
405C22×Q8C23×C5911yescharacteristic
406C22×Q8C23×C5911yescharacteristic
407C22×D4C23×C5911yescharacteristic
408C23×C4—21no—
409C22×C8C23×C5911yescharacteristic
410C22×C8C23×C5911yescharacteristic
411C22×C8C23×C5911yescharacteristic
412C22×C8C23×C5911yescharacteristic
413C4⋊Q8—22no—
414C4⋊Q8—22no—
415#126—28no—
416#126—28no—
417#125—22no—
418#125—22no—
419#124—22no—
420#124—22no—
421#124—22no—
422#124D4×C5914yes—
423C22⋊Q8—28no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8D4×C5914yes—
430C4×D4—22no—
431C4×D4—22no—
432#117—28no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C5911yescharacteristic
444C2×C4⋊C4D4×C5911yescharacteristic
445C2×C4⋊C4D4×C5911yescharacteristic
446C2×C4⋊C4C23×C5911yescharacteristic
447C2×C4⋊C4C23×C5911yescharacteristic
448C2×C4⋊C4C23×C5911yescharacteristic
449C2×C4⋊C4C23×C5911yescharacteristic
450C2×C4⋊C4C23×C5911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C5911yescharacteristic
460C2×C42C23×C5911yescharacteristic
461C2×C42C23×C5911yescharacteristic
462#107—22no—
463#106—22no—
464C4⋊C8—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477C4×C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483C24—21no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8C2×D4×C5912yes—
498C2×Q8C2×D4×C5912yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C5912yes—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4C2×D4×C5911yescharacteristic
516C22×C4C2×D4×C5911yescharacteristic
517C22×C4C2×D4×C5911yescharacteristic
518C22×C4C2×D4×C5911yescharacteristic
519C22×C4C2×D4×C5911yescharacteristic
520C22×C4C2×D4×C5911yescharacteristic
521C22×C4C24×C5911yescharacteristic
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C2×D4×C5912yes—
555C4⋊C4#41×C5912yes—
556C4⋊C4#41×C5912yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C42—24no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42C2×D4×C5912yes—
570C42C2×D4×C5912yes—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C5911yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—44no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4#120×C5912yes—
630C2×C4#120×C5912yes—
631C2×C4#135×C5912yes—
632C2×C4C22×D4×C5911yescharacteristic
633C2×C4C22×D4×C5911yescharacteristic
634C2×C4C2×#41×C5911yescharacteristic
635C2×C4C2×#41×C5911yescharacteristic
636C2×C42−1+4×C5911yescharacteristic
637C2×C42−1+4×C5911yescharacteristic
638C8—41no—
639C8—41no—
640C8—41no—
641C8—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×#120×C5911yescharacteristic
650C22C59×#54811yescharacteristic
651C22C59×#54811yescharacteristic
652C22C2×#135×C5911yescharacteristic
653C22C59×#57511yescharacteristic
654C22C59×#57711yescharacteristic
655C22C59×#57811yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—41no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4C59×#53211yescharacteristic
670C4C59×#53611yescharacteristic
671C4C59×#54711yescharacteristic
672C4C59×#54711yescharacteristic
673C2—82no—
674C2C59×#243211yescharacteristic
675C2C59×#300211yescharacteristic
676C2C59×#301311yescharacteristic
677C2C59×#336011yescharacteristic
678C2C59×#336411yescharacteristic
679C2C59×#337611yescharacteristic
680C2C59×#337711yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC22×D4×C59C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×Q8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C59×#479C2semidirect
4. C59×#2584C2semidirect
5. C59×#2043C2semidirect
6. C59×#2043C2semidirect
9. C59×#1984C2semidirect
11. C59×#1865C2semidirect
13. C59×#1863C2semidirect
15. C4×#103×C59C2semidirect
301. #25654C59direct (N × H)
335. C2×#479C2×C59semidirect
336. #2584C2×C59semidirect
337. #2043C2×C59semidirect
338. #2043C2×C59semidirect
341. #1984C2×C59semidirect
343. #1865C2×C59semidirect
345. #1863C2×C59semidirect
347. C4×#103C2×C59semidirect
403. C59#25654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5562
C2×C59×#4882
C2×C59×#4792
C59×#25842
C59×#20432
C59×#20422
C59×#19842
C59×#19832
C59×#18652
C59×#18642
C59×#18632
C59×#18622
C4×#103×C592
#2565459