Finite Group Databasebeta

← C59×#16681 #28428790

Subgroups — C59×#16681 #28428790

Order 15104.

1858 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C59C211yesmaximal, characteristic
2C2×C59×#395C211yesmaximal, characteristic, complemented
3C2×C59×#394C211yesmaximal, characteristic
4C2×C59×#387C211yesmaximal, characteristic, complemented
5C59×#1446C211yesmaximal, characteristic, complemented
6C59×#1440C212yesmaximal, complemented
7C59×#1439C212yesmaximal, complemented
8C59×#1439C212yesmaximal, complemented
9C59×#1439C212yesmaximal, complemented
10C59×#1438C211yesmaximal, characteristic
11C59×#1434C211yesmaximal, characteristic, complemented
12C23×Q8×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C2×#124×C59—24no—
15C2×#124×C59—24no—
16C2×#124×C59—24no—
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2212yes—
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2212yes—
25C22×C22⋊C4×C59C2212yes—
26C22×C42×C59C2211yescharacteristic
27C59×#395—24no—
28C59×#394—24no—
29C59×#387—24no—
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C25×C59C2312yes—
42C22×Q8×C59—22no—
43C22×Q8×C59—22no—
44C22×Q8×C59—42no—
45C22×Q8×C59—42no—
46C22×Q8×C59D414yes—
47C22×D4×C59—22no—
48C22×D4×C59—22no—
49C22×D4×C59—42no—
50C22×D4×C59—42no—
51C22×D4×C59D414yes—
52C23×C4×C59C2311yescharacteristic
53C23×C4×C59C2312yes—
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2312yes—
58C23×C4×C59C2311yescharacteristic
59C23×C4×C59C2312yes—
60C23×C4×C59C2311yescharacteristic
61C23×C4×C59C2311yescharacteristic
62#124×C59—232no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—22no—
68C2×C4⋊C4×C59—24no—
69C2×C4⋊C4×C59—22no—
70C2×C4⋊C4×C59—42no—
71C2×C4⋊C4×C59—42no—
72C2×C22⋊C4×C59—24no—
73C2×C22⋊C4×C59—24no—
74C2×C22⋊C4×C59—24no—
75C2×C22⋊C4×C59—24no—
76C2×C22⋊C4×C59—24no—
77C2×C22⋊C4×C59—24no—
78C2×C22⋊C4×C59—24no—
79C2×C22⋊C4×C59—24no—
80C2×C22⋊C4×C59—24no—
81C2×C22⋊C4×C59—24no—
82C2×C22⋊C4×C59—24no—
83C2×C22⋊C4×C59—24no—
84C2×C22⋊C4×C59—42no—
85C2×C22⋊C4×C59—42no—
86C2×C22⋊C4×C59—42no—
87C2×C22⋊C4×C59—42no—
88C2×C22⋊C4×C59—42no—
89C2×C22⋊C4×C59—42no—
90C2×C42×C59—22no—
91C2×C42×C59—22no—
92C2×C42×C59D414yes—
93#95×C59—22no—
94#95×C59—22no—
95#95×C59—22no—
96#95×C59—22no—
97#95×C59—22no—
98#95×C59—24no—
99#95×C59—22no—
100#95×C59—24no—
101#95×C59—42no—
102#95×C59—42no—
103#95×C59—42no—
104C24×C59—22no—
105C24×C59—22no—
106C24×C59—22no—
107C24×C59—22no—
108C24×C59—22no—
109C24×C59—22no—
110C24×C59—22no—
111C24×C59—22no—
112C24×C59—22no—
113C24×C59—22no—
114C24×C59—22no—
115C24×C59—22no—
116C24×C59—22no—
117C24×C59—22no—
118C24×C59C2×D414yes—
119C24×C59C2411yescharacteristic
120C2×Q8×C59—28no—
121C2×Q8×C59—48no—
122C2×Q8×C59—48no—
123C2×Q8×C59—44no—
124C2×Q8×C59—44no—
125C2×D4×C59—28no—
126C2×D4×C59—48no—
127C2×D4×C59—48no—
128C2×D4×C59—44no—
129C2×D4×C59—44no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—21no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—22no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—22no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—21no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—21no—
180C22×C4×C59—22no—
181C22×C4×C59C2×D412yes—
182C22×C4×C59C2×D412yes—
183C22×C4×C59C2×D414yes—
184C22×C4×C59C2×D412yes—
185C22×C4×C59C2×D412yes—
186C22×C4×C59C2×D412yes—
187C22×C4×C59#4114yes—
188C22×C4×C59#4112yes—
189C22×C4×C59#4112yes—
190C4⋊C4×C59—28no—
191C4⋊C4×C59—48no—
192C4⋊C4×C59—44no—
193C22⋊C4×C59—216no—
194C22⋊C4×C59—216no—
195C22⋊C4×C59—48no—
196C22⋊C4×C59—48no—
197C22⋊C4×C59—48no—
198C22⋊C4×C59—48no—
199C42×C59—28no—
200C23×C59—24no—
201C23×C59—24no—
202C23×C59—24no—
203C23×C59—24no—
204C23×C59—24no—
205C23×C59—24no—
206C23×C59—24no—
207C23×C59—42no—
208C23×C59—42no—
209C23×C59—42no—
210C23×C59—42no—
211C23×C59—42no—
212C23×C59—42no—
213C23×C59—42no—
214C23×C59—42no—
215C23×C59—42no—
216C23×C59—42no—
217C23×C59—42no—
218C23×C59—42no—
219C23×C59—42no—
220C23×C59—42no—
221C23×C59—42no—
222C23×C59—42no—
223C23×C59—42no—
224C23×C59—42no—
225C23×C59—42no—
226C23×C59—42no—
227C23×C59—42no—
228C23×C59—42no—
229C23×C59—42no—
230C23×C59—42no—
231C23×C59—42no—
232C23×C59—42no—
233C23×C59—42no—
234C23×C59—42no—
235C23×C59C22×D411yescharacteristic
236C23×C59C22×D411yescharacteristic
237C23×C59C22×D411yescharacteristic
238C23×C59C2×#4111yescharacteristic
239C23×C59C2×#4111yescharacteristic
240C23×C59C2×#4112yes—
241C23×C59H(5,𝔽2)12yes—
242C23×C59H(5,𝔽2)12yes—
243C23×C59H(5,𝔽2)11yescharacteristic
244C23×C592−1+412yes—
245C23×C592−1+411yescharacteristic
246Q8×C59—416no—
247D4×C59—416no—
248C2×C4×C59—24no—
249C2×C4×C59—24no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—24no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—24no—
260C2×C4×C59—24no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—24no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—24no—
267C2×C4×C59—24no—
268C2×C4×C59—24no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—41no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—41no—
278C2×C4×C59—42no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—42no—
283C2×C4×C59—41no—
284C2×C4×C59—42no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59#12014yes—
308#16681C5911yesmaximal, characteristic, direct product factor, Sylow
309C22×C59—44no—
310C22×C59—44no—
311C22×C59—44no—
312C22×C59—44no—
313C22×C59—44no—
314C22×C59—44no—
315C22×C59—44no—
316C22×C59—82no—
317C22×C59—82no—
318C22×C59—82no—
319C22×C59—82no—
320C22×C59—82no—
321C22×C59—82no—
322C22×C59—82no—
323C22×C59—82no—
324C22×C59C2×#12011yescharacteristic
325C22×C59#52511yescharacteristic
326C22×C59#53211yescharacteristic
327C22×C59#53412yes—
328C22×C59#53412yes—
329C22×C59#53511yescharacteristic
330C22×C59#53511yescharacteristic
331C22×C59#53611yescharacteristic
332C22×C59#53711yescharacteristic
333C22×C59#53812yes—
334C22×C59#54212yes—
335C22×C59#54212yes—
336C22×C59#54212yes—
337C22×C59#54611yescharacteristic
338C22×C59#54711yescharacteristic
339C22×C59#54712yes—
340C22×C59#54811yescharacteristic
341C22×C59#54812yes—
342C22×C59#55011yescharacteristic
343C22×C59#55112yes—
344C22×C59#55512yes—
345C22×C59#56212yes—
346C22×C59#56312yes—
347C4×C59—24no—
348C4×C59—42no—
349C4×C59—44no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59—44no—
354C4×C59—81no—
355C4×C59—81no—
356C4×C59—82no—
357C22×#124C2×C5911yescharacteristic
358C2×#395C2×C5911yescharacteristic, complemented
359C2×#394C2×C5911yescharacteristic
360C2×#387C2×C5911yescharacteristic, complemented
361#1446C2×C5911yescharacteristic, complemented
362#1440C2×C5912yescomplemented
363#1439C2×C5912yescomplemented
364#1439C2×C5912yescomplemented
365#1439C2×C5912yescomplemented
366#1438C2×C5911yescharacteristic
367#1434C2×C5911yescharacteristic, complemented
368C2×C59—84no—
369C2×C59#240711yescharacteristic
370C2×C59#243211yescharacteristic
371C2×C59#261011yescharacteristic
372C2×C59#261311yescharacteristic
373C2×C59#263211yescharacteristic
374C2×C59#266211yescharacteristic
375C2×C59#268612yes—
376C2×C59#271712yes—
377C2×C59#273012yes—
378C2×C59#273112yes—
379C2×C59#282011yescharacteristic
380C23×Q8C22×C5911yescharacteristic
381C23×D4C22×C5911yescharacteristic
382C2×#124—24no—
383C2×#124—24no—
384C2×#124—24no—
385C22×C4⋊C4C22×C5911yescharacteristic
386C22×C4⋊C4C22×C5911yescharacteristic
387C22×C4⋊C4C22×C5912yes—
388C22×C22⋊C4C22×C5912yes—
389C22×C22⋊C4C22×C5912yes—
390C22×C22⋊C4C22×C5912yes—
391C22×C22⋊C4C22×C5912yes—
392C22×C22⋊C4C22×C5912yes—
393C22×C22⋊C4C22×C5912yes—
394C22×C42C22×C5911yescharacteristic
395#395—24no—
396#394—24no—
397#387—24no—
398C2×#95C22×C5911yescharacteristic
399C2×#95C22×C5911yescharacteristic
400C2×#95C22×C5912yes—
401C2×#95C22×C5912yes—
402C2×#95C22×C5911yescharacteristic
403C2×#95C22×C5911yescharacteristic
404C2×#95C22×C5911yescharacteristic
405C2×#95C22×C5911yescharacteristic
406C2×#95C22×C5912yes—
407C2×#95C22×C5912yes—
408C2×#95C22×C5912yes—
409C59#1668111yescharacteristic, direct product factor, Sylow
410C25C23×C5912yes—
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—42no—
414C22×Q8—42no—
415C22×Q8D4×C5914yes—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—42no—
419C22×D4—42no—
420C22×D4D4×C5914yes—
421C23×C4C23×C5911yescharacteristic
422C23×C4C23×C5911yescharacteristic
423C23×C4C23×C5912yes—
424C23×C4C23×C5912yes—
425C23×C4C23×C5911yescharacteristic
426C23×C4C23×C5911yescharacteristic
427C23×C4C23×C5911yescharacteristic
428C23×C4C23×C5911yescharacteristic
429C23×C4C23×C5912yes—
430C23×C4C23×C5911yescharacteristic
431#124—232no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42D4×C5914yes—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—24no—
468#95—22no—
469#95—24no—
470#95—42no—
471#95—42no—
472#95—42no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24C2×D4×C5914yes—
488C24C24×C5911yescharacteristic
489C2×Q8—28no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×D4—28no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—44no—
498C2×D4—44no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4C2×D4×C5912yes—
551C22×C4C2×D4×C5912yes—
552C22×C4C2×D4×C5914yes—
553C22×C4C2×D4×C5912yes—
554C22×C4C2×D4×C5912yes—
555C22×C4C2×D4×C5912yes—
556C22×C4#41×C5914yes—
557C22×C4#41×C5912yes—
558C22×C4#41×C5912yes—
559C4⋊C4—28no—
560C4⋊C4—48no—
561C4⋊C4—44no—
562C22⋊C4—216no—
563C22⋊C4—216no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C42—28no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23C22×D4×C5911yescharacteristic
605C23C22×D4×C5911yescharacteristic
606C23C22×D4×C5911yescharacteristic
607C23C2×#41×C5911yescharacteristic
608C23C2×#41×C5911yescharacteristic
609C23C2×#41×C5912yes—
610C23H(5,𝔽2)×C5912yes—
611C23H(5,𝔽2)×C5912yes—
612C23H(5,𝔽2)×C5911yescharacteristic
613C232−1+4×C5912yes—
614C232−1+4×C5911yescharacteristic
615Q8—416no—
616D4—416no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4#120×C5914yes—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22C2×#120×C5911yescharacteristic
693C22C59×#52511yescharacteristic
694C22C59×#53211yescharacteristic
695C22C59×#53412yes—
696C22C59×#53412yes—
697C22C59×#53511yescharacteristic
698C22C59×#53511yescharacteristic
699C22C59×#53611yescharacteristic
700C22C59×#53711yescharacteristic
701C22C59×#53812yes—
702C22C59×#54212yes—
703C22C59×#54212yes—
704C22C59×#54212yes—
705C22C59×#54611yescharacteristic
706C22C59×#54711yescharacteristic
707C22C59×#54712yes—
708C22C59×#54811yescharacteristic
709C22C59×#54812yes—
710C22C59×#55011yescharacteristic
711C22C59×#55112yes—
712C22C59×#55512yes—
713C22C59×#56212yes—
714C22C59×#56312yes—
715C4—24no—
716C4—42no—
717C4—44no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—44no—
722C4—81no—
723C4—81no—
724C4—82no—
725C2—84no—
726C2C59×#240711yescharacteristic
727C2C59×#243211yescharacteristic
728C2C59×#261011yescharacteristic
729C2C59×#261311yescharacteristic
730C2C59×#263211yescharacteristic
731C2C59×#266211yescharacteristic
732C2C59×#268612yes—
733C2C59×#271712yes—
734C2C59×#273012yes—
735C2C59×#273112yes—
736C2C59×#282011yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC23×D4×C59C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#395C2semidirect
4. C2×C59×#387C2semidirect
5. C59×#1446C2semidirect
6. C59×#1440C2semidirect
7. C59×#1439C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
11. C59×#1434C2semidirect
308. #16681C59direct (N × H)
358. C2×#395C2×C59semidirect
360. C2×#387C2×C59semidirect
361. #1446C2×C59semidirect
362. #1440C2×C59semidirect
363. #1439C2×C59semidirect
364. #1439C2×C59semidirect
365. #1439C2×C59semidirect
367. #1434C2×C59semidirect
409. C59#16681direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#124×C592
C2×C59×#3952
C2×C59×#3942
C2×C59×#3872
C59×#14462
C59×#14402
C59×#14392
C59×#14382
C59×#14342
#1668159