Finite Group Databasebeta

← C59×#16505 #28428614

Subgroups — C59×#16505 #28428614

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C59C211yesmaximal, characteristic
2C2×C59×#396C212yesmaximal, complemented
3C2×C59×#395C211yesmaximal, characteristic, complemented
4C2×C59×#394C211yesmaximal, characteristic
5C2×C59×#387C211yesmaximal, characteristic, complemented
6C59×#1446C211yesmaximal, characteristic, complemented
7C59×#1440C212yesmaximal, complemented
8C59×#1439C212yesmaximal, complemented
9C59×#1439C212yesmaximal, complemented
10C59×#1438C211yesmaximal, characteristic
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Q8×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C2×#124×C59—28no—
15C2×#124×C59—24no—
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2211yescharacteristic
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×#396—28no—
28C59×#395—24no—
29C59×#394—24no—
30C59×#387—24no—
31C2×#95×C59C2211yescharacteristic
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2211yescharacteristic
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C25×C59C2312yes—
42C22×Q8×C59—24no—
43C22×Q8×C59—22no—
44C22×Q8×C59—22no—
45C22×Q8×C59—22no—
46C22×Q8×C59—42no—
47C22×D4×C59—24no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—22no—
51C22×D4×C59—42no—
52C23×C4×C59C2311yescharacteristic
53C23×C4×C59C2311yescharacteristic
54C23×C4×C59C2312yes—
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—24no—
67C2×C4⋊C4×C59—24no—
68C2×C4⋊C4×C59—24no—
69C2×C4⋊C4×C59—24no—
70C2×C4⋊C4×C59—24no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59—42no—
73C2×C4⋊C4×C59D414yes—
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—24no—
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×C22⋊C4×C59—42no—
91C2×C22⋊C4×C59D418yes—
92C2×C42×C59—24no—
93C2×C42×C59D414yes—
94#95×C59—22no—
95#95×C59—22no—
96#95×C59—22no—
97#95×C59—22no—
98#95×C59—22no—
99#95×C59—22no—
100#95×C59—24no—
101#95×C59—24no—
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—22no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—22no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—22no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—22no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—22no—
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2×D412yes—
180C22×C4×C59C2×D414yes—
181C22×C4×C59C2×D412yes—
182C22×C4×C59C2×D412yes—
183C22×C4×C59C2×D414yes—
184C22×C4×C59C2×D412yes—
185C22×C4×C59C2×D412yes—
186C22×C4×C59#4114yes—
187C22×C4×C59#4112yes—
188C4⋊C4×C59—28no—
189C4⋊C4×C59—48no—
190C4⋊C4×C59—48no—
191C4⋊C4×C59—44no—
192C22⋊C4×C59—216no—
193C22⋊C4×C59—216no—
194C22⋊C4×C59—48no—
195C22⋊C4×C59—48no—
196C22⋊C4×C59—48no—
197C22⋊C4×C59—48no—
198C42×C59—28no—
199C23×C59—24no—
200C23×C59—24no—
201C23×C59—24no—
202C23×C59—24no—
203C23×C59—24no—
204C23×C59—24no—
205C23×C59—24no—
206C23×C59—42no—
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×C59C22×D411yescharacteristic
235C23×C59C22×D412yes—
236C23×C59C22×D411yescharacteristic
237C23×C59C2×#4111yescharacteristic
238C23×C59C2×#4112yes—
239C23×C59H(5,𝔽2)11yescharacteristic
240C23×C59H(5,𝔽2)11yescharacteristic
241C23×C59H(5,𝔽2)12yes—
242C23×C592−1+411yescharacteristic
243C23×C592−1+412yes—
244C23×C592−1+411yescharacteristic
245Q8×C59—416no—
246D4×C59—416no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—24no—
252C2×C4×C59—24no—
253C2×C4×C59—24no—
254C2×C4×C59—24no—
255C2×C4×C59—22no—
256C2×C4×C59—24no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—24no—
264C2×C4×C59—24no—
265C2×C4×C59—24no—
266C2×C4×C59—24no—
267C2×C4×C59—24no—
268C2×C4×C59—24no—
269C2×C4×C59—41no—
270C2×C4×C59—42no—
271C2×C4×C59—41no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—42no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—42no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—42no—
293C2×C4×C59—41no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59#12014yes—
304C2×C4×C59#12114yes—
305#16505C5911yesmaximal, characteristic, direct product factor, Sylow
306C22×C59—44no—
307C22×C59—44no—
308C22×C59—44no—
309C22×C59—44no—
310C22×C59—44no—
311C22×C59—44no—
312C22×C59—44no—
313C22×C59—82no—
314C22×C59—82no—
315C22×C59—82no—
316C22×C59—82no—
317C22×C59—82no—
318C22×C59—82no—
319C22×C59—82no—
320C22×C59—82no—
321C22×C59C2×#12011yescharacteristic
322C22×C59C2×#12111yescharacteristic
323C22×C59#53211yescharacteristic
324C22×C59#53511yescharacteristic
325C22×C59#53511yescharacteristic
326C22×C59#53611yescharacteristic
327C22×C59#53612yes—
328C22×C59#53611yescharacteristic
329C22×C59#53711yescharacteristic
330C22×C59#53711yescharacteristic
331C22×C59#53712yes—
332C22×C59#53812yes—
333C22×C59#54211yescharacteristic
334C22×C59#54211yescharacteristic
335C22×C59#54212yes—
336C22×C59D4212yes—
337C22×C59#54612yes—
338C22×C59#54612yes—
339C22×C59#54712yes—
340C22×C59#54812yes—
341C22×C59#55612yes—
342C22×C59#56212yes—
343C22×C59#56312yes—
344C4×C59—24no—
345C4×C59—24no—
346C4×C59—42no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59—44no—
350C4×C59—44no—
351C4×C59—81no—
352C4×C59—82no—
353C4×C59—81no—
354C22×#124C2×C5911yescharacteristic
355C2×#396C2×C5912yescomplemented
356C2×#395C2×C5911yescharacteristic, complemented
357C2×#394C2×C5911yescharacteristic
358C2×#387C2×C5911yescharacteristic, complemented
359#1446C2×C5911yescharacteristic, complemented
360#1440C2×C5912yescomplemented
361#1439C2×C5912yescomplemented
362#1439C2×C5912yescomplemented
363#1438C2×C5911yescharacteristic
364C4⋊#95C2×C5911yescharacteristic, complemented
365C2×C59—84no—
366C2×C59#240811yescharacteristic
367C2×C59#243011yescharacteristic
368C2×C59#254511yescharacteristic
369C2×C59#261611yescharacteristic
370C2×C59#262011yescharacteristic
371C2×C59#266211yescharacteristic
372C2×C59#267412yes—
373C2×C59#267612yes—
374C2×C59#270012yes—
375C2×C59#271512yes—
376C2×C59#282011yescharacteristic
377C23×Q8C22×C5911yescharacteristic
378C23×D4C22×C5911yescharacteristic
379C2×#124—28no—
380C2×#124—24no—
381C22×C4⋊C4C22×C5911yescharacteristic
382C22×C4⋊C4C22×C5912yes—
383C22×C4⋊C4C22×C5912yes—
384C22×C4⋊C4C22×C5911yescharacteristic
385C22×C22⋊C4C22×C5912yes—
386C22×C22⋊C4C22×C5912yes—
387C22×C22⋊C4C22×C5912yes—
388C22×C22⋊C4C22×C5912yes—
389C22×C22⋊C4C22×C5912yes—
390C22×C22⋊C4C22×C5912yes—
391C22×C42C22×C5911yescharacteristic
392#396—28no—
393#395—24no—
394#394—24no—
395#387—24no—
396C2×#95C22×C5911yescharacteristic
397C2×#95C22×C5911yescharacteristic
398C2×#95C22×C5912yes—
399C2×#95C22×C5912yes—
400C2×#95C22×C5911yescharacteristic
401C2×#95C22×C5911yescharacteristic
402C2×#95C22×C5911yescharacteristic
403C2×#95C22×C5911yescharacteristic
404C2×#95C22×C5912yes—
405C2×#95C22×C5912yes—
406C59#1650511yescharacteristic, direct product factor, Sylow
407C25C23×C5912yes—
408C22×Q8—24no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—22no—
412C22×Q8—42no—
413C22×D4—24no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—42no—
418C23×C4C23×C5911yescharacteristic
419C23×C4C23×C5912yes—
420C23×C4C23×C5911yescharacteristic
421C23×C4C23×C5911yescharacteristic
422C23×C4C23×C5912yes—
423C23×C4C23×C5911yescharacteristic
424C23×C4C23×C5911yescharacteristic
425C23×C4C23×C5912yes—
426C23×C4C23×C5911yescharacteristic
427C23×C4C23×C5911yescharacteristic
428#124—232no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4D4×C5914yes—
440C2×C22⋊C4—24no—
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—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4D4×C5918yes—
458C2×C42—24no—
459C2×C42D4×C5914yes—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—24no—
467#95—24no—
468#95—42no—
469#95—42no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×D4×C5914yes—
485C24C24×C5911yescharacteristic
486C2×Q8—28no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—28no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—44no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4C2×D4×C5912yes—
545C22×C4C2×D4×C5912yes—
546C22×C4C2×D4×C5914yes—
547C22×C4C2×D4×C5912yes—
548C22×C4C2×D4×C5912yes—
549C22×C4C2×D4×C5914yes—
550C22×C4C2×D4×C5912yes—
551C22×C4C2×D4×C5912yes—
552C22×C4#41×C5914yes—
553C22×C4#41×C5912yes—
554C4⋊C4—28no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—44no—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C42—28no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
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—
600C23C22×D4×C5911yescharacteristic
601C23C22×D4×C5912yes—
602C23C22×D4×C5911yescharacteristic
603C23C2×#41×C5911yescharacteristic
604C23C2×#41×C5912yes—
605C23H(5,𝔽2)×C5911yescharacteristic
606C23H(5,𝔽2)×C5911yescharacteristic
607C23H(5,𝔽2)×C5912yes—
608C232−1+4×C5911yescharacteristic
609C232−1+4×C5912yes—
610C232−1+4×C5911yescharacteristic
611Q8—416no—
612D4—416no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4#120×C5914yes—
670C2×C4#121×C5914yes—
671C22—44no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22C2×#120×C5911yescharacteristic
687C22C2×#121×C5911yescharacteristic
688C22C59×#53211yescharacteristic
689C22C59×#53511yescharacteristic
690C22C59×#53511yescharacteristic
691C22C59×#53611yescharacteristic
692C22C59×#53612yes—
693C22C59×#53611yescharacteristic
694C22C59×#53711yescharacteristic
695C22C59×#53711yescharacteristic
696C22C59×#53712yes—
697C22C59×#53812yes—
698C22C59×#54211yescharacteristic
699C22C59×#54211yescharacteristic
700C22C59×#54212yes—
701C22D42×C5912yes—
702C22C59×#54612yes—
703C22C59×#54612yes—
704C22C59×#54712yes—
705C22C59×#54812yes—
706C22C59×#55612yes—
707C22C59×#56212yes—
708C22C59×#56312yes—
709C4—24no—
710C4—24no—
711C4—42no—
712C4—42no—
713C4—44no—
714C4—42no—
715C4—44no—
716C4—81no—
717C4—82no—
718C4—81no—
719C2—84no—
720C2C59×#240811yescharacteristic
721C2C59×#243011yescharacteristic
722C2C59×#254511yescharacteristic
723C2C59×#261611yescharacteristic
724C2C59×#262011yescharacteristic
725C2C59×#266211yescharacteristic
726C2C59×#267412yes—
727C2C59×#267612yes—
728C2C59×#270012yes—
729C2C59×#271512yes—
730C2C59×#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×#396C2semidirect
3. C2×C59×#395C2semidirect
5. C2×C59×#387C2semidirect
6. C59×#1446C2semidirect
7. C59×#1440C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
11. C59×C4⋊#95C2semidirect
305. #16505C59direct (N × H)
355. C2×#396C2×C59semidirect
356. C2×#395C2×C59semidirect
358. C2×#387C2×C59semidirect
359. #1446C2×C59semidirect
360. #1440C2×C59semidirect
361. #1439C2×C59semidirect
362. #1439C2×C59semidirect
364. C4⋊#95C2×C59semidirect
406. C59#16505direct (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×#3962
C2×C59×#3952
C2×C59×#3942
C2×C59×#3872
C59×#14462
C59×#14402
C59×#14392
C59×#14382
C59×C4⋊#952
#1650559