Finite Group Databasebeta

← C59×#16519 #28428628

Subgroups — C59×#16519 #28428628

Order 15104.

1690 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#396C212yesmaximal, complemented
2C2×C59×#394C211yesmaximal, characteristic
3C2×C59×#390C211yesmaximal, characteristic
4C2×C59×#387C211yesmaximal, characteristic, complemented
5C2×C59×#382C211yesmaximal, characteristic, complemented
6C59×#1444C211yesmaximal, characteristic, complemented
7C59×#1441C211yesmaximal, characteristic, complemented
8C59×#1440C212yesmaximal, complemented
9C59×#1439C212yesmaximal, complemented
10C59×#1439C212yesmaximal, complemented
11C59×#1438C211yesmaximal, characteristic
12C23×D4×C59C2211yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C4⋊C4×C59C2212yes—
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2212yes—
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C42×C59C2211yescharacteristic
25C59×#396—28no—
26C59×#394—24no—
27C59×#390—24no—
28C59×#387—24no—
29C59×#382—24no—
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C25×C59C2312yes—
41C22×D4×C59—24no—
42C22×D4×C59—22no—
43C22×D4×C59—22no—
44C22×D4×C59—22no—
45C22×D4×C59—42no—
46C23×C4×C59C2311yescharacteristic
47C23×C4×C59C2312yes—
48C23×C4×C59C2311yescharacteristic
49C23×C4×C59C2312yes—
50C23×C4×C59C2311yescharacteristic
51C23×C4×C59C2311yescharacteristic
52C23×C4×C59C2312yes—
53C23×C4×C59C2311yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—24no—
59C2×C4⋊C4×C59—22no—
60C2×C4⋊C4×C59—22no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—24no—
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—42no—
66C2×C4⋊C4×C59—42no—
67C2×C4⋊C4×C59—42no—
68C2×C4⋊C4×C59—42no—
69C2×C4⋊C4×C59D414yescomplemented
70C2×C22⋊C4×C59—24no—
71C2×C22⋊C4×C59—24no—
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—42no—
81C2×C22⋊C4×C59—42no—
82C2×C22⋊C4×C59—42no—
83C2×C22⋊C4×C59—42no—
84C2×C22⋊C4×C59—42no—
85C2×C22⋊C4×C59—42no—
86C2×C22⋊C4×C59—42no—
87C2×C22⋊C4×C59—42no—
88C2×C42×C59—22no—
89C2×C42×C59—22no—
90C2×C42×C59D414yes—
91#95×C59—24no—
92#95×C59—22no—
93#95×C59—22no—
94#95×C59—22no—
95#95×C59—22no—
96#95×C59—22no—
97#95×C59—24no—
98#95×C59—42no—
99#95×C59—42no—
100#95×C59D414yes—
101C24×C59—22no—
102C24×C59—22no—
103C24×C59—22no—
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#4114yes—
116C24×C59C2411yescharacteristic
117C2×D4×C59—28no—
118C2×D4×C59—48no—
119C2×D4×C59—48no—
120C2×D4×C59—44no—
121C2×D4×C59—44no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—22no—
125C22×C4×C59—21no—
126C22×C4×C59—22no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
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—22no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—21no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—21no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—21no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—21no—
171C22×C4×C59—22no—
172C22×C4×C59C2×D412yes—
173C22×C4×C59C2×D412yes—
174C22×C4×C59C2×D414yes—
175C22×C4×C59C2×D412yes—
176C22×C4×C59C2×D412yes—
177C22×C4×C59C2×D412yes—
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2×D412yes—
180C22×C4×C59#4112yes—
181C22×C4×C59#4112yes—
182C4⋊C4×C59—28no—
183C4⋊C4×C59—48no—
184C4⋊C4×C59—44no—
185C4⋊C4×C59—48no—
186C4⋊C4×C59—44no—
187C22⋊C4×C59—48no—
188C22⋊C4×C59—48no—
189C22⋊C4×C59—48no—
190C22⋊C4×C59—48no—
191C22⋊C4×C59—48no—
192C22⋊C4×C59—48no—
193C42×C59—28no—
194C23×C59—24no—
195C23×C59—24no—
196C23×C59—24no—
197C23×C59—24no—
198C23×C59—24no—
199C23×C59—24no—
200C23×C59—24no—
201C23×C59—42no—
202C23×C59—42no—
203C23×C59—42no—
204C23×C59—42no—
205C23×C59—42no—
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×C59C22×D411yescharacteristic
230C23×C59C22×D411yescharacteristic
231C23×C59C22×D411yescharacteristic
232C23×C59C2×#4111yescharacteristic
233C23×C59C2×#4111yescharacteristic
234C23×C59C2×#4112yes—
235C23×C59H(5,𝔽2)12yes—
236C23×C59H(5,𝔽2)12yes—
237C23×C59H(5,𝔽2)11yescharacteristic
238C23×C592−1+412yes—
239C23×C592−1+411yescharacteristic
240D4×C59—416no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—24no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—24no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—24no—
256C2×C4×C59—22no—
257C2×C4×C59—24no—
258C2×C4×C59—22no—
259C2×C4×C59—24no—
260C2×C4×C59—24no—
261C2×C4×C59—22no—
262C2×C4×C59—41no—
263C2×C4×C59—42no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—42no—
267C2×C4×C59—41no—
268C2×C4×C59—42no—
269C2×C4×C59—42no—
270C2×C4×C59—42no—
271C2×C4×C59—41no—
272C2×C4×C59—42no—
273C2×C4×C59—41no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—42no—
280C2×C4×C59—42no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59#12114yes—
300C2×C4×C59#12114yes—
301#16519C5911yesmaximal, characteristic, direct product factor, Sylow
302C22×C59—44no—
303C22×C59—44no—
304C22×C59—44no—
305C22×C59—44no—
306C22×C59—44no—
307C22×C59—44no—
308C22×C59—44no—
309C22×C59—82no—
310C22×C59—82no—
311C22×C59—82no—
312C22×C59—82no—
313C22×C59—82no—
314C22×C59—82no—
315C22×C59—82no—
316C22×C59—82no—
317C22×C59C2×#12111yescharacteristic
318C22×C59C2×#12111yescharacteristic
319C22×C59#52511yescharacteristic
320C22×C59#53511yescharacteristic
321C22×C59#53511yescharacteristic
322C22×C59#53512yes—
323C22×C59#53611yescharacteristic
324C22×C59#53711yescharacteristic
325C22×C59#53712yes—
326C22×C59#53812yes—
327C22×C59#53912yes—
328C22×C59#54012yes—
329C22×C59#54212yes—
330C22×C59D4211yescharacteristic
331C22×C59#54612yes—
332C22×C59#54711yescharacteristic
333C22×C59#54811yescharacteristic
334C22×C59#54812yes—
335C22×C59#55112yes—
336C22×C59#55212yes—
337C22×C59#55311yescharacteristic
338C22×C59#56212yes—
339C22×C59#56312yes—
340C4×C59—24no—
341C4×C59—24no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59—44no—
346C4×C59—82no—
347C4×C59—81no—
348C4×C59—81no—
349C4×C59—82no—
350C2×#396C2×C5912yescomplemented
351C2×#394C2×C5911yescharacteristic
352C2×#390C2×C5911yescharacteristic
353C2×#387C2×C5911yescharacteristic, complemented
354C2×#382C2×C5911yescharacteristic, complemented
355#1444C2×C5911yescharacteristic, complemented
356#1441C2×C5911yescharacteristic, complemented
357#1440C2×C5912yescomplemented
358#1439C2×C5912yescomplemented
359#1439C2×C5912yescomplemented
360#1438C2×C5911yescharacteristic
361C2×C59—84no—
362C2×C59#241111yescharacteristic
363C2×C59#241611yescharacteristic
364C2×C59#253611yescharacteristic
365C2×C59#261911yescharacteristic
366C2×C59#262011yescharacteristic
367C2×C59#263611yescharacteristic
368C2×C59#267612yes—
369C2×C59#270712yes—
370C2×C59#272312yes—
371C2×C59#276112yes—
372C2×C59#282011yescharacteristic
373C23×D4C22×C5911yescharacteristic
374C22×C4⋊C4C22×C5911yescharacteristic
375C22×C4⋊C4C22×C5912yes—
376C22×C4⋊C4C22×C5911yescharacteristic
377C22×C4⋊C4C22×C5912yes—
378C22×C4⋊C4C22×C5911yescharacteristic
379C22×C22⋊C4C22×C5912yes—
380C22×C22⋊C4C22×C5912yes—
381C22×C22⋊C4C22×C5912yes—
382C22×C22⋊C4C22×C5912yes—
383C22×C22⋊C4C22×C5912yes—
384C22×C22⋊C4C22×C5912yes—
385C22×C42C22×C5911yescharacteristic
386#396—28no—
387#394—24no—
388#390—24no—
389#387—24no—
390#382—24no—
391C2×#95C22×C5912yes—
392C2×#95C22×C5911yescharacteristic
393C2×#95C22×C5911yescharacteristic
394C2×#95C22×C5911yescharacteristic
395C2×#95C22×C5911yescharacteristic
396C2×#95C22×C5912yes—
397C2×#95C22×C5911yescharacteristic
398C2×#95C22×C5912yes—
399C2×#95C22×C5912yes—
400C2×#95C22×C5911yescharacteristic
401C59#1651911yescharacteristic, direct product factor, Sylow
402C25C23×C5912yes—
403C22×D4—24no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—42no—
408C23×C4C23×C5912yes—
409C23×C4C23×C5912yes—
410C23×C4C23×C5911yescharacteristic
411C23×C4C23×C5911yescharacteristic
412C23×C4C23×C5911yescharacteristic
413C23×C4C23×C5911yescharacteristic
414C23×C4C23×C5912yes—
415C23×C4C23×C5911yescharacteristic
416C23×C4C23×C5911yescharacteristic
417C23×C4C23×C5911yescharacteristic
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4D4×C5914yescomplemented
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42D4×C5914yes—
453#95—24no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—42no—
461#95—42no—
462#95D4×C5914yes—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24#41×C5914yes—
478C24C24×C5911yescharacteristic
479C2×D4—28no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—44no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4C2×D4×C5912yes—
535C22×C4C2×D4×C5912yes—
536C22×C4C2×D4×C5914yes—
537C22×C4C2×D4×C5912yes—
538C22×C4C2×D4×C5912yes—
539C22×C4C2×D4×C5912yes—
540C22×C4C2×D4×C5912yes—
541C22×C4C2×D4×C5912yes—
542C22×C4#41×C5912yes—
543C22×C4#41×C5912yes—
544C4⋊C4—28no—
545C4⋊C4—48no—
546C4⋊C4—44no—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C42—28no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
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—
591C23C22×D4×C5911yescharacteristic
592C23C22×D4×C5911yescharacteristic
593C23C22×D4×C5911yescharacteristic
594C23C2×#41×C5911yescharacteristic
595C23C2×#41×C5911yescharacteristic
596C23C2×#41×C5912yes—
597C23H(5,𝔽2)×C5912yes—
598C23H(5,𝔽2)×C5912yes—
599C23H(5,𝔽2)×C5911yescharacteristic
600C232−1+4×C5912yes—
601C232−1+4×C5911yescharacteristic
602D4—416no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4#121×C5914yes—
662C2×C4#121×C5914yes—
663C22—44no—
664C22—44no—
665C22—44no—
666C22—44no—
667C22—44no—
668C22—44no—
669C22—44no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22C2×#121×C5911yescharacteristic
679C22C2×#121×C5911yescharacteristic
680C22C59×#52511yescharacteristic
681C22C59×#53511yescharacteristic
682C22C59×#53511yescharacteristic
683C22C59×#53512yes—
684C22C59×#53611yescharacteristic
685C22C59×#53711yescharacteristic
686C22C59×#53712yes—
687C22C59×#53812yes—
688C22C59×#53912yes—
689C22C59×#54012yes—
690C22C59×#54212yes—
691C22D42×C5911yescharacteristic
692C22C59×#54612yes—
693C22C59×#54711yescharacteristic
694C22C59×#54812yes—
695C22C59×#54811yescharacteristic
696C22C59×#55112yes—
697C22C59×#55212yes—
698C22C59×#55311yescharacteristic
699C22C59×#56212yes—
700C22C59×#56312yes—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—44no—
707C4—82no—
708C4—81no—
709C4—81no—
710C4—82no—
711C2—84no—
712C2C59×#241111yescharacteristic
713C2C59×#241611yescharacteristic
714C2C59×#253611yescharacteristic
715C2C59×#261911yescharacteristic
716C2C59×#262011yescharacteristic
717C2C59×#263611yescharacteristic
718C2C59×#267612yes—
719C2C59×#270712yes—
720C2C59×#272312yes—
721C2C59×#276112yes—
722C2C59×#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
1. C2×C59×#396C2semidirect
4. C2×C59×#387C2semidirect
5. C2×C59×#382C2semidirect
6. C59×#1444C2semidirect
7. C59×#1441C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
69. C2×C4⋊C4×C59D4semidirect
301. #16519C59direct (N × H)
350. C2×#396C2×C59semidirect
353. C2×#387C2×C59semidirect
354. C2×#382C2×C59semidirect
355. #1444C2×C59semidirect
356. #1441C2×C59semidirect
357. #1440C2×C59semidirect
358. #1439C2×C59semidirect
359. #1439C2×C59semidirect
401. C59#16519direct (N × H)
431. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3962
C2×C59×#3942
C2×C59×#3902
C2×C59×#3872
C2×C59×#3822
C59×#14442
C59×#14412
C59×#14402
C59×#14392
C59×#14382
#1651959