Finite Group Databasebeta

← C59×#14887 #28426996

Subgroups — C59×#14887 #28426996

Order 15104.

1894 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C59C211yesmaximal, characteristic
2C2×C59×#395C211yesmaximal, characteristic, complemented
3C2×C59×#393C211yesmaximal, characteristic
4C2×C59×#391C211yesmaximal, characteristic, complemented
5C59×#1442C212yesmaximal, complemented
6C59×#1441C211yesmaximal, characteristic, complemented
7C59×#1439C212yesmaximal
8C59×#1439C211yesmaximal, characteristic
9C59×#1436C212yesmaximal, complemented
10C59×#1434C211yesmaximal, characteristic, complemented
11C59×C22⋊#95C212yesmaximal
12C23×Q8×C59C2211yescharacteristic
13C24×C4×C59C2211yescharacteristic
14C2×#117×C59—24no—
15C2×#117×C59—24no—
16C2×#117×C59—24no—
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C42×C59C2211yescharacteristic
26C22×C42×C59C2211yescharacteristic
27C59×#395—24no—
28C59×#393—24no—
29C59×#391—24no—
30C2×#95×C59C2212yes—
31C2×#95×C59C2212yes—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C2×#95×C59C2212yes—
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C25×C59C2311yescharacteristic
42C22×Q8×C59—22no—
43C22×Q8×C59—22no—
44C22×Q8×C59—22no—
45C22×Q8×C59—24no—
46C22×Q8×C59—42no—
47C23×C4×C59—22no—
48C23×C4×C59—22no—
49C23×C4×C59—22no—
50C23×C4×C59—22no—
51C23×C4×C59—22no—
52C23×C4×C59—22no—
53C23×C4×C59Q814yescomplemented
54C23×C4×C59C2312yes—
55C23×C4×C59C2312yes—
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2311yescharacteristic
58C23×C4×C59C2311yescharacteristic
59C23×C4×C59C2312yes—
60C23×C4×C59C2312yes—
61C23×C4×C59C2311yescharacteristic
62C23×C4×C59C2311yescharacteristic
63C23×C4×C59C2311yescharacteristic
64#117×C59—232no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—22no—
68C2×C4⋊C4×C59—22no—
69C2×C4⋊C4×C59—22no—
70C2×C4⋊C4×C59—22no—
71C2×C4⋊C4×C59—24no—
72C2×C4⋊C4×C59—24no—
73C2×C4⋊C4×C59—42no—
74C2×C4⋊C4×C59—42no—
75C2×C4⋊C4×C59D414yes—
76C2×C22⋊C4×C59—22no—
77C2×C22⋊C4×C59—22no—
78C2×C22⋊C4×C59—22no—
79C2×C22⋊C4×C59—22no—
80C2×C22⋊C4×C59—22no—
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×C59D414yes—
88C2×C42×C59—22no—
89C2×C42×C59—22no—
90C2×C42×C59—22no—
91C2×C42×C59—22no—
92C2×C42×C59—22no—
93C2×C42×C59D414yes—
94#95×C59—24no—
95#95×C59—24no—
96#95×C59—24no—
97#95×C59—22no—
98#95×C59—22no—
99#95×C59—24no—
100#95×C59—24no—
101#95×C59—24no—
102#95×C59—24no—
103#95×C59—24no—
104#95×C59—42no—
105C24×C59—21no—
106C24×C59—21no—
107C24×C59—22no—
108C24×C59—22no—
109C24×C59—21no—
110C24×C59—21no—
111C24×C59—22no—
112C24×C59—22no—
113C24×C59C2×D412yes—
114C24×C59C2×Q812yes—
115C24×C59#4112yes—
116C24×C59C2411yescharacteristic
117C2×Q8×C59—28no—
118C2×Q8×C59—48no—
119C2×Q8×C59—48no—
120C2×Q8×C59—44no—
121C2×Q8×C59—44no—
122C22×C4×C59—28no—
123C22×C4×C59—28no—
124C22×C4×C59—28no—
125C22×C4×C59—28no—
126C22×C4×C59—28no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—28no—
138C22×C4×C59—28no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
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—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
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—22no—
177C22×C4×C59C2×D412yes—
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2×D412yes—
180C22×C4×C59C2×D412yes—
181C22×C4×C59C2×D412yes—
182C22×C4×C59C2×D412yes—
183C22×C4×C59C2×D412yes—
184C22×C4×C59C2×D412yes—
185C22×C4×C59C2×Q812yes—
186C22×C4×C59C2×Q812yes—
187C22×C4×C59#4114yes—
188C22×C4×C59#4114yes—
189C22×C4×C59#4112yes—
190C22×C4×C59#4112yes—
191C4⋊C4×C59—28no—
192C4⋊C4×C59—28no—
193C4⋊C4×C59—48no—
194C4⋊C4×C59—44no—
195C22⋊C4×C59—28no—
196C22⋊C4×C59—28no—
197C22⋊C4×C59—48no—
198C22⋊C4×C59—48no—
199C42×C59—28no—
200C42×C59—28no—
201C23×C59—22no—
202C23×C59—22no—
203C23×C59—22no—
204C23×C59—22no—
205C23×C59—22no—
206C23×C59—22no—
207C23×C59—24no—
208C23×C59—24no—
209C23×C59—24no—
210C23×C59—24no—
211C23×C59—24no—
212C23×C59—24no—
213C23×C59—41no—
214C23×C59—42no—
215C23×C59—41no—
216C23×C59—41no—
217C23×C59—41no—
218C23×C59—42no—
219C23×C59—42no—
220C23×C59—42no—
221C23×C59—42no—
222C23×C59—42no—
223C23×C59C22⋊Q814yes—
224C23×C59C22×D411yescharacteristic
225C23×C59C22×D411yescharacteristic
226C23×C59C22×D411yescharacteristic
227C23×C59C22×Q811yescharacteristic
228C23×C59C2×#4111yescharacteristic
229C23×C59C2×#4111yescharacteristic
230C23×C59C2×#4111yescharacteristic
231C23×C59C2×#4112yes—
232C23×C59C2×#4112yes—
233C23×C59H(5,𝔽2)12yes—
234C23×C592−1+412yes—
235Q8×C59—416no—
236C2×C4×C59—232no—
237C2×C4×C59—22no—
238C2×C4×C59—22no—
239C2×C4×C59—22no—
240C2×C4×C59—22no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
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—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—24no—
257C2×C4×C59—24no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—24no—
261C2×C4×C59—24no—
262C2×C4×C59—24no—
263C2×C4×C59—24no—
264C2×C4×C59—24no—
265C2×C4×C59—24no—
266C2×C4×C59—42no—
267C2×C4×C59—41no—
268C2×C4×C59—42no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—42no—
272C2×C4×C59—41no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—42no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
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#12014yes—
297C2×C4×C59C22⋊Q814yes—
298C2×C4×C59C22⋊Q814yes—
299#14887C5911yesmaximal, characteristic, direct product factor, Sylow
300C22×C59—24no—
301C22×C59—28no—
302C22×C59—42no—
303C22×C59—42no—
304C22×C59—42no—
305C22×C59—42no—
306C22×C59—42no—
307C22×C59—42no—
308C22×C59—44no—
309C22×C59—44no—
310C22×C59—44no—
311C22×C59C2×#12011yescharacteristic
312C22×C59C2×C22⋊Q811yescharacteristic
313C22×C59C2×C22⋊Q811yescharacteristic
314C22×C59C2×C22⋊Q811yescharacteristic
315C22×C59#52511yescharacteristic
316C22×C59#52511yescharacteristic
317C22×C59#52511yescharacteristic
318C22×C59#52511yescharacteristic
319C22×C59#52912yes—
320C22×C59#53211yescharacteristic
321C22×C59#53312yes—
322C22×C59#53511yescharacteristic
323C22×C59#53611yescharacteristic
324C22×C59#54212yes—
325C22×C59#54412yes—
326C22×C59#54612yes—
327C22×C59#54612yes—
328C22×C59#54712yes—
329C22×C59#54812yes—
330C22×C59#55112yes—
331C22×C59#55212yes—
332C22×C59#55512yes—
333C22×C59#55612yes—
334C4×C59—24no—
335C4×C59—24no—
336C4×C59—24no—
337C4×C59—42no—
338C4×C59—44no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—44no—
342C4×C59—82no—
343C4×C59—82no—
344C22×#117C2×C5911yescharacteristic
345C2×#395C2×C5911yescharacteristic, complemented
346C2×#393C2×C5911yescharacteristic
347C2×#391C2×C5911yescharacteristic, complemented
348#1442C2×C5912yescomplemented
349#1441C2×C5911yescharacteristic, complemented
350#1439C2×C5912yes—
351#1439C2×C5911yescharacteristic
352#1436C2×C5912yescomplemented
353#1434C2×C5911yescharacteristic, complemented
354C22⋊#95C2×C5912yes—
355C2×C59—44no—
356C2×C59#239611yescharacteristic
357C2×C59#240411yescharacteristic
358C2×C59#243211yescharacteristic
359C2×C59#243812yes—
360C2×C59#243912yes—
361C2×C59#247412yes—
362C2×C59#247712yes—
363C2×C59#259911yescharacteristic
364C2×C59#261011yescharacteristic
365C2×C59#262811yescharacteristic
366C2×C59#284811yescharacteristic
367C23×Q8C22×C5911yescharacteristic
368C24×C4C22×C5911yescharacteristic
369C2×#117—24no—
370C2×#117—24no—
371C2×#117—24no—
372C22×C4⋊C4C22×C5911yescharacteristic
373C22×C4⋊C4C22×C5912yes—
374C22×C4⋊C4C22×C5911yescharacteristic
375C22×C4⋊C4C22×C5911yescharacteristic
376C22×C22⋊C4C22×C5911yescharacteristic
377C22×C22⋊C4C22×C5912yes—
378C22×C22⋊C4C22×C5912yes—
379C22×C22⋊C4C22×C5911yescharacteristic
380C22×C42C22×C5911yescharacteristic
381C22×C42C22×C5911yescharacteristic
382#395—24no—
383#393—24no—
384#391—24no—
385C2×#95C22×C5911yescharacteristic
386C2×#95C22×C5912yes—
387C2×#95C22×C5912yes—
388C2×#95C22×C5911yescharacteristic
389C2×#95C22×C5912yes—
390C2×#95C22×C5912yes—
391C2×#95C22×C5912yes—
392C2×#95C22×C5912yes—
393C2×#95C22×C5912yes—
394C2×#95C22×C5912yes—
395C2×#95C22×C5912yes—
396C59#1488711yescharacteristic, direct product factor, Sylow
397C25C23×C5911yescharacteristic
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—24no—
402C22×Q8—42no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4Q8×C5914yescomplemented
410C23×C4C23×C5912yes—
411C23×C4C23×C5912yes—
412C23×C4C23×C5911yescharacteristic
413C23×C4C23×C5911yescharacteristic
414C23×C4C23×C5911yescharacteristic
415C23×C4C23×C5912yes—
416C23×C4C23×C5912yes—
417C23×C4C23×C5911yescharacteristic
418C23×C4C23×C5911yescharacteristic
419C23×C4C23×C5911yescharacteristic
420#117—232no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4D4×C5914yes—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4D4×C5914yes—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42D4×C5914yes—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—22no—
454#95—22no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—42no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24C2×D4×C5912yes—
470C24C2×Q8×C5912yes—
471C24#41×C5912yes—
472C24C24×C5911yescharacteristic
473C2×Q8—28no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—44no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4C2×D4×C5912yes—
534C22×C4C2×D4×C5912yes—
535C22×C4C2×D4×C5912yes—
536C22×C4C2×D4×C5912yes—
537C22×C4C2×D4×C5912yes—
538C22×C4C2×D4×C5912yes—
539C22×C4C2×D4×C5912yes—
540C22×C4C2×D4×C5912yes—
541C22×C4C2×Q8×C5912yes—
542C22×C4C2×Q8×C5912yes—
543C22×C4#41×C5914yes—
544C22×C4#41×C5914yes—
545C22×C4#41×C5912yes—
546C22×C4#41×C5912yes—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C22⋊C4—28no—
552C22⋊C4—28no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C42—28no—
556C42—28no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—41no—
570C23—42no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23C22⋊Q8×C5914yes—
580C23C22×D4×C5911yescharacteristic
581C23C22×D4×C5911yescharacteristic
582C23C22×D4×C5911yescharacteristic
583C23C22×Q8×C5911yescharacteristic
584C23C2×#41×C5911yescharacteristic
585C23C2×#41×C5911yescharacteristic
586C23C2×#41×C5911yescharacteristic
587C23C2×#41×C5912yes—
588C23C2×#41×C5912yes—
589C23H(5,𝔽2)×C5912yes—
590C232−1+4×C5912yes—
591Q8—416no—
592C2×C4—232no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4#120×C5914yes—
653C2×C4C22⋊Q8×C5914yes—
654C2×C4C22⋊Q8×C5914yes—
655C22—24no—
656C22—28no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—44no—
664C22—44no—
665C22—44no—
666C22C2×#120×C5911yescharacteristic
667C22C2×C22⋊Q8×C5911yescharacteristic
668C22C2×C22⋊Q8×C5911yescharacteristic
669C22C2×C22⋊Q8×C5911yescharacteristic
670C22C59×#52511yescharacteristic
671C22C59×#52511yescharacteristic
672C22C59×#52511yescharacteristic
673C22C59×#52511yescharacteristic
674C22C59×#52912yes—
675C22C59×#53211yescharacteristic
676C22C59×#53312yes—
677C22C59×#53511yescharacteristic
678C22C59×#53611yescharacteristic
679C22C59×#54212yes—
680C22C59×#54412yes—
681C22C59×#54612yes—
682C22C59×#54612yes—
683C22C59×#54712yes—
684C22C59×#54812yes—
685C22C59×#55112yes—
686C22C59×#55212yes—
687C22C59×#55512yes—
688C22C59×#55612yes—
689C4—24no—
690C4—24no—
691C4—24no—
692C4—44no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—44no—
697C4—82no—
698C4—82no—
699C2—44no—
700C2C59×#239611yescharacteristic
701C2C59×#240411yescharacteristic
702C2C59×#243211yescharacteristic
703C2C59×#243812yes—
704C2C59×#243912yes—
705C2C59×#247412yes—
706C2C59×#247712yes—
707C2C59×#259911yescharacteristic
708C2C59×#261011yescharacteristic
709C2C59×#262811yescharacteristic
710C2C59×#284811yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
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×#391C2semidirect
5. C59×#1442C2semidirect
6. C59×#1441C2semidirect
9. C59×#1436C2semidirect
10. C59×#1434C2semidirect
53. C23×C4×C59Q8semidirect
299. #14887C59direct (N × H)
345. C2×#395C2×C59semidirect
347. C2×#391C2×C59semidirect
348. #1442C2×C59semidirect
349. #1441C2×C59semidirect
352. #1436C2×C59semidirect
353. #1434C2×C59semidirect
396. C59#14887direct (N × H)
409. C23×C4Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C592
C2×C59×#3952
C2×C59×#3932
C2×C59×#3912
C59×#14422
C59×#14412
C59×#14392
C59×#14362
C59×#14342
C59×C22⋊#952
#1488759