Finite Group Databasebeta

← C59×#14912 #28427021

Subgroups — C59×#14912 #28427021

Order 15104.

2314 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C59C211yesmaximal, characteristic
2C2×C59×#386C211yesmaximal, characteristic
3C2×C59×#386C211yesmaximal, characteristic
4C2×C59×#385C211yesmaximal, characteristic, complemented
5C2×C59×#381C211yesmaximal, characteristic, complemented
6C22×#95×C59C211yesmaximal, characteristic, complemented
7C59×#1442C212yesmaximal, complemented
8C59×#1441C212yesmaximal, complemented
9C59×#1440C212yesmaximal, complemented
10C59×#1439C212yesmaximal, complemented
11C59×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C59C2211yescharacteristic
13C24×C4×C59C2211yescharacteristic
14C24×C4×C59C2211yescharacteristic
15C24×C4×C59C2211yescharacteristic
16C2×#123×C59—24no—
17C2×#123×C59—24no—
18C2×#123×C59—24no—
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2212yes—
22C22×C22⋊C4×C59C2211yescharacteristic
23C22×C22⋊C4×C59C2211yescharacteristic
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2212yes—
26C22×C22⋊C4×C59C2212yes—
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C59×#386—24no—
30C59×#386—24no—
31C59×#385—24no—
32C59×#381—24no—
33C2×#95×C59—24no—
34C2×#95×C59C2212yes—
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2212yes—
41C2×#95×C59C2212yes—
42C2×#95×C59C2212yes—
43C25×C59C2311yescharacteristic
44C25×C59C2311yescharacteristic
45C22×D4×C59—22no—
46C22×D4×C59—22no—
47C22×D4×C59—22no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—22no—
51C22×D4×C59D414yes—
52C23×C4×C59—22no—
53C23×C4×C59—22no—
54C23×C4×C59—22no—
55C23×C4×C59—22no—
56C23×C4×C59—22no—
57C23×C4×C59—22no—
58C23×C4×C59—22no—
59C23×C4×C59—22no—
60C23×C4×C59—24no—
61C23×C4×C59—24no—
62C23×C4×C59—22no—
63C23×C4×C59—22no—
64C23×C4×C59—22no—
65C23×C4×C59—22no—
66C23×C4×C59—42no—
67C23×C4×C59—42no—
68C23×C4×C59D414yes—
69C23×C4×C59C2312yes—
70C23×C4×C59C2312yes—
71C23×C4×C59C2311yescharacteristic
72C23×C4×C59C2311yescharacteristic
73C23×C4×C59C2311yescharacteristic
74C23×C4×C59C2311yescharacteristic
75C23×C4×C59C2311yescharacteristic
76C23×C4×C59C2312yes—
77C23×C4×C59C2312yes—
78#123×C59—232no—
79C2×C4⋊C4×C59—22no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—24no—
86C2×C4⋊C4×C59—24no—
87C2×C4⋊C4×C59—42no—
88C2×C22⋊C4×C59—22no—
89C2×C22⋊C4×C59—22no—
90C2×C22⋊C4×C59—22no—
91C2×C22⋊C4×C59—22no—
92C2×C22⋊C4×C59—22no—
93C2×C22⋊C4×C59—22no—
94C2×C22⋊C4×C59—22no—
95C2×C22⋊C4×C59—22no—
96C2×C22⋊C4×C59—22no—
97C2×C22⋊C4×C59—22no—
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—24no—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—22no—
102C2×C22⋊C4×C59—24no—
103C2×C22⋊C4×C59—24no—
104C2×C22⋊C4×C59—24no—
105C2×C22⋊C4×C59—42no—
106C2×C22⋊C4×C59—42no—
107C2×C22⋊C4×C59D414yes—
108C2×C22⋊C4×C59D414yes—
109#95×C59—24no—
110#95×C59—24no—
111#95×C59—24no—
112#95×C59—24no—
113#95×C59—24no—
114#95×C59—24no—
115#95×C59—24no—
116#95×C59—24no—
117#95×C59—42no—
118C24×C59—22no—
119C24×C59—22no—
120C24×C59—22no—
121C24×C59—22no—
122C24×C59—21no—
123C24×C59—21no—
124C24×C59—21no—
125C24×C59—22no—
126C24×C59—22no—
127C24×C59—21no—
128C24×C59—21no—
129C24×C59—21no—
130C24×C59—22no—
131C24×C59—22no—
132C24×C59C2×D412yes—
133C24×C59C2×D412yes—
134C24×C59C2×D412yes—
135C24×C59C2×D412yes—
136C24×C59C2×D412yes—
137C24×C59#4112yes—
138C24×C59#4112yes—
139C24×C59#4112yes—
140C24×C59C2411yescharacteristic
141C2×D4×C59—28no—
142C2×D4×C59—28no—
143C2×D4×C59—28no—
144C2×D4×C59—44no—
145C2×D4×C59—44no—
146C2×D4×C59—44no—
147C2×D4×C59—44no—
148C22×C4×C59—28no—
149C22×C4×C59—28no—
150C22×C4×C59—28no—
151C22×C4×C59—28no—
152C22×C4×C59—28no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—21no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
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—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—48no—
205C22×C4×C59—48no—
206C22×C4×C59—48no—
207C22×C4×C59—48no—
208C22×C4×C59—44no—
209C22×C4×C59—44no—
210C22×C4×C59—44no—
211C22×C4×C59—44no—
212C22×C4×C59—44no—
213C22×C4×C59—44no—
214C22×C4×C59—44no—
215C22×C4×C59—44no—
216C22×C4×C59C2×D414yes—
217C22×C4×C59C2×D412yes—
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D412yes—
222C22×C4×C59#4114yes—
223C22×C4×C59#4114yes—
224C4⋊C4×C59—28no—
225C4⋊C4×C59—28no—
226C4⋊C4×C59—48no—
227C22⋊C4×C59—28no—
228C22⋊C4×C59—28no—
229C22⋊C4×C59—28no—
230C22⋊C4×C59—28no—
231C22⋊C4×C59—48no—
232C22⋊C4×C59—48no—
233C22⋊C4×C59—44no—
234C23×C59—22no—
235C23×C59—22no—
236C23×C59—24no—
237C23×C59—24no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—24no—
241C23×C59—24no—
242C23×C59—24no—
243C23×C59—24no—
244C23×C59—24no—
245C23×C59—24no—
246C23×C59—24no—
247C23×C59—24no—
248C23×C59—24no—
249C23×C59—24no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—24no—
254C23×C59—24no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—42no—
262C23×C59—42no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59#12014yes—
274C23×C59#12114yes—
275C23×C59#12114yes—
276C23×C59#12114yes—
277C23×C59#12314yes—
278C23×C59#12314yes—
279C23×C59#12414yes—
280C23×C59C22×D411yescharacteristic
281C23×C59C22×D411yescharacteristic
282C23×C59C22×D411yescharacteristic
283C23×C59C22×D411yescharacteristic
284C23×C59C2×#4111yescharacteristic
285C23×C59C2×#4111yescharacteristic
286C23×C59C2×#4111yescharacteristic
287C23×C59C2×#4112yes—
288C23×C59C2×#4112yes—
289C23×C59H(5,𝔽2)12yes—
290C23×C592−1+412yes—
291D4×C59—416no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—24no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—24no—
305C2×C4×C59—24no—
306C2×C4×C59—24no—
307C2×C4×C59—24no—
308C2×C4×C59—24no—
309C2×C4×C59—24no—
310C2×C4×C59—24no—
311C2×C4×C59—24no—
312C2×C4×C59—24no—
313C2×C4×C59—24no—
314C2×C4×C59—416no—
315C2×C4×C59—416no—
316C2×C4×C59—42no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—42no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59—41no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
331C2×C4×C59—41no—
332C2×C4×C59—42no—
333C2×C4×C59—41no—
334C2×C4×C59—42no—
335C2×C4×C59—42no—
336C2×C4×C59—41no—
337C2×C4×C59—42no—
338C2×C4×C59—42no—
339C2×C4×C59—42no—
340C2×C4×C59—42no—
341C2×C4×C59—42no—
342C2×C4×C59—42no—
343C2×C4×C59—42no—
344C2×C4×C59—42no—
345C2×C4×C59—42no—
346C2×C4×C59—416no—
347C2×C4×C59—42no—
348C2×C4×C59—42no—
349C2×C4×C59—42no—
350C2×C4×C59—42no—
351C2×C4×C59—42no—
352C2×C4×C59—42no—
353C2×C4×C59—42no—
354#14912C5911yesmaximal, characteristic, direct product factor, Sylow
355C22×C59—24no—
356C22×C59—24no—
357C22×C59—24no—
358C22×C59—24no—
359C22×C59—24no—
360C22×C59—24no—
361C22×C59—28no—
362C22×C59—28no—
363C22×C59—28no—
364C22×C59—28no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—44no—
369C22×C59—44no—
370C22×C59—81no—
371C22×C59—81no—
372C22×C59—81no—
373C22×C59—81no—
374C22×C59—82no—
375C22×C59—82no—
376C22×C59#39418yes—
377C22×C59C2×#12011yescharacteristic
378C22×C59C2×#12111yescharacteristic
379C22×C59C2×#12111yescharacteristic
380C22×C59C2×#12111yescharacteristic
381C22×C59C2×#12311yescharacteristic
382C22×C59C2×#12311yescharacteristic
383C22×C59#52511yescharacteristic
384C22×C59#52511yescharacteristic
385C22×C59C2×#12411yescharacteristic
386C22×C59#52912yes—
387C22×C59#52912yes—
388C22×C59#53511yescharacteristic
389C22×C59#53611yescharacteristic
390C22×C59#53912yes—
391C22×C59#53912yes—
392C22×C59#54612yes—
393C22×C59#54612yes—
394C22×C59#54612yes—
395C22×C59#54712yes—
396C22×C59#54712yes—
397C22×C59#54712yes—
398C22×C59#55112yes—
399C22×C59#55212yes—
400C4×C59—42no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59—42no—
404C4×C59—44no—
405C4×C59—42no—
406C4×C59—44no—
407C4×C59—44no—
408C4×C59—82no—
409C22×#123C2×C5911yescharacteristic
410C2×#386C2×C5911yescharacteristic
411C2×#386C2×C5911yescharacteristic
412C2×#385C2×C5911yescharacteristic, complemented
413C2×#381C2×C5911yescharacteristic, complemented
414C22×#95C2×C5911yescharacteristic, complemented
415#1442C2×C5912yescomplemented
416#1441C2×C5912yescomplemented
417#1440C2×C5912yescomplemented
418#1439C2×C5912yescomplemented
419C22⋊#95C2×C5911yescharacteristic, complemented
420C2×C59—28no—
421C2×C59—82no—
422C2×C59C2×#39411yescharacteristic
423C2×C59#240411yescharacteristic
424C2×C59#240611yescharacteristic
425C2×C59#241111yescharacteristic
426C2×C59#241311yescharacteristic
427C2×C59#241912yes—
428C2×C59#242512yes—
429C2×C59#242512yes—
430C2×C59#248812yes—
431C2×C59#262311yescharacteristic
432C2×C59#285311yescharacteristic
433C23×D4C22×C5911yescharacteristic
434C24×C4C22×C5911yescharacteristic
435C24×C4C22×C5911yescharacteristic
436C24×C4C22×C5911yescharacteristic
437C2×#123—24no—
438C2×#123—24no—
439C2×#123—24no—
440C22×C4⋊C4C22×C5911yescharacteristic
441C22×C4⋊C4C22×C5911yescharacteristic
442C22×C4⋊C4C22×C5912yes—
443C22×C22⋊C4C22×C5911yescharacteristic
444C22×C22⋊C4C22×C5911yescharacteristic
445C22×C22⋊C4C22×C5911yescharacteristic
446C22×C22⋊C4C22×C5912yes—
447C22×C22⋊C4C22×C5912yes—
448C22×C22⋊C4C22×C5911yescharacteristic
449C22×C22⋊C4C22×C5911yescharacteristic
450#386—24no—
451#386—24no—
452#385—24no—
453#381—24no—
454C2×#95—24no—
455C2×#95C22×C5912yes—
456C2×#95C22×C5912yes—
457C2×#95C22×C5912yes—
458C2×#95C22×C5912yes—
459C2×#95C22×C5912yes—
460C2×#95C22×C5912yes—
461C2×#95C22×C5912yes—
462C2×#95C22×C5912yes—
463C2×#95C22×C5912yes—
464C59#1491211yescharacteristic, direct product factor, Sylow
465C25C23×C5911yescharacteristic
466C25C23×C5911yescharacteristic
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4D4×C5914yes—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—22no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4D4×C5914yes—
491C23×C4C23×C5912yes—
492C23×C4C23×C5911yescharacteristic
493C23×C4C23×C5912yes—
494C23×C4C23×C5911yescharacteristic
495C23×C4C23×C5911yescharacteristic
496C23×C4C23×C5911yescharacteristic
497C23×C4C23×C5911yescharacteristic
498C23×C4C23×C5912yes—
499C23×C4C23×C5912yes—
500#123—232no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—42no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4D4×C5914yes—
530C2×C22⋊C4D4×C5914yes—
531#95—24no—
532#95—24no—
533#95—24no—
534#95—24no—
535#95—24no—
536#95—24no—
537#95—24no—
538#95—24no—
539#95—42no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—22no—
553C24—22no—
554C24C2×D4×C5912yes—
555C24C2×D4×C5912yes—
556C24C2×D4×C5912yes—
557C24C2×D4×C5912yes—
558C24C2×D4×C5912yes—
559C24#41×C5912yes—
560C24#41×C5912yes—
561C24#41×C5912yes—
562C24C24×C5911yescharacteristic
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4C2×D4×C5914yes—
639C22×C4C2×D4×C5912yes—
640C22×C4C2×D4×C5912yes—
641C22×C4C2×D4×C5912yes—
642C22×C4C2×D4×C5912yes—
643C22×C4C2×D4×C5912yes—
644C22×C4#41×C5914yes—
645C22×C4#41×C5914yes—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—48no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—44no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23#120×C5914yes—
696C23#121×C5914yes—
697C23#121×C5914yes—
698C23#121×C5914yes—
699C23#123×C5914yes—
700C23#123×C5914yes—
701C23#124×C5914yes—
702C23C22×D4×C5911yescharacteristic
703C23C22×D4×C5911yescharacteristic
704C23C22×D4×C5911yescharacteristic
705C23C22×D4×C5911yescharacteristic
706C23C2×#41×C5911yescharacteristic
707C23C2×#41×C5911yescharacteristic
708C23C2×#41×C5911yescharacteristic
709C23C2×#41×C5912yes—
710C23C2×#41×C5912yes—
711C23H(5,𝔽2)×C5912yes—
712C232−1+4×C5912yes—
713D4—416no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C22—28no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—28no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—82no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—82no—
797C22C59×#39418yes—
798C22C2×#120×C5911yescharacteristic
799C22C2×#121×C5911yescharacteristic
800C22C2×#121×C5911yescharacteristic
801C22C2×#121×C5911yescharacteristic
802C22C2×#123×C5911yescharacteristic
803C22C2×#123×C5911yescharacteristic
804C22C59×#52511yescharacteristic
805C22C59×#52511yescharacteristic
806C22C2×#124×C5911yescharacteristic
807C22C59×#52912yes—
808C22C59×#52912yes—
809C22C59×#53511yescharacteristic
810C22C59×#53611yescharacteristic
811C22C59×#53912yes—
812C22C59×#53912yes—
813C22C59×#54612yes—
814C22C59×#54612yes—
815C22C59×#54612yes—
816C22C59×#54712yes—
817C22C59×#54712yes—
818C22C59×#54712yes—
819C22C59×#55112yes—
820C22C59×#55212yes—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—42no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—82no—
830C2—28no—
831C2—82no—
832C2C2×C59×#39411yescharacteristic
833C2C59×#240411yescharacteristic
834C2C59×#240611yescharacteristic
835C2C59×#241111yescharacteristic
836C2C59×#241311yescharacteristic
837C2C59×#241912yes—
838C2C59×#242512yes—
839C2C59×#242512yes—
840C2C59×#248812yes—
841C2C59×#262311yescharacteristic
842C2C59×#285311yescharacteristic
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
4. C2×C59×#385C2semidirect
5. C2×C59×#381C2semidirect
6. C22×#95×C59C2semidirect
7. C59×#1442C2semidirect
8. C59×#1441C2semidirect
9. C59×#1440C2semidirect
10. C59×#1439C2semidirect
11. C59×C22⋊#95C2semidirect
354. #14912C59direct (N × H)
412. C2×#385C2×C59semidirect
413. C2×#381C2×C59semidirect
414. C22×#95C2×C59semidirect
415. #1442C2×C59semidirect
416. #1441C2×C59semidirect
417. #1440C2×C59semidirect
418. #1439C2×C59semidirect
419. C22⋊#95C2×C59semidirect
464. C59#14912direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C592
C2×C59×#3862
C2×C59×#3852
C2×C59×#3812
C22×#95×C592
C59×#14422
C59×#14412
C59×#14402
C59×#14392
C59×C22⋊#952
#1491259