Finite Group Databasebeta

← C59×#16809 #28428918

Subgroups — C59×#16809 #28428918

Order 15104.

2006 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#400C211yesmaximal, characteristic, complemented
2C2×C59×#399C211yesmaximal, characteristic, complemented
3C2×C59×#394C211yesmaximal, characteristic, complemented
4C2×C59×#392C211yesmaximal, characteristic
5C2×C59×#390C211yesmaximal, characteristic, complemented
6C2×C59×#388C211yesmaximal, characteristic, complemented
7C59×#1439C212yesmaximal, complemented
8C59×#1439C212yesmaximal, complemented
9C59×#1438C212yesmaximal, complemented
10C59×#1438C212yesmaximal, complemented
11C59×#1434C211yesmaximal, characteristic, complemented
12C23×D4×C59C2211yescharacteristic
13C23×D4×C59C2212yes—
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2212yes—
17C22×C22⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2212yes—
25C22×C22⋊C4×C59C2212yes—
26C22×C42×C59C2211yescharacteristic
27C59×#400—24no—
28C59×#399—24no—
29C59×#394—24no—
30C59×#392—24no—
31C59×#390—24no—
32C59×#388—24no—
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C2×#95×C59C2211yescharacteristic
41C25×C59C2311yescharacteristic
42C25×C59C2312yes—
43C22×D4×C59—24no—
44C22×D4×C59—24no—
45C22×D4×C59—24no—
46C22×D4×C59—22no—
47C22×D4×C59—24no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—42no—
51C22×D4×C59—42no—
52C22×D4×C59—42no—
53C22×D4×C59—42no—
54C22×D4×C59—42no—
55C23×C4×C59C2311yescharacteristic
56C23×C4×C59C2311yescharacteristic
57C23×C4×C59C2312yes—
58C23×C4×C59C2312yes—
59C23×C4×C59C2311yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C23×C4×C59C2312yes—
62C23×C4×C59C2311yescharacteristic
63C23×C4×C59C2311yescharacteristic
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—22no—
67C2×C4⋊C4×C59—24no—
68C2×C4⋊C4×C59—22no—
69C2×C4⋊C4×C59—22no—
70C2×C4⋊C4×C59—22no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59—42no—
73C2×C22⋊C4×C59—22no—
74C2×C22⋊C4×C59—22no—
75C2×C22⋊C4×C59—22no—
76C2×C22⋊C4×C59—24no—
77C2×C22⋊C4×C59—22no—
78C2×C22⋊C4×C59—22no—
79C2×C22⋊C4×C59—24no—
80C2×C22⋊C4×C59—24no—
81C2×C22⋊C4×C59—24no—
82C2×C22⋊C4×C59—22no—
83C2×C22⋊C4×C59—24no—
84C2×C22⋊C4×C59—24no—
85C2×C22⋊C4×C59—24no—
86C2×C22⋊C4×C59—22no—
87C2×C22⋊C4×C59—24no—
88C2×C22⋊C4×C59—42no—
89C2×C22⋊C4×C59—42no—
90C2×C22⋊C4×C59—42no—
91C2×C22⋊C4×C59—42no—
92C2×C22⋊C4×C59—42no—
93C2×C22⋊C4×C59—42no—
94C2×C22⋊C4×C59—42no—
95C2×C22⋊C4×C59—42no—
96C2×C22⋊C4×C59—42no—
97C2×C22⋊C4×C59—42no—
98C2×C22⋊C4×C59—42no—
99C2×C42×C59—42no—
100C2×C42×C59D414yescomplemented
101#95×C59—22no—
102#95×C59—22no—
103#95×C59—24no—
104#95×C59—24no—
105#95×C59—42no—
106#95×C59—42no—
107#95×C59D414yes—
108#95×C59D414yescomplemented
109C24×C59—21no—
110C24×C59—21no—
111C24×C59—22no—
112C24×C59—22no—
113C24×C59—21no—
114C24×C59—22no—
115C24×C59—21no—
116C24×C59—22no—
117C24×C59—22no—
118C24×C59—22no—
119C24×C59—22no—
120C24×C59—22no—
121C24×C59—22no—
122C24×C59—22no—
123C24×C59—22no—
124C24×C59—22no—
125C24×C59—22no—
126C24×C59—22no—
127C24×C59—22no—
128C24×C59—22no—
129C24×C59—22no—
130C24×C59—21no—
131C24×C59—22no—
132C24×C59—21no—
133C24×C59#4112yes—
134C24×C59#4114yes—
135C24×C59C2411yescharacteristic
136C2×D4×C59—28no—
137C2×D4×C59—48no—
138C2×D4×C59—48no—
139C2×D4×C59—48no—
140C2×D4×C59—48no—
141C2×D4×C59—44no—
142C2×D4×C59—48no—
143C2×D4×C59—48no—
144C2×D4×C59—48no—
145C2×D4×C59—48no—
146C2×D4×C59—48no—
147C2×D4×C59—44no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—21no—
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—21no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—22no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—22no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59C2×D414yes—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×D414yes—
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2×D412yes—
200C22×C4×C59#4112yes—
201C4⋊C4×C59—48no—
202C4⋊C4×C59—44no—
203C4⋊C4×C59—44no—
204C22⋊C4×C59—28no—
205C22⋊C4×C59—48no—
206C22⋊C4×C59—48no—
207C22⋊C4×C59—44no—
208C22⋊C4×C59—48no—
209C22⋊C4×C59—48no—
210C22⋊C4×C59—48no—
211C22⋊C4×C59—48no—
212C22⋊C4×C59—44no—
213C42×C59—44no—
214C23×C59—22no—
215C23×C59—24no—
216C23×C59—24no—
217C23×C59—24no—
218C23×C59—24no—
219C23×C59—24no—
220C23×C59—22no—
221C23×C59—24no—
222C23×C59—22no—
223C23×C59—24no—
224C23×C59—24no—
225C23×C59—24no—
226C23×C59—42no—
227C23×C59—41no—
228C23×C59—41no—
229C23×C59—42no—
230C23×C59—41no—
231C23×C59—42no—
232C23×C59—42no—
233C23×C59—42no—
234C23×C59—42no—
235C23×C59—42no—
236C23×C59—42no—
237C23×C59—42no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—42no—
241C23×C59—42no—
242C23×C59—42no—
243C23×C59—41no—
244C23×C59—42no—
245C23×C59—42no—
246C23×C59—42no—
247C23×C59—42no—
248C23×C59—42no—
249C23×C59—42no—
250C23×C59—42no—
251C23×C59—42no—
252C23×C59—42no—
253C23×C59—42no—
254C23×C59—42no—
255C23×C59—42no—
256C23×C59—42no—
257C23×C59—42no—
258C23×C59—42no—
259C23×C59—41no—
260C23×C59—42no—
261C23×C59—42no—
262C23×C59—41no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59C22×D411yescharacteristic
273C23×C59C22×D411yescharacteristic
274C23×C59C22×D411yescharacteristic
275C23×C59C2×#4111yescharacteristic
276C23×C59C2×#4112yes—
277C23×C59C2×#4111yescharacteristic
278C23×C59H(5,𝔽2)12yes—
279C23×C59H(5,𝔽2)12yes—
280C23×C59H(5,𝔽2)12yes—
281C23×C59H(5,𝔽2)11yescharacteristic
282C23×C592−1+411yescharacteristic
283D4×C59—416no—
284D4×C59—432no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—24no—
288C2×C4×C59—24no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—24no—
296C2×C4×C59—24no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—24no—
300C2×C4×C59—24no—
301C2×C4×C59—24no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—42no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—42no—
334C2×C4×C59—42no—
335C2×C4×C59—42no—
336C2×C4×C59—42no—
337C2×C4×C59#12714yes—
338#16809C5911yesmaximal, characteristic, direct product factor, Sylow
339C22×C59—42no—
340C22×C59—44no—
341C22×C59—42no—
342C22×C59—44no—
343C22×C59—44no—
344C22×C59—44no—
345C22×C59—44no—
346C22×C59—44no—
347C22×C59—44no—
348C22×C59—44no—
349C22×C59—44no—
350C22×C59—42no—
351C22×C59—82no—
352C22×C59—81no—
353C22×C59—81no—
354C22×C59—82no—
355C22×C59—82no—
356C22×C59—82no—
357C22×C59—82no—
358C22×C59—82no—
359C22×C59—82no—
360C22×C59—82no—
361C22×C59—81no—
362C22×C59—82no—
363C22×C59—81no—
364C22×C59—82no—
365C22×C59#52511yescharacteristic
366C22×C59#52511yescharacteristic
367C22×C59C2×#12711yescharacteristic
368C22×C59#53411yescharacteristic
369C22×C59#53511yescharacteristic
370C22×C59#53511yescharacteristic
371C22×C59#53512yes—
372C22×C59#53512yes—
373C22×C59#53711yescharacteristic
374C22×C59#53812yes—
375C22×C59#53812yes—
376C22×C59#53912yes—
377C22×C59#54012yes—
378C22×C59#54611yescharacteristic
379C22×C59#54612yes—
380C22×C59#54612yes—
381C22×C59#54611yescharacteristic
382C22×C59#54811yescharacteristic
383C22×C59#54811yescharacteristic
384C22×C59#55112yes—
385C22×C59#55312yes—
386C22×C59#56012yes—
387C22×C59#56212yes—
388C4×C59—24no—
389C4×C59—42no—
390C4×C59—44no—
391C4×C59—44no—
392C4×C59—42no—
393C4×C59—42no—
394C4×C59—81no—
395C4×C59—82no—
396C4×C59—81no—
397C2×#400C2×C5911yescharacteristic, complemented
398C2×#399C2×C5911yescharacteristic, complemented
399C2×#394C2×C5911yescharacteristic, complemented
400C2×#392C2×C5911yescharacteristic
401C2×#390C2×C5911yescharacteristic, complemented
402C2×#388C2×C5911yescharacteristic, complemented
403#1439C2×C5912yescomplemented
404#1439C2×C5912yescomplemented
405#1438C2×C5912yescomplemented
406#1438C2×C5912yescomplemented
407#1434C2×C5911yescharacteristic, complemented
408C2×C59—82no—
409C2×C59—84no—
410C2×C59#253911yescharacteristic
411C2×C59#254011yescharacteristic
412C2×C59#259811yescharacteristic
413C2×C59#263511yescharacteristic
414C2×C59#263611yescharacteristic
415C2×C59#265711yescharacteristic
416C2×C59#268512yes—
417C2×C59#269612yes—
418C2×C59#270312yes—
419C2×C59#271112yes—
420C2×C59#281311yescharacteristic
421C23×D4C22×C5911yescharacteristic
422C23×D4C22×C5912yes—
423C22×C4⋊C4C22×C5911yescharacteristic
424C22×C4⋊C4C22×C5911yescharacteristic
425C22×C4⋊C4C22×C5912yes—
426C22×C22⋊C4C22×C5911yescharacteristic
427C22×C22⋊C4C22×C5911yescharacteristic
428C22×C22⋊C4C22×C5912yes—
429C22×C22⋊C4C22×C5912yes—
430C22×C22⋊C4C22×C5912yes—
431C22×C22⋊C4C22×C5912yes—
432C22×C22⋊C4C22×C5911yescharacteristic
433C22×C22⋊C4C22×C5912yes—
434C22×C22⋊C4C22×C5912yes—
435C22×C42C22×C5911yescharacteristic
436#400—24no—
437#399—24no—
438#394—24no—
439#392—24no—
440#390—24no—
441#388—24no—
442C2×#95C22×C5912yes—
443C2×#95C22×C5912yes—
444C2×#95C22×C5911yescharacteristic
445C2×#95C22×C5911yescharacteristic
446C2×#95C22×C5912yes—
447C2×#95C22×C5912yes—
448C2×#95C22×C5911yescharacteristic
449C2×#95C22×C5911yescharacteristic
450C59#1680911yescharacteristic, direct product factor, Sylow
451C25C23×C5911yescharacteristic
452C25C23×C5912yes—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—22no—
457C22×D4—24no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4—42no—
463C22×D4—42no—
464C22×D4—42no—
465C23×C4C23×C5911yescharacteristic
466C23×C4C23×C5912yes—
467C23×C4C23×C5911yescharacteristic
468C23×C4C23×C5912yes—
469C23×C4C23×C5911yescharacteristic
470C23×C4C23×C5911yescharacteristic
471C23×C4C23×C5912yes—
472C23×C4C23×C5911yescharacteristic
473C23×C4C23×C5911yescharacteristic
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C42—42no—
510C2×C42D4×C5914yescomplemented
511#95—22no—
512#95—22no—
513#95—24no—
514#95—24no—
515#95—42no—
516#95—42no—
517#95D4×C5914yes—
518#95D4×C5914yescomplemented
519C24—21no—
520C24—21no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—22no—
542C24—21no—
543C24#41×C5912yes—
544C24#41×C5914yes—
545C24C24×C5911yescharacteristic
546C2×D4—28no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—44no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—44no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
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—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4C2×D4×C5914yes—
604C22×C4C2×D4×C5912yes—
605C22×C4C2×D4×C5912yes—
606C22×C4C2×D4×C5914yes—
607C22×C4C2×D4×C5912yes—
608C22×C4C2×D4×C5912yes—
609C22×C4C2×D4×C5912yes—
610C22×C4#41×C5912yes—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C22⋊C4—28no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C42—44no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23C22×D4×C5911yescharacteristic
683C23C22×D4×C5911yescharacteristic
684C23C22×D4×C5911yescharacteristic
685C23C2×#41×C5911yescharacteristic
686C23C2×#41×C5912yes—
687C23C2×#41×C5911yescharacteristic
688C23H(5,𝔽2)×C5912yes—
689C23H(5,𝔽2)×C5912yes—
690C23H(5,𝔽2)×C5912yes—
691C23H(5,𝔽2)×C5911yescharacteristic
692C232−1+4×C5911yescharacteristic
693D4—416no—
694D4—432no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4#127×C5914yes—
748C22—44no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—81no—
761C22—82no—
762C22—81no—
763C22—82no—
764C22—82no—
765C22—81no—
766C22—81no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C59×#52511yescharacteristic
775C22C59×#52511yescharacteristic
776C22C2×#127×C5911yescharacteristic
777C22C59×#53411yescharacteristic
778C22C59×#53511yescharacteristic
779C22C59×#53511yescharacteristic
780C22C59×#53512yes—
781C22C59×#53512yes—
782C22C59×#53711yescharacteristic
783C22C59×#53812yes—
784C22C59×#53812yes—
785C22C59×#53912yes—
786C22C59×#54012yes—
787C22C59×#54612yes—
788C22C59×#54612yes—
789C22C59×#54611yescharacteristic
790C22C59×#54611yescharacteristic
791C22C59×#54811yescharacteristic
792C22C59×#54811yescharacteristic
793C22C59×#55112yes—
794C22C59×#55312yes—
795C22C59×#56012yes—
796C22C59×#56212yes—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—44no—
802C4—44no—
803C4—81no—
804C4—81no—
805C4—82no—
806C2—84no—
807C2—82no—
808C2C59×#253911yescharacteristic
809C2C59×#254011yescharacteristic
810C2C59×#259811yescharacteristic
811C2C59×#263511yescharacteristic
812C2C59×#263611yescharacteristic
813C2C59×#265711yescharacteristic
814C2C59×#268512yes—
815C2C59×#269612yes—
816C2C59×#270312yes—
817C2C59×#271112yes—
818C2C59×#281311yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC2×C59×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#400C2semidirect
2. C2×C59×#399C2semidirect
3. C2×C59×#394C2semidirect
5. C2×C59×#390C2semidirect
6. C2×C59×#388C2semidirect
7. C59×#1439C2semidirect
8. C59×#1439C2semidirect
9. C59×#1438C2semidirect
10. C59×#1438C2semidirect
11. C59×#1434C2semidirect
100. C2×C42×C59D4semidirect
108. #95×C59D4semidirect
338. #16809C59direct (N × H)
397. C2×#400C2×C59semidirect
398. C2×#399C2×C59semidirect
399. C2×#394C2×C59semidirect
401. C2×#390C2×C59semidirect
402. C2×#388C2×C59semidirect
403. #1439C2×C59semidirect
404. #1439C2×C59semidirect
405. #1438C2×C59semidirect
406. #1438C2×C59semidirect
407. #1434C2×C59semidirect
450. C59#16809direct (N × H)
510. C2×C42D4×C59semidirect
518. #95D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4002
C2×C59×#3992
C2×C59×#3942
C2×C59×#3922
C2×C59×#3902
C2×C59×#3882
C59×#14392
C59×#14382
C59×#14342
#1680959