Finite Group Databasebeta

← C59×#16516 #28428625

Subgroups — C59×#16516 #28428625

Order 15104.

2014 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#394C212yesmaximal, complemented
2C2×C59×#392C211yesmaximal, characteristic
3C2×C59×#390C211yesmaximal, characteristic, complemented
4C2×C59×#388C211yesmaximal, characteristic, complemented
5C2×C59×#382C211yesmaximal, characteristic, complemented
6C59×#1442C211yesmaximal, characteristic, complemented
7C59×#1439C212yesmaximal, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1439C212yesmaximal, complemented
10C59×#1438C211yesmaximal, characteristic, complemented
11C59×#1438C212yesmaximal, complemented
12C23×D4×C59C2211yescharacteristic
13C23×D4×C59C2212yes—
14C22×C4⋊C4×C59C2212yes—
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2212yes—
20C22×C22⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2212yes—
25C22×C22⋊C4×C59C2212yes—
26C22×C42×C59C2211yescharacteristic
27C59×#394—28no—
28C59×#392—24no—
29C59×#390—24no—
30C59×#388—24no—
31C59×#382—24no—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2212yes—
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2211yescharacteristic
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C25×C59C2311yescharacteristic
41C25×C59C2312yes—
42C22×D4×C59—24no—
43C22×D4×C59—24no—
44C22×D4×C59—24no—
45C22×D4×C59—22no—
46C22×D4×C59—24no—
47C22×D4×C59—22no—
48C22×D4×C59—22no—
49C22×D4×C59—42no—
50C22×D4×C59—42no—
51C22×D4×C59—42no—
52C22×D4×C59—42no—
53C22×D4×C59—42no—
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2312yes—
56C23×C4×C59C2312yes—
57C23×C4×C59C2311yescharacteristic
58C23×C4×C59C2312yes—
59C23×C4×C59C2311yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C23×C4×C59C2311yescharacteristic
62C23×C4×C59C2311yescharacteristic
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—22no—
65C2×C4⋊C4×C59—22no—
66C2×C4⋊C4×C59—24no—
67C2×C4⋊C4×C59—42no—
68C2×C4⋊C4×C59—42no—
69C2×C4⋊C4×C59—42no—
70C2×C22⋊C4×C59—22no—
71C2×C22⋊C4×C59—22no—
72C2×C22⋊C4×C59—24no—
73C2×C22⋊C4×C59—24no—
74C2×C22⋊C4×C59—22no—
75C2×C22⋊C4×C59—22no—
76C2×C22⋊C4×C59—24no—
77C2×C22⋊C4×C59—24no—
78C2×C22⋊C4×C59—24no—
79C2×C22⋊C4×C59—22no—
80C2×C22⋊C4×C59—24no—
81C2×C22⋊C4×C59—24no—
82C2×C22⋊C4×C59—22no—
83C2×C22⋊C4×C59—24no—
84C2×C22⋊C4×C59—42no—
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×C59—42no—
92C2×C22⋊C4×C59—42no—
93C2×C22⋊C4×C59—42no—
94C2×C22⋊C4×C59—42no—
95C2×C22⋊C4×C59D414yescomplemented
96C2×C42×C59—22no—
97C2×C42×C59—22no—
98C2×C42×C59D414yescomplemented
99#95×C59—24no—
100#95×C59—22no—
101#95×C59—22no—
102#95×C59—22no—
103#95×C59—24no—
104#95×C59—42no—
105#95×C59—42no—
106#95×C59D414yes—
107C24×C59—21no—
108C24×C59—22no—
109C24×C59—22no—
110C24×C59—21no—
111C24×C59—22no—
112C24×C59—21no—
113C24×C59—21no—
114C24×C59—22no—
115C24×C59—22no—
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—21no—
128C24×C59—22no—
129C24×C59—22no—
130C24×C59—21no—
131C24×C59C2×D412yes—
132C24×C59#4114yes—
133C24×C59C2411yescharacteristic
134C2×D4×C59—28no—
135C2×D4×C59—48no—
136C2×D4×C59—48no—
137C2×D4×C59—48no—
138C2×D4×C59—48no—
139C2×D4×C59—44no—
140C2×D4×C59—48no—
141C2×D4×C59—48no—
142C2×D4×C59—48no—
143C2×D4×C59—48no—
144C2×D4×C59—48no—
145C2×D4×C59—44no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—22no—
149C22×C4×C59—21no—
150C22×C4×C59—22no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—22no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
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—21no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—21no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—21no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59—21no—
190C22×C4×C59C2×D412yes—
191C22×C4×C59C2×D414yes—
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×D412yes—
197C22×C4×C59#4112yes—
198C22×C4×C59#4112yes—
199C4⋊C4×C59—48no—
200C4⋊C4×C59—44no—
201C4⋊C4×C59—44no—
202C22⋊C4×C59—28no—
203C22⋊C4×C59—48no—
204C22⋊C4×C59—48no—
205C22⋊C4×C59—44no—
206C22⋊C4×C59—48no—
207C22⋊C4×C59—48no—
208C22⋊C4×C59—48no—
209C22⋊C4×C59—44no—
210C22⋊C4×C59—48no—
211C42×C59—28no—
212C23×C59—22no—
213C23×C59—24no—
214C23×C59—24no—
215C23×C59—24no—
216C23×C59—24no—
217C23×C59—22no—
218C23×C59—24no—
219C23×C59—24no—
220C23×C59—24no—
221C23×C59—22no—
222C23×C59—24no—
223C23×C59—24no—
224C23×C59—41no—
225C23×C59—42no—
226C23×C59—42no—
227C23×C59—41no—
228C23×C59—42no—
229C23×C59—42no—
230C23×C59—41no—
231C23×C59—42no—
232C23×C59—42no—
233C23×C59—42no—
234C23×C59—42no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59—42no—
238C23×C59—42no—
239C23×C59—42no—
240C23×C59—41no—
241C23×C59—42no—
242C23×C59—42no—
243C23×C59—42no—
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—41no—
257C23×C59—42no—
258C23×C59—42no—
259C23×C59—42no—
260C23×C59—41no—
261C23×C59—42no—
262C23×C59—42no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59C22×D411yescharacteristic
271C23×C59C22×D411yescharacteristic
272C23×C59C22×D411yescharacteristic
273C23×C59C2×#4111yescharacteristic
274C23×C59C2×#4111yescharacteristic
275C23×C59C2×#4112yes—
276C23×C59H(5,𝔽2)12yes—
277C23×C59H(5,𝔽2)12yes—
278C23×C59H(5,𝔽2)12yes—
279C23×C59H(5,𝔽2)11yescharacteristic
280C23×C592−1+411yescharacteristic
281D4×C59—416no—
282D4×C59—432no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—24no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—24no—
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—24no—
299C2×C4×C59—24no—
300C2×C4×C59—24no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—41no—
311C2×C4×C59—42no—
312C2×C4×C59—41no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59—41no—
324C2×C4×C59—42no—
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—42no—
332C2×C4×C59—42no—
333C2×C4×C59—42no—
334C2×C4×C59#12114yes—
335C2×C4×C59#12114yes—
336#16516C5911yesmaximal, characteristic, direct product factor, Sylow
337C22×C59—42no—
338C22×C59—44no—
339C22×C59—44no—
340C22×C59—44no—
341C22×C59—44no—
342C22×C59—42no—
343C22×C59—44no—
344C22×C59—44no—
345C22×C59—44no—
346C22×C59—44no—
347C22×C59—42no—
348C22×C59—44no—
349C22×C59—81no—
350C22×C59—82no—
351C22×C59—81no—
352C22×C59—82no—
353C22×C59—82no—
354C22×C59—81no—
355C22×C59—81no—
356C22×C59—82no—
357C22×C59—82no—
358C22×C59—82no—
359C22×C59—82no—
360C22×C59—82no—
361C22×C59—82no—
362C22×C59—82no—
363C22×C59C2×#12111yescharacteristic
364C22×C59C2×#12111yescharacteristic
365C22×C59#52511yescharacteristic
366C22×C59#53511yescharacteristic
367C22×C59#53511yescharacteristic
368C22×C59#53511yescharacteristic
369C22×C59#53512yes—
370C22×C59#53512yes—
371C22×C59#53711yescharacteristic
372C22×C59#53812yes—
373C22×C59#53912yes—
374C22×C59#54012yes—
375C22×C59#54012yes—
376C22×C59D4211yescharacteristic
377C22×C59#54612yes—
378C22×C59#54612yes—
379C22×C59#54711yescharacteristic
380C22×C59#54811yescharacteristic
381C22×C59#55112yes—
382C22×C59#55311yescharacteristic
383C22×C59#55312yes—
384C22×C59H(3,𝔽4)12yes—
385C22×C59#56212yes—
386C4×C59—24no—
387C4×C59—24no—
388C4×C59—42no—
389C4×C59—44no—
390C4×C59—42no—
391C4×C59—81no—
392C4×C59—81no—
393C4×C59—82no—
394C4×C59—82no—
395C2×#394C2×C5912yescomplemented
396C2×#392C2×C5911yescharacteristic
397C2×#390C2×C5911yescharacteristic, complemented
398C2×#388C2×C5911yescharacteristic, complemented
399C2×#382C2×C5911yescharacteristic, complemented
400#1442C2×C5911yescharacteristic, complemented
401#1439C2×C5911yescharacteristic, complemented
402#1439C2×C5912yescomplemented
403#1439C2×C5912yescomplemented
404#1438C2×C5911yescharacteristic, complemented
405#1438C2×C5912yescomplemented
406C2×C59—82no—
407C2×C59—84no—
408C2×C59#241111yescharacteristic
409C2×C59#241611yescharacteristic
410C2×C59#253511yescharacteristic
411C2×C59#261911yescharacteristic
412C2×C59#261911yescharacteristic
413C2×C59#263611yescharacteristic
414C2×C59#267012yes—
415C2×C59#270612yes—
416C2×C59#271112yes—
417C2×C59#275312yes—
418C2×C59#281911yescharacteristic
419C23×D4C22×C5911yescharacteristic
420C23×D4C22×C5912yes—
421C22×C4⋊C4C22×C5912yes—
422C22×C4⋊C4C22×C5911yescharacteristic
423C22×C4⋊C4C22×C5911yescharacteristic
424C22×C22⋊C4C22×C5911yescharacteristic
425C22×C22⋊C4C22×C5912yes—
426C22×C22⋊C4C22×C5912yes—
427C22×C22⋊C4C22×C5911yescharacteristic
428C22×C22⋊C4C22×C5912yes—
429C22×C22⋊C4C22×C5912yes—
430C22×C22⋊C4C22×C5911yescharacteristic
431C22×C22⋊C4C22×C5912yes—
432C22×C22⋊C4C22×C5912yes—
433C22×C42C22×C5911yescharacteristic
434#394—28no—
435#392—24no—
436#390—24no—
437#388—24no—
438#382—24no—
439C2×#95C22×C5912yes—
440C2×#95C22×C5911yescharacteristic
441C2×#95C22×C5912yes—
442C2×#95C22×C5911yescharacteristic
443C2×#95C22×C5911yescharacteristic
444C2×#95C22×C5912yes—
445C2×#95C22×C5912yes—
446C2×#95C22×C5911yescharacteristic
447C59#1651611yescharacteristic, direct product factor, Sylow
448C25C23×C5911yescharacteristic
449C25C23×C5912yes—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—22no—
454C22×D4—24no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—42no—
462C23×C4C23×C5912yes—
463C23×C4C23×C5912yes—
464C23×C4C23×C5911yescharacteristic
465C23×C4C23×C5911yescharacteristic
466C23×C4C23×C5911yescharacteristic
467C23×C4C23×C5911yescharacteristic
468C23×C4C23×C5912yes—
469C23×C4C23×C5911yescharacteristic
470C23×C4C23×C5911yescharacteristic
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4D4×C5914yescomplemented
504C2×C42—22no—
505C2×C42—22no—
506C2×C42D4×C5914yescomplemented
507#95—24no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—24no—
512#95—42no—
513#95—42no—
514#95D4×C5914yes—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—22no—
538C24—21no—
539C24C2×D4×C5912yes—
540C24#41×C5914yes—
541C24C24×C5911yescharacteristic
542C2×D4—28no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—44no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—44no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4C2×D4×C5912yes—
599C22×C4C2×D4×C5914yes—
600C22×C4C2×D4×C5912yes—
601C22×C4C2×D4×C5912yes—
602C22×C4C2×D4×C5912yes—
603C22×C4C2×D4×C5912yes—
604C22×C4C2×D4×C5912yes—
605C22×C4#41×C5912yes—
606C22×C4#41×C5912yes—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—44no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C42—28no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C22×D4×C5911yescharacteristic
679C23C22×D4×C5911yescharacteristic
680C23C22×D4×C5911yescharacteristic
681C23C2×#41×C5911yescharacteristic
682C23C2×#41×C5911yescharacteristic
683C23C2×#41×C5912yes—
684C23H(5,𝔽2)×C5912yes—
685C23H(5,𝔽2)×C5912yes—
686C23H(5,𝔽2)×C5912yes—
687C23H(5,𝔽2)×C5911yescharacteristic
688C232−1+4×C5911yescharacteristic
689D4—416no—
690D4—432no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4#121×C5914yes—
743C2×C4#121×C5914yes—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—82no—
757C22—82no—
758C22—81no—
759C22—82no—
760C22—81no—
761C22—82no—
762C22—82no—
763C22—81no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22C2×#121×C5911yescharacteristic
771C22C2×#121×C5911yescharacteristic
772C22C59×#52511yescharacteristic
773C22C59×#53511yescharacteristic
774C22C59×#53511yescharacteristic
775C22C59×#53511yescharacteristic
776C22C59×#53512yes—
777C22C59×#53512yes—
778C22C59×#53711yescharacteristic
779C22C59×#53812yes—
780C22C59×#53912yes—
781C22C59×#54012yes—
782C22C59×#54012yes—
783C22D42×C5911yescharacteristic
784C22C59×#54612yes—
785C22C59×#54612yes—
786C22C59×#54711yescharacteristic
787C22C59×#54811yescharacteristic
788C22C59×#55112yes—
789C22C59×#55311yescharacteristic
790C22C59×#55312yes—
791C22C59×H(3,𝔽4)12yes—
792C22C59×#56212yes—
793C4—24no—
794C4—24no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—81no—
799C4—81no—
800C4—82no—
801C4—82no—
802C2—84no—
803C2—82no—
804C2C59×#241111yescharacteristic
805C2C59×#241611yescharacteristic
806C2C59×#253511yescharacteristic
807C2C59×#261911yescharacteristic
808C2C59×#261911yescharacteristic
809C2C59×#263611yescharacteristic
810C2C59×#267012yes—
811C2C59×#270612yes—
812C2C59×#271112yes—
813C2C59×#275312yes—
814C2C59×#281911yescharacteristic
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×#394C2semidirect
3. C2×C59×#390C2semidirect
4. C2×C59×#388C2semidirect
5. C2×C59×#382C2semidirect
6. C59×#1442C2semidirect
7. C59×#1439C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
10. C59×#1438C2semidirect
11. C59×#1438C2semidirect
95. C2×C22⋊C4×C59D4semidirect
98. C2×C42×C59D4semidirect
336. #16516C59direct (N × H)
395. C2×#394C2×C59semidirect
397. C2×#390C2×C59semidirect
398. C2×#388C2×C59semidirect
399. C2×#382C2×C59semidirect
400. #1442C2×C59semidirect
401. #1439C2×C59semidirect
402. #1439C2×C59semidirect
403. #1439C2×C59semidirect
404. #1438C2×C59semidirect
405. #1438C2×C59semidirect
447. C59#16516direct (N × H)
503. C2×C22⋊C4D4×C59semidirect
506. C2×C42D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3942
C2×C59×#3922
C2×C59×#3902
C2×C59×#3882
C2×C59×#3822
C59×#14422
C59×#14392
C59×#14382
#1651659