Finite Group Databasebeta

← C59×#25587 #28437696

Subgroups — C59×#25587 #28437696

Order 15104.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#2561C211yesmaximal, characteristic, complemented
3C59×#2539C211yesmaximal, characteristic, complemented
4C59×#2534C211yesmaximal, characteristic, complemented
5C59×#2022C212yesmaximal, complemented
6C59×#2021C212yesmaximal, complemented
7C59×#1996C211yesmaximal, characteristic, complemented
8C59×#1964C211yesmaximal, characteristic, complemented
9C59×#1890C212yesmaximal, complemented
10C59×#1889C212yesmaximal, complemented
11C4×#99×C59C211yesmaximal, characteristic, complemented
12C59×#553—22no—
13C59×#553—21no—
14C59×#552—21no—
15C59×#551—22no—
16C59×#548—21no—
17C59×#546—21no—
18C59×#539—21no—
19C59×#538—21no—
20C59×#534C2212yes—
21C59×#529—21no—
22C59×#525—21no—
23C2×#123×C59C2212yes—
24C2×#123×C59C2211yescharacteristic
25C2×C22⋊Q8×C59C2211yescharacteristic
26C2×#121×C59C2211yescharacteristic
27C2×#120×C59C2212yes—
28C2×#120×C59C2211yescharacteristic
29C59×#518C2212yes—
30C2×C4×D4×C59C2211yescharacteristic
31C22×C22⋊C4×C59C2211yescharacteristic
32C2×#99×C59C2212yes—
33C2×#99×C59C2212yes—
34C2×#99×C59C2212yes—
35C59×#399—21no—
36C59×#397—21no—
37C59×#396—21no—
38C59×#394—21no—
39C59×#393—21no—
40C59×#392—21no—
41C59×#390—22no—
42C59×#388—22no—
43C59×#388—21no—
44C59×#386—21no—
45C59×#381C2212yes—
46C59×#381C2211yescharacteristic
47C59×#380C2211yescharacteristic
48C59×#379C2212yes—
49C59×#379C2211yescharacteristic
50C4×C22⋊C4×C59C2211yescharacteristic
51C4×C22⋊C4×C59C2211yescharacteristic
52C59×#342C2212yes—
53C59×#342C2212yes—
54C59×#342C2212yes—
55C25×C59C2311yescharacteristic
56C2×#41×C59—21no—
57C22×Q8×C59D411yescharacteristic, complemented
58C22×D4×C59—21no—
59C22×D4×C59—22no—
60C22×D4×C59D411yescharacteristic, complemented
61C22×D4×C59C2311yescharacteristic
62C22×D4×C59C2312yes—
63C23×C4×C59D411yescharacteristic, complemented
64C23×C4×C59C2311yescharacteristic
65C23×C4×C59C2311yescharacteristic
66#126×C59—22no—
67#126×C59—22no—
68#126×C59—22no—
69#125×C59—21no—
70#125×C59—22no—
71#124×C59—21no—
72#124×C59—22no—
73#123×C59—22no—
74#123×C59—22no—
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78#123×C59—24no—
79#123×C59—42no—
80#123×C59—42no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—22no—
83C22⋊Q8×C59—21no—
84C22⋊Q8×C59—21no—
85C22⋊Q8×C59—21no—
86C22⋊Q8×C59—21no—
87#121×C59—21no—
88#121×C59—22no—
89#121×C59—21no—
90#121×C59—21no—
91#121×C59—21no—
92#121×C59—21no—
93#121×C59—22no—
94#121×C59—22no—
95#120×C59—22no—
96#120×C59—22no—
97#120×C59—24no—
98#120×C59—42no—
99#120×C59—42no—
100C4×Q8×C59—21no—
101C4×D4×C59—22no—
102C4×D4×C59—21no—
103C4×D4×C59—21no—
104C4×D4×C59—21no—
105C4×D4×C59—21no—
106C4×D4×C59—21no—
107C4×D4×C59—22no—
108C4×D4×C59—22no—
109C4×D4×C59—22no—
110C4×D4×C59—22no—
111#117×C59—21no—
112#117×C59—22no—
113#117×C59—22no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—22no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59D412yescomplemented
118C2×C4⋊C4×C59D411yescharacteristic, complemented
119C2×C4⋊C4×C59D411yescharacteristic, complemented
120C2×C4⋊C4×C59D411yescharacteristic, complemented
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59D412yescomplemented
137C2×C22⋊C4×C59D411yescharacteristic, complemented
138C2×C22⋊C4×C59C2311yescharacteristic
139C2×C22⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59C2312yes—
141C2×C22⋊C4×C59C2311yescharacteristic
142C2×C22⋊C4×C59C2312yes—
143C2×C22⋊C4×C59C2312yes—
144C2×C42×C59—21no—
145C2×C42×C59—21no—
146C2×C42×C59D411yescharacteristic, complemented
147#99×C59—24no—
148#99×C59—42no—
149#99×C59—42no—
150#95×C59—21no—
151#95×C59—21no—
152#95×C59—21no—
153#95×C59—21no—
154#95×C59—22no—
155#95×C59—21no—
156#95×C59—22no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—22no—
161C24×C59—22no—
162C24×C59—42no—
163C24×C59—81no—
164C24×C59C2×D412yes—
165C24×C59C2×D411yescharacteristic
166C24×C59C2411yescharacteristic
167#41×C59—82no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—81no—
171C2×D4×C59—21no—
172C2×D4×C59—22no—
173C2×D4×C59—21no—
174C2×D4×C59—22no—
175C2×D4×C59—22no—
176C2×D4×C59—22no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—22no—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—22no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—44no—
186C2×D4×C59—42no—
187C2×D4×C59—44no—
188C2×D4×C59—42no—
189C2×D4×C59—81no—
190C2×D4×C59—82no—
191C2×D4×C59—81no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—81no—
206C22×C4×C59—81no—
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C4⋊C4×C59—22no—
220C4⋊C4×C59—22no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—22no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—22no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—22no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—44no—
232C4⋊C4×C59—42no—
233C4⋊C4×C59—81no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—22no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—22no—
240C22⋊C4×C59—21no—
241C22⋊C4×C59—22no—
242C22⋊C4×C59—21no—
243C22⋊C4×C59—22no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—22no—
246C22⋊C4×C59—21no—
247C22⋊C4×C59—21no—
248C22⋊C4×C59—22no—
249C22⋊C4×C59—22no—
250C22⋊C4×C59—22no—
251C22⋊C4×C59—22no—
252C22⋊C4×C59—22no—
253C22⋊C4×C59—44no—
254C22⋊C4×C59—44no—
255C22⋊C4×C59—42no—
256C22⋊C4×C59—44no—
257C22⋊C4×C59—42no—
258C22⋊C4×C59—42no—
259C22⋊C4×C59—41no—
260C22⋊C4×C59—41no—
261C22⋊C4×C59—41no—
262C22⋊C4×C59—41no—
263C22⋊C4×C59—81no—
264C22⋊C4×C59—82no—
265C22⋊C4×C59#4114yescomplemented
266C42×C59—22no—
267C42×C59—22no—
268C42×C59—21no—
269C42×C59—21no—
270C42×C59—81no—
271C42×C59—81no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59—21no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—41no—
282C23×C59—41no—
283C23×C59—41no—
284C23×C59—41no—
285C23×C59—42no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—42no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59—84no—
300C23×C59—84no—
301C23×C59C22×D411yescharacteristic
302C23×C59C22×D411yescharacteristic
303C23×C59C22×D411yescharacteristic
304C23×C59C2×#4112yes—
305C23×C59H(5,𝔽2)12yes—
306Q8×C59—42no—
307Q8×C59—81no—
308D4×C59—42no—
309D4×C59—42no—
310D4×C59—42no—
311D4×C59—42no—
312D4×C59—42no—
313D4×C59—42no—
314D4×C59—42no—
315D4×C59—81no—
316D4×C59—82no—
317D4×C59—82no—
318D4×C59—88no—
319D4×C59—84no—
320C2×C4×C59—21no—
321C2×C4×C59—22no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—24no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—42no—
338C2×C4×C59—42no—
339C2×C4×C59—42no—
340C2×C4×C59—41no—
341C2×C4×C59—42no—
342C2×C4×C59—41no—
343C2×C4×C59—42no—
344C2×C4×C59—42no—
345C2×C4×C59—42no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—42no—
358C2×C4×C59—81no—
359C2×C4×C59—82no—
360C2×C4×C59—82no—
361C2×C4×C59#12011yescharacteristic
362C2×C4×C59#12011yescharacteristic
363C2×C4×C59#12011yescharacteristic
364C2×C4×C59#12011yescharacteristic
365#25587C5911yesmaximal, characteristic, direct product factor, Sylow
366C22×C59—21no—
367C22×C59—21no—
368C22×C59—21no—
369C22×C59—21no—
370C22×C59—21no—
371C22×C59—21no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—44no—
376C22×C59—42no—
377C22×C59—44no—
378C22×C59—42no—
379C22×C59—41no—
380C22×C59—42no—
381C22×C59—42no—
382C22×C59—41no—
383C22×C59—42no—
384C22×C59—41no—
385C22×C59—42no—
386C22×C59—82no—
387C22×C59—82no—
388C22×C59—81no—
389C22×C59—82no—
390C22×C59—81no—
391C22×C59—82no—
392C22×C59—81no—
393C22×C59—81no—
394C22×C59—81no—
395C22×C59C2×#12011yescharacteristic
396C22×C59#53211yescharacteristic
397C22×C59#53511yescharacteristic
398C22×C59#54612yes—
399C22×C59#55012yes—
400C4×C59—21no—
401C4×C59—21no—
402C4×C59—21no—
403C4×C59—21no—
404C4×C59—44no—
405C4×C59—41no—
406C4×C59—42no—
407C4×C59—41no—
408C4×C59—42no—
409C4×C59—41no—
410C4×C59—42no—
411C4×C59—81no—
412C4×C59—82no—
413C4×C59—81no—
414C4×C59—81no—
415#3505C2×C5911yescharacteristic, complemented
416#2561C2×C5911yescharacteristic, complemented
417#2539C2×C5911yescharacteristic, complemented
418#2534C2×C5911yescharacteristic, complemented
419#2022C2×C5912yescomplemented
420#2021C2×C5912yescomplemented
421#1996C2×C5911yescharacteristic, complemented
422#1964C2×C5911yescharacteristic, complemented
423#1890C2×C5912yescomplemented
424#1889C2×C5912yescomplemented
425C4×#99C2×C5911yescharacteristic, complemented
426C2×C59—22no—
427C2×C59—21no—
428C2×C59—22no—
429C2×C59—21no—
430C2×C59—82no—
431C2×C59—81no—
432C2×C59—82no—
433C2×C59#243111yescharacteristic
434C2×C59#302511yescharacteristic
435C2×C59#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C5912yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C5912yes—
448C2×#123C22×C5911yescharacteristic
449C2×C22⋊Q8C22×C5911yescharacteristic
450C2×#121C22×C5911yescharacteristic
451C2×#120C22×C5912yes—
452C2×#120C22×C5911yescharacteristic
453#518C22×C5912yes—
454C2×C4×D4C22×C5911yescharacteristic
455C22×C22⋊C4C22×C5911yescharacteristic
456C2×#99C22×C5912yes—
457C2×#99C22×C5912yes—
458C2×#99C22×C5912yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C5912yes—
470#381C22×C5911yescharacteristic
471#380C22×C5911yescharacteristic
472#379C22×C5912yes—
473#379C22×C5911yescharacteristic
474C4×C22⋊C4C22×C5911yescharacteristic
475C4×C22⋊C4C22×C5911yescharacteristic
476#342C22×C5912yes—
477#342C22×C5912yes—
478#342C22×C5912yes—
479C59#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C5911yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C5911yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C5911yescharacteristic, complemented
486C22×D4C23×C5911yescharacteristic
487C22×D4C23×C5912yes—
488C23×C4D4×C5911yescharacteristic, complemented
489C23×C4C23×C5911yescharacteristic
490C23×C4C23×C5911yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C5911yescharacteristic, complemented
543C2×C4⋊C4D4×C5911yescharacteristic, complemented
544C2×C4⋊C4D4×C5912yescomplemented
545C2×C4⋊C4D4×C5911yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C5911yescharacteristic, complemented
562C2×C22⋊C4D4×C5912yescomplemented
563C2×C22⋊C4C23×C5911yescharacteristic
564C2×C22⋊C4C23×C5911yescharacteristic
565C2×C22⋊C4C23×C5912yes—
566C2×C22⋊C4C23×C5911yescharacteristic
567C2×C22⋊C4C23×C5912yes—
568C2×C22⋊C4C23×C5912yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C5911yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C5912yes—
590C24C2×D4×C5911yescharacteristic
591C24C24×C5911yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C5911yescharacteristic
633C22×C4C2×D4×C5912yes—
634C22×C4C2×D4×C5911yescharacteristic
635C22×C4C2×D4×C5912yes—
636C22×C4C2×D4×C5911yescharacteristic
637C22×C4C2×D4×C5912yes—
638C22×C4C2×D4×C5911yescharacteristic
639C22×C4C2×D4×C5911yescharacteristic
640C22×C4C2×D4×C5911yescharacteristic
641C22×C4C2×D4×C5911yescharacteristic
642C22×C4C2×D4×C5911yescharacteristic
643C22×C4C2×D4×C5911yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C5914yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C5911yescharacteristic
727C23C22×D4×C5911yescharacteristic
728C23C22×D4×C5911yescharacteristic
729C23C2×#41×C5912yes—
730C23H(5,𝔽2)×C5912yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C5911yescharacteristic
787C2×C4#120×C5911yescharacteristic
788C2×C4#120×C5911yescharacteristic
789C2×C4#120×C5911yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C5911yescharacteristic
820C22C59×#53211yescharacteristic
821C22C59×#53511yescharacteristic
822C22C59×#54612yes—
823C22C59×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C59×#243111yescharacteristic
847C2C59×#302511yescharacteristic
848C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3505C2semidirect
2. C59×#2561C2semidirect
3. C59×#2539C2semidirect
4. C59×#2534C2semidirect
5. C59×#2022C2semidirect
6. C59×#2021C2semidirect
7. C59×#1996C2semidirect
8. C59×#1964C2semidirect
9. C59×#1890C2semidirect
10. C59×#1889C2semidirect
11. C4×#99×C59C2semidirect
57. C22×Q8×C59D4semidirect
60. C22×D4×C59D4semidirect
63. C23×C4×C59D4semidirect
117. C2×C4⋊C4×C59D4semidirect
118. C2×C4⋊C4×C59D4semidirect
119. C2×C4⋊C4×C59D4semidirect
120. C2×C4⋊C4×C59D4semidirect
136. C2×C22⋊C4×C59D4semidirect
137. C2×C22⋊C4×C59D4semidirect
146. C2×C42×C59D4semidirect
265. C22⋊C4×C59#41semidirect
365. #25587C59direct (N × H)
415. #3505C2×C59semidirect
416. #2561C2×C59semidirect
417. #2539C2×C59semidirect
418. #2534C2×C59semidirect
419. #2022C2×C59semidirect
420. #2021C2×C59semidirect
421. #1996C2×C59semidirect
422. #1964C2×C59semidirect
423. #1890C2×C59semidirect
424. #1889C2×C59semidirect
425. C4×#99C2×C59semidirect
479. C59#25587direct (N × H)
482. C22×Q8D4×C59semidirect
485. C22×D4D4×C59semidirect
488. C23×C4D4×C59semidirect
542. C2×C4⋊C4D4×C59semidirect
543. C2×C4⋊C4D4×C59semidirect
544. C2×C4⋊C4D4×C59semidirect
545. C2×C4⋊C4D4×C59semidirect
561. C2×C22⋊C4D4×C59semidirect
562. C2×C22⋊C4D4×C59semidirect
571. C2×C42D4×C59semidirect
690. C22⋊C4#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35052
C59×#25612
C59×#25392
C59×#25342
C59×#20222
C59×#20212
C59×#19962
C59×#19642
C59×#18902
C59×#18892
C4×#99×C592
#2558759