Finite Group Databasebeta

← C59×#23850 #28435959

Subgroups — C59×#23850 #28435959

Order 15104.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C59C211yesmaximal, characteristic, complemented
2C2×C59×#546C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#450C211yesmaximal, characteristic, complemented
5C2×C59×#447C211yesmaximal, characteristic, complemented
6C59×#2407C211yesmaximal, characteristic, complemented
7C59×#2015C211yesmaximal, characteristic, complemented
8C59×#2012C211yesmaximal, characteristic, complemented
9C59×#2001C211yesmaximal, characteristic, complemented
10C59×#2000C211yesmaximal, characteristic, complemented
11C59×#1893C211yesmaximal, characteristic, complemented
12C59×#1879C211yesmaximal, characteristic, complemented
13C59×#1877C211yesmaximal, characteristic, complemented
14C59×#1869C211yesmaximal, characteristic, complemented
15C59×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic, complemented
18C23×D4×C59C2211yescharacteristic
19C2×#135×C59—24no—
20C2×#135×C59—24no—
21C2×#135×C59—24no—
22C22×Q16×C59C2211yescharacteristic, complemented
23C22×SD16×C59C2211yescharacteristic
24C22×SD16×C59C2211yescharacteristic
25C22×SD16×C59C2211yescharacteristic, complemented
26C22×D8×C59C2211yescharacteristic
27C22×D8×C59C2211yescharacteristic
28C23×C8×C59C2211yescharacteristic, complemented
29C59×#546—24no—
30C59×#546—24no—
31C2×#124×C59C2211yescharacteristic
32C2×#123×C59—21no—
33C2×C22⋊Q8×C59C2211yescharacteristic
34C2×C22⋊Q8×C59C2211yescharacteristic
35C2×#121×C59—21no—
36C2×#121×C59C2211yescharacteristic
37C2×#121×C59C2211yescharacteristic
38C2×#120×C59—21no—
39C2×C4×D4×C59C2211yescharacteristic
40C2×C4×D4×C59C2211yescharacteristic
41C22×C22⋊C4×C59—21no—
42C59×#450—24no—
43C59×#449—24no—
44C59×#447—24no—
45C2×#103×C59C2211yescharacteristic, complemented
46C2×#103×C59C2211yescharacteristic, complemented
47C2×#103×C59C2211yescharacteristic, complemented
48C2×#102×C59C2211yescharacteristic
49C2×#102×C59C2211yescharacteristic
50C2×#102×C59C2211yescharacteristic
51C2×#102×C59C2211yescharacteristic
52C2×#102×C59C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic
55C2×C22⋊C8×C59C2211yescharacteristic, complemented
56C59×#394—21no—
57C59×#392—21no—
58C59×#391C2211yescharacteristic, complemented
59C59×#390C2211yescharacteristic, complemented
60C59×#386—21no—
61C59×#385—21no—
62C59×#380C2211yescharacteristic, complemented
63C59×#340C2211yescharacteristic, complemented
64C59×#340C2211yescharacteristic, complemented
65C59×#336C2211yescharacteristic, complemented
66C59×#336C2211yescharacteristic, complemented
67C25×C59—21no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—22no—
71C2×#41×C59—22no—
72C2×#41×C59—22no—
73C2×#41×C59—22no—
74C2×#41×C59—22no—
75C2×#41×C59—41no—
76C2×#41×C59—41no—
77C2×#41×C59—41no—
78C2×#41×C59—41no—
79C2×#41×C59D414yescomplemented
80C22×Q8×C59C2311yescharacteristic
81C22×Q8×C59C2311yescharacteristic
82C22×D4×C59—21no—
83C22×D4×C59—21no—
84C22×D4×C59—22no—
85C22×D4×C59—22no—
86C22×D4×C59—22no—
87C22×D4×C59—22no—
88C22×D4×C59—21no—
89C22×D4×C59—21no—
90C22×D4×C59—21no—
91C22×D4×C59—41no—
92C22×D4×C59—41no—
93C22×D4×C59D411yescharacteristic
94C22×D4×C59C2311yescharacteristic
95C22×D4×C59C2311yescharacteristic
96C22×D4×C59C2311yescharacteristic
97C23×C4×C59—21no—
98C23×C4×C59—21no—
99C23×C4×C59—21no—
100C23×C4×C59C2311yescharacteristic
101C23×C4×C59C2311yescharacteristic
102#135×C59—232no—
103C2×Q16×C59—22no—
104C2×Q16×C59—22no—
105C2×Q16×C59—22no—
106C2×SD16×C59—22no—
107C2×SD16×C59—22no—
108C2×SD16×C59—22no—
109C2×SD16×C59—22no—
110C2×SD16×C59—22no—
111C2×SD16×C59—22no—
112C2×SD16×C59—22no—
113C2×SD16×C59—41no—
114C2×SD16×C59D414yescomplemented
115C2×D8×C59—22no—
116C2×D8×C59—22no—
117C2×D8×C59—22no—
118C2×D8×C59—22no—
119C2×D8×C59—41no—
120C2×D8×C59D414yescomplemented
121C22×C8×C59—22no—
122C22×C8×C59—22no—
123C22×C8×C59—22no—
124C22×C8×C59C2311yescharacteristic
125C22×C8×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128#124×C59—22no—
129#124×C59—22no—
130#123×C59—28no—
131C22⋊Q8×C59—22no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59—22no—
134C22⋊Q8×C59—41no—
135#121×C59—28no—
136#121×C59—22no—
137#121×C59—22no—
138#121×C59—41no—
139#121×C59D414yescomplemented
140#120×C59—28no—
141C4×D4×C59—22no—
142C4×D4×C59—22no—
143C4×D4×C59—22no—
144C4×D4×C59—22no—
145C2×C4⋊C4×C59—21no—
146C2×C4⋊C4×C59—21no—
147C2×C4⋊C4×C59D411yescharacteristic
148C2×C4⋊C4×C59C2311yescharacteristic
149C2×C4⋊C4×C59C2311yescharacteristic
150C2×C4⋊C4×C59C2311yescharacteristic
151C2×C22⋊C4×C59—28no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59—21no—
156C2×C22⋊C4×C59—21no—
157C2×C22⋊C4×C59—21no—
158C2×C22⋊C4×C59—21no—
159C2×C22⋊C4×C59—21no—
160C2×C22⋊C4×C59—21no—
161C2×C22⋊C4×C59—21no—
162C2×C22⋊C4×C59D411yescharacteristic
163C2×C22⋊C4×C59D411yescharacteristic
164C2×C42×C59C2311yescharacteristic
165#103×C59—22no—
166#103×C59—41no—
167#103×C59—41no—
168#102×C59—22no—
169#102×C59—22no—
170#102×C59—22no—
171#102×C59—22no—
172#102×C59—22no—
173C22⋊C8×C59—22no—
174C22⋊C8×C59—22no—
175C22⋊C8×C59—22no—
176#95×C59—21no—
177#95×C59—21no—
178#95×C59—21no—
179C24×C59—21no—
180C24×C59—24no—
181C24×C59—21no—
182C24×C59—21no—
183C24×C59—42no—
184C24×C59—42no—
185C24×C59—42no—
186C24×C59—42no—
187C24×C59—81no—
188C24×C59—81no—
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191#41×C59—28no—
192#41×C59—28no—
193#41×C59—44no—
194#41×C59—44no—
195#41×C59—44no—
196#41×C59—44no—
197#41×C59—44no—
198#41×C59—44no—
199C2×Q8×C59—21no—
200C2×Q8×C59—21no—
201C2×Q8×C59—21no—
202C2×Q8×C59—21no—
203C2×Q8×C59—21no—
204C2×Q8×C59—21no—
205C2×Q8×C59—21no—
206C2×Q8×C59—21no—
207C2×Q8×C59—21no—
208C2×Q8×C59—21no—
209C2×Q8×C59C2×D412yes—
210C2×Q8×C59C2×D412yes—
211C2×D4×C59—24no—
212C2×D4×C59—22no—
213C2×D4×C59—24no—
214C2×D4×C59—22no—
215C2×D4×C59—24no—
216C2×D4×C59—21no—
217C2×D4×C59—21no—
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—21no—
228C2×D4×C59—21no—
229C2×D4×C59—41no—
230C2×D4×C59—42no—
231C2×D4×C59—42no—
232C2×D4×C59—42no—
233C2×D4×C59—44no—
234C2×D4×C59—44no—
235C2×D4×C59—44no—
236C2×D4×C59—42no—
237C2×D4×C59—42no—
238C2×D4×C59—42no—
239C2×D4×C59—42no—
240C2×D4×C59—44no—
241C2×D4×C59—42no—
242C2×D4×C59—42no—
243C2×D4×C59—81no—
244C2×D4×C59—81no—
245C2×D4×C59—81no—
246C2×D4×C59C2×D412yes—
247C2×D4×C59C2×D412yes—
248C2×D4×C59C2×D412yes—
249C2×D4×C59C2×D412yes—
250C2×D4×C59C2×D412yes—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—24no—
259C22×C4×C59—24no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59—21no—
264C22×C4×C59—21no—
265C22×C4×C59—21no—
266C22×C4×C59—21no—
267C22×C4×C59—21no—
268C22×C4×C59—42no—
269C22×C4×C59—42no—
270C22×C4×C59—42no—
271C22×C4×C59—42no—
272C22×C4×C59—42no—
273C22×C4×C59—81no—
274C22×C4×C59—81no—
275C22×C4×C59C2×D411yescharacteristic
276C22×C4×C59C2×D411yescharacteristic
277C22×C4×C59C2×D411yescharacteristic
278C22×C4×C59C2×D411yescharacteristic
279C22×C4×C59C2×D412yes—
280C22×C4×C59C2×D412yes—
281C22×C4×C59C2411yescharacteristic
282Q16×C59—28no—
283SD16×C59—28no—
284SD16×C59—28no—
285SD16×C59—44no—
286D8×C59—28no—
287D8×C59—44no—
288C2×C8×C59—28no—
289C2×C8×C59—21no—
290C2×C8×C59—21no—
291C2×C8×C59—21no—
292C2×C8×C59—21no—
293C2×C8×C59—21no—
294C2×C8×C59—21no—
295C2×C8×C59—21no—
296C2×C8×C59—21no—
297C2×C8×C59—21no—
298C2×C8×C59—21no—
299C2×C8×C59C2×D412yes—
300C2×C8×C59C2×D412yes—
301C4⋊C4×C59—24no—
302C4⋊C4×C59—22no—
303C4⋊C4×C59—21no—
304C4⋊C4×C59—21no—
305C4⋊C4×C59—21no—
306C4⋊C4×C59—21no—
307C4⋊C4×C59—21no—
308C4⋊C4×C59—42no—
309C4⋊C4×C59C2×D412yes—
310C22⋊C4×C59—24no—
311C22⋊C4×C59—24no—
312C22⋊C4×C59—24no—
313C22⋊C4×C59—24no—
314C22⋊C4×C59—22no—
315C22⋊C4×C59—22no—
316C22⋊C4×C59—24no—
317C22⋊C4×C59—42no—
318C22⋊C4×C59—42no—
319C22⋊C4×C59—42no—
320C22⋊C4×C59—81no—
321C22⋊C4×C59—81no—
322C42×C59—21no—
323C42×C59—21no—
324C23×C59—21no—
325C23×C59—22no—
326C23×C59—21no—
327C23×C59—21no—
328C23×C59—21no—
329C23×C59—21no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—21no—
333C23×C59—21no—
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—21no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—48no—
342C23×C59—48no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—84no—
360C23×C59—84no—
361C23×C59—84no—
362C23×C59—84no—
363C23×C59—84no—
364C23×C59#12012yes—
365C23×C59#13512yescomplemented
366C23×C59C22×D411yescharacteristic
367Q8×C59—22no—
368Q8×C59—22no—
369Q8×C59—22no—
370Q8×C59—22no—
371Q8×C59—41no—
372Q8×C59—41no—
373Q8×C59—41no—
374Q8×C59—41no—
375D4×C59—22no—
376D4×C59—22no—
377D4×C59—22no—
378D4×C59—22no—
379D4×C59—22no—
380D4×C59—22no—
381D4×C59—22no—
382D4×C59—44no—
383D4×C59—48no—
384D4×C59—48no—
385D4×C59—48no—
386D4×C59—41no—
387D4×C59—41no—
388D4×C59—41no—
389D4×C59—41no—
390D4×C59—84no—
391D4×C59—84no—
392D4×C59#12014yes—
393C2×C4×C59—21no—
394C2×C4×C59—21no—
395C2×C4×C59—22no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—21no—
400C2×C4×C59—21no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—21no—
404C2×C4×C59—21no—
405C2×C4×C59—22no—
406C2×C4×C59—21no—
407C2×C4×C59—21no—
408C2×C4×C59—21no—
409C2×C4×C59—21no—
410C2×C4×C59—21no—
411C2×C4×C59—48no—
412C2×C4×C59—48no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—84no—
430C2×C4×C59#12012yes—
431C2×C4×C59C22×D411yescharacteristic
432C2×C4×C59C22×D411yescharacteristic
433C2×C4×C59C22×D411yescharacteristic
434C2×C4×C59C22×D411yescharacteristic
435C2×C4×C59H(5,𝔽2)11yescharacteristic
436C2×C4×C59H(5,𝔽2)11yescharacteristic
437C8×C59—22no—
438C8×C59—22no—
439C8×C59—41no—
440C8×C59—41no—
441#23850C5911yesmaximal, characteristic, direct product factor, Sylow
442C22×C59—22no—
443C22×C59—24no—
444C22×C59—22no—
445C22×C59—22no—
446C22×C59—22no—
447C22×C59—22no—
448C22×C59—22no—
449C22×C59—41no—
450C22×C59—42no—
451C22×C59—41no—
452C22×C59—41no—
453C22×C59—42no—
454C22×C59—42no—
455C22×C59—41no—
456C22×C59—41no—
457C22×C59—41no—
458C22×C59—42no—
459C22×C59—41no—
460C22×C59—42no—
461C22×C59—41no—
462C22×C59—42no—
463C22×C59—42no—
464C22×C59—42no—
465C22×C59—42no—
466C22×C59—42no—
467C22×C59—42no—
468C22×C59—42no—
469C22×C59—816no—
470C22×C59—81no—
471C22×C59—81no—
472C22×C59—81no—
473C22×C59—81no—
474C22×C59—81no—
475C22×C59—81no—
476C22×C59—81no—
477C22×C59—81no—
478C22×C59C2×#12011yescharacteristic
479C22×C59D4211yescharacteristic
480C22×C59D4211yescharacteristic
481C22×C59C2×#13511yescharacteristic
482C22×C59#57511yescharacteristic
483C22×C59#57611yescharacteristic
484C22×C59#57711yescharacteristic
485C4×C59—22no—
486C4×C59—41no—
487C4×C59—42no—
488C4×C59—42no—
489C4×C59—41no—
490C4×C59—41no—
491C4×C59—42no—
492C4×C59—81no—
493C4×C59—81no—
494C4×C59C2×#12011yescharacteristic
495C4×C59#53411yescharacteristic
496C4×C59D4211yescharacteristic
497C4×C59D4211yescharacteristic
498C22×#135C2×C5911yescharacteristic, complemented
499C2×#546C2×C5911yescharacteristic, complemented
500C2×#449C2×C5911yescharacteristic, complemented
501C2×#450C2×C5911yescharacteristic, complemented
502C2×#447C2×C5911yescharacteristic, complemented
503#2407C2×C5911yescharacteristic, complemented
504#2015C2×C5911yescharacteristic, complemented
505#2012C2×C5911yescharacteristic, complemented
506#2001C2×C5911yescharacteristic, complemented
507#2000C2×C5911yescharacteristic, complemented
508#1893C2×C5911yescharacteristic, complemented
509#1879C2×C5911yescharacteristic, complemented
510#1877C2×C5911yescharacteristic, complemented
511#1869C2×C5911yescharacteristic, complemented
512#1788C2×C5911yescharacteristic, complemented
513C2×C59—42no—
514C2×C59—42no—
515C2×C59—44no—
516C2×C59—82no—
517C2×C59—82no—
518C2×C59#240311yescharacteristic
519C2×C59#300211yescharacteristic
520C2×C59#301211yescharacteristic
521C2×C59#326711yescharacteristic
522C2×C59#326811yescharacteristic
523C2×C59#328011yescharacteristic
524C2×C59#328211yescharacteristic
525C22×#41C22×C5911yescharacteristic
526C22×#41C22×C5911yescharacteristic, complemented
527C23×D4C22×C5911yescharacteristic
528C2×#135—24no—
529C2×#135—24no—
530C2×#135—24no—
531C22×Q16C22×C5911yescharacteristic, complemented
532C22×SD16C22×C5911yescharacteristic
533C22×SD16C22×C5911yescharacteristic
534C22×SD16C22×C5911yescharacteristic, complemented
535C22×D8C22×C5911yescharacteristic
536C22×D8C22×C5911yescharacteristic
537C23×C8C22×C5911yescharacteristic, complemented
538#546—24no—
539#546—24no—
540C2×#124C22×C5911yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8C22×C5911yescharacteristic
543C2×C22⋊Q8C22×C5911yescharacteristic
544C2×#121—21no—
545C2×#121C22×C5911yescharacteristic
546C2×#121C22×C5911yescharacteristic
547C2×#120—21no—
548C2×C4×D4C22×C5911yescharacteristic
549C2×C4×D4C22×C5911yescharacteristic
550C22×C22⋊C4—21no—
551#450—24no—
552#449—24no—
553#447—24no—
554C2×#103C22×C5911yescharacteristic, complemented
555C2×#103C22×C5911yescharacteristic, complemented
556C2×#103C22×C5911yescharacteristic, complemented
557C2×#102C22×C5911yescharacteristic
558C2×#102C22×C5911yescharacteristic
559C2×#102C22×C5911yescharacteristic
560C2×#102C22×C5911yescharacteristic
561C2×#102C22×C5911yescharacteristic, complemented
562C2×C22⋊C8C22×C5911yescharacteristic
563C2×C22⋊C8C22×C5911yescharacteristic
564C2×C22⋊C8C22×C5911yescharacteristic, complemented
565#394—21no—
566#392—21no—
567#391C22×C5911yescharacteristic, complemented
568#390C22×C5911yescharacteristic, complemented
569#386—21no—
570#385—21no—
571#380C22×C5911yescharacteristic, complemented
572#340C22×C5911yescharacteristic, complemented
573#340C22×C5911yescharacteristic, complemented
574#336C22×C5911yescharacteristic, complemented
575#336C22×C5911yescharacteristic, complemented
576C59#2385011yescharacteristic, direct product factor, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C5914yescomplemented
590C22×Q8C23×C5911yescharacteristic
591C22×Q8C23×C5911yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C5911yescharacteristic
604C22×D4C23×C5911yescharacteristic
605C22×D4C23×C5911yescharacteristic
606C22×D4C23×C5911yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C5911yescharacteristic
611C23×C4C23×C5911yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C5914yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C5914yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C5911yescharacteristic
635C22×C8C23×C5911yescharacteristic
636C22×C8C23×C5911yescharacteristic
637C22×C8C23×C5911yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C5914yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C5911yescharacteristic
658C2×C4⋊C4C23×C5911yescharacteristic
659C2×C4⋊C4C23×C5911yescharacteristic
660C2×C4⋊C4C23×C5911yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C5911yescharacteristic
673C2×C22⋊C4D4×C5911yescharacteristic
674C2×C42C23×C5911yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C5911yescharacteristic
700C24C2×D4×C5911yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C5912yes—
720C2×Q8C2×D4×C5912yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C5912yes—
757C2×D4C2×D4×C5912yes—
758C2×D4C2×D4×C5912yes—
759C2×D4C2×D4×C5912yes—
760C2×D4C2×D4×C5912yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C5911yescharacteristic
786C22×C4C2×D4×C5911yescharacteristic
787C22×C4C2×D4×C5911yescharacteristic
788C22×C4C2×D4×C5911yescharacteristic
789C22×C4C2×D4×C5912yes—
790C22×C4C2×D4×C5912yes—
791C22×C4C24×C5911yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C5912yes—
810C2×C8C2×D4×C5912yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C5912yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C5912yes—
875C23#135×C5912yescomplemented
876C23C22×D4×C5911yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C5914yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C5912yes—
941C2×C4C22×D4×C5911yescharacteristic
942C2×C4C22×D4×C5911yescharacteristic
943C2×C4C22×D4×C5911yescharacteristic
944C2×C4C22×D4×C5911yescharacteristic
945C2×C4H(5,𝔽2)×C5911yescharacteristic
946C2×C4H(5,𝔽2)×C5911yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C5911yescharacteristic
988C22D42×C5911yescharacteristic
989C22D42×C5911yescharacteristic
990C22C2×#135×C5911yescharacteristic
991C22C59×#57511yescharacteristic
992C22C59×#57611yescharacteristic
993C22C59×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—41no—
997C4—42no—
998C4—41no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C5911yescharacteristic
1004C4C59×#53411yescharacteristic
1005C4D42×C5911yescharacteristic
1006C4D42×C5911yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C59×#240311yescharacteristic
1013C2C59×#300211yescharacteristic
1014C2C59×#301211yescharacteristic
1015C2C59×#326711yescharacteristic
1016C2C59×#326811yescharacteristic
1017C2C59×#328011yescharacteristic
1018C2C59×#328211yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C59C2semidirect
2. C2×C59×#546C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#450C2semidirect
5. C2×C59×#447C2semidirect
6. C59×#2407C2semidirect
7. C59×#2015C2semidirect
8. C59×#2012C2semidirect
9. C59×#2001C2semidirect
10. C59×#2000C2semidirect
11. C59×#1893C2semidirect
12. C59×#1879C2semidirect
13. C59×#1877C2semidirect
14. C59×#1869C2semidirect
15. C59×#1788C2semidirect
17. C22×#41×C59C22semidirect
22. C22×Q16×C59C22semidirect
25. C22×SD16×C59C22semidirect
28. C23×C8×C59C22semidirect
45. C2×#103×C59C22semidirect
46. C2×#103×C59C22semidirect
47. C2×#103×C59C22semidirect
52. C2×#102×C59C22semidirect
55. C2×C22⋊C8×C59C22semidirect
58. C59×#391C22semidirect
59. C59×#390C22semidirect
62. C59×#380C22semidirect
63. C59×#340C22semidirect
64. C59×#340C22semidirect
65. C59×#336C22semidirect
66. C59×#336C22semidirect
79. C2×#41×C59D4semidirect
114. C2×SD16×C59D4semidirect
120. C2×D8×C59D4semidirect
139. #121×C59D4semidirect
365. C23×C59#135semidirect
441. #23850C59direct (N × H)
498. C22×#135C2×C59semidirect
499. C2×#546C2×C59semidirect
500. C2×#449C2×C59semidirect
501. C2×#450C2×C59semidirect
502. C2×#447C2×C59semidirect
503. #2407C2×C59semidirect
504. #2015C2×C59semidirect
505. #2012C2×C59semidirect
506. #2001C2×C59semidirect
507. #2000C2×C59semidirect
508. #1893C2×C59semidirect
509. #1879C2×C59semidirect
510. #1877C2×C59semidirect
511. #1869C2×C59semidirect
512. #1788C2×C59semidirect
526. C22×#41C22×C59semidirect
531. C22×Q16C22×C59semidirect
534. C22×SD16C22×C59semidirect
537. C23×C8C22×C59semidirect
554. C2×#103C22×C59semidirect
555. C2×#103C22×C59semidirect
556. C2×#103C22×C59semidirect
561. C2×#102C22×C59semidirect
564. C2×C22⋊C8C22×C59semidirect
567. #391C22×C59semidirect
568. #390C22×C59semidirect
571. #380C22×C59semidirect
572. #340C22×C59semidirect
573. #340C22×C59semidirect
574. #336C22×C59semidirect
575. #336C22×C59semidirect
576. C59#23850direct (N × H)
589. C2×#41D4×C59semidirect
624. C2×SD16D4×C59semidirect
630. C2×D8D4×C59semidirect
649. #121D4×C59semidirect
875. C23#135×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C592
C2×C59×#5462
C2×C59×#4492
C2×C59×#4502
C2×C59×#4472
C59×#24072
C59×#20152
C59×#20122
C59×#20012
C59×#20002
C59×#18932
C59×#18792
C59×#18772
C59×#18692
C59×#17882
#2385059