Finite Group Databasebeta

← C59×#24444 #28436553

Subgroups — C59×#24444 #28436553

Order 15104.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#546C211yesmaximal, characteristic, complemented
2C2×C59×#469C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#447C211yesmaximal, characteristic, complemented
5C2×C59×#417C211yesmaximal, characteristic, complemented
6C59×#2416C211yesmaximal, characteristic, complemented
7C59×#2042C211yesmaximal, characteristic, complemented
8C59×#2035C211yesmaximal, characteristic, complemented
9C59×#2012C211yesmaximal, characteristic, complemented
10C59×#2000C211yesmaximal, characteristic, complemented
11C59×#1879C211yesmaximal, characteristic, complemented
12C59×#1874C211yesmaximal, characteristic, complemented
13C59×#1870C211yesmaximal, characteristic, complemented
14C59×#1864C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic, complemented
19C22×D8×C59C2211yescharacteristic
20C22×D8×C59C2211yescharacteristic
21C22×M16×C59C2211yescharacteristic, complemented
22C59×#546—24no—
23C59×#546—24no—
24C2×#124×C59C2211yescharacteristic
25C2×#123×C59—21no—
26C2×C22⋊Q8×C59C2211yescharacteristic
27C2×#121×C59—21no—
28C2×#121×C59—21no—
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C2×#121×C59C2211yescharacteristic, complemented
32C2×#120×C59—21no—
33C2×C4×D4×C59C2211yescharacteristic
34C2×C4×D4×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic, complemented
36C22×C22⋊C4×C59—21no—
37C59×#469—24no—
38C59×#449—24no—
39C59×#447—24no—
40C2×#106×C59C2211yescharacteristic, complemented
41C59×#417—24no—
42C2×#103×C59C2211yescharacteristic, complemented
43C2×#103×C59C2211yescharacteristic, complemented
44C2×#103×C59C2211yescharacteristic, complemented
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C2×#102×C59C2211yescharacteristic
50C2×#102×C59C2211yescharacteristic
51C2×#102×C59C2211yescharacteristic, complemented
52C2×C22⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic, complemented
55C59×#396—21no—
56C59×#394—21no—
57C59×#390C2211yescharacteristic, complemented
58C59×#389C2211yescharacteristic, complemented
59C59×#386—21no—
60C59×#380C2211yescharacteristic
61C59×#340C2211yescharacteristic, complemented
62C59×#340C2211yescharacteristic, complemented
63C59×#336C2211yescharacteristic, complemented
64C59×#336C2211yescharacteristic, complemented
65C25×C59—21no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—41no—
70C2×#41×C59—41no—
71C2×#41×C59D414yescomplemented
72C22×Q8×C59C2311yescharacteristic
73C22×D4×C59—21no—
74C22×D4×C59—21no—
75C22×D4×C59—22no—
76C22×D4×C59—22no—
77C22×D4×C59—22no—
78C22×D4×C59—22no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59—41no—
83C22×D4×C59—41no—
84C22×D4×C59D411yescharacteristic
85C22×D4×C59C2311yescharacteristic
86C22×D4×C59C2311yescharacteristic
87C22×D4×C59C2311yescharacteristic
88C23×C4×C59—21no—
89C23×C4×C59—21no—
90C23×C4×C59—21no—
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
93C2×SD16×C59—22no—
94C2×SD16×C59—41no—
95C2×SD16×C59—41no—
96C2×D8×C59—22no—
97C2×D8×C59—22no—
98C2×D8×C59—22no—
99C2×D8×C59—22no—
100C2×D8×C59—22no—
101C2×D8×C59—41no—
102C2×M16×C59—22no—
103C2×M16×C59—22no—
104C2×M16×C59—41no—
105C22×C8×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109#124×C59—22no—
110#124×C59—22no—
111#123×C59—28no—
112C22⋊Q8×C59—22no—
113C22⋊Q8×C59—22no—
114#121×C59—28no—
115#121×C59—22no—
116#121×C59—22no—
117#121×C59—22no—
118#121×C59—22no—
119#121×C59—41no—
120#121×C59—44no—
121#121×C59D414yescomplemented
122#120×C59—28no—
123C4×D4×C59—22no—
124C4×D4×C59—22no—
125C4×D4×C59—22no—
126C4×D4×C59—22no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—22no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—41no—
132C2×C4⋊C4×C59D411yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C22⋊C4×C59—28no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—21no—
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C22⋊C4×C59D411yescharacteristic
150C2×C42×C59C2311yescharacteristic
151#106×C59—22no—
152#103×C59—22no—
153#103×C59—22no—
154#103×C59—22no—
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—22no—
158#102×C59—22no—
159#102×C59—22no—
160#102×C59—41no—
161#102×C59D414yescomplemented
162C22⋊C8×C59—22no—
163C22⋊C8×C59—22no—
164C22⋊C8×C59—41no—
165#95×C59—21no—
166#95×C59—21no—
167C24×C59—21no—
168C24×C59—24no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—42no—
172C24×C59—42no—
173C24×C59—42no—
174C24×C59—42no—
175C24×C59—81no—
176C24×C59—81no—
177C24×C59C2×D411yescharacteristic
178C24×C59C2×D411yescharacteristic
179#41×C59—28no—
180#41×C59—44no—
181#41×C59—44no—
182#41×C59—44no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—21no—
188C2×Q8×C59C2×D412yes—
189C2×D4×C59—24no—
190C2×D4×C59—22no—
191C2×D4×C59—24no—
192C2×D4×C59—22no—
193C2×D4×C59—24no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—21no—
198C2×D4×C59—21no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—41no—
209C2×D4×C59—42no—
210C2×D4×C59—42no—
211C2×D4×C59—42no—
212C2×D4×C59—44no—
213C2×D4×C59—44no—
214C2×D4×C59—44no—
215C2×D4×C59—42no—
216C2×D4×C59—42no—
217C2×D4×C59—44no—
218C2×D4×C59—42no—
219C2×D4×C59—42no—
220C2×D4×C59—42no—
221C2×D4×C59—42no—
222C2×D4×C59—81no—
223C2×D4×C59—81no—
224C2×D4×C59—81no—
225C2×D4×C59C2×D412yes—
226C2×D4×C59C2×D412yes—
227C2×D4×C59C2×D412yes—
228C2×D4×C59#4112yes—
229C22×C4×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—24no—
237C22×C4×C59—24no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—42no—
247C22×C4×C59—42no—
248C22×C4×C59—42no—
249C22×C4×C59—42no—
250C22×C4×C59—81no—
251C22×C4×C59—81no—
252C22×C4×C59—81no—
253C22×C4×C59C2×D411yescharacteristic
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D412yes—
258C22×C4×C59C2×D412yes—
259C22×C4×C59C2411yescharacteristic
260SD16×C59—44no—
261D8×C59—44no—
262D8×C59—44no—
263M16×C59—44no—
264C2×C8×C59—21no—
265C2×C8×C59—21no—
266C2×C8×C59—21no—
267C2×C8×C59—21no—
268C2×C8×C59—21no—
269C2×C8×C59—21no—
270C2×C8×C59—21no—
271C2×C8×C59—21no—
272C2×C8×C59—21no—
273C2×C8×C59—21no—
274C2×C8×C59—21no—
275C2×C8×C59C2×D412yes—
276C4⋊C4×C59—24no—
277C4⋊C4×C59—22no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—42no—
285C4⋊C4×C59—42no—
286C4⋊C4×C59C2×D412yes—
287C4⋊C4×C59C2×D412yes—
288C22⋊C4×C59—24no—
289C22⋊C4×C59—24no—
290C22⋊C4×C59—24no—
291C22⋊C4×C59—24no—
292C22⋊C4×C59—22no—
293C22⋊C4×C59—22no—
294C22⋊C4×C59—24no—
295C22⋊C4×C59—42no—
296C22⋊C4×C59—42no—
297C22⋊C4×C59—42no—
298C22⋊C4×C59—42no—
299C22⋊C4×C59—81no—
300C42×C59—21no—
301C42×C59—21no—
302C23×C59—21no—
303C23×C59—22no—
304C23×C59—21no—
305C23×C59—21no—
306C23×C59—22no—
307C23×C59—21no—
308C23×C59—21no—
309C23×C59—22no—
310C23×C59—21no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—21no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—22no—
318C23×C59—48no—
319C23×C59—48no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—84no—
338C23×C59—84no—
339C23×C59—84no—
340C23×C59—84no—
341C23×C59—84no—
342C23×C59#12012yes—
343C23×C59AGL(1,ℤ/8)12yes—
344C23×C59C22×D411yescharacteristic
345Q8×C59—22no—
346Q8×C59—22no—
347Q8×C59—41no—
348Q8×C59—41no—
349D4×C59—22no—
350D4×C59—22no—
351D4×C59—22no—
352D4×C59—22no—
353D4×C59—22no—
354D4×C59—44no—
355D4×C59—48no—
356D4×C59—48no—
357D4×C59—41no—
358D4×C59—41no—
359D4×C59—41no—
360D4×C59—41no—
361D4×C59—41no—
362D4×C59—41no—
363D4×C59—84no—
364D4×C59—84no—
365D4×C59—84no—
366D4×C59#12114yescomplemented
367C2×C4×C59—21no—
368C2×C4×C59—21no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—21no—
378C2×C4×C59—21no—
379C2×C4×C59—22no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—21no—
384C2×C4×C59—21no—
385C2×C4×C59—48no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—84no—
403C2×C4×C59—84no—
404C2×C4×C59#12012yes—
405C2×C4×C59C22×D411yescharacteristic
406C2×C4×C59C22×D411yescharacteristic
407C2×C4×C59C22×D411yescharacteristic
408C2×C4×C59C2×#4111yescharacteristic
409C2×C4×C59H(5,𝔽2)11yescharacteristic
410C2×C4×C59H(5,𝔽2)11yescharacteristic
411C8×C59—22no—
412C8×C59—41no—
413C8×C59—41no—
414C8×C59—41no—
415#24444C5911yesmaximal, characteristic, direct product factor, Sylow
416C22×C59—22no—
417C22×C59—24no—
418C22×C59—22no—
419C22×C59—22no—
420C22×C59—22no—
421C22×C59—22no—
422C22×C59—22no—
423C22×C59—41no—
424C22×C59—42no—
425C22×C59—41no—
426C22×C59—42no—
427C22×C59—42no—
428C22×C59—41no—
429C22×C59—41no—
430C22×C59—41no—
431C22×C59—42no—
432C22×C59—41no—
433C22×C59—42no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—42no—
437C22×C59—42no—
438C22×C59—42no—
439C22×C59—42no—
440C22×C59—816no—
441C22×C59—81no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59—81no—
449C22×C59—81no—
450C22×C59—81no—
451C22×C59—81no—
452C22×C59C2×#12011yescharacteristic
453C22×C59D4211yescharacteristic
454C22×C59#54611yescharacteristic
455C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C59#57511yescharacteristic
457C22×C59#57611yescharacteristic
458C22×C59#57711yescharacteristic
459C4×C59—22no—
460C4×C59—41no—
461C4×C59—42no—
462C4×C59—41no—
463C4×C59—42no—
464C4×C59—41no—
465C4×C59—42no—
466C4×C59—81no—
467C4×C59—81no—
468C4×C59C2×#12111yescharacteristic
469C4×C59#53411yescharacteristic
470C4×C59D4211yescharacteristic
471C4×C59#54611yescharacteristic
472C2×#546C2×C5911yescharacteristic, complemented
473C2×#469C2×C5911yescharacteristic, complemented
474C2×#449C2×C5911yescharacteristic, complemented
475C2×#447C2×C5911yescharacteristic, complemented
476C2×#417C2×C5911yescharacteristic, complemented
477#2416C2×C5911yescharacteristic, complemented
478#2042C2×C5911yescharacteristic, complemented
479#2035C2×C5911yescharacteristic, complemented
480#2012C2×C5911yescharacteristic, complemented
481#2000C2×C5911yescharacteristic, complemented
482#1879C2×C5911yescharacteristic, complemented
483#1874C2×C5911yescharacteristic, complemented
484#1870C2×C5911yescharacteristic, complemented
485#1864C2×C5911yescharacteristic, complemented
486#1786C2×C5911yescharacteristic, complemented
487C2×C59—42no—
488C2×C59—42no—
489C2×C59—44no—
490C2×C59—82no—
491C2×C59—161no—
492C2×C59#241011yescharacteristic
493C2×C59#300611yescharacteristic
494C2×C59#301211yescharacteristic
495C2×C59#326411yescharacteristic
496C2×C59#327511yescharacteristic
497C2×C59#330611yescharacteristic
498C2×C59#332211yescharacteristic
499C22×#41C22×C5911yescharacteristic
500C23×D4C22×C5911yescharacteristic
501C22×SD16C22×C5911yescharacteristic, complemented
502C22×D8C22×C5911yescharacteristic
503C22×D8C22×C5911yescharacteristic
504C22×M16C22×C5911yescharacteristic, complemented
505#546—24no—
506#546—24no—
507C2×#124C22×C5911yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C22×C5911yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C5911yescharacteristic
513C2×#121C22×C5911yescharacteristic
514C2×#121C22×C5911yescharacteristic, complemented
515C2×#120—21no—
516C2×C4×D4C22×C5911yescharacteristic
517C2×C4×D4C22×C5911yescharacteristic
518C22×C4⋊C4C22×C5911yescharacteristic, complemented
519C22×C22⋊C4—21no—
520#469—24no—
521#449—24no—
522#447—24no—
523C2×#106C22×C5911yescharacteristic, complemented
524#417—24no—
525C2×#103C22×C5911yescharacteristic, complemented
526C2×#103C22×C5911yescharacteristic, complemented
527C2×#103C22×C5911yescharacteristic, complemented
528C2×#102C22×C5911yescharacteristic
529C2×#102C22×C5911yescharacteristic
530C2×#102C22×C5911yescharacteristic
531C2×#102C22×C5911yescharacteristic
532C2×#102C22×C5911yescharacteristic
533C2×#102C22×C5911yescharacteristic
534C2×#102C22×C5911yescharacteristic, complemented
535C2×C22⋊C8C22×C5911yescharacteristic
536C2×C22⋊C8C22×C5911yescharacteristic
537C2×C22⋊C8C22×C5911yescharacteristic, complemented
538#396—21no—
539#394—21no—
540#390C22×C5911yescharacteristic, complemented
541#389C22×C5911yescharacteristic, complemented
542#386—21no—
543#380C22×C5911yescharacteristic
544#340C22×C5911yescharacteristic, complemented
545#340C22×C5911yescharacteristic, complemented
546#336C22×C5911yescharacteristic, complemented
547#336C22×C5911yescharacteristic, complemented
548C59#2444411yescharacteristic, direct product factor, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C5914yescomplemented
556C22×Q8C23×C5911yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4D4×C5911yescharacteristic
569C22×D4C23×C5911yescharacteristic
570C22×D4C23×C5911yescharacteristic
571C22×D4C23×C5911yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C5911yescharacteristic
576C23×C4C23×C5911yescharacteristic
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—41no—
589C22×C8C23×C5911yescharacteristic
590C22×C8C23×C5911yescharacteristic
591C22×C8C23×C5911yescharacteristic
592C22×C8C23×C5911yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—44no—
605#121D4×C5914yescomplemented
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C5911yescharacteristic
617C2×C4⋊C4C23×C5911yescharacteristic
618C2×C4⋊C4C23×C5911yescharacteristic
619C2×C4⋊C4C23×C5911yescharacteristic
620C2×C4⋊C4C23×C5911yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C5911yescharacteristic
633C2×C22⋊C4D4×C5911yescharacteristic
634C2×C42C23×C5911yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645#102D4×C5914yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—24no—
653C24—21no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C5911yescharacteristic
662C24C2×D4×C5911yescharacteristic
663#41—28no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C5912yes—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C5912yes—
710C2×D4C2×D4×C5912yes—
711C2×D4C2×D4×C5912yes—
712C2×D4#41×C5912yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C2×D4×C5911yescharacteristic
739C22×C4C2×D4×C5911yescharacteristic
740C22×C4C2×D4×C5911yescharacteristic
741C22×C4C2×D4×C5912yes—
742C22×C4C2×D4×C5912yes—
743C22×C4C24×C5911yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747M16—44no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8C2×D4×C5912yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C5912yes—
771C4⋊C4C2×D4×C5912yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23#120×C5912yes—
827C23AGL(1,ℤ/8)×C5912yes—
828C23C22×D4×C5911yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C5914yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C5912yes—
889C2×C4C22×D4×C5911yescharacteristic
890C2×C4C22×D4×C5911yescharacteristic
891C2×C4C22×D4×C5911yescharacteristic
892C2×C4C2×#41×C5911yescharacteristic
893C2×C4H(5,𝔽2)×C5911yescharacteristic
894C2×C4H(5,𝔽2)×C5911yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×#120×C5911yescharacteristic
936C22D42×C5911yescharacteristic
937C22C59×#54611yescharacteristic
938C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
939C22C59×#57511yescharacteristic
940C22C59×#57611yescharacteristic
941C22C59×#57711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C5911yescharacteristic
952C4C59×#53411yescharacteristic
953C4D42×C5911yescharacteristic
954C4C59×#54611yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2C59×#241011yescharacteristic
961C2C59×#300611yescharacteristic
962C2C59×#301211yescharacteristic
963C2C59×#326411yescharacteristic
964C2C59×#327511yescharacteristic
965C2C59×#330611yescharacteristic
966C2C59×#332211yescharacteristic
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. C2×C59×#546C2semidirect
2. C2×C59×#469C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#447C2semidirect
5. C2×C59×#417C2semidirect
6. C59×#2416C2semidirect
7. C59×#2042C2semidirect
8. C59×#2035C2semidirect
9. C59×#2012C2semidirect
10. C59×#2000C2semidirect
11. C59×#1879C2semidirect
12. C59×#1874C2semidirect
13. C59×#1870C2semidirect
14. C59×#1864C2semidirect
15. C59×#1786C2semidirect
18. C22×SD16×C59C22semidirect
21. C22×M16×C59C22semidirect
31. C2×#121×C59C22semidirect
35. C22×C4⋊C4×C59C22semidirect
40. C2×#106×C59C22semidirect
42. C2×#103×C59C22semidirect
43. C2×#103×C59C22semidirect
44. C2×#103×C59C22semidirect
51. C2×#102×C59C22semidirect
54. C2×C22⋊C8×C59C22semidirect
57. C59×#390C22semidirect
58. C59×#389C22semidirect
61. C59×#340C22semidirect
62. C59×#340C22semidirect
63. C59×#336C22semidirect
64. C59×#336C22semidirect
71. C2×#41×C59D4semidirect
121. #121×C59D4semidirect
161. #102×C59D4semidirect
366. D4×C59#121semidirect
415. #24444C59direct (N × H)
472. C2×#546C2×C59semidirect
473. C2×#469C2×C59semidirect
474. C2×#449C2×C59semidirect
475. C2×#447C2×C59semidirect
476. C2×#417C2×C59semidirect
477. #2416C2×C59semidirect
478. #2042C2×C59semidirect
479. #2035C2×C59semidirect
480. #2012C2×C59semidirect
481. #2000C2×C59semidirect
482. #1879C2×C59semidirect
483. #1874C2×C59semidirect
484. #1870C2×C59semidirect
485. #1864C2×C59semidirect
486. #1786C2×C59semidirect
501. C22×SD16C22×C59semidirect
504. C22×M16C22×C59semidirect
514. C2×#121C22×C59semidirect
518. C22×C4⋊C4C22×C59semidirect
523. C2×#106C22×C59semidirect
525. C2×#103C22×C59semidirect
526. C2×#103C22×C59semidirect
527. C2×#103C22×C59semidirect
534. C2×#102C22×C59semidirect
537. C2×C22⋊C8C22×C59semidirect
540. #390C22×C59semidirect
541. #389C22×C59semidirect
544. #340C22×C59semidirect
545. #340C22×C59semidirect
546. #336C22×C59semidirect
547. #336C22×C59semidirect
548. C59#24444direct (N × H)
555. C2×#41D4×C59semidirect
605. #121D4×C59semidirect
645. #102D4×C59semidirect
850. D4#121×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5462
C2×C59×#4692
C2×C59×#4492
C2×C59×#4472
C2×C59×#4172
C59×#24162
C59×#20422
C59×#20352
C59×#20122
C59×#20002
C59×#18792
C59×#18742
C59×#18702
C59×#18642
C59×#17862
#2444459