Finite Group Databasebeta

← C59×#24245 #28436354

Subgroups — C59×#24245 #28436354

Order 15104.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#546C211yesmaximal, characteristic, complemented
2C2×C59×#463C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#447C211yesmaximal, characteristic, complemented
5C2×C4×D8×C59C211yesmaximal, characteristic, complemented
6C59×#2535C211yesmaximal, characteristic, complemented
7C59×#2036C211yesmaximal, characteristic, complemented
8C59×#2033C211yesmaximal, characteristic, complemented
9C59×#2000C211yesmaximal, characteristic, complemented
10C59×#1999C211yesmaximal, characteristic, complemented
11C59×#1958C211yesmaximal, characteristic, complemented
12C59×#1954C211yesmaximal, characteristic, complemented
13C59×#1804C211yesmaximal, characteristic, complemented
14C59×#1788C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic, complemented
19C22×D8×C59C2211yescharacteristic
20C22×D8×C59C2211yescharacteristic
21C59×#546—24no—
22C59×#546—24no—
23C2×#124×C59C2211yescharacteristic
24C2×#123×C59—21no—
25C2×C22⋊Q8×C59C2211yescharacteristic
26C2×#121×C59—21no—
27C2×#121×C59C2211yescharacteristic
28C2×#121×C59C2211yescharacteristic
29C2×#121×C59C2211yescharacteristic, complemented
30C2×#120×C59—21no—
31C2×C4×D4×C59C2211yescharacteristic
32C2×C4×D4×C59C2211yescharacteristic
33C2×C4×D4×C59C2211yescharacteristic, complemented
34C22×C22⋊C4×C59—21no—
35C59×#463—24no—
36C59×#449—24no—
37C59×#447—24no—
38C4×D8×C59—24no—
39C2×#107×C59C2211yescharacteristic, complemented
40C2×C4⋊C8×C59C2211yescharacteristic, complemented
41C2×#103×C59C2211yescharacteristic, complemented
42C2×#103×C59C2211yescharacteristic, complemented
43C2×#103×C59C2211yescharacteristic, complemented
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C2×#102×C59C2211yescharacteristic
50C2×#102×C59C2211yescharacteristic, complemented
51C2×C22⋊C8×C59C2211yescharacteristic
52C2×C22⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C2×C22⋊C8×C59C2211yescharacteristic, complemented
55C2×C4×C8×C59C2211yescharacteristic, complemented
56C59×#397—21no—
57C59×#392—21no—
58C59×#386—21no—
59C59×#386—21no—
60C59×#382C2211yescharacteristic, complemented
61C59×#380C2211yescharacteristic
62C59×#380C2211yescharacteristic, complemented
63C59×#340C2211yescharacteristic, complemented
64C59×#340C2211yescharacteristic, complemented
65C25×C59—21no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—41no—
71C2×#41×C59—41no—
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—22no—
95C2×SD16×C59—41no—
96C2×D8×C59—22no—
97C2×D8×C59—22no—
98C2×D8×C59—22no—
99C2×D8×C59—22no—
100C2×D8×C59—41no—
101C2×D8×C59D414yescomplemented
102C22×C8×C59C2311yescharacteristic
103C22×C8×C59C2311yescharacteristic
104C22×C8×C59C2311yescharacteristic
105C22×C8×C59C2311yescharacteristic
106#124×C59—22no—
107#124×C59D414yescomplemented
108#123×C59—28no—
109C22⋊Q8×C59—22no—
110C22⋊Q8×C59—22no—
111#121×C59—28no—
112#121×C59—22no—
113#121×C59—22no—
114#121×C59—22no—
115#121×C59—22no—
116#121×C59—41no—
117#121×C59—41no—
118#120×C59—28no—
119C4×D4×C59—22no—
120C4×D4×C59—22no—
121C4×D4×C59—22no—
122C4×D4×C59—22no—
123C4×D4×C59—22no—
124C4×D4×C59D414yescomplemented
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59D411yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C22⋊C4×C59—28no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—21no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—21no—
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59D411yescharacteristic
143C2×C22⋊C4×C59D411yescharacteristic
144C2×C42×C59C2311yescharacteristic
145#107×C59—22no—
146C4⋊C8×C59—22no—
147#103×C59—22no—
148#103×C59—22no—
149#103×C59—41no—
150#102×C59—22no—
151#102×C59—22no—
152#102×C59—22no—
153#102×C59—22no—
154#102×C59—22no—
155#102×C59—22no—
156#102×C59—41no—
157C22⋊C8×C59—22no—
158C22⋊C8×C59—22no—
159C22⋊C8×C59—41no—
160C22⋊C8×C59—41no—
161C4×C8×C59—22no—
162#95×C59—21no—
163#95×C59—21no—
164#95×C59—21no—
165#95×C59—21no—
166C24×C59—21no—
167C24×C59—24no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—42no—
171C24×C59—42no—
172C24×C59—42no—
173C24×C59—42no—
174C24×C59—81no—
175C24×C59—81no—
176C24×C59C2×D411yescharacteristic
177C24×C59C2×D411yescharacteristic
178#41×C59—44no—
179#41×C59—44no—
180#41×C59—44no—
181#41×C59—44no—
182C2×Q8×C59—21no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59C2×D412yes—
188C2×D4×C59—24no—
189C2×D4×C59—24no—
190C2×D4×C59—22no—
191C2×D4×C59—24no—
192C2×D4×C59—22no—
193C2×D4×C59—21no—
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—41no—
207C2×D4×C59—42no—
208C2×D4×C59—42no—
209C2×D4×C59—44no—
210C2×D4×C59—44no—
211C2×D4×C59—44no—
212C2×D4×C59—42no—
213C2×D4×C59—42no—
214C2×D4×C59—44no—
215C2×D4×C59—42no—
216C2×D4×C59—42no—
217C2×D4×C59—42no—
218C2×D4×C59—42no—
219C2×D4×C59—81no—
220C2×D4×C59—81no—
221C2×D4×C59—81no—
222C2×D4×C59—81no—
223C2×D4×C59C2×D412yes—
224C2×D4×C59C2×D412yes—
225C2×D4×C59C2×D412yes—
226C2×D4×C59C2×D412yes—
227C2×D4×C59#4112yes—
228C22×C4×C59—24no—
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—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—24no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
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×C59—81no—
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2411yescharacteristic
259SD16×C59—44no—
260D8×C59—28no—
261D8×C59—44no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
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×C59C2×D412yes—
274C4⋊C4×C59—24no—
275C4⋊C4×C59—22no—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59C2×D412yes—
284C22⋊C4×C59—24no—
285C22⋊C4×C59—24no—
286C22⋊C4×C59—22no—
287C22⋊C4×C59—24no—
288C22⋊C4×C59—24no—
289C22⋊C4×C59—24no—
290C22⋊C4×C59—22no—
291C22⋊C4×C59—42no—
292C22⋊C4×C59—42no—
293C22⋊C4×C59—42no—
294C22⋊C4×C59—81no—
295C22⋊C4×C59—81no—
296C42×C59C2×D412yes—
297C42×C59C2×D412yes—
298C23×C59—21no—
299C23×C59—22no—
300C23×C59—21no—
301C23×C59—22no—
302C23×C59—21no—
303C23×C59—22no—
304C23×C59—21no—
305C23×C59—21no—
306C23×C59—21no—
307C23×C59—22no—
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—48no—
317C23×C59—48no—
318C23×C59—41no—
319C23×C59—41no—
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—84no—
335C23×C59—84no—
336C23×C59—84no—
337C23×C59—84no—
338C23×C59—84no—
339C23×C59#13512yes—
340C23×C59C22×D411yescharacteristic
341Q8×C59—22no—
342Q8×C59—22no—
343Q8×C59—41no—
344Q8×C59—41no—
345D4×C59—22no—
346D4×C59—22no—
347D4×C59—22no—
348D4×C59—22no—
349D4×C59—22no—
350D4×C59—22no—
351D4×C59—22no—
352D4×C59—44no—
353D4×C59—48no—
354D4×C59—48no—
355D4×C59—41no—
356D4×C59—41no—
357D4×C59—41no—
358D4×C59—41no—
359D4×C59—84no—
360D4×C59—84no—
361D4×C59—84no—
362D4×C59#12114yes—
363C2×C4×C59—21no—
364C2×C4×C59—21no—
365C2×C4×C59—21no—
366C2×C4×C59—21no—
367C2×C4×C59—22no—
368C2×C4×C59—21no—
369C2×C4×C59—22no—
370C2×C4×C59—21no—
371C2×C4×C59—21no—
372C2×C4×C59—21no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—48no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
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—84no—
398C2×C4×C59—84no—
399C2×C4×C59#12012yes—
400C2×C4×C59#12012yes—
401C2×C4×C59C22×D411yescharacteristic
402C2×C4×C59C22×D411yescharacteristic
403C2×C4×C59C22×D411yescharacteristic
404C2×C4×C59C2×#4111yescharacteristic
405C2×C4×C59H(5,𝔽2)11yescharacteristic
406C2×C4×C59H(5,𝔽2)11yescharacteristic
407C8×C59—22no—
408C8×C59—41no—
409C8×C59—41no—
410C8×C59—41no—
411#24245C5911yesmaximal, characteristic, direct product factor, Sylow
412C22×C59—24no—
413C22×C59—22no—
414C22×C59—22no—
415C22×C59—22no—
416C22×C59—41no—
417C22×C59—42no—
418C22×C59—42no—
419C22×C59—41no—
420C22×C59—41no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59—42no—
424C22×C59—41no—
425C22×C59—42no—
426C22×C59—41no—
427C22×C59—42no—
428C22×C59—42no—
429C22×C59—41no—
430C22×C59—42no—
431C22×C59—41no—
432C22×C59—42no—
433C22×C59—41no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—41no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—816no—
440C22×C59—81no—
441C22×C59—81no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59C2×#12011yescharacteristic
449C22×C59D4211yescharacteristic
450C22×C59#54611yescharacteristic
451C22×C59C2×#13511yescharacteristic
452C22×C59#57511yescharacteristic
453C22×C59#57611yescharacteristic
454C22×C59#57611yescharacteristic
455C4×C59—22no—
456C4×C59—22no—
457C4×C59—41no—
458C4×C59—41no—
459C4×C59—42no—
460C4×C59—42no—
461C4×C59—81no—
462C4×C59—81no—
463C4×C59—81no—
464C4×C59C2×#12111yescharacteristic
465C4×C59#53511yescharacteristic
466C4×C59D4211yescharacteristic
467C4×C59#54611yescharacteristic
468C2×#546C2×C5911yescharacteristic, complemented
469C2×#463C2×C5911yescharacteristic, complemented
470C2×#449C2×C5911yescharacteristic, complemented
471C2×#447C2×C5911yescharacteristic, complemented
472C2×C4×D8C2×C5911yescharacteristic, complemented
473#2535C2×C5911yescharacteristic, complemented
474#2036C2×C5911yescharacteristic, complemented
475#2033C2×C5911yescharacteristic, complemented
476#2000C2×C5911yescharacteristic, complemented
477#1999C2×C5911yescharacteristic, complemented
478#1958C2×C5911yescharacteristic, complemented
479#1954C2×C5911yescharacteristic, complemented
480#1804C2×C5911yescharacteristic, complemented
481#1788C2×C5911yescharacteristic, complemented
482#1786C2×C5911yescharacteristic, complemented
483C2×C59—42no—
484C2×C59—44no—
485C2×C59—81no—
486C2×C59—82no—
487C2×C59—82no—
488C2×C59#240811yescharacteristic
489C2×C59#300211yescharacteristic
490C2×C59#300811yescharacteristic
491C2×C59#327311yescharacteristic
492C2×C59#328011yescharacteristic
493C2×C59#329711yescharacteristic
494C2×C59#332211yescharacteristic
495C22×#41C22×C5911yescharacteristic
496C23×D4C22×C5911yescharacteristic
497C22×SD16C22×C5911yescharacteristic, complemented
498C22×D8C22×C5911yescharacteristic
499C22×D8C22×C5911yescharacteristic
500#546—24no—
501#546—24no—
502C2×#124C22×C5911yescharacteristic
503C2×#123—21no—
504C2×C22⋊Q8C22×C5911yescharacteristic
505C2×#121—21no—
506C2×#121C22×C5911yescharacteristic
507C2×#121C22×C5911yescharacteristic
508C2×#121C22×C5911yescharacteristic, complemented
509C2×#120—21no—
510C2×C4×D4C22×C5911yescharacteristic
511C2×C4×D4C22×C5911yescharacteristic
512C2×C4×D4C22×C5911yescharacteristic, complemented
513C22×C22⋊C4—21no—
514#463—24no—
515#449—24no—
516#447—24no—
517C4×D8—24no—
518C2×#107C22×C5911yescharacteristic, complemented
519C2×C4⋊C8C22×C5911yescharacteristic, complemented
520C2×#103C22×C5911yescharacteristic, complemented
521C2×#103C22×C5911yescharacteristic, complemented
522C2×#103C22×C5911yescharacteristic, complemented
523C2×#102C22×C5911yescharacteristic
524C2×#102C22×C5911yescharacteristic
525C2×#102C22×C5911yescharacteristic
526C2×#102C22×C5911yescharacteristic
527C2×#102C22×C5911yescharacteristic
528C2×#102C22×C5911yescharacteristic
529C2×#102C22×C5911yescharacteristic, complemented
530C2×C22⋊C8C22×C5911yescharacteristic
531C2×C22⋊C8C22×C5911yescharacteristic
532C2×C22⋊C8C22×C5911yescharacteristic, complemented
533C2×C22⋊C8C22×C5911yescharacteristic, complemented
534C2×C4×C8C22×C5911yescharacteristic, complemented
535#397—21no—
536#392—21no—
537#386—21no—
538#386—21no—
539#382C22×C5911yescharacteristic, complemented
540#380C22×C5911yescharacteristic
541#380C22×C5911yescharacteristic, complemented
542#340C22×C5911yescharacteristic, complemented
543#340C22×C5911yescharacteristic, complemented
544C59#2424511yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C5911yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C5911yescharacteristic
565C22×D4C23×C5911yescharacteristic
566C22×D4C23×C5911yescharacteristic
567C22×D4C23×C5911yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C5911yescharacteristic
572C23×C4C23×C5911yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C5914yescomplemented
582C22×C8C23×C5911yescharacteristic
583C22×C8C23×C5911yescharacteristic
584C22×C8C23×C5911yescharacteristic
585C22×C8C23×C5911yescharacteristic
586#124—22no—
587#124D4×C5914yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C5914yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C5911yescharacteristic
607C2×C4⋊C4C23×C5911yescharacteristic
608C2×C4⋊C4C23×C5911yescharacteristic
609C2×C4⋊C4C23×C5911yescharacteristic
610C2×C4⋊C4C23×C5911yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C5911yescharacteristic
623C2×C22⋊C4D4×C5911yescharacteristic
624C2×C42C23×C5911yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C5911yescharacteristic
657C24C2×D4×C5911yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C5912yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
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—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C5912yes—
704C2×D4C2×D4×C5912yes—
705C2×D4C2×D4×C5912yes—
706C2×D4C2×D4×C5912yes—
707C2×D4#41×C5912yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C5911yescharacteristic
735C22×C4C2×D4×C5911yescharacteristic
736C22×C4C2×D4×C5911yescharacteristic
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C24×C5911yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C5912yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C5912yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C5912yes—
777C42C2×D4×C5912yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C5912yes—
820C23C22×D4×C5911yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C5914yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C5912yes—
880C2×C4#120×C5912yes—
881C2×C4C22×D4×C5911yescharacteristic
882C2×C4C22×D4×C5911yescharacteristic
883C2×C4C22×D4×C5911yescharacteristic
884C2×C4C2×#41×C5911yescharacteristic
885C2×C4H(5,𝔽2)×C5911yescharacteristic
886C2×C4H(5,𝔽2)×C5911yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C5911yescharacteristic
928C22D42×C5911yescharacteristic
929C22C59×#54611yescharacteristic
930C22C2×#135×C5911yescharacteristic
931C22C59×#57511yescharacteristic
932C22C59×#57611yescharacteristic
933C22C59×#57611yescharacteristic
934C4—22no—
935C4—22no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C5911yescharacteristic
944C4C59×#53511yescharacteristic
945C4D42×C5911yescharacteristic
946C4C59×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C59×#240811yescharacteristic
953C2C59×#300211yescharacteristic
954C2C59×#300811yescharacteristic
955C2C59×#327311yescharacteristic
956C2C59×#328011yescharacteristic
957C2C59×#329711yescharacteristic
958C2C59×#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×#463C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#447C2semidirect
5. C2×C4×D8×C59C2semidirect
6. C59×#2535C2semidirect
7. C59×#2036C2semidirect
8. C59×#2033C2semidirect
9. C59×#2000C2semidirect
10. C59×#1999C2semidirect
11. C59×#1958C2semidirect
12. C59×#1954C2semidirect
13. C59×#1804C2semidirect
14. C59×#1788C2semidirect
15. C59×#1786C2semidirect
18. C22×SD16×C59C22semidirect
29. C2×#121×C59C22semidirect
33. C2×C4×D4×C59C22semidirect
39. C2×#107×C59C22semidirect
40. C2×C4⋊C8×C59C22semidirect
41. C2×#103×C59C22semidirect
42. C2×#103×C59C22semidirect
43. C2×#103×C59C22semidirect
50. C2×#102×C59C22semidirect
53. C2×C22⋊C8×C59C22semidirect
54. C2×C22⋊C8×C59C22semidirect
55. C2×C4×C8×C59C22semidirect
60. C59×#382C22semidirect
62. C59×#380C22semidirect
63. C59×#340C22semidirect
64. C59×#340C22semidirect
101. C2×D8×C59D4semidirect
107. #124×C59D4semidirect
124. C4×D4×C59D4semidirect
411. #24245C59direct (N × H)
468. C2×#546C2×C59semidirect
469. C2×#463C2×C59semidirect
470. C2×#449C2×C59semidirect
471. C2×#447C2×C59semidirect
472. C2×C4×D8C2×C59semidirect
473. #2535C2×C59semidirect
474. #2036C2×C59semidirect
475. #2033C2×C59semidirect
476. #2000C2×C59semidirect
477. #1999C2×C59semidirect
478. #1958C2×C59semidirect
479. #1954C2×C59semidirect
480. #1804C2×C59semidirect
481. #1788C2×C59semidirect
482. #1786C2×C59semidirect
497. C22×SD16C22×C59semidirect
508. C2×#121C22×C59semidirect
512. C2×C4×D4C22×C59semidirect
518. C2×#107C22×C59semidirect
519. C2×C4⋊C8C22×C59semidirect
520. C2×#103C22×C59semidirect
521. C2×#103C22×C59semidirect
522. C2×#103C22×C59semidirect
529. C2×#102C22×C59semidirect
532. C2×C22⋊C8C22×C59semidirect
533. C2×C22⋊C8C22×C59semidirect
534. C2×C4×C8C22×C59semidirect
539. #382C22×C59semidirect
541. #380C22×C59semidirect
542. #340C22×C59semidirect
543. #340C22×C59semidirect
544. C59#24245direct (N × H)
581. C2×D8D4×C59semidirect
587. #124D4×C59semidirect
604. C4×D4D4×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×#4632
C2×C59×#4492
C2×C59×#4472
C2×C4×D8×C592
C59×#25352
C59×#20362
C59×#20332
C59×#20002
C59×#19992
C59×#19582
C59×#19542
C59×#18042
C59×#17882
C59×#17862
#2424559