Finite Group Databasebeta

← C59×#24397 #28436506

Subgroups — C59×#24397 #28436506

Order 15104.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#537C211yesmaximal, characteristic, complemented
2C2×C59×#469C211yesmaximal, characteristic, complemented
3C2×C59×#465C211yesmaximal, characteristic, complemented
4C2×C59×#449C211yesmaximal, characteristic, complemented
5C2×C59×#408C211yesmaximal, characteristic, complemented
6C59×#2615C211yesmaximal, characteristic, complemented
7C59×#2035C211yesmaximal, characteristic, complemented
8C59×#2034C211yesmaximal, characteristic, complemented
9C59×#2000C211yesmaximal, characteristic, complemented
10C59×#1999C211yesmaximal, characteristic, complemented
11C59×#1894C211yesmaximal, characteristic, complemented
12C59×#1893C211yesmaximal, characteristic, complemented
13C59×#1874C211yesmaximal, characteristic, complemented
14C59×#1853C211yesmaximal, characteristic, complemented
15C59×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic
19C22×D8×C59C2211yescharacteristic
20C22×M16×C59C2211yescharacteristic
21C23×C8×C59C2211yescharacteristic
22C59×#537—24no—
23C59×#537—24no—
24C2×C22⋊Q8×C59—21no—
25C2×C22⋊Q8×C59C2211yescharacteristic
26C2×C22⋊Q8×C59C2211yescharacteristic
27C2×#121×C59—21no—
28C2×#121×C59—21no—
29C2×#121×C59—21no—
30C2×#121×C59C2211yescharacteristic
31C2×#121×C59C2211yescharacteristic
32C2×#121×C59C2211yescharacteristic
33C2×#121×C59C2211yescharacteristic
34C2×#121×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic
36C59×#469—24no—
37C59×#465—24no—
38C59×#449—24no—
39C2×#106×C59C2211yescharacteristic
40C2×#106×C59C2211yescharacteristic
41C2×#103×C59C2211yescharacteristic
42C2×#103×C59C2211yescharacteristic
43C2×#103×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C59×#408—24no—
50C2×C22⋊C8×C59C2211yescharacteristic
51C2×C22⋊C8×C59C2211yescharacteristic
52C2×C22⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C59×#393—21no—
55C59×#392—21no—
56C59×#392—21no—
57C59×#392—21no—
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C59×#340C2211yescharacteristic
63C59×#340C2211yescharacteristic
64C59×#340C2211yescharacteristic
65C2×#41×C59—22no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—22no—
71C2×#41×C59—22no—
72C2×#41×C59—22no—
73C2×#41×C59—41no—
74C2×#41×C59—41no—
75C2×#41×C59—41no—
76C2×#41×C59—41no—
77C22×Q8×C59D411yescharacteristic
78C22×Q8×C59C2311yescharacteristic
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59—21no—
83C22×D4×C59—21no—
84C22×D4×C59—21no—
85C22×D4×C59D411yescharacteristic
86C22×D4×C59D411yescharacteristic
87C22×D4×C59D411yescharacteristic
88C22×D4×C59C2311yescharacteristic
89C22×D4×C59C2311yescharacteristic
90C23×C4×C59—21no—
91C23×C4×C59—21no—
92C23×C4×C59C2311yescharacteristic
93C23×C4×C59C2311yescharacteristic
94C23×C4×C59C2311yescharacteristic
95C2×SD16×C59—22no—
96C2×SD16×C59—22no—
97C2×SD16×C59—41no—
98C2×D8×C59—22no—
99C2×D8×C59—22no—
100C2×D8×C59—41no—
101C2×M16×C59—22no—
102C2×M16×C59—22no—
103C2×M16×C59—41no—
104C22×C8×C59—22no—
105C22×C8×C59—22no—
106C22×C8×C59—41no—
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C22⋊Q8×C59—28no—
112C22⋊Q8×C59—22no—
113C22⋊Q8×C59—22no—
114C22⋊Q8×C59—22no—
115C22⋊Q8×C59D414yescomplemented
116#121×C59—28no—
117#121×C59—28no—
118#121×C59—28no—
119#121×C59—22no—
120#121×C59—22no—
121#121×C59—22no—
122#121×C59—22no—
123#121×C59—22no—
124#121×C59—22no—
125#121×C59—22no—
126#121×C59—41no—
127#121×C59—41no—
128#121×C59D414yescomplemented
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59—22no—
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
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×C59—21no—
149#106×C59—22no—
150#106×C59—22no—
151#103×C59—22no—
152#103×C59—22no—
153#103×C59—41no—
154#102×C59—22no—
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—22no—
158#102×C59—41no—
159C22⋊C8×C59—22no—
160C22⋊C8×C59—22no—
161C22⋊C8×C59—22no—
162C22⋊C8×C59D414yescomplemented
163#95×C59—21no—
164#95×C59—21no—
165#95×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59C2×D411yescharacteristic
169C24×C59C2×D411yescharacteristic
170C24×C59C2×D411yescharacteristic
171#41×C59—44no—
172#41×C59—44no—
173#41×C59—44no—
174#41×C59—44no—
175#41×C59—44no—
176#41×C59—44no—
177#41×C59—44no—
178#41×C59—44no—
179C2×Q8×C59—22no—
180C2×Q8×C59—22no—
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—41no—
187C2×Q8×C59C2×D412yes—
188C2×D4×C59—24no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59—24no—
194C2×D4×C59—24no—
195C2×D4×C59—22no—
196C2×D4×C59—22no—
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—41no—
210C2×D4×C59—41no—
211C2×D4×C59—42no—
212C2×D4×C59—42no—
213C2×D4×C59—42no—
214C2×D4×C59—42no—
215C2×D4×C59—42no—
216C2×D4×C59—81no—
217C2×D4×C59—81no—
218C2×D4×C59—81no—
219C2×D4×C59—81no—
220C2×D4×C59—81no—
221C2×D4×C59—81no—
222C2×D4×C59—81no—
223C2×D4×C59—81no—
224C2×D4×C59—81no—
225C2×D4×C59—81no—
226C2×D4×C59C2×D412yes—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
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—24no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—24no—
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—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—42no—
250C22×C4×C59—42no—
251C22×C4×C59—81no—
252C22×C4×C59—81no—
253C22×C4×C59C2×D411yescharacteristic
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D412yes—
256C22×C4×C59C2×D412yes—
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2×D412yes—
259C22×C4×C59#4112yes—
260C22×C4×C59C2411yescharacteristic
261SD16×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—44no—
275C2×C8×C59C2×D412yes—
276C2×C8×C59C2×D412yes—
277C4⋊C4×C59—24no—
278C4⋊C4×C59—24no—
279C4⋊C4×C59—24no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59C2×D412yes—
289C4⋊C4×C59C2×D412yes—
290C22⋊C4×C59—24no—
291C22⋊C4×C59—24no—
292C22⋊C4×C59—24no—
293C22⋊C4×C59—24no—
294C22⋊C4×C59—42no—
295C22⋊C4×C59—42no—
296C22⋊C4×C59—42no—
297C22⋊C4×C59—81no—
298C22⋊C4×C59—81no—
299C22⋊C4×C59—81no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—21no—
303C23×C59—21no—
304C23×C59—21no—
305C23×C59—21no—
306C23×C59—21no—
307C23×C59—21no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—21no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—22no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—21no—
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#12012yes—
334C23×C59#12112yes—
335C23×C59C22×D411yescharacteristic
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—44no—
339Q8×C59—41no—
340Q8×C59—41no—
341D4×C59—22no—
342D4×C59—22no—
343D4×C59—44no—
344D4×C59—44no—
345D4×C59—44no—
346D4×C59—48no—
347D4×C59—41no—
348D4×C59—41no—
349D4×C59—41no—
350D4×C59—41no—
351D4×C59—41no—
352D4×C59—41no—
353D4×C59—84no—
354D4×C59—84no—
355D4×C59—84no—
356D4×C59—84no—
357D4×C59—84no—
358C2×C4×C59—21no—
359C2×C4×C59—21no—
360C2×C4×C59—21no—
361C2×C4×C59—21no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
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—21no—
376C2×C4×C59—48no—
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—84no—
397C2×C4×C59#12012yes—
398C2×C4×C59#12112yes—
399C2×C4×C59C22×D411yescharacteristic
400C2×C4×C59C22×D411yescharacteristic
401C2×C4×C59C22×D411yescharacteristic
402C2×C4×C59C2×#4111yescharacteristic
403C2×C4×C59H(5,𝔽2)11yescharacteristic
404C2×C4×C59H(5,𝔽2)11yescharacteristic
405C8×C59—22no—
406C8×C59—22no—
407C8×C59—41no—
408C8×C59—41no—
409#24397C5911yesmaximal, characteristic, direct product factor, Sylow
410C22×C59—22no—
411C22×C59—22no—
412C22×C59—22no—
413C22×C59—22no—
414C22×C59—22no—
415C22×C59—22no—
416C22×C59—41no—
417C22×C59—41no—
418C22×C59—41no—
419C22×C59—41no—
420C22×C59—41no—
421C22×C59—41no—
422C22×C59—41no—
423C22×C59—41no—
424C22×C59—42no—
425C22×C59—41no—
426C22×C59—41no—
427C22×C59—41no—
428C22×C59—41no—
429C22×C59—42no—
430C22×C59—41no—
431C22×C59—42no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—81no—
435C22×C59—81no—
436C22×C59—81no—
437C22×C59—81no—
438C22×C59—81no—
439C22×C59—81no—
440C22×C59—81no—
441C22×C59—81no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59C2×#12011yescharacteristic
446C22×C59C2×#12111yescharacteristic
447C22×C59#53411yescharacteristic
448C22×C59#57611yescharacteristic
449C22×C59#57711yescharacteristic
450C22×C59#57711yescharacteristic
451C22×C59#57711yescharacteristic
452C4×C59—22no—
453C4×C59—22no—
454C4×C59—41no—
455C4×C59—42no—
456C4×C59—42no—
457C4×C59—42no—
458C4×C59—81no—
459C4×C59—81no—
460C4×C59—81no—
461C4×C59D4211yescharacteristic
462C4×C59D4211yescharacteristic
463C4×C59#54611yescharacteristic
464C4×C59#54611yescharacteristic
465C2×#537C2×C5911yescharacteristic, complemented
466C2×#469C2×C5911yescharacteristic, complemented
467C2×#465C2×C5911yescharacteristic, complemented
468C2×#449C2×C5911yescharacteristic, complemented
469C2×#408C2×C5911yescharacteristic, complemented
470#2615C2×C5911yescharacteristic, complemented
471#2035C2×C5911yescharacteristic, complemented
472#2034C2×C5911yescharacteristic, complemented
473#2000C2×C5911yescharacteristic, complemented
474#1999C2×C5911yescharacteristic, complemented
475#1894C2×C5911yescharacteristic, complemented
476#1893C2×C5911yescharacteristic, complemented
477#1874C2×C5911yescharacteristic, complemented
478#1853C2×C5911yescharacteristic, complemented
479#1788C2×C5911yescharacteristic, complemented
480C2×C59—42no—
481C2×C59—42no—
482C2×C59—81no—
483C2×C59—82no—
484C2×C59—161no—
485C2×C59#241011yescharacteristic
486C2×C59#301011yescharacteristic
487C2×C59#301211yescharacteristic
488C2×C59#306011yescharacteristic
489C2×C59#306211yescharacteristic
490C2×C59#319811yescharacteristic
491C2×C59#320411yescharacteristic
492C22×#41C22×C5911yescharacteristic
493C22×#41C22×C5911yescharacteristic
494C22×SD16C22×C5911yescharacteristic
495C22×D8C22×C5911yescharacteristic
496C22×M16C22×C5911yescharacteristic
497C23×C8C22×C5911yescharacteristic
498#537—24no—
499#537—24no—
500C2×C22⋊Q8—21no—
501C2×C22⋊Q8C22×C5911yescharacteristic
502C2×C22⋊Q8C22×C5911yescharacteristic
503C2×#121—21no—
504C2×#121—21no—
505C2×#121—21no—
506C2×#121C22×C5911yescharacteristic
507C2×#121C22×C5911yescharacteristic
508C2×#121C22×C5911yescharacteristic
509C2×#121C22×C5911yescharacteristic
510C2×#121C22×C5911yescharacteristic
511C22×C4⋊C4C22×C5911yescharacteristic
512#469—24no—
513#465—24no—
514#449—24no—
515C2×#106C22×C5911yescharacteristic
516C2×#106C22×C5911yescharacteristic
517C2×#103C22×C5911yescharacteristic
518C2×#103C22×C5911yescharacteristic
519C2×#103C22×C5911yescharacteristic
520C2×#102C22×C5911yescharacteristic
521C2×#102C22×C5911yescharacteristic
522C2×#102C22×C5911yescharacteristic
523C2×#102C22×C5911yescharacteristic
524C2×#102C22×C5911yescharacteristic
525#408—24no—
526C2×C22⋊C8C22×C5911yescharacteristic
527C2×C22⋊C8C22×C5911yescharacteristic
528C2×C22⋊C8C22×C5911yescharacteristic
529C2×C22⋊C8C22×C5911yescharacteristic
530#393—21no—
531#392—21no—
532#392—21no—
533#392—21no—
534#380C22×C5911yescharacteristic
535#380C22×C5911yescharacteristic
536#380C22×C5911yescharacteristic
537#340C22×C5911yescharacteristic
538#340C22×C5911yescharacteristic
539#340C22×C5911yescharacteristic
540#340C22×C5911yescharacteristic
541C59#2439711yescharacteristic, direct product factor, Sylow
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C5911yescharacteristic
555C22×Q8C23×C5911yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C5911yescharacteristic
563C22×D4D4×C5911yescharacteristic
564C22×D4D4×C5911yescharacteristic
565C22×D4C23×C5911yescharacteristic
566C22×D4C23×C5911yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C5911yescharacteristic
570C23×C4C23×C5911yescharacteristic
571C23×C4C23×C5911yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C5911yescharacteristic
585C22×C8C23×C5911yescharacteristic
586C22×C8C23×C5911yescharacteristic
587C22×C8C23×C5911yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C5914yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C5914yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C5911yescharacteristic
612C2×C4⋊C4C23×C5911yescharacteristic
613C2×C4⋊C4C23×C5911yescharacteristic
614C2×C4⋊C4C23×C5911yescharacteristic
615C2×C4⋊C4C23×C5911yescharacteristic
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⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C5914yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C5911yescharacteristic
646C24C2×D4×C5911yescharacteristic
647C24C2×D4×C5911yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C5912yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
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—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C5912yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C5911yescharacteristic
731C22×C4C2×D4×C5911yescharacteristic
732C22×C4C2×D4×C5912yes—
733C22×C4C2×D4×C5912yes—
734C22×C4C2×D4×C5911yescharacteristic
735C22×C4C2×D4×C5912yes—
736C22×C4#41×C5912yes—
737C22×C4C24×C5911yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
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—44no—
752C2×C8C2×D4×C5912yes—
753C2×C8C2×D4×C5912yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C5912yes—
766C4⋊C4C2×D4×C5912yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
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#120×C5912yes—
811C23#121×C5912yes—
812C23C22×D4×C5911yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
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—84no—
874C2×C4#120×C5912yes—
875C2×C4#121×C5912yes—
876C2×C4C22×D4×C5911yescharacteristic
877C2×C4C22×D4×C5911yescharacteristic
878C2×C4C22×D4×C5911yescharacteristic
879C2×C4C2×#41×C5911yescharacteristic
880C2×C4H(5,𝔽2)×C5911yescharacteristic
881C2×C4H(5,𝔽2)×C5911yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C5911yescharacteristic
922C22C2×#121×C5911yescharacteristic
923C22C59×#53411yescharacteristic
924C22C59×#57611yescharacteristic
925C22C59×#57711yescharacteristic
926C22C59×#57711yescharacteristic
927C22C59×#57711yescharacteristic
928C4—22no—
929C4—22no—
930C4—42no—
931C4—42no—
932C4—41no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C5911yescharacteristic
938C4D42×C5911yescharacteristic
939C4C59×#54611yescharacteristic
940C4C59×#54611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C59×#241011yescharacteristic
947C2C59×#301011yescharacteristic
948C2C59×#301211yescharacteristic
949C2C59×#306011yescharacteristic
950C2C59×#306211yescharacteristic
951C2C59×#319811yescharacteristic
952C2C59×#320411yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#537C2semidirect
2. C2×C59×#469C2semidirect
3. C2×C59×#465C2semidirect
4. C2×C59×#449C2semidirect
5. C2×C59×#408C2semidirect
6. C59×#2615C2semidirect
7. C59×#2035C2semidirect
8. C59×#2034C2semidirect
9. C59×#2000C2semidirect
10. C59×#1999C2semidirect
11. C59×#1894C2semidirect
12. C59×#1893C2semidirect
13. C59×#1874C2semidirect
14. C59×#1853C2semidirect
15. C59×#1788C2semidirect
115. C22⋊Q8×C59D4semidirect
128. #121×C59D4semidirect
162. C22⋊C8×C59D4semidirect
409. #24397C59direct (N × H)
465. C2×#537C2×C59semidirect
466. C2×#469C2×C59semidirect
467. C2×#465C2×C59semidirect
468. C2×#449C2×C59semidirect
469. C2×#408C2×C59semidirect
470. #2615C2×C59semidirect
471. #2035C2×C59semidirect
472. #2034C2×C59semidirect
473. #2000C2×C59semidirect
474. #1999C2×C59semidirect
475. #1894C2×C59semidirect
476. #1893C2×C59semidirect
477. #1874C2×C59semidirect
478. #1853C2×C59semidirect
479. #1788C2×C59semidirect
541. C59#24397direct (N × H)
592. C22⋊Q8D4×C59semidirect
605. #121D4×C59semidirect
639. C22⋊C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5372
C2×C59×#4692
C2×C59×#4652
C2×C59×#4492
C2×C59×#4082
C59×#26152
C59×#20352
C59×#20342
C59×#20002
C59×#19992
C59×#18942
C59×#18932
C59×#18742
C59×#18532
C59×#17882
#2439759