Finite Group Databasebeta

← C59×#25610 #28437719

Subgroups — C59×#25610 #28437719

Order 15104.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#542C211yesmaximal, characteristic, complemented
2C2×C59×#495C211yesmaximal, characteristic, complemented
3C2×C59×#489C211yesmaximal, characteristic, complemented
4C59×#2620C211yesmaximal, characteristic, complemented
5C59×#2001C211yesmaximal, characteristic, complemented
6C59×#2000C211yesmaximal, characteristic, complemented
7C59×#2000C211yesmaximal, characteristic, complemented
8C59×#1999C211yesmaximal, characteristic
9C59×#1990C211yesmaximal, characteristic, complemented
10C59×#1959C211yesmaximal, characteristic, complemented
11C59×#1880C211yesmaximal, characteristic, complemented
12C59×#1879C211yesmaximal, characteristic, complemented
13C59×#1878C211yesmaximal, characteristic, complemented
14C59×#1877C211yesmaximal, characteristic, complemented
15C59×#1750C211yesmaximal, characteristic, complemented
16C22×Q16×C59C2211yescharacteristic
17C22×SD16×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic
19C22×D8×C59C2211yescharacteristic
20C59×#542—24no—
21C59×#542—24no—
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×#126×C59—21no—
24C2×#124×C59—21no—
25C2×#124×C59C2211yescharacteristic
26C2×#124×C59C2211yescharacteristic
27C2×#123×C59—21no—
28C2×C22⋊Q8×C59—21no—
29C2×C22⋊Q8×C59C2211yescharacteristic
30C2×C22⋊Q8×C59C2211yescharacteristic
31C2×#121×C59C2211yescharacteristic
32C2×#121×C59C2211yescharacteristic
33C2×C4×Q8×C59C2211yescharacteristic
34C2×C4×D4×C59C2211yescharacteristic
35C2×#117×C59C2211yescharacteristic
36C59×#495—24no—
37C59×#489—24no—
38C2×#103×C59C2211yescharacteristic
39C2×#103×C59C2211yescharacteristic
40C2×#103×C59C2211yescharacteristic
41C2×#103×C59C2211yescharacteristic
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×C22⋊C8×C59C2211yescharacteristic
47C2×C22⋊C8×C59C2211yescharacteristic
48C2×#97×C59C2211yescharacteristic
49C2×C4×C8×C59C2211yescharacteristic
50C59×#396—21no—
51C59×#396—21no—
52C59×#394—21no—
53C59×#394—21no—
54C59×#391C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#384C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×Q8×C59—21no—
64C22×Q8×C59C2311yescharacteristic
65C22×Q8×C59C2311yescharacteristic
66C22×D4×C59—21no—
67C22×D4×C59—21no—
68C22×D4×C59C2311yescharacteristic
69C22×D4×C59C2311yescharacteristic
70C23×C4×C59—21no—
71C23×C4×C59C2311yescharacteristic
72C2×Q16×C59—22no—
73C2×Q16×C59—22no—
74C2×Q16×C59—41no—
75C2×SD16×C59—22no—
76C2×SD16×C59—22no—
77C2×SD16×C59—22no—
78C2×SD16×C59—22no—
79C2×SD16×C59—41no—
80C2×SD16×C59—41no—
81C2×D8×C59—22no—
82C2×D8×C59—22no—
83C2×D8×C59—41no—
84C22×C8×C59C2311yescharacteristic
85C22×C8×C59C2311yescharacteristic
86C22×C8×C59C2311yescharacteristic
87C22×C8×C59C2311yescharacteristic
88C4⋊Q8×C59—22no—
89C4⋊Q8×C59D414yescomplemented
90#126×C59—28no—
91#124×C59—28no—
92#124×C59—22no—
93#124×C59—22no—
94#124×C59—22no—
95#124×C59D414yescomplemented
96#123×C59—28no—
97C22⋊Q8×C59—28no—
98C22⋊Q8×C59—22no—
99C22⋊Q8×C59—22no—
100C22⋊Q8×C59—41no—
101C22⋊Q8×C59—41no—
102#121×C59—22no—
103#121×C59—22no—
104#121×C59—41no—
105#121×C59—41no—
106C4×Q8×C59—22no—
107C4×Q8×C59—22no—
108C4×D4×C59—22no—
109C4×D4×C59—22no—
110#117×C59—22no—
111#117×C59—22no—
112C2×C4⋊C4×C59—21no—
113C2×C4⋊C4×C59—21no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59D411yescharacteristic
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59D411yescharacteristic
136C2×C22⋊C4×C59D411yescharacteristic
137C2×C42×C59—21no—
138C2×C42×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140#103×C59—22no—
141#103×C59—22no—
142#103×C59—41no—
143#103×C59—41no—
144#102×C59—22no—
145#102×C59—22no—
146#102×C59—41no—
147#102×C59—41no—
148C22⋊C8×C59—22no—
149C22⋊C8×C59—22no—
150#97×C59—22no—
151C4×C8×C59—22no—
152#95×C59—21no—
153#95×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59C2×D411yescharacteristic
157C2×Q8×C59—24no—
158C2×Q8×C59—21no—
159C2×Q8×C59—21no—
160C2×Q8×C59—21no—
161C2×Q8×C59—21no—
162C2×Q8×C59—21no—
163C2×Q8×C59—21no—
164C2×Q8×C59—21no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—21no—
169C2×Q8×C59—81no—
170C2×Q8×C59—81no—
171C2×Q8×C59C2×D412yes—
172C2×D4×C59—24no—
173C2×D4×C59—21no—
174C2×D4×C59—21no—
175C2×D4×C59—21no—
176C2×D4×C59—21no—
177C2×D4×C59—21no—
178C2×D4×C59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—42no—
185C2×D4×C59—81no—
186C2×D4×C59—81no—
187C2×D4×C59—81no—
188C2×D4×C59—81no—
189C2×D4×C59C2×D412yes—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—24no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—81no—
204C22×C4×C59—81no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2411yescharacteristic
211Q16×C59—44no—
212SD16×C59—44no—
213SD16×C59—44no—
214D8×C59—44no—
215C2×C8×C59—21no—
216C2×C8×C59—21no—
217C2×C8×C59—21no—
218C2×C8×C59—21no—
219C2×C8×C59—21no—
220C2×C8×C59—21no—
221C2×C8×C59—21no—
222C2×C8×C59—21no—
223C2×C8×C59—21no—
224C2×C8×C59—21no—
225C2×C8×C59#4112yes—
226C2×C8×C59#4112yes—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—22no—
231C4⋊C4×C59—22no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—42no—
239C4⋊C4×C59—81no—
240C4⋊C4×C59—81no—
241C4⋊C4×C59C2×D412yes—
242C4⋊C4×C59C2×D412yes—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59—22no—
249C22⋊C4×C59—22no—
250C22⋊C4×C59—42no—
251C22⋊C4×C59—42no—
252C22⋊C4×C59—42no—
253C22⋊C4×C59—42no—
254C22⋊C4×C59—81no—
255C22⋊C4×C59—81no—
256C42×C59—24no—
257C42×C59—21no—
258C42×C59—21no—
259C42×C59C2×D412yes—
260C42×C59C2×D412yes—
261C23×C59—21no—
262C23×C59—22no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59—41no—
273C23×C59—41no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—41no—
279C23×C59—41no—
280C23×C59—41no—
281C23×C59—41no—
282C23×C59C22×D411yescharacteristic
283Q8×C59—22no—
284Q8×C59—22no—
285Q8×C59—41no—
286Q8×C59—41no—
287Q8×C59—41no—
288Q8×C59—41no—
289Q8×C59—41no—
290Q8×C59—41no—
291Q8×C59—84no—
292D4×C59—22no—
293D4×C59—22no—
294D4×C59—41no—
295D4×C59—41no—
296D4×C59—41no—
297D4×C59—41no—
298D4×C59—41no—
299D4×C59—41no—
300D4×C59—84no—
301D4×C59—84no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—22no—
308C2×C4×C59—21no—
309C2×C4×C59—22no—
310C2×C4×C59—21no—
311C2×C4×C59—22no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59—41no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—84no—
338C2×C4×C59#12012yes—
339C2×C4×C59#12012yes—
340C2×C4×C59C22×D411yescharacteristic
341C2×C4×C59C22×D411yescharacteristic
342C2×C4×C59C2×#4111yescharacteristic
343C2×C4×C59C2×#4111yescharacteristic
344C2×C4×C59H(5,𝔽2)11yescharacteristic
345C2×C4×C59H(5,𝔽2)11yescharacteristic
346C8×C59—22no—
347C8×C59—22no—
348C8×C59—41no—
349C8×C59—41no—
350#25610C5911yesmaximal, characteristic, direct product factor, Sylow
351C22×C59—41no—
352C22×C59—41no—
353C22×C59—41no—
354C22×C59—42no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59—42no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—42no—
361C22×C59—81no—
362C22×C59—81no—
363C22×C59—81no—
364C22×C59—81no—
365C22×C59—81no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—81no—
369C22×C59—81no—
370C22×C59—81no—
371C22×C59—81no—
372C22×C59C2×#12011yescharacteristic
373C22×C59#53211yescharacteristic
374C22×C59#53511yescharacteristic
375C22×C59#57611yescharacteristic
376C22×C59#57711yescharacteristic
377C22×C59#57711yescharacteristic
378C22×C59#57811yescharacteristic
379C4×C59—22no—
380C4×C59—22no—
381C4×C59—41no—
382C4×C59—42no—
383C4×C59—41no—
384C4×C59—42no—
385C4×C59—42no—
386C4×C59—41no—
387C4×C59—81no—
388C4×C59—81no—
389C4×C59—81no—
390C4×C59#54611yescharacteristic
391C4×C59#54611yescharacteristic
392C4×C59#55011yescharacteristic
393C4×C59#55011yescharacteristic
394C2×#542C2×C5911yescharacteristic, complemented
395C2×#495C2×C5911yescharacteristic, complemented
396C2×#489C2×C5911yescharacteristic, complemented
397#2620C2×C5911yescharacteristic, complemented
398#2001C2×C5911yescharacteristic, complemented
399#2000C2×C5911yescharacteristic, complemented
400#2000C2×C5911yescharacteristic, complemented
401#1999C2×C5911yescharacteristic
402#1990C2×C5911yescharacteristic, complemented
403#1959C2×C5911yescharacteristic, complemented
404#1880C2×C5911yescharacteristic, complemented
405#1879C2×C5911yescharacteristic, complemented
406#1878C2×C5911yescharacteristic, complemented
407#1877C2×C5911yescharacteristic, complemented
408#1750C2×C5911yescharacteristic, complemented
409C2×C59—81no—
410C2×C59—82no—
411C2×C59—161no—
412C2×C59#243111yescharacteristic
413C2×C59#301211yescharacteristic
414C2×C59#301311yescharacteristic
415C2×C59#317311yescharacteristic
416C2×C59#317511yescharacteristic
417C2×C59#322411yescharacteristic
418C2×C59#322511yescharacteristic
419C22×Q16C22×C5911yescharacteristic
420C22×SD16C22×C5911yescharacteristic
421C22×SD16C22×C5911yescharacteristic
422C22×D8C22×C5911yescharacteristic
423#542—24no—
424#542—24no—
425C2×C4⋊Q8C22×C5911yescharacteristic
426C2×#126—21no—
427C2×#124—21no—
428C2×#124C22×C5911yescharacteristic
429C2×#124C22×C5911yescharacteristic
430C2×#123—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8C22×C5911yescharacteristic
433C2×C22⋊Q8C22×C5911yescharacteristic
434C2×#121C22×C5911yescharacteristic
435C2×#121C22×C5911yescharacteristic
436C2×C4×Q8C22×C5911yescharacteristic
437C2×C4×D4C22×C5911yescharacteristic
438C2×#117C22×C5911yescharacteristic
439#495—24no—
440#489—24no—
441C2×#103C22×C5911yescharacteristic
442C2×#103C22×C5911yescharacteristic
443C2×#103C22×C5911yescharacteristic
444C2×#103C22×C5911yescharacteristic
445C2×#102C22×C5911yescharacteristic
446C2×#102C22×C5911yescharacteristic
447C2×#102C22×C5911yescharacteristic
448C2×#102C22×C5911yescharacteristic
449C2×C22⋊C8C22×C5911yescharacteristic
450C2×C22⋊C8C22×C5911yescharacteristic
451C2×#97C22×C5911yescharacteristic
452C2×C4×C8C22×C5911yescharacteristic
453#396—21no—
454#396—21no—
455#394—21no—
456#394—21no—
457#391C22×C5911yescharacteristic
458#390C22×C5911yescharacteristic
459#384C22×C5911yescharacteristic
460#340C22×C5911yescharacteristic
461#340C22×C5911yescharacteristic
462#340C22×C5911yescharacteristic
463#340C22×C5911yescharacteristic
464#336C22×C5911yescharacteristic
465#336C22×C5911yescharacteristic
466C59#2561011yescharacteristic, direct product factor, Sylow
467C22×Q8—21no—
468C22×Q8C23×C5911yescharacteristic
469C22×Q8C23×C5911yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C23×C5911yescharacteristic
473C22×D4C23×C5911yescharacteristic
474C23×C4—21no—
475C23×C4C23×C5911yescharacteristic
476C2×Q16—22no—
477C2×Q16—22no—
478C2×Q16—41no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—41no—
484C2×SD16—41no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C22×C8C23×C5911yescharacteristic
489C22×C8C23×C5911yescharacteristic
490C22×C8C23×C5911yescharacteristic
491C22×C8C23×C5911yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8D4×C5914yescomplemented
494#126—28no—
495#124—28no—
496#124—22no—
497#124—22no—
498#124—22no—
499#124D4×C5914yescomplemented
500#123—28no—
501C22⋊Q8—28no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—41no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4D4×C5911yescharacteristic
523C2×C4⋊C4D4×C5911yescharacteristic
524C2×C4⋊C4C23×C5911yescharacteristic
525C2×C4⋊C4C23×C5911yescharacteristic
526C2×C4⋊C4C23×C5911yescharacteristic
527C2×C4⋊C4C23×C5911yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C5911yescharacteristic
540C2×C22⋊C4D4×C5911yescharacteristic
541C2×C42—21no—
542C2×C42C23×C5911yescharacteristic
543C2×C42C23×C5911yescharacteristic
544#103—22no—
545#103—22no—
546#103—41no—
547#103—41no—
548#102—22no—
549#102—22no—
550#102—41no—
551#102—41no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554#97—22no—
555C4×C8—22no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C5911yescharacteristic
561C2×Q8—24no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—81no—
574C2×Q8—81no—
575C2×Q8C2×D4×C5912yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4C2×D4×C5912yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C5911yescharacteristic
610C22×C4C2×D4×C5911yescharacteristic
611C22×C4C2×D4×C5911yescharacteristic
612C22×C4C2×D4×C5911yescharacteristic
613C22×C4C2×D4×C5911yescharacteristic
614C22×C4C24×C5911yescharacteristic
615Q16—44no—
616SD16—44no—
617SD16—44no—
618D8—44no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8#41×C5912yes—
630C2×C8#41×C5912yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4C2×D4×C5912yes—
646C4⋊C4C2×D4×C5912yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C42—24no—
661C42—21no—
662C42—21no—
663C42C2×D4×C5912yes—
664C42C2×D4×C5912yes—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23C22×D4×C5911yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695Q8—84no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—84no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4#120×C5912yes—
743C2×C4#120×C5912yes—
744C2×C4C22×D4×C5911yescharacteristic
745C2×C4C22×D4×C5911yescharacteristic
746C2×C4C2×#41×C5911yescharacteristic
747C2×C4C2×#41×C5911yescharacteristic
748C2×C4H(5,𝔽2)×C5911yescharacteristic
749C2×C4H(5,𝔽2)×C5911yescharacteristic
750C8—22no—
751C8—22no—
752C8—41no—
753C8—41no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22C2×#120×C5911yescharacteristic
776C22C59×#53211yescharacteristic
777C22C59×#53511yescharacteristic
778C22C59×#57611yescharacteristic
779C22C59×#57711yescharacteristic
780C22C59×#57711yescharacteristic
781C22C59×#57811yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4C59×#54611yescharacteristic
794C4C59×#54611yescharacteristic
795C4C59×#55011yescharacteristic
796C4C59×#55011yescharacteristic
797C2—81no—
798C2—82no—
799C2—161no—
800C2C59×#243111yescharacteristic
801C2C59×#301211yescharacteristic
802C2C59×#301311yescharacteristic
803C2C59×#317311yescharacteristic
804C2C59×#317511yescharacteristic
805C2C59×#322411yescharacteristic
806C2C59×#322511yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#542C2semidirect
2. C2×C59×#495C2semidirect
3. C2×C59×#489C2semidirect
4. C59×#2620C2semidirect
5. C59×#2001C2semidirect
6. C59×#2000C2semidirect
7. C59×#2000C2semidirect
9. C59×#1990C2semidirect
10. C59×#1959C2semidirect
11. C59×#1880C2semidirect
12. C59×#1879C2semidirect
13. C59×#1878C2semidirect
14. C59×#1877C2semidirect
15. C59×#1750C2semidirect
89. C4⋊Q8×C59D4semidirect
95. #124×C59D4semidirect
350. #25610C59direct (N × H)
394. C2×#542C2×C59semidirect
395. C2×#495C2×C59semidirect
396. C2×#489C2×C59semidirect
397. #2620C2×C59semidirect
398. #2001C2×C59semidirect
399. #2000C2×C59semidirect
400. #2000C2×C59semidirect
402. #1990C2×C59semidirect
403. #1959C2×C59semidirect
404. #1880C2×C59semidirect
405. #1879C2×C59semidirect
406. #1878C2×C59semidirect
407. #1877C2×C59semidirect
408. #1750C2×C59semidirect
466. C59#25610direct (N × H)
493. C4⋊Q8D4×C59semidirect
499. #124D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5422
C2×C59×#4952
C2×C59×#4892
C59×#26202
C59×#20012
C59×#20002
C59×#19992
C59×#19902
C59×#19592
C59×#18802
C59×#18792
C59×#18782
C59×#18772
C59×#17502
#2561059