Finite Group Databasebeta

← C59×#23580 #28435689

Subgroups — C59×#23580 #28435689

Order 15104.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#540C211yesmaximal, characteristic, complemented
2C2×C59×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C59C211yesmaximal, characteristic, complemented
4C59×#2324C211yesmaximal, characteristic, complemented
5C59×#2059C211yesmaximal, characteristic, complemented
6C59×#2041C211yesmaximal, characteristic, complemented
7C59×#2034C211yesmaximal, characteristic, complemented
8C59×#2033C211yesmaximal, characteristic, complemented
9C59×#2025C211yesmaximal, characteristic, complemented
10C59×#2011C211yesmaximal, characteristic, complemented
11C59×#1999C211yesmaximal, characteristic, complemented
12C59×#1999C211yesmaximal, characteristic, complemented
13C59×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C59C211yesmaximal, characteristic, complemented
15C59×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C59C2211yescharacteristic
17C22×D8×C59C2211yescharacteristic
18C59×#540—24no—
19C59×#540—24no—
20C2×#127×C59C2211yescharacteristic
21C2×#125×C59C2211yescharacteristic
22C2×#123×C59—21no—
23C2×#123×C59—21no—
24C2×#121×C59—21no—
25C2×#121×C59—21no—
26C2×#121×C59C2211yescharacteristic
27C2×#121×C59C2211yescharacteristic
28C2×#121×C59C2211yescharacteristic
29C2×C4×D4×C59C2211yescharacteristic
30C2×C4×D4×C59C2211yescharacteristic
31C2×C4×D4×C59C2211yescharacteristic
32C2×#117×C59C2211yescharacteristic
33C59×#442—24no—
34C4×D8×C59—24no—
35C2×#107×C59C2211yescharacteristic
36C2×#106×C59C2211yescharacteristic
37C2×#102×C59C2211yescharacteristic
38C2×#102×C59C2211yescharacteristic
39C2×#102×C59C2211yescharacteristic
40C2×#102×C59C2211yescharacteristic
41C2×#102×C59C2211yescharacteristic
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×C22⋊C8×C59C2211yescharacteristic
46C2×C22⋊C8×C59C2211yescharacteristic
47C2×#97×C59C2211yescharacteristic
48C2×C4×C8×C59C2211yescharacteristic
49C59×#390—21no—
50C59×#390C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#388—21no—
53C59×#386—21no—
54C59×#385—21no—
55C59×#380C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×D4×C59—21no—
64C22×D4×C59—21no—
65C22×D4×C59—21no—
66C22×D4×C59—21no—
67C22×D4×C59—21no—
68C22×D4×C59C2311yescharacteristic
69C22×D4×C59C2311yescharacteristic
70C22×D4×C59C2311yescharacteristic
71C23×C4×C59—21no—
72C23×C4×C59—21no—
73C23×C4×C59—21no—
74C23×C4×C59C2311yescharacteristic
75C2×D8×C59—22no—
76C2×D8×C59—22no—
77C2×D8×C59—22no—
78C2×D8×C59—22no—
79C2×D8×C59—22no—
80C2×D8×C59—22no—
81C22×C8×C59C2311yescharacteristic
82C22×C8×C59C2311yescharacteristic
83C22×C8×C59C2311yescharacteristic
84C22×C8×C59C2311yescharacteristic
85#127×C59—22no—
86#127×C59—22no—
87#125×C59—22no—
88#125×C59—22no—
89#123×C59—28no—
90#123×C59—28no—
91#121×C59—28no—
92#121×C59—28no—
93#121×C59—22no—
94#121×C59—22no—
95#121×C59—22no—
96#121×C59—22no—
97#121×C59—22no—
98#121×C59—22no—
99C4×D4×C59—22no—
100C4×D4×C59—22no—
101C4×D4×C59—22no—
102C4×D4×C59—22no—
103C4×D4×C59D414yescomplemented
104C4×D4×C59D414yescomplemented
105#117×C59—22no—
106#117×C59—22no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59—21no—
110C2×C4⋊C4×C59D411yescharacteristic
111C2×C4⋊C4×C59D411yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C22⋊C4×C59—21no—
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59—21no—
129C2×C42×C59C2311yescharacteristic
130C2×C42×C59C2311yescharacteristic
131#107×C59—22no—
132#106×C59—22no—
133#102×C59—22no—
134#102×C59—22no—
135#102×C59—22no—
136#102×C59—22no—
137#102×C59—22no—
138#102×C59—22no—
139#102×C59—22no—
140#102×C59—22no—
141C22⋊C8×C59—22no—
142C22⋊C8×C59—22no—
143#97×C59—22no—
144C4×C8×C59—22no—
145#95×C59—21no—
146#95×C59—21no—
147#95×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59C2×D411yescharacteristic
152C2×D4×C59—24no—
153C2×D4×C59—24no—
154C2×D4×C59—24no—
155C2×D4×C59—24no—
156C2×D4×C59—24no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—21no—
172C2×D4×C59—81no—
173C2×D4×C59—81no—
174C2×D4×C59—81no—
175C2×D4×C59—81no—
176C2×D4×C59—81no—
177C2×D4×C59—81no—
178C2×D4×C59—81no—
179C2×D4×C59—81no—
180C2×D4×C59—81no—
181C2×D4×C59—81no—
182C2×D4×C59C2×D412yes—
183C2×D4×C59C2×D412yes—
184C2×D4×C59#4112yes—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—24no—
195C22×C4×C59—24no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—42no—
199C22×C4×C59—81no—
200C22×C4×C59—81no—
201C22×C4×C59—81no—
202C22×C4×C59—81no—
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
211D8×C59—28no—
212D8×C59—28no—
213C2×C8×C59—21no—
214C2×C8×C59—21no—
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#4112yes—
224C2×C8×C59#4112yes—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—22no—
228C4⋊C4×C59—22no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—81no—
237C4⋊C4×C59C2×D412yes—
238C4⋊C4×C59C2×D412yes—
239C4⋊C4×C59#4112yes—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—22no—
246C22⋊C4×C59—22no—
247C22⋊C4×C59—42no—
248C22⋊C4×C59—81no—
249C22⋊C4×C59—81no—
250C22⋊C4×C59—81no—
251C42×C59—21no—
252C42×C59—21no—
253C42×C59—81no—
254C42×C59C2×D412yes—
255C42×C59C2×D412yes—
256C23×C59—21no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
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×C59—41no—
283C23×C59—41no—
284C23×C59C22×D411yescharacteristic
285D4×C59—22no—
286D4×C59—22no—
287D4×C59—22no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—41no—
292D4×C59—41no—
293D4×C59—41no—
294D4×C59—41no—
295D4×C59—41no—
296D4×C59—41no—
297D4×C59—84no—
298D4×C59—84no—
299D4×C59—84no—
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—21no—
308C2×C4×C59—21no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—21no—
312C2×C4×C59—22no—
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—84no—
335C2×C4×C59—84no—
336C2×C4×C59—84no—
337C2×C4×C59#12012yes—
338C2×C4×C59#12012yes—
339C2×C4×C59C22×D411yescharacteristic
340C2×C4×C59C22×D411yescharacteristic
341C2×C4×C59C2×#4111yescharacteristic
342C2×C4×C59C2×#4111yescharacteristic
343C2×C4×C59C2×#4111yescharacteristic
344C2×C4×C59C2×#4111yescharacteristic
345C8×C59—22no—
346C8×C59—22no—
347C8×C59—41no—
348C8×C59—41no—
349#23580C5911yesmaximal, characteristic, direct product factor, Sylow
350C22×C59—41no—
351C22×C59—42no—
352C22×C59—41no—
353C22×C59—42no—
354C22×C59—41no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—42no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—42no—
361C22×C59—41no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—41no—
365C22×C59—42no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—81no—
369C22×C59—81no—
370C22×C59—81no—
371C22×C59—81no—
372C22×C59—81no—
373C22×C59—81no—
374C22×C59—81no—
375C22×C59—81no—
376C22×C59—81no—
377C22×C59—81no—
378C22×C59C2×#12011yescharacteristic
379C22×C59#52511yescharacteristic
380C22×C59#53211yescharacteristic
381C22×C59#57611yescharacteristic
382C22×C59#57611yescharacteristic
383C22×C59#57611yescharacteristic
384C22×C59#57711yescharacteristic
385C4×C59—22no—
386C4×C59—22no—
387C4×C59—42no—
388C4×C59—41no—
389C4×C59—41no—
390C4×C59—42no—
391C4×C59—41no—
392C4×C59—42no—
393C4×C59—81no—
394C4×C59—81no—
395C4×C59#52511yescharacteristic
396C4×C59#52511yescharacteristic
397C4×C59#53211yescharacteristic
398C4×C59#53211yescharacteristic
399C2×#540C2×C5911yescharacteristic, complemented
400C2×#442C2×C5911yescharacteristic, complemented
401C2×C4×D8C2×C5911yescharacteristic, complemented
402#2324C2×C5911yescharacteristic, complemented
403#2059C2×C5911yescharacteristic, complemented
404#2041C2×C5911yescharacteristic, complemented
405#2034C2×C5911yescharacteristic, complemented
406#2033C2×C5911yescharacteristic, complemented
407#2025C2×C5911yescharacteristic, complemented
408#2011C2×C5911yescharacteristic, complemented
409#1999C2×C5911yescharacteristic, complemented
410#1999C2×C5911yescharacteristic, complemented
411#1762C2×C5911yescharacteristic, complemented
412C4×#102C2×C5911yescharacteristic, complemented
413#1750C2×C5911yescharacteristic, complemented
414C2×C59—81no—
415C2×C59—82no—
416C2×C59—82no—
417C2×C59—82no—
418C2×C59#238811yescharacteristic
419C2×C59#300811yescharacteristic
420C2×C59#301211yescharacteristic
421C2×C59#311911yescharacteristic
422C2×C59#312211yescharacteristic
423C2×C59#317611yescharacteristic
424C2×C59#317911yescharacteristic
425C22×D8C22×C5911yescharacteristic
426C22×D8C22×C5911yescharacteristic
427#540—24no—
428#540—24no—
429C2×#127C22×C5911yescharacteristic
430C2×#125C22×C5911yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C5911yescharacteristic
436C2×#121C22×C5911yescharacteristic
437C2×#121C22×C5911yescharacteristic
438C2×C4×D4C22×C5911yescharacteristic
439C2×C4×D4C22×C5911yescharacteristic
440C2×C4×D4C22×C5911yescharacteristic
441C2×#117C22×C5911yescharacteristic
442#442—24no—
443C4×D8—24no—
444C2×#107C22×C5911yescharacteristic
445C2×#106C22×C5911yescharacteristic
446C2×#102C22×C5911yescharacteristic
447C2×#102C22×C5911yescharacteristic
448C2×#102C22×C5911yescharacteristic
449C2×#102C22×C5911yescharacteristic
450C2×#102C22×C5911yescharacteristic
451C2×#102C22×C5911yescharacteristic
452C2×#102C22×C5911yescharacteristic
453C2×#102C22×C5911yescharacteristic
454C2×C22⋊C8C22×C5911yescharacteristic
455C2×C22⋊C8C22×C5911yescharacteristic
456C2×#97C22×C5911yescharacteristic
457C2×C4×C8C22×C5911yescharacteristic
458#390—21no—
459#390C22×C5911yescharacteristic
460#389C22×C5911yescharacteristic
461#388—21no—
462#386—21no—
463#385—21no—
464#380C22×C5911yescharacteristic
465C4×C4⋊C4C22×C5911yescharacteristic
466#340C22×C5911yescharacteristic
467#340C22×C5911yescharacteristic
468#340C22×C5911yescharacteristic
469#340C22×C5911yescharacteristic
470#336C22×C5911yescharacteristic
471#336C22×C5911yescharacteristic
472C59#2358011yescharacteristic, direct product factor, Sylow
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C5911yescharacteristic
479C22×D4C23×C5911yescharacteristic
480C22×D4C23×C5911yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C5911yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C5911yescharacteristic
492C22×C8C23×C5911yescharacteristic
493C22×C8C23×C5911yescharacteristic
494C22×C8C23×C5911yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C5914yescomplemented
514C4×D4D4×C5914yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C5911yescharacteristic
521C2×C4⋊C4D4×C5911yescharacteristic
522C2×C4⋊C4C23×C5911yescharacteristic
523C2×C4⋊C4C23×C5911yescharacteristic
524C2×C4⋊C4C23×C5911yescharacteristic
525C2×C4⋊C4C23×C5911yescharacteristic
526C2×C4⋊C4C23×C5911yescharacteristic
527C2×C22⋊C4—21no—
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⋊C4D4×C5911yescharacteristic
537C2×C22⋊C4D4×C5911yescharacteristic
538C2×C42—21no—
539C2×C42C23×C5911yescharacteristic
540C2×C42C23×C5911yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C5911yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C5912yes—
593C2×D4C2×D4×C5912yes—
594C2×D4#41×C5912yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C5911yescharacteristic
616C22×C4C2×D4×C5911yescharacteristic
617C22×C4C2×D4×C5911yescharacteristic
618C22×C4C2×D4×C5911yescharacteristic
619C22×C4C2×D4×C5911yescharacteristic
620C22×C4C24×C5911yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C5912yes—
634C2×C8#41×C5912yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C5912yes—
648C4⋊C4C2×D4×C5912yes—
649C4⋊C4#41×C5912yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C5912yes—
665C42C2×D4×C5912yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C5911yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C5912yes—
748C2×C4#120×C5912yes—
749C2×C4C22×D4×C5911yescharacteristic
750C2×C4C22×D4×C5911yescharacteristic
751C2×C4C2×#41×C5911yescharacteristic
752C2×C4C2×#41×C5911yescharacteristic
753C2×C4C2×#41×C5911yescharacteristic
754C2×C4C2×#41×C5911yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C5911yescharacteristic
788C22C59×#52511yescharacteristic
789C22C59×#53211yescharacteristic
790C22C59×#57611yescharacteristic
791C22C59×#57611yescharacteristic
792C22C59×#57611yescharacteristic
793C22C59×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—81no—
803C4—81no—
804C4C59×#52511yescharacteristic
805C4C59×#52511yescharacteristic
806C4C59×#53211yescharacteristic
807C4C59×#53211yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C59×#238811yescharacteristic
813C2C59×#300811yescharacteristic
814C2C59×#301211yescharacteristic
815C2C59×#311911yescharacteristic
816C2C59×#312211yescharacteristic
817C2C59×#317611yescharacteristic
818C2C59×#317911yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
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×#540C2semidirect
2. C2×C59×#442C2semidirect
3. C2×C4×D8×C59C2semidirect
4. C59×#2324C2semidirect
5. C59×#2059C2semidirect
6. C59×#2041C2semidirect
7. C59×#2034C2semidirect
8. C59×#2033C2semidirect
9. C59×#2025C2semidirect
10. C59×#2011C2semidirect
11. C59×#1999C2semidirect
12. C59×#1999C2semidirect
13. C59×#1762C2semidirect
14. C4×#102×C59C2semidirect
15. C59×#1750C2semidirect
103. C4×D4×C59D4semidirect
104. C4×D4×C59D4semidirect
349. #23580C59direct (N × H)
399. C2×#540C2×C59semidirect
400. C2×#442C2×C59semidirect
401. C2×C4×D8C2×C59semidirect
402. #2324C2×C59semidirect
403. #2059C2×C59semidirect
404. #2041C2×C59semidirect
405. #2034C2×C59semidirect
406. #2033C2×C59semidirect
407. #2025C2×C59semidirect
408. #2011C2×C59semidirect
409. #1999C2×C59semidirect
410. #1999C2×C59semidirect
411. #1762C2×C59semidirect
412. C4×#102C2×C59semidirect
413. #1750C2×C59semidirect
472. C59#23580direct (N × H)
513. C4×D4D4×C59semidirect
514. 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×#5402
C2×C59×#4422
C2×C4×D8×C592
C59×#23242
C59×#20592
C59×#20412
C59×#20342
C59×#20332
C59×#20252
C59×#20112
C59×#19992
C59×#17622
C4×#102×C592
C59×#17502
#2358059