Finite Group Databasebeta

← C59×#26720 #28438829

Subgroups — C59×#26720 #28438829

Order 15104.

910 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2491C211yesmaximal, characteristic, complemented
2C59×#2361C211yesmaximal, characteristic, complemented
3C59×#2054C211yesmaximal, characteristic, complemented
4C59×#2033C211yesmaximal, characteristic, complemented
5C59×#2023C211yesmaximal, characteristic, complemented
6C59×#1999C211yesmaximal, characteristic
7C59×#1988C211yesmaximal, characteristic, complemented
8C59×#1934C211yesmaximal, characteristic, complemented
9C59×#1925C211yesmaximal, characteristic, complemented
10C59×#1923C211yesmaximal, characteristic, complemented
11C59×#1918C211yesmaximal, characteristic, complemented
12C59×#1879C211yesmaximal, characteristic, complemented
13C59×#1874C211yesmaximal, characteristic, complemented
14C59×#1823C211yesmaximal, characteristic, complemented
15C4×#102×C59C211yesmaximal, characteristic, complemented
16C22×D8×C59C2211yescharacteristic
17C2×C4⋊Q8×C59C2211yescharacteristic
18C2×#124×C59—21no—
19C2×#121×C59C2211yescharacteristic
20C2×#121×C59C2211yescharacteristic
21C2×C4×D4×C59—21no—
22C2×C4×D4×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C2×#107×C59C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×#102×C59C2211yescharacteristic
27C2×#102×C59C2211yescharacteristic
28C2×#102×C59C2211yescharacteristic
29C2×#102×C59C2211yescharacteristic
30C2×#102×C59C2211yescharacteristic
31C2×#102×C59C2211yescharacteristic
32C2×C22⋊C8×C59C2211yescharacteristic
33C2×C22⋊C8×C59C2211yescharacteristic
34C2×C4×C8×C59C2211yescharacteristic
35C59×#394—21no—
36C59×#393—21no—
37C59×#390C2211yescharacteristic
38C59×#390C2211yescharacteristic
39C59×#390C2211yescharacteristic
40C59×#389C2211yescharacteristic
41C59×#388—21no—
42C59×#388—21no—
43C59×#386—21no—
44C59×#385—21no—
45C59×#380C2211yescharacteristic
46C4×C4⋊C4×C59C2211yescharacteristic
47C4×C4⋊C4×C59C2211yescharacteristic
48C4×C22⋊C4×C59C2211yescharacteristic
49C59×#340C2211yescharacteristic
50C59×#340C2211yescharacteristic
51C59×#340C2211yescharacteristic
52C59×#340C2211yescharacteristic
53C59×#340C2211yescharacteristic
54C59×#340C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×Q8×C59—21no—
60C22×D4×C59—21no—
61C22×D4×C59—21no—
62C22×D4×C59C2311yescharacteristic
63C22×D4×C59C2311yescharacteristic
64C23×C4×C59—21no—
65C23×C4×C59—21no—
66C23×C4×C59C2311yescharacteristic
67C2×D8×C59—22no—
68C2×D8×C59—41no—
69C2×D8×C59—41no—
70C22×C8×C59C2311yescharacteristic
71C22×C8×C59C2311yescharacteristic
72C22×C8×C59C2311yescharacteristic
73C22×C8×C59C2311yescharacteristic
74C4⋊Q8×C59—22no—
75C4⋊Q8×C59—41no—
76#124×C59—44no—
77#121×C59—22no—
78#121×C59—22no—
79#121×C59—22no—
80#121×C59—41no—
81C4×D4×C59—22no—
82C4×D4×C59—41no—
83C4×D4×C59—44no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—21no—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59—41no—
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C4⋊C4×C59C2311yescharacteristic
93C2×C4⋊C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59C2311yescharacteristic
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—21no—
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—21no—
100C2×C22⋊C4×C59—21no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59D411yescharacteristic
106C2×C22⋊C4×C59D411yescharacteristic
107C2×C42×C59—21no—
108C2×C42×C59—21no—
109C2×C42×C59C2311yescharacteristic
110C2×C42×C59C2311yescharacteristic
111#107×C59—22no—
112C4⋊C8×C59—41no—
113#102×C59—22no—
114#102×C59—22no—
115#102×C59—22no—
116#102×C59—22no—
117#102×C59—41no—
118#102×C59—41no—
119C22⋊C8×C59—41no—
120C22⋊C8×C59—41no—
121C4×C8×C59—41no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126#95×C59D411yescharacteristic
127#95×C59D411yescharacteristic
128C24×C59—21no—
129C24×C59—21no—
130C24×C59C2×D411yescharacteristic
131C2×Q8×C59—42no—
132C2×Q8×C59—42no—
133C2×Q8×C59—81no—
134C2×D4×C59—24no—
135C2×D4×C59—21no—
136C2×D4×C59—21no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—42no—
147C2×D4×C59—42no—
148C2×D4×C59—42no—
149C2×D4×C59—42no—
150C2×D4×C59—81no—
151C2×D4×C59#4112yes—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—42no—
165C22×C4×C59—42no—
166C22×C4×C59—42no—
167C22×C4×C59—42no—
168C22×C4×C59—81no—
169C22×C4×C59—81no—
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2411yescharacteristic
176D8×C59—44no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59—21no—
180C2×C8×C59—21no—
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—42no—
199C4⋊C4×C59—42no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59#4112yes—
202C4⋊C4×C59#4112yes—
203C4⋊C4×C59#4112yes—
204C22⋊C4×C59—24no—
205C22⋊C4×C59—41no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—42no—
209C22⋊C4×C59—42no—
210C22⋊C4×C59—42no—
211C22⋊C4×C59—42no—
212C22⋊C4×C59—42no—
213C22⋊C4×C59—81no—
214C22⋊C4×C59—81no—
215C22⋊C4×C59D814yescomplemented
216C42×C59—21no—
217C42×C59—21no—
218C42×C59—21no—
219C42×C59—21no—
220C42×C59—42no—
221C42×C59—42no—
222C23×C59—21no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59—21no—
228C23×C59—22no—
229C23×C59—41no—
230C23×C59—41no—
231C23×C59—41no—
232C23×C59—41no—
233C23×C59—41no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59C2×D812yes—
243C23×C59C22×D411yescharacteristic
244Q8×C59—84no—
245D4×C59—22no—
246D4×C59—22no—
247D4×C59—48no—
248D4×C59—41no—
249D4×C59—41no—
250D4×C59—41no—
251D4×C59—41no—
252D4×C59—41no—
253D4×C59—41no—
254D4×C59—84no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—84no—
291C2×C4×C59—84no—
292C2×C4×C59C2×D812yes—
293C2×C4×C59C2×D812yes—
294C2×C4×C59C2×#4111yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59C2×#4111yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C2×C4×C59H(5,𝔽2)11yescharacteristic
300C8×C59—41no—
301C8×C59—41no—
302C8×C59—41no—
303C8×C59—41no—
304#26720C5911yesmaximal, characteristic, direct product factor, Sylow
305C22×C59—22no—
306C22×C59—22no—
307C22×C59—22no—
308C22×C59—41no—
309C22×C59—41no—
310C22×C59—41no—
311C22×C59—41no—
312C22×C59—42no—
313C22×C59—42no—
314C22×C59—42no—
315C22×C59—81no—
316C22×C59—81no—
317C22×C59—81no—
318C22×C59—81no—
319C22×C59—81no—
320C22×C59—81no—
321C22×C59—81no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59#52511yescharacteristic
327C22×C59#54611yescharacteristic
328C22×C59#54611yescharacteristic
329C22×C59C22×D811yescharacteristic
330C22×C59#57511yescharacteristic
331C22×C59#57711yescharacteristic
332C22×C59#57711yescharacteristic
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—41no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59—41no—
340C4×C59—41no—
341C4×C59—81no—
342C4×C59—81no—
343C4×C59—81no—
344C4×C59#52911yescharacteristic
345C4×C59#53811yescharacteristic
346C4×C59#55511yescharacteristic
347C4×C59#55911yescharacteristic
348#2491C2×C5911yescharacteristic, complemented
349#2361C2×C5911yescharacteristic, complemented
350#2054C2×C5911yescharacteristic, complemented
351#2033C2×C5911yescharacteristic, complemented
352#2023C2×C5911yescharacteristic, complemented
353#1999C2×C5911yescharacteristic
354#1988C2×C5911yescharacteristic, complemented
355#1934C2×C5911yescharacteristic, complemented
356#1925C2×C5911yescharacteristic, complemented
357#1923C2×C5911yescharacteristic, complemented
358#1918C2×C5911yescharacteristic, complemented
359#1879C2×C5911yescharacteristic, complemented
360#1874C2×C5911yescharacteristic, complemented
361#1823C2×C5911yescharacteristic, complemented
362C4×#102C2×C5911yescharacteristic, complemented
363C2×C59—42no—
364C2×C59—82no—
365C2×C59—161no—
366C2×C59#245911yescharacteristic
367C2×C59#310011yescharacteristic
368C2×C59#312511yescharacteristic
369C2×C59#329411yescharacteristic
370C2×C59#329411yescharacteristic
371C2×C59#332111yescharacteristic
372C2×C59#332611yescharacteristic
373C22×D8C22×C5911yescharacteristic
374C2×C4⋊Q8C22×C5911yescharacteristic
375C2×#124—21no—
376C2×#121C22×C5911yescharacteristic
377C2×#121C22×C5911yescharacteristic
378C2×C4×D4—21no—
379C2×C4×D4C22×C5911yescharacteristic
380C22×C4⋊C4C22×C5911yescharacteristic
381C2×#107C22×C5911yescharacteristic
382C2×C4⋊C8C22×C5911yescharacteristic
383C2×#102C22×C5911yescharacteristic
384C2×#102C22×C5911yescharacteristic
385C2×#102C22×C5911yescharacteristic
386C2×#102C22×C5911yescharacteristic
387C2×#102C22×C5911yescharacteristic
388C2×#102C22×C5911yescharacteristic
389C2×C22⋊C8C22×C5911yescharacteristic
390C2×C22⋊C8C22×C5911yescharacteristic
391C2×C4×C8C22×C5911yescharacteristic
392#394—21no—
393#393—21no—
394#390C22×C5911yescharacteristic
395#390C22×C5911yescharacteristic
396#390C22×C5911yescharacteristic
397#389C22×C5911yescharacteristic
398#388—21no—
399#388—21no—
400#386—21no—
401#385—21no—
402#380C22×C5911yescharacteristic
403C4×C4⋊C4C22×C5911yescharacteristic
404C4×C4⋊C4C22×C5911yescharacteristic
405C4×C22⋊C4C22×C5911yescharacteristic
406#340C22×C5911yescharacteristic
407#340C22×C5911yescharacteristic
408#340C22×C5911yescharacteristic
409#340C22×C5911yescharacteristic
410#340C22×C5911yescharacteristic
411#340C22×C5911yescharacteristic
412#340C22×C5911yescharacteristic
413#340C22×C5911yescharacteristic
414#336C22×C5911yescharacteristic
415#336C22×C5911yescharacteristic
416C59#2672011yescharacteristic, direct product factor, Sylow
417C22×Q8—21no—
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C23×C5911yescharacteristic
421C22×D4C23×C5911yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C23×C5911yescharacteristic
425C2×D8—22no—
426C2×D8—41no—
427C2×D8—41no—
428C22×C8C23×C5911yescharacteristic
429C22×C8C23×C5911yescharacteristic
430C22×C8C23×C5911yescharacteristic
431C22×C8C23×C5911yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434#124—44no—
435#121—22no—
436#121—22no—
437#121—22no—
438#121—41no—
439C4×D4—22no—
440C4×D4—41no—
441C4×D4—44no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4C23×C5911yescharacteristic
448C2×C4⋊C4C23×C5911yescharacteristic
449C2×C4⋊C4C23×C5911yescharacteristic
450C2×C4⋊C4C23×C5911yescharacteristic
451C2×C4⋊C4C23×C5911yescharacteristic
452C2×C4⋊C4C23×C5911yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C5911yescharacteristic
464C2×C22⋊C4D4×C5911yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C5911yescharacteristic
468C2×C42C23×C5911yescharacteristic
469#107—22no—
470C4⋊C8—41no—
471#102—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—41no—
476#102—41no—
477C22⋊C8—41no—
478C22⋊C8—41no—
479C4×C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C5911yescharacteristic
485#95D4×C5911yescharacteristic
486C24—21no—
487C24—21no—
488C24C2×D4×C5911yescharacteristic
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—81no—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—81no—
509C2×D4#41×C5912yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×D4×C5911yescharacteristic
529C22×C4C2×D4×C5911yescharacteristic
530C22×C4C2×D4×C5911yescharacteristic
531C22×C4C2×D4×C5911yescharacteristic
532C22×C4C2×D4×C5911yescharacteristic
533C22×C4C24×C5911yescharacteristic
534D8—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4#41×C5912yes—
560C4⋊C4#41×C5912yes—
561C4⋊C4#41×C5912yes—
562C22⋊C4—24no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4D8×C5914yescomplemented
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C42—42no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×D8×C5912yes—
601C23C22×D4×C5911yescharacteristic
602Q8—84no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4C2×D8×C5912yes—
651C2×C4C2×D8×C5912yes—
652C2×C4C2×#41×C5911yescharacteristic
653C2×C4C2×#41×C5911yescharacteristic
654C2×C4C2×#41×C5911yescharacteristic
655C2×C4C2×#41×C5911yescharacteristic
656C2×C4H(5,𝔽2)×C5911yescharacteristic
657C2×C4H(5,𝔽2)×C5911yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C59×#52511yescharacteristic
684C22C59×#54611yescharacteristic
685C22C59×#54611yescharacteristic
686C22C22×D8×C5911yescharacteristic
687C22C59×#57511yescharacteristic
688C22C59×#57711yescharacteristic
689C22C59×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C59×#52911yescharacteristic
702C4C59×#53811yescharacteristic
703C4C59×#55511yescharacteristic
704C4C59×#55911yescharacteristic
705C2—42no—
706C2—82no—
707C2—161no—
708C2C59×#245911yescharacteristic
709C2C59×#310011yescharacteristic
710C2C59×#312511yescharacteristic
711C2C59×#329411yescharacteristic
712C2C59×#329411yescharacteristic
713C2C59×#332111yescharacteristic
714C2C59×#332611yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC59×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2491C2semidirect
2. C59×#2361C2semidirect
3. C59×#2054C2semidirect
4. C59×#2033C2semidirect
5. C59×#2023C2semidirect
7. C59×#1988C2semidirect
8. C59×#1934C2semidirect
9. C59×#1925C2semidirect
10. C59×#1923C2semidirect
11. C59×#1918C2semidirect
12. C59×#1879C2semidirect
13. C59×#1874C2semidirect
14. C59×#1823C2semidirect
15. C4×#102×C59C2semidirect
215. C22⋊C4×C59D8semidirect
304. #26720C59direct (N × H)
348. #2491C2×C59semidirect
349. #2361C2×C59semidirect
350. #2054C2×C59semidirect
351. #2033C2×C59semidirect
352. #2023C2×C59semidirect
354. #1988C2×C59semidirect
355. #1934C2×C59semidirect
356. #1925C2×C59semidirect
357. #1923C2×C59semidirect
358. #1918C2×C59semidirect
359. #1879C2×C59semidirect
360. #1874C2×C59semidirect
361. #1823C2×C59semidirect
362. C4×#102C2×C59semidirect
416. C59#26720direct (N × H)
573. C22⋊C4D8×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#24912
C59×#23612
C59×#20542
C59×#20332
C59×#20232
C59×#19992
C59×#19882
C59×#19342
C59×#19252
C59×#19232
C59×#19182
C59×#18792
C59×#18742
C59×#18232
C4×#102×C592
#2672059