Finite Group Databasebeta

← C59×#24847 #28436956

Subgroups — C59×#24847 #28436956

Order 15104.

852 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#474C211yesmaximal, characteristic, complemented
2C2×C59×#424C211yesmaximal, characteristic, complemented
3C59×#2628C211yesmaximal, characteristic, complemented
4C59×#2324C211yesmaximal, characteristic
5C59×#2087C211yesmaximal, characteristic, complemented
6C59×#2086C211yesmaximal, characteristic, complemented
7C59×#2067C211yesmaximal, characteristic, complemented
8C59×#2065C211yesmaximal, characteristic, complemented
9C59×#1987C211yesmaximal, characteristic, complemented
10C59×#1949C211yesmaximal, characteristic, complemented
11C59×#1895C211yesmaximal, characteristic
12C59×#1893C211yesmaximal, characteristic
13C59×#1809C211yesmaximal, characteristic, complemented
14C59×#1808C211yesmaximal, characteristic, complemented
15C59×#1804C211yesmaximal, characteristic, complemented
16C22×M16×C59C2211yescharacteristic
17C23×C8×C59C2211yescharacteristic
18C2×C4⋊Q8×C59C2211yescharacteristic
19C2×#121×C59C2211yescharacteristic
20C2×C4×D4×C59C2211yescharacteristic
21C2×#117×C59C2211yescharacteristic
22C59×#474—24no—
23C2×#107×C59C2211yescharacteristic
24C2×#107×C59C2211yescharacteristic
25C2×#107×C59C2211yescharacteristic
26C2×#106×C59C2211yescharacteristic
27C59×#424—24no—
28C2×C4⋊C8×C59C2211yescharacteristic
29C2×C4⋊C8×C59C2211yescharacteristic
30C2×C4⋊C8×C59C2211yescharacteristic
31C2×C4⋊C8×C59C2211yescharacteristic
32C2×#102×C59C2211yescharacteristic
33C2×#102×C59C2211yescharacteristic
34C2×#102×C59C2211yescharacteristic
35C2×#102×C59C2211yescharacteristic
36C59×#400—21no—
37C59×#399—21no—
38C59×#395—21no—
39C59×#393—21no—
40C59×#390—21no—
41C59×#390C2211yescharacteristic
42C59×#389C2211yescharacteristic
43C59×#389C2211yescharacteristic
44C59×#389C2211yescharacteristic
45C59×#388—21no—
46C59×#386—21no—
47C59×#385—21no—
48C59×#382C2211yescharacteristic
49C59×#380C2211yescharacteristic
50C59×#380C2211yescharacteristic
51C59×#380C2211yescharacteristic
52C4×C4⋊C4×C59C2211yescharacteristic
53C59×#340C2211yescharacteristic
54C59×#340C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C22×Q8×C59—21no—
62C22×D4×C59—21no—
63C22×D4×C59C2311yescharacteristic
64C23×C4×C59—21no—
65C23×C4×C59C2311yescharacteristic
66C2×M16×C59—22no—
67C2×M16×C59—22no—
68C2×M16×C59—41no—
69C22×C8×C59—22no—
70C22×C8×C59—22no—
71C22×C8×C59—41no—
72C22×C8×C59C2311yescharacteristic
73C22×C8×C59C2311yescharacteristic
74C22×C8×C59C2311yescharacteristic
75C22×C8×C59C2311yescharacteristic
76C4⋊Q8×C59—22no—
77C4⋊Q8×C59—22no—
78#121×C59—22no—
79#121×C59Q814yescomplemented
80C4×D4×C59—22no—
81C4×D4×C59—22no—
82#117×C59—22no—
83#117×C59—22no—
84C2×C4⋊C4×C59—21no—
85C2×C4⋊C4×C59—21no—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59D411yescharacteristic
89C2×C4⋊C4×C59D411yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C4⋊C4×C59C2311yescharacteristic
93C2×C4⋊C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59C2311yescharacteristic
95C2×C4⋊C4×C59C2311yescharacteristic
96C2×C4⋊C4×C59C2311yescharacteristic
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×C59D411yescharacteristic
105C2×C22⋊C4×C59D411yescharacteristic
106C2×C42×C59—21no—
107C2×C42×C59C2311yescharacteristic
108C2×C42×C59C2311yescharacteristic
109#107×C59—22no—
110#107×C59—22no—
111#107×C59—41no—
112#106×C59—41no—
113C4⋊C8×C59—22no—
114C4⋊C8×C59—22no—
115C4⋊C8×C59—22no—
116C4⋊C8×C59D414yescomplemented
117#102×C59—22no—
118#102×C59—22no—
119#102×C59—41no—
120#102×C59—41no—
121#95×C59—21no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126#95×C59—21no—
127#95×C59—21no—
128#95×C59—21no—
129#95×C59—21no—
130C24×C59—21no—
131C24×C59C2×D411yescharacteristic
132C2×Q8×C59—42no—
133C2×Q8×C59—81no—
134C2×Q8×C59—81no—
135C2×D4×C59—24no—
136C2×D4×C59—21no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—81no—
142C2×D4×C59—81no—
143C2×D4×C59C2×Q812yes—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—42no—
156C22×C4×C59—81no—
157C22×C4×C59—81no—
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×Q812yes—
164C22×C4×C59#4112yes—
165C22×C4×C59C2411yescharacteristic
166M16×C59—44no—
167C2×C8×C59—21no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—44no—
178C2×C8×C59C2×D412yes—
179C2×C8×C59C2×D412yes—
180C4⋊C4×C59—22no—
181C4⋊C4×C59—22no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×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—42no—
196C4⋊C4×C59—81no—
197C4⋊C4×C59—81no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C2×Q812yes—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—24no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—81no—
205C22⋊C4×C59—81no—
206C22⋊C4×C59—81no—
207C22⋊C4×C59—81no—
208C22⋊C4×C59—81no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—81no—
212C42×C59C2×D412yes—
213C42×C59#4112yes—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—22no—
221C23×C59—41no—
222C23×C59—41no—
223C23×C59—41no—
224C23×C59—41no—
225C23×C59—41no—
226C23×C59—41no—
227C23×C59C22⋊Q812yes—
228C23×C59C22×D411yescharacteristic
229Q8×C59—84no—
230D4×C59—22no—
231D4×C59—22no—
232D4×C59—41no—
233D4×C59—41no—
234D4×C59—84no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—22no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—41no—
253C2×C4×C59—41no—
254C2×C4×C59—41no—
255C2×C4×C59—41no—
256C2×C4×C59—41no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—84no—
273C2×C4×C59#12112yes—
274C2×C4×C59#12112yes—
275C2×C4×C59C22⋊Q812yes—
276C2×C4×C59C22×D411yescharacteristic
277C2×C4×C59C22×Q811yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×C4×C59H(5,𝔽2)11yescharacteristic
281C2×C4×C592−1+411yescharacteristic
282C8×C59—22no—
283C8×C59—22no—
284C8×C59—41no—
285C8×C59—41no—
286#24847C5911yesmaximal, characteristic, direct product factor, Sylow
287C22×C59—22no—
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—41no—
291C22×C59—41no—
292C22×C59—41no—
293C22×C59—41no—
294C22×C59—42no—
295C22×C59—42no—
296C22×C59—42no—
297C22×C59—81no—
298C22×C59—81no—
299C22×C59—81no—
300C22×C59—81no—
301C22×C59C2×#12111yescharacteristic
302C22×C59C2×C22⋊Q811yescharacteristic
303C22×C59#53711yescharacteristic
304C22×C59#57611yescharacteristic
305C22×C59#57611yescharacteristic
306C22×C59#57711yescharacteristic
307C22×C59#57811yescharacteristic
308C4×C59—22no—
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—42no—
312C4×C59—41no—
313C4×C59—41no—
314C4×C59—81no—
315C4×C59—81no—
316C4×C59—81no—
317C4×C59—81no—
318C4×C59—81no—
319C4×C59—81no—
320C4×C59#54611yescharacteristic
321C4×C59D4×Q811yescharacteristic
322C4×C59#55211yescharacteristic
323C4×C59#55411yescharacteristic
324C2×#474C2×C5911yescharacteristic, complemented
325C2×#424C2×C5911yescharacteristic, complemented
326#2628C2×C5911yescharacteristic, complemented
327#2324C2×C5911yescharacteristic
328#2087C2×C5911yescharacteristic, complemented
329#2086C2×C5911yescharacteristic, complemented
330#2067C2×C5911yescharacteristic, complemented
331#2065C2×C5911yescharacteristic, complemented
332#1987C2×C5911yescharacteristic, complemented
333#1949C2×C5911yescharacteristic, complemented
334#1895C2×C5911yescharacteristic
335#1893C2×C5911yescharacteristic
336#1809C2×C5911yescharacteristic, complemented
337#1808C2×C5911yescharacteristic, complemented
338#1804C2×C5911yescharacteristic, complemented
339C2×C59—42no—
340C2×C59—82no—
341C2×C59#241711yescharacteristic
342C2×C59#305811yescharacteristic
343C2×C59#306311yescharacteristic
344C2×C59#308111yescharacteristic
345C2×C59#308311yescharacteristic
346C2×C59#325711yescharacteristic
347C2×C59#326211yescharacteristic
348C22×M16C22×C5911yescharacteristic
349C23×C8C22×C5911yescharacteristic
350C2×C4⋊Q8C22×C5911yescharacteristic
351C2×#121C22×C5911yescharacteristic
352C2×C4×D4C22×C5911yescharacteristic
353C2×#117C22×C5911yescharacteristic
354#474—24no—
355C2×#107C22×C5911yescharacteristic
356C2×#107C22×C5911yescharacteristic
357C2×#107C22×C5911yescharacteristic
358C2×#106C22×C5911yescharacteristic
359#424—24no—
360C2×C4⋊C8C22×C5911yescharacteristic
361C2×C4⋊C8C22×C5911yescharacteristic
362C2×C4⋊C8C22×C5911yescharacteristic
363C2×C4⋊C8C22×C5911yescharacteristic
364C2×#102C22×C5911yescharacteristic
365C2×#102C22×C5911yescharacteristic
366C2×#102C22×C5911yescharacteristic
367C2×#102C22×C5911yescharacteristic
368#400—21no—
369#399—21no—
370#395—21no—
371#393—21no—
372#390—21no—
373#390C22×C5911yescharacteristic
374#389C22×C5911yescharacteristic
375#389C22×C5911yescharacteristic
376#389C22×C5911yescharacteristic
377#388—21no—
378#386—21no—
379#385—21no—
380#382C22×C5911yescharacteristic
381#380C22×C5911yescharacteristic
382#380C22×C5911yescharacteristic
383#380C22×C5911yescharacteristic
384C4×C4⋊C4C22×C5911yescharacteristic
385#340C22×C5911yescharacteristic
386#340C22×C5911yescharacteristic
387#340C22×C5911yescharacteristic
388#340C22×C5911yescharacteristic
389#340C22×C5911yescharacteristic
390#340C22×C5911yescharacteristic
391#340C22×C5911yescharacteristic
392#340C22×C5911yescharacteristic
393C59#2484711yescharacteristic, direct product factor, Sylow
394C22×Q8—21no—
395C22×D4—21no—
396C22×D4C23×C5911yescharacteristic
397C23×C4—21no—
398C23×C4C23×C5911yescharacteristic
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—41no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—41no—
405C22×C8C23×C5911yescharacteristic
406C22×C8C23×C5911yescharacteristic
407C22×C8C23×C5911yescharacteristic
408C22×C8C23×C5911yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—22no—
411#121—22no—
412#121Q8×C5914yescomplemented
413C4×D4—22no—
414C4×D4—22no—
415#117—22no—
416#117—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4D4×C5911yescharacteristic
422C2×C4⋊C4D4×C5911yescharacteristic
423C2×C4⋊C4C23×C5911yescharacteristic
424C2×C4⋊C4C23×C5911yescharacteristic
425C2×C4⋊C4C23×C5911yescharacteristic
426C2×C4⋊C4C23×C5911yescharacteristic
427C2×C4⋊C4C23×C5911yescharacteristic
428C2×C4⋊C4C23×C5911yescharacteristic
429C2×C4⋊C4C23×C5911yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4D4×C5911yescharacteristic
438C2×C22⋊C4D4×C5911yescharacteristic
439C2×C42—21no—
440C2×C42C23×C5911yescharacteristic
441C2×C42C23×C5911yescharacteristic
442#107—22no—
443#107—22no—
444#107—41no—
445#106—41no—
446C4⋊C8—22no—
447C4⋊C8—22no—
448C4⋊C8—22no—
449C4⋊C8D4×C5914yescomplemented
450#102—22no—
451#102—22no—
452#102—41no—
453#102—41no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463C24—21no—
464C24C2×D4×C5911yescharacteristic
465C2×Q8—42no—
466C2×Q8—81no—
467C2×Q8—81no—
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4C2×Q8×C5912yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4C2×D4×C5911yescharacteristic
492C22×C4C2×D4×C5911yescharacteristic
493C22×C4C2×D4×C5911yescharacteristic
494C22×C4C2×D4×C5911yescharacteristic
495C22×C4C2×D4×C5911yescharacteristic
496C22×C4C2×Q8×C5912yes—
497C22×C4#41×C5912yes—
498C22×C4C24×C5911yescharacteristic
499M16—44no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—44no—
511C2×C8C2×D4×C5912yes—
512C2×C8C2×D4×C5912yes—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4—81no—
532C4⋊C4C2×Q8×C5912yes—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C42—21no—
543C42—21no—
544C42—81no—
545C42C2×D4×C5912yes—
546C42#41×C5912yes—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—22no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23C22⋊Q8×C5912yes—
561C23C22×D4×C5911yescharacteristic
562Q8—84no—
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—84no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4#121×C5912yes—
607C2×C4#121×C5912yes—
608C2×C4C22⋊Q8×C5912yes—
609C2×C4C22×D4×C5911yescharacteristic
610C2×C4C22×Q8×C5911yescharacteristic
611C2×C4C2×#41×C5911yescharacteristic
612C2×C4C2×#41×C5911yescharacteristic
613C2×C4H(5,𝔽2)×C5911yescharacteristic
614C2×C42−1+4×C5911yescharacteristic
615C8—22no—
616C8—22no—
617C8—41no—
618C8—41no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×#121×C5911yescharacteristic
634C22C2×C22⋊Q8×C5911yescharacteristic
635C22C59×#53711yescharacteristic
636C22C59×#57611yescharacteristic
637C22C59×#57611yescharacteristic
638C22C59×#57711yescharacteristic
639C22C59×#57811yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4C59×#54611yescharacteristic
653C4D4×Q8×C5911yescharacteristic
654C4C59×#55211yescharacteristic
655C4C59×#55411yescharacteristic
656C2—42no—
657C2—82no—
658C2C59×#241711yescharacteristic
659C2C59×#305811yescharacteristic
660C2C59×#306311yescharacteristic
661C2C59×#308111yescharacteristic
662C2C59×#308311yescharacteristic
663C2C59×#325711yescharacteristic
664C2C59×#326211yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×#121×C59C22
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×#474C2semidirect
2. C2×C59×#424C2semidirect
3. C59×#2628C2semidirect
5. C59×#2087C2semidirect
6. C59×#2086C2semidirect
7. C59×#2067C2semidirect
8. C59×#2065C2semidirect
9. C59×#1987C2semidirect
10. C59×#1949C2semidirect
13. C59×#1809C2semidirect
14. C59×#1808C2semidirect
15. C59×#1804C2semidirect
79. #121×C59Q8semidirect
116. C4⋊C8×C59D4semidirect
286. #24847C59direct (N × H)
324. C2×#474C2×C59semidirect
325. C2×#424C2×C59semidirect
326. #2628C2×C59semidirect
328. #2087C2×C59semidirect
329. #2086C2×C59semidirect
330. #2067C2×C59semidirect
331. #2065C2×C59semidirect
332. #1987C2×C59semidirect
333. #1949C2×C59semidirect
336. #1809C2×C59semidirect
337. #1808C2×C59semidirect
338. #1804C2×C59semidirect
393. C59#24847direct (N × H)
412. #121Q8×C59semidirect
449. C4⋊C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4742
C2×C59×#4242
C59×#26282
C59×#23242
C59×#20872
C59×#20862
C59×#20672
C59×#20652
C59×#19872
C59×#19492
C59×#18952
C59×#18932
C59×#18092
C59×#18082
C59×#18042
#2484759