Finite Group Databasebeta

← C59×#24142 #28436251

Subgroups — C59×#24142 #28436251

Order 15104.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#2626C211yesmaximal, characteristic, complemented
3C59×#2617C211yesmaximal, characteristic, complemented
4C59×#2321C211yesmaximal, characteristic, complemented
5C59×#2044C212yesmaximal, complemented
6C59×#2021C212yesmaximal, complemented
7C59×#1996C211yesmaximal, characteristic, complemented
8C59×#1964C211yesmaximal, characteristic, complemented
9C59×#1889C212yesmaximal, complemented
10C59×#1867C212yesmaximal, complemented
11C59×#1799C211yesmaximal, characteristic, complemented
12C59×#553—22no—
13C59×#553—21no—
14C59×#552—21no—
15C59×#551—22no—
16C59×#548—21no—
17C59×#546—21no—
18C59×#539—21no—
19C59×#538—21no—
20C59×#534C2212yes—
21C59×#529—21no—
22C59×#525—21no—
23C2×C22⋊Q8×C59C2211yescharacteristic
24C2×#121×C59C2211yescharacteristic
25C2×#120×C59C2211yescharacteristic
26C2×#120×C59C2212yes—
27C59×#518C2212yes—
28C2×C4×D4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2211yescharacteristic
30C2×#99×C59C2212yes—
31C2×#99×C59C2212yes—
32C2×#99×C59C2212yes—
33C59×#399—21no—
34C59×#397—21no—
35C59×#396—22no—
36C59×#394—22no—
37C59×#393—21no—
38C59×#392—21no—
39C59×#390—21no—
40C59×#388—21no—
41C59×#388—21no—
42C59×#386—21no—
43C59×#386C2211yescharacteristic
44C59×#386C2212yes—
45C59×#385C2212yes—
46C59×#385C2211yescharacteristic
47C59×#380C2211yescharacteristic
48C59×#380C2211yescharacteristic
49C59×#379C2212yes—
50C59×#379C2211yescharacteristic
51C4×C22⋊C4×C59C2211yescharacteristic
52C59×#342C2212yes—
53C59×#342C2212yes—
54C59×#342C2212yes—
55C25×C59C2311yescharacteristic
56C2×#41×C59—21no—
57C22×Q8×C59D411yescharacteristic, complemented
58C22×D4×C59—21no—
59C22×D4×C59—22no—
60C22×D4×C59D411yescharacteristic, complemented
61C22×D4×C59C2311yescharacteristic
62C22×D4×C59C2312yes—
63C23×C4×C59D411yescharacteristic, complemented
64C23×C4×C59C2311yescharacteristic
65C23×C4×C59C2311yescharacteristic
66#126×C59—22no—
67#126×C59—22no—
68#126×C59—22no—
69#125×C59—21no—
70#125×C59—22no—
71#124×C59—21no—
72#124×C59—22no—
73#123×C59—22no—
74#123×C59—22no—
75#123×C59—22no—
76#123×C59—22no—
77#123×C59—22no—
78C22⋊Q8×C59—21no—
79C22⋊Q8×C59—22no—
80C22⋊Q8×C59—21no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59—21no—
84#121×C59—21no—
85#121×C59—22no—
86#121×C59—21no—
87#121×C59—21no—
88#121×C59—21no—
89#121×C59—21no—
90#121×C59—22no—
91#121×C59—22no—
92#120×C59—22no—
93#120×C59—22no—
94#120×C59—22no—
95#120×C59—22no—
96#120×C59—24no—
97#120×C59—42no—
98C4×Q8×C59—21no—
99C4×D4×C59—22no—
100C4×D4×C59—21no—
101C4×D4×C59—21no—
102C4×D4×C59—21no—
103C4×D4×C59—21no—
104C4×D4×C59—21no—
105C4×D4×C59—22no—
106C4×D4×C59—22no—
107C4×D4×C59—22no—
108C4×D4×C59—22no—
109#117×C59—21no—
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—22no—
116C2×C4⋊C4×C59D411yescharacteristic, complemented
117C2×C4⋊C4×C59D412yescomplemented
118C2×C4⋊C4×C59D411yescharacteristic, complemented
119C2×C4⋊C4×C59D411yescharacteristic, complemented
120C2×C22⋊C4×C59—22no—
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×C59—21no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59D411yescharacteristic, complemented
136C2×C22⋊C4×C59D412yescomplemented
137C2×C22⋊C4×C59C2312yes—
138C2×C22⋊C4×C59C2311yescharacteristic
139C2×C22⋊C4×C59C2312yes—
140C2×C22⋊C4×C59C2311yescharacteristic
141C2×C22⋊C4×C59C2312yes—
142C2×C22⋊C4×C59C2311yescharacteristic
143C2×C42×C59—21no—
144C2×C42×C59D411yescharacteristic, complemented
145#99×C59—24no—
146#99×C59—42no—
147#99×C59—42no—
148#95×C59—21no—
149#95×C59—21no—
150#95×C59—21no—
151#95×C59—21no—
152#95×C59—22no—
153#95×C59—21no—
154#95×C59—22no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—81no—
162C24×C59—81no—
163C24×C59C2×D412yes—
164C24×C59C2×D411yescharacteristic
165C24×C59#4112yescomplemented
166C24×C59C2411yescharacteristic
167#41×C59—82no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—81no—
171C2×D4×C59—21no—
172C2×D4×C59—22no—
173C2×D4×C59—21no—
174C2×D4×C59—22no—
175C2×D4×C59—22no—
176C2×D4×C59—21no—
177C2×D4×C59—21no—
178C2×D4×C59—22no—
179C2×D4×C59—21no—
180C2×D4×C59—22no—
181C2×D4×C59—21no—
182C2×D4×C59—22no—
183C2×D4×C59—22no—
184C2×D4×C59—22no—
185C2×D4×C59—24no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—44no—
189C2×D4×C59—81no—
190C2×D4×C59—81no—
191C2×D4×C59—81no—
192C2×D4×C59—82no—
193C2×D4×C59—82no—
194C22×C4×C59—21no—
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—21no—
205C22×C4×C59—81no—
206C22×C4×C59—81no—
207C22×C4×C59—81no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C4⋊C4×C59—22no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—22no—
223C4⋊C4×C59—22no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—22no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—22no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—81no—
233C4⋊C4×C59—81no—
234C4⋊C4×C59—81no—
235C4⋊C4×C59—82no—
236C22⋊C4×C59—22no—
237C22⋊C4×C59—22no—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—22no—
240C22⋊C4×C59—22no—
241C22⋊C4×C59—22no—
242C22⋊C4×C59—22no—
243C22⋊C4×C59—21no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—21no—
246C22⋊C4×C59—22no—
247C22⋊C4×C59—21no—
248C22⋊C4×C59—22no—
249C22⋊C4×C59—21no—
250C22⋊C4×C59—21no—
251C22⋊C4×C59—22no—
252C22⋊C4×C59—22no—
253C22⋊C4×C59—22no—
254C22⋊C4×C59—21no—
255C22⋊C4×C59—22no—
256C22⋊C4×C59—22no—
257C22⋊C4×C59—21no—
258C22⋊C4×C59—44no—
259C22⋊C4×C59—41no—
260C22⋊C4×C59—41no—
261C22⋊C4×C59—41no—
262C22⋊C4×C59—41no—
263C22⋊C4×C59—81no—
264C22⋊C4×C59—82no—
265C22⋊C4×C59—81no—
266C22⋊C4×C59—82no—
267C22⋊C4×C59—81no—
268C22⋊C4×C59—82no—
269C22⋊C4×C59#4112yescomplemented
270C42×C59—22no—
271C42×C59—22no—
272C42×C59—21no—
273C42×C59—21no—
274C42×C59—81no—
275C23×C59—21no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—21no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—21no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—41no—
285C23×C59—41no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—42no—
289C23×C59—41no—
290C23×C59—42no—
291C23×C59—41no—
292C23×C59—41no—
293C23×C59—42no—
294C23×C59—41no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—82no—
303C23×C59—82no—
304C23×C59—82no—
305C23×C59—82no—
306C23×C59C22×D411yescharacteristic
307C23×C59C22×D411yescharacteristic
308C23×C59C22×D411yescharacteristic
309C23×C59C2×#4111yescharacteristic
310C23×C59C2×#4111yescharacteristic
311C23×C59H(5,𝔽2)11yescharacteristic
312C23×C592−1+411yescharacteristic
313Q8×C59—42no—
314Q8×C59—81no—
315D4×C59—42no—
316D4×C59—42no—
317D4×C59—42no—
318D4×C59—41no—
319D4×C59—41no—
320D4×C59—41no—
321D4×C59—42no—
322D4×C59—42no—
323D4×C59—41no—
324D4×C59—81no—
325D4×C59—82no—
326D4×C59—84no—
327D4×C59—82no—
328D4×C59—88no—
329C2×C4×C59—21no—
330C2×C4×C59—22no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—21no—
336C2×C4×C59—22no—
337C2×C4×C59—21no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—42no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—42no—
351C2×C4×C59—41no—
352C2×C4×C59—42no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—41no—
358C2×C4×C59—42no—
359C2×C4×C59—42no—
360C2×C4×C59—42no—
361C2×C4×C59—41no—
362C2×C4×C59—42no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—42no—
366C2×C4×C59—42no—
367C2×C4×C59—81no—
368C2×C4×C59—82no—
369C2×C4×C59—82no—
370C2×C4×C59#12011yescharacteristic
371C2×C4×C59#12011yescharacteristic
372C2×C4×C59#12011yescharacteristic
373C2×C4×C59#12011yescharacteristic
374#24142C5911yesmaximal, characteristic, direct product factor, Sylow
375C22×C59—21no—
376C22×C59—21no—
377C22×C59—21no—
378C22×C59—21no—
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—41no—
382C22×C59—41no—
383C22×C59—41no—
384C22×C59—41no—
385C22×C59—42no—
386C22×C59—42no—
387C22×C59—44no—
388C22×C59—42no—
389C22×C59—44no—
390C22×C59—41no—
391C22×C59—42no—
392C22×C59—42no—
393C22×C59—41no—
394C22×C59—42no—
395C22×C59—42no—
396C22×C59—41no—
397C22×C59—82no—
398C22×C59—81no—
399C22×C59—82no—
400C22×C59—82no—
401C22×C59—81no—
402C22×C59—81no—
403C22×C59—82no—
404C22×C59—81no—
405C22×C59—81no—
406C22×C59C2×#12011yescharacteristic
407C22×C59#52511yescharacteristic
408C22×C59#53711yescharacteristic
409C22×C59#54611yescharacteristic
410C22×C59#54711yescharacteristic
411C22×C59#54811yescharacteristic
412C22×C59#55011yescharacteristic
413C4×C59—21no—
414C4×C59—21no—
415C4×C59—21no—
416C4×C59—21no—
417C4×C59—42no—
418C4×C59—41no—
419C4×C59—42no—
420C4×C59—41no—
421C4×C59—42no—
422C4×C59—41no—
423C4×C59—42no—
424C4×C59—82no—
425C4×C59—81no—
426C4×C59—82no—
427C4×C59—81no—
428#3505C2×C5911yescharacteristic, complemented
429#2626C2×C5911yescharacteristic, complemented
430#2617C2×C5911yescharacteristic, complemented
431#2321C2×C5911yescharacteristic, complemented
432#2044C2×C5912yescomplemented
433#2021C2×C5912yescomplemented
434#1996C2×C5911yescharacteristic, complemented
435#1964C2×C5911yescharacteristic, complemented
436#1889C2×C5912yescomplemented
437#1867C2×C5912yescomplemented
438#1799C2×C5911yescharacteristic, complemented
439C2×C59—21no—
440C2×C59—21no—
441C2×C59—21no—
442C2×C59—21no—
443C2×C59—21no—
444C2×C59—21no—
445C2×C59—82no—
446C2×C59—81no—
447C2×C59—82no—
448C2×C59#240711yescharacteristic
449C2×C59#302611yescharacteristic
450C2×C59#302711yescharacteristic
451#553—22no—
452#553—21no—
453#552—21no—
454#551—22no—
455#548—21no—
456#546—21no—
457#539—21no—
458#538—21no—
459#534C22×C5912yes—
460#529—21no—
461#525—21no—
462C2×C22⋊Q8C22×C5911yescharacteristic
463C2×#121C22×C5911yescharacteristic
464C2×#120C22×C5911yescharacteristic
465C2×#120C22×C5912yes—
466#518C22×C5912yes—
467C2×C4×D4C22×C5911yescharacteristic
468C22×C22⋊C4C22×C5911yescharacteristic
469C2×#99C22×C5912yes—
470C2×#99C22×C5912yes—
471C2×#99C22×C5912yes—
472#399—21no—
473#397—21no—
474#396—22no—
475#394—22no—
476#393—21no—
477#392—21no—
478#390—21no—
479#388—21no—
480#388—21no—
481#386—21no—
482#386C22×C5911yescharacteristic
483#386C22×C5912yes—
484#385C22×C5911yescharacteristic
485#385C22×C5912yes—
486#380C22×C5911yescharacteristic
487#380C22×C5911yescharacteristic
488#379C22×C5911yescharacteristic
489#379C22×C5912yes—
490C4×C22⋊C4C22×C5911yescharacteristic
491#342C22×C5912yes—
492#342C22×C5912yes—
493#342C22×C5912yes—
494C59#2414211yescharacteristic, direct product factor, Sylow
495C25C23×C5911yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C5911yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C5911yescharacteristic, complemented
501C22×D4C23×C5911yescharacteristic
502C22×D4C23×C5912yes—
503C23×C4D4×C5911yescharacteristic, complemented
504C23×C4C23×C5911yescharacteristic
505C23×C4C23×C5911yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C5911yescharacteristic, complemented
557C2×C4⋊C4D4×C5911yescharacteristic, complemented
558C2×C4⋊C4D4×C5912yescomplemented
559C2×C4⋊C4D4×C5911yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C5911yescharacteristic, complemented
576C2×C22⋊C4D4×C5912yescomplemented
577C2×C22⋊C4C23×C5912yes—
578C2×C22⋊C4C23×C5911yescharacteristic
579C2×C22⋊C4C23×C5912yes—
580C2×C22⋊C4C23×C5911yescharacteristic
581C2×C22⋊C4C23×C5912yes—
582C2×C22⋊C4C23×C5911yescharacteristic
583C2×C42—21no—
584C2×C42D4×C5911yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C5912yes—
604C24C2×D4×C5911yescharacteristic
605C24#41×C5912yescomplemented
606C24C24×C5911yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C5911yescharacteristic
649C22×C4C2×D4×C5912yes—
650C22×C4C2×D4×C5911yescharacteristic
651C22×C4C2×D4×C5912yes—
652C22×C4C2×D4×C5911yescharacteristic
653C22×C4C2×D4×C5912yes—
654C22×C4C2×D4×C5911yescharacteristic
655C22×C4C2×D4×C5911yescharacteristic
656C22×C4C2×D4×C5911yescharacteristic
657C22×C4C2×D4×C5911yescharacteristic
658C22×C4C2×D4×C5911yescharacteristic
659C22×C4C2×D4×C5911yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C5912yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C5911yescharacteristic
747C23C22×D4×C5911yescharacteristic
748C23C22×D4×C5911yescharacteristic
749C23C2×#41×C5911yescharacteristic
750C23C2×#41×C5911yescharacteristic
751C23H(5,𝔽2)×C5911yescharacteristic
752C232−1+4×C5911yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—82no—
766D4—84no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C5911yescharacteristic
811C2×C4#120×C5911yescharacteristic
812C2×C4#120×C5911yescharacteristic
813C2×C4#120×C5911yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C5911yescharacteristic
846C22C59×#52511yescharacteristic
847C22C59×#53711yescharacteristic
848C22C59×#54611yescharacteristic
849C22C59×#54711yescharacteristic
850C22C59×#54811yescharacteristic
851C22C59×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C59×#240711yescharacteristic
877C2C59×#302611yescharacteristic
878C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3505C2semidirect
2. C59×#2626C2semidirect
3. C59×#2617C2semidirect
4. C59×#2321C2semidirect
5. C59×#2044C2semidirect
6. C59×#2021C2semidirect
7. C59×#1996C2semidirect
8. C59×#1964C2semidirect
9. C59×#1889C2semidirect
10. C59×#1867C2semidirect
11. C59×#1799C2semidirect
57. C22×Q8×C59D4semidirect
60. C22×D4×C59D4semidirect
63. C23×C4×C59D4semidirect
116. C2×C4⋊C4×C59D4semidirect
117. C2×C4⋊C4×C59D4semidirect
118. C2×C4⋊C4×C59D4semidirect
119. C2×C4⋊C4×C59D4semidirect
135. C2×C22⋊C4×C59D4semidirect
136. C2×C22⋊C4×C59D4semidirect
144. C2×C42×C59D4semidirect
165. C24×C59#41semidirect
269. C22⋊C4×C59#41semidirect
374. #24142C59direct (N × H)
428. #3505C2×C59semidirect
429. #2626C2×C59semidirect
430. #2617C2×C59semidirect
431. #2321C2×C59semidirect
432. #2044C2×C59semidirect
433. #2021C2×C59semidirect
434. #1996C2×C59semidirect
435. #1964C2×C59semidirect
436. #1889C2×C59semidirect
437. #1867C2×C59semidirect
438. #1799C2×C59semidirect
494. C59#24142direct (N × H)
497. C22×Q8D4×C59semidirect
500. C22×D4D4×C59semidirect
503. C23×C4D4×C59semidirect
556. C2×C4⋊C4D4×C59semidirect
557. C2×C4⋊C4D4×C59semidirect
558. C2×C4⋊C4D4×C59semidirect
559. C2×C4⋊C4D4×C59semidirect
575. C2×C22⋊C4D4×C59semidirect
576. C2×C22⋊C4D4×C59semidirect
584. C2×C42D4×C59semidirect
605. C24#41×C59semidirect
709. C22⋊C4#41×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35052
C59×#26262
C59×#26172
C59×#23212
C59×#20442
C59×#20212
C59×#19962
C59×#19642
C59×#18892
C59×#18672
C59×#17992
#2414259