Finite Group Databasebeta

← C59×#24140 #28436249

Subgroups — C59×#24140 #28436249

Order 15104.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3505C211yesmaximal, characteristic, complemented
2C59×#2848C211yesmaximal, characteristic, complemented
3C59×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C59C211yesmaximal, 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
12C24×C4×C59C2211yescharacteristic
13C59×#553—21no—
14C59×#553—22no—
15C59×#552—21no—
16C59×#551—22no—
17C59×#548—21no—
18C59×#546—21no—
19C59×#539—21no—
20C59×#538—21no—
21C59×#534C2212yes—
22C59×#529—21no—
23C59×#525—21no—
24C2×C22⋊Q8×C59—21no—
25C2×C22⋊Q8×C59C2211yescharacteristic
26C2×#121×C59—21no—
27C2×#121×C59C2211yescharacteristic
28C2×#120×C59C2211yescharacteristic
29C2×#120×C59C2212yes—
30C59×#518C2212yes—
31C2×C4×D4×C59—21no—
32C2×C4×D4×C59C2211yescharacteristic
33C2×#99×C59C2212yes—
34C2×#99×C59C2212yes—
35C2×#99×C59C2212yes—
36C59×#386—21no—
37C59×#386—22no—
38C59×#386C2211yescharacteristic
39C59×#386C2212yes—
40C59×#385—21no—
41C59×#385—22no—
42C59×#385C2211yescharacteristic
43C59×#385C2212yes—
44C59×#380—21no—
45C59×#380—21no—
46C59×#380C2211yescharacteristic
47C59×#380C2211yescharacteristic
48C59×#379C2212yes—
49C59×#379C2211yescharacteristic
50C4×C22⋊C4×C59—21no—
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×C59—21no—
64C23×C4×C59—21no—
65C23×C4×C59—21no—
66C23×C4×C59—21no—
67C23×C4×C59—21no—
68C23×C4×C59—21no—
69C23×C4×C59—44no—
70C23×C4×C59D411yescharacteristic, complemented
71C23×C4×C59C2311yescharacteristic
72C23×C4×C59C2311yescharacteristic
73#126×C59—22no—
74#126×C59—22no—
75#126×C59—22no—
76#125×C59—21no—
77#125×C59—22no—
78#124×C59—21no—
79#124×C59—22no—
80#123×C59—22no—
81#123×C59—22no—
82#123×C59—22no—
83#123×C59—22no—
84#123×C59—22no—
85C22⋊Q8×C59—21no—
86C22⋊Q8×C59—22no—
87C22⋊Q8×C59—21no—
88C22⋊Q8×C59—21no—
89C22⋊Q8×C59—21no—
90C22⋊Q8×C59—21no—
91C22⋊Q8×C59—44no—
92#121×C59—21no—
93#121×C59—22no—
94#121×C59—21no—
95#121×C59—21no—
96#121×C59—21no—
97#121×C59—21no—
98#121×C59—22no—
99#121×C59—22no—
100#121×C59—44no—
101#120×C59—22no—
102#120×C59—22no—
103#120×C59—22no—
104#120×C59—22no—
105#120×C59—24no—
106#120×C59—42no—
107C4×Q8×C59—21no—
108C4×D4×C59—22no—
109C4×D4×C59—21no—
110C4×D4×C59—21no—
111C4×D4×C59—21no—
112C4×D4×C59—21no—
113C4×D4×C59—21no—
114C4×D4×C59—22no—
115C4×D4×C59—22no—
116C4×D4×C59—22no—
117C4×D4×C59—22no—
118C4×D4×C59—44no—
119#117×C59—21no—
120#117×C59—22no—
121#117×C59—22no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—22no—
126C2×C4⋊C4×C59D411yescharacteristic, complemented
127C2×C4⋊C4×C59D411yescharacteristic, complemented
128C2×C4⋊C4×C59D411yescharacteristic, complemented
129C2×C4⋊C4×C59D412yescomplemented
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59—22no—
138C2×C22⋊C4×C59—22no—
139C2×C22⋊C4×C59D411yescharacteristic, complemented
140C2×C22⋊C4×C59D412yescomplemented
141C2×C22⋊C4×C59C2312yes—
142C2×C22⋊C4×C59C2311yescharacteristic
143C2×C22⋊C4×C59C2312yes—
144C2×C22⋊C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59C2312yes—
146C2×C22⋊C4×C59C2311yescharacteristic
147C2×C42×C59—21no—
148C2×C42×C59D411yescharacteristic, complemented
149#99×C59—24no—
150#99×C59—42no—
151#99×C59—42no—
152#95×C59—21no—
153#95×C59—21no—
154#95×C59—21no—
155#95×C59—22no—
156#95×C59—22no—
157#95×C59—21no—
158#95×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—42no—
166C24×C59—42no—
167C24×C59C2×D412yes—
168C24×C59C2×D411yescharacteristic
169C24×C59#4112yescomplemented
170C24×C59C2411yescharacteristic
171#41×C59—82no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59—42no—
175C2×D4×C59—24no—
176C2×D4×C59—21no—
177C2×D4×C59—22no—
178C2×D4×C59—21no—
179C2×D4×C59—22no—
180C2×D4×C59—22no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—22no—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—42no—
193C2×D4×C59—42no—
194C2×D4×C59—42no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C2×D4×C59—44no—
198C22×C4×C59—24no—
199C22×C4×C59—24no—
200C22×C4×C59—24no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—22no—
211C22×C4×C59—22no—
212C22×C4×C59—42no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59—42no—
216C22×C4×C59—42no—
217C22×C4×C59—42no—
218C22×C4×C59—42no—
219C22×C4×C59—42no—
220C22×C4×C59—42no—
221C22×C4×C59—42no—
222C22×C4×C59—42no—
223C22×C4×C59—42no—
224C22×C4×C59—41no—
225C22×C4×C59—41no—
226C22×C4×C59—41no—
227C22×C4×C59—41no—
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D412yes—
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59C2×D411yescharacteristic
234C22×C4×C59C2×D412yes—
235C22×C4×C59C2×D411yescharacteristic
236C22×C4×C59C2×D412yes—
237C22×C4×C59C2×D411yescharacteristic
238C22×C4×C59C2×D411yescharacteristic
239C22×C4×C59C2×D411yescharacteristic
240C4⋊C4×C59—22no—
241C4⋊C4×C59—22no—
242C4⋊C4×C59—22no—
243C4⋊C4×C59—22no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—22no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—22no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—42no—
253C4⋊C4×C59—42no—
254C4⋊C4×C59—42no—
255C4⋊C4×C59—44no—
256C22⋊C4×C59—22no—
257C22⋊C4×C59—22no—
258C22⋊C4×C59—24no—
259C22⋊C4×C59—22no—
260C22⋊C4×C59—22no—
261C22⋊C4×C59—22no—
262C22⋊C4×C59—22no—
263C22⋊C4×C59—21no—
264C22⋊C4×C59—22no—
265C22⋊C4×C59—21no—
266C22⋊C4×C59—22no—
267C22⋊C4×C59—21no—
268C22⋊C4×C59—22no—
269C22⋊C4×C59—21no—
270C22⋊C4×C59—21no—
271C22⋊C4×C59—22no—
272C22⋊C4×C59—22no—
273C22⋊C4×C59—22no—
274C22⋊C4×C59—21no—
275C22⋊C4×C59—22no—
276C22⋊C4×C59—22no—
277C22⋊C4×C59—21no—
278C22⋊C4×C59—44no—
279C22⋊C4×C59—42no—
280C22⋊C4×C59—44no—
281C22⋊C4×C59—44no—
282C22⋊C4×C59—42no—
283C22⋊C4×C59—42no—
284C22⋊C4×C59—44no—
285C22⋊C4×C59#4112yescomplemented
286C42×C59—22no—
287C42×C59—22no—
288C42×C59—21no—
289C42×C59—21no—
290C42×C59—42no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—21no—
301C23×C59—22no—
302C23×C59—21no—
303C23×C59—21no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—41no—
307C23×C59—44no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—44no—
316C23×C59—44no—
317C23×C59—44no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59C22×D411yescharacteristic
327C23×C59C22×D411yescharacteristic
328C23×C59C22×D411yescharacteristic
329C23×C59C2×#4111yescharacteristic
330C23×C59C2×#4111yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C592−1+411yescharacteristic
333Q8×C59—42no—
334Q8×C59—81no—
335D4×C59—48no—
336D4×C59—42no—
337D4×C59—42no—
338D4×C59—41no—
339D4×C59—41no—
340D4×C59—41no—
341D4×C59—42no—
342D4×C59—42no—
343D4×C59—41no—
344D4×C59—42no—
345D4×C59—81no—
346D4×C59—82no—
347D4×C59—82no—
348D4×C59—88no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—21no—
356C2×C4×C59—22no—
357C2×C4×C59—21no—
358C2×C4×C59—21no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—21no—
362C2×C4×C59—22no—
363C2×C4×C59—21no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—44no—
370C2×C4×C59—44no—
371C2×C4×C59—44no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—44no—
379C2×C4×C59—42no—
380C2×C4×C59—41no—
381C2×C4×C59—42no—
382C2×C4×C59—41no—
383C2×C4×C59—42no—
384C2×C4×C59—41no—
385C2×C4×C59—42no—
386C2×C4×C59—42no—
387C2×C4×C59—42no—
388C2×C4×C59—41no—
389C2×C4×C59—42no—
390C2×C4×C59—41no—
391C2×C4×C59—42no—
392C2×C4×C59—42no—
393C2×C4×C59—81no—
394C2×C4×C59—82no—
395C2×C4×C59—82no—
396C2×C4×C59#12011yescharacteristic
397C2×C4×C59#12011yescharacteristic
398C2×C4×C59#12011yescharacteristic
399C2×C4×C59#12011yescharacteristic
400#24140C5911yesmaximal, characteristic, direct product factor, Sylow
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—21no—
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—21no—
407C22×C59—24no—
408C22×C59—24no—
409C22×C59—24no—
410C22×C59—41no—
411C22×C59—41no—
412C22×C59—41no—
413C22×C59—41no—
414C22×C59—42no—
415C22×C59—42no—
416C22×C59—42no—
417C22×C59—42no—
418C22×C59—42no—
419C22×C59—42no—
420C22×C59—42no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59—42no—
424C22×C59—42no—
425C22×C59—42no—
426C22×C59—42no—
427C22×C59—41no—
428C22×C59—42no—
429C22×C59—41no—
430C22×C59—42no—
431C22×C59—42no—
432C22×C59—41no—
433C22×C59—82no—
434C22×C59—81no—
435C22×C59—82no—
436C22×C59C2×#12011yescharacteristic
437C22×C59#52511yescharacteristic
438C22×C59#53711yescharacteristic
439C22×C59#54611yescharacteristic
440C22×C59#54711yescharacteristic
441C22×C59#54811yescharacteristic
442C22×C59#55011yescharacteristic
443C4×C59—21no—
444C4×C59—21no—
445C4×C59—21no—
446C4×C59—42no—
447C4×C59—41no—
448C4×C59—42no—
449C4×C59—42no—
450C4×C59—41no—
451C4×C59—42no—
452C4×C59—41no—
453C4×C59—42no—
454C4×C59—82no—
455C4×C59—81no—
456C4×C59—82no—
457C4×C59B(4,𝔽2)12yes—
458#3505C2×C5911yescharacteristic, complemented
459#2848C2×C5911yescharacteristic, complemented
460#2847C2×C5911yescharacteristic, complemented
461C4×#120C2×C5911yescharacteristic, complemented
462#2044C2×C5912yescomplemented
463#2021C2×C5912yescomplemented
464#1996C2×C5911yescharacteristic, complemented
465#1964C2×C5911yescharacteristic, complemented
466#1889C2×C5912yescomplemented
467#1867C2×C5912yescomplemented
468#1799C2×C5911yescharacteristic, complemented
469C2×C59—21no—
470C2×C59—21no—
471C2×C59—21no—
472C2×C59—21no—
473C2×C59—21no—
474C2×C59—21no—
475C2×C59—44no—
476C2×C59—81no—
477C2×C59—82no—
478C2×C59#240711yescharacteristic
479C2×C59C2×B(4,𝔽2)11yescharacteristic
480C2×C59#302511yescharacteristic
481C24×C4C22×C5911yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C5912yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C5911yescharacteristic
495C2×#121—21no—
496C2×#121C22×C5911yescharacteristic
497C2×#120C22×C5911yescharacteristic
498C2×#120C22×C5912yes—
499#518C22×C5912yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C5911yescharacteristic
502C2×#99C22×C5912yes—
503C2×#99C22×C5912yes—
504C2×#99C22×C5912yes—
505#386—22no—
506#386—21no—
507#386C22×C5912yes—
508#386C22×C5911yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C5912yes—
512#385C22×C5911yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C5911yescharacteristic
516#380C22×C5911yescharacteristic
517#379C22×C5912yes—
518#379C22×C5911yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C5911yescharacteristic
521#342C22×C5912yes—
522#342C22×C5912yes—
523#342C22×C5912yes—
524C59#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C5911yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C5911yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C5911yescharacteristic, complemented
531C22×D4C23×C5911yescharacteristic
532C22×D4C23×C5912yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C5911yescharacteristic, complemented
541C23×C4C23×C5911yescharacteristic
542C23×C4C23×C5911yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C5911yescharacteristic, complemented
597C2×C4⋊C4D4×C5911yescharacteristic, complemented
598C2×C4⋊C4D4×C5911yescharacteristic, complemented
599C2×C4⋊C4D4×C5912yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C5911yescharacteristic, complemented
610C2×C22⋊C4D4×C5912yescomplemented
611C2×C22⋊C4C23×C5912yes—
612C2×C22⋊C4C23×C5911yescharacteristic
613C2×C22⋊C4C23×C5912yes—
614C2×C22⋊C4C23×C5911yescharacteristic
615C2×C22⋊C4C23×C5912yes—
616C2×C22⋊C4C23×C5911yescharacteristic
617C2×C42—21no—
618C2×C42D4×C5911yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C5912yes—
638C24C2×D4×C5911yescharacteristic
639C24#41×C5912yescomplemented
640C24C24×C5911yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C5911yescharacteristic
699C22×C4C2×D4×C5912yes—
700C22×C4C2×D4×C5911yescharacteristic
701C22×C4C2×D4×C5911yescharacteristic
702C22×C4C2×D4×C5911yescharacteristic
703C22×C4C2×D4×C5911yescharacteristic
704C22×C4C2×D4×C5912yes—
705C22×C4C2×D4×C5911yescharacteristic
706C22×C4C2×D4×C5912yes—
707C22×C4C2×D4×C5911yescharacteristic
708C22×C4C2×D4×C5911yescharacteristic
709C22×C4C2×D4×C5911yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C5912yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C5911yescharacteristic
797C23C22×D4×C5911yescharacteristic
798C23C22×D4×C5911yescharacteristic
799C23C2×#41×C5911yescharacteristic
800C23C2×#41×C5911yescharacteristic
801C23H(5,𝔽2)×C5911yescharacteristic
802C232−1+4×C5911yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C5911yescharacteristic
867C2×C4#120×C5911yescharacteristic
868C2×C4#120×C5911yescharacteristic
869C2×C4#120×C5911yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C5911yescharacteristic
906C22C59×#52511yescharacteristic
907C22C59×#53711yescharacteristic
908C22C59×#54611yescharacteristic
909C22C59×#54711yescharacteristic
910C22C59×#54811yescharacteristic
911C22C59×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C59×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C59×#240711yescharacteristic
937C2C2×C59×B(4,𝔽2)11yescharacteristic
938C2C59×#302511yescharacteristic
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×#2848C2semidirect
3. C59×#2847C2semidirect
4. C4×#120×C59C2semidirect
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
70. C23×C4×C59D4semidirect
126. C2×C4⋊C4×C59D4semidirect
127. C2×C4⋊C4×C59D4semidirect
128. C2×C4⋊C4×C59D4semidirect
129. C2×C4⋊C4×C59D4semidirect
139. C2×C22⋊C4×C59D4semidirect
140. C2×C22⋊C4×C59D4semidirect
148. C2×C42×C59D4semidirect
169. C24×C59#41semidirect
285. C22⋊C4×C59#41semidirect
400. #24140C59direct (N × H)
458. #3505C2×C59semidirect
459. #2848C2×C59semidirect
460. #2847C2×C59semidirect
461. C4×#120C2×C59semidirect
462. #2044C2×C59semidirect
463. #2021C2×C59semidirect
464. #1996C2×C59semidirect
465. #1964C2×C59semidirect
466. #1889C2×C59semidirect
467. #1867C2×C59semidirect
468. #1799C2×C59semidirect
524. C59#24140direct (N × H)
527. C22×Q8D4×C59semidirect
530. C22×D4D4×C59semidirect
540. C23×C4D4×C59semidirect
596. C2×C4⋊C4D4×C59semidirect
597. C2×C4⋊C4D4×C59semidirect
598. C2×C4⋊C4D4×C59semidirect
599. C2×C4⋊C4D4×C59semidirect
609. C2×C22⋊C4D4×C59semidirect
610. C2×C22⋊C4D4×C59semidirect
618. C2×C42D4×C59semidirect
639. C24#41×C59semidirect
755. 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×#28482
C59×#28472
C4×#120×C592
C59×#20442
C59×#20212
C59×#19962
C59×#19642
C59×#18892
C59×#18672
C59×#17992
#2414059