Finite Group Databasebeta

← C59×#24405 #28436514

Subgroups — C59×#24405 #28436514

Order 15104.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3484C211yesmaximal, characteristic
2C2×C59×#458C211yesmaximal, characteristic, complemented
3C22×#99×C59C211yesmaximal, characteristic, complemented
4C59×#2412C212yesmaximal, complemented
5C59×#2405C211yesmaximal, characteristic, complemented
6C59×#2044C212yesmaximal, complemented
7C59×#2022C212yesmaximal, complemented
8C59×#1898C212yesmaximal, complemented
9C59×#1890C211yesmaximal, characteristic, complemented
10C59×#1867C211yesmaximal, characteristic, complemented
11C59×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C59×#546—22no—
15C59×#546—22no—
16D42×C59—22no—
17D42×C59—22no—
18C59×#535—21no—
19C59×#534—21no—
20C59×#534C2212yes—
21C59×#525—21no—
22C2×#123×C59C2211yescharacteristic
23C2×#123×C59C2212yescomplemented
24C2×#123×C59C2211yescharacteristic, complemented
25C2×#120×C59—21no—
26C2×#120×C59C2212yes—
27C59×#518C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic, complemented
29C22×C22⋊C4×C59C2212yescomplemented
30C59×#458—24no—
31C2×#99×C59—24no—
32C2×#99×C59C2211yescharacteristic
33C2×#99×C59C2211yescharacteristic
34C2×#99×C59C2212yescomplemented
35C2×#99×C59C2212yescomplemented
36C2×#99×C59C2212yescomplemented
37C59×#397—22no—
38C59×#394—21no—
39C59×#394—21no—
40C59×#394—22no—
41C59×#386—22no—
42C59×#386C2211yescharacteristic
43C59×#386C2211yescharacteristic, complemented
44C59×#386C2212yescomplemented
45C59×#385—21no—
46C59×#385C2212yescomplemented
47C59×#381C2212yescomplemented
48C59×#380—22no—
49C59×#379—21no—
50C59×#379C2211yescharacteristic, complemented
51C59×#342C2212yescomplemented
52C59×#342C2212yescomplemented
53C25×C59D411yescharacteristic
54C25×C59C2311yescharacteristic
55H(5,𝔽2)×C59—22no—
56H(5,𝔽2)×C59—22no—
57H(5,𝔽2)×C59—42no—
58C2×#41×C59—21no—
59C2×#41×C59—22no—
60C22×D4×C59—21no—
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—21no—
65C22×D4×C59—21no—
66C22×D4×C59—22no—
67C22×D4×C59—22no—
68C22×D4×C59—42no—
69C22×D4×C59D411yescharacteristic
70C22×D4×C59D411yescharacteristic
71C22×D4×C59D412yes—
72C22×D4×C59D412yes—
73C22×D4×C59C2312yes—
74C22×D4×C59C2311yescharacteristic
75C22×D4×C59C2311yescharacteristic
76C23×C4×C59—22no—
77C23×C4×C59D411yescharacteristic
78C23×C4×C59C2311yescharacteristic
79C23×C4×C59C2311yescharacteristic
80#127×C59—22no—
81#124×C59—22no—
82#123×C59—22no—
83#123×C59—22no—
84#123×C59—22no—
85#123×C59—22no—
86#123×C59—22no—
87#123×C59—24no—
88#123×C59—42no—
89#123×C59—42no—
90C22⋊Q8×C59—21no—
91C22⋊Q8×C59—21no—
92#121×C59—21no—
93#121×C59—21no—
94#121×C59—22no—
95#121×C59—22no—
96#121×C59—22no—
97#121×C59—22no—
98#121×C59—22no—
99#121×C59—22no—
100#120×C59—22no—
101#120×C59—22no—
102#120×C59—22no—
103#120×C59—22no—
104#120×C59—22no—
105#120×C59—22no—
106#120×C59—22no—
107#120×C59—22no—
108#120×C59—22no—
109C4×D4×C59—22no—
110C4×D4×C59—22no—
111C4×D4×C59—22no—
112C4×D4×C59—22no—
113#117×C59—21no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—22no—
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—24no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—22no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—42no—
136C2×C22⋊C4×C59D412yes—
137C2×C22⋊C4×C59D412yes—
138C2×C22⋊C4×C59C2311yescharacteristic
139C2×C22⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59C2312yes—
141C2×C22⋊C4×C59C2312yes—
142C2×C22⋊C4×C59C2312yes—
143#99×C59—22no—
144#99×C59—24no—
145#99×C59—24no—
146#99×C59—42no—
147#99×C59D414yescomplemented
148#95×C59—22no—
149#95×C59—22no—
150#95×C59—22no—
151#95×C59—21no—
152#95×C59—21no—
153#95×C59—22no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—22no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—22no—
161C24×C59—41no—
162C24×C59—42no—
163C24×C59—42no—
164C24×C59—81no—
165C24×C59—81no—
166C24×C59C2×D411yescharacteristic
167C24×C59C2×D412yes—
168C24×C59C2×D411yescharacteristic
169C24×C59C2×D412yes—
170C24×C59C2×D412yes—
171C24×C59C2×D411yescharacteristic
172C24×C59C2×D411yescharacteristic
173C24×C59C2411yescharacteristic
174#41×C59—44no—
175#41×C59—44no—
176#41×C59—42no—
177#41×C59—42no—
178C2×Q8×C59—21no—
179C2×D4×C59—22no—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—21no—
183C2×D4×C59—22no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59—21no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59—22no—
197C2×D4×C59—22no—
198C2×D4×C59—22no—
199C2×D4×C59—22no—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59—22no—
203C2×D4×C59—41no—
204C2×D4×C59—41no—
205C2×D4×C59—44no—
206C2×D4×C59—44no—
207C2×D4×C59—44no—
208C2×D4×C59—44no—
209C2×D4×C59—44no—
210C2×D4×C59—44no—
211C2×D4×C59—42no—
212C2×D4×C59—42no—
213C2×D4×C59—44no—
214C2×D4×C59—82no—
215C2×D4×C59—82no—
216C2×D4×C59—82no—
217C2×D4×C59C2×D412yes—
218C2×D4×C59#4112yes—
219C22×C4×C59—21no—
220C22×C4×C59—22no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—22no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—22no—
227C22×C4×C59—22no—
228C22×C4×C59—21no—
229C22×C4×C59—22no—
230C22×C4×C59—22no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—22no—
237C22×C4×C59—41no—
238C22×C4×C59—44no—
239C22×C4×C59—44no—
240C22×C4×C59—81no—
241C22×C4×C59—82no—
242C22×C4×C59C2×D412yes—
243C22×C4×C59C2×D411yescharacteristic
244C22×C4×C59C2×D411yescharacteristic
245C22×C4×C59C2×D412yes—
246C22×C4×C59C2×D412yes—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—22no—
250C4⋊C4×C59—22no—
251C4⋊C4×C59—44no—
252C4⋊C4×C59—42no—
253C4⋊C4×C59—42no—
254C4⋊C4×C59—82no—
255C22⋊C4×C59—22no—
256C22⋊C4×C59—22no—
257C22⋊C4×C59—22no—
258C22⋊C4×C59—22no—
259C22⋊C4×C59—22no—
260C22⋊C4×C59—22no—
261C22⋊C4×C59—22no—
262C22⋊C4×C59—22no—
263C22⋊C4×C59—22no—
264C22⋊C4×C59—22no—
265C22⋊C4×C59—22no—
266C22⋊C4×C59—22no—
267C22⋊C4×C59—22no—
268C22⋊C4×C59—21no—
269C22⋊C4×C59—21no—
270C22⋊C4×C59—22no—
271C22⋊C4×C59—22no—
272C22⋊C4×C59—44no—
273C22⋊C4×C59—44no—
274C22⋊C4×C59—42no—
275C22⋊C4×C59—42no—
276C22⋊C4×C59—41no—
277C22⋊C4×C59—42no—
278C22⋊C4×C59—41no—
279C22⋊C4×C59—42no—
280C22⋊C4×C59—81no—
281C22⋊C4×C59—81no—
282C22⋊C4×C59—81no—
283C22⋊C4×C59—82no—
284C22⋊C4×C59C2×D414yescomplemented
285C42×C59—22no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—24no—
293C23×C59—21no—
294C23×C59—21no—
295C23×C59—21no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—21no—
299C23×C59—22no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—42no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—42no—
310C23×C59—42no—
311C23×C59—41no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—42no—
319C23×C59—42no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—42no—
323C23×C59—81no—
324C23×C59—81no—
325C23×C59—82no—
326C23×C59—82no—
327C23×C59—84no—
328C23×C59—81no—
329C23×C59—81no—
330C23×C59—84no—
331C23×C59—84no—
332C23×C59#12011yescharacteristic
333C23×C59#12012yes—
334C23×C59#12011yescharacteristic
335C23×C59#12112yes—
336C23×C59C22×D411yescharacteristic
337C23×C59C22×D412yes—
338C23×C59C22×D411yescharacteristic
339C23×C59C2×#4111yescharacteristic
340C23×C59H(5,𝔽2)12yes—
341Q8×C59—42no—
342D4×C59—24no—
343D4×C59—24no—
344D4×C59—44no—
345D4×C59—42no—
346D4×C59—44no—
347D4×C59—44no—
348D4×C59—44no—
349D4×C59—42no—
350D4×C59—42no—
351D4×C59—42no—
352D4×C59—42no—
353D4×C59—42no—
354D4×C59—42no—
355D4×C59—44no—
356D4×C59—82no—
357D4×C59—82no—
358D4×C59—82no—
359D4×C59—82no—
360C2×C4×C59—21no—
361C2×C4×C59—21no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—21no—
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—24no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—42no—
372C2×C4×C59—42no—
373C2×C4×C59—44no—
374C2×C4×C59—42no—
375C2×C4×C59—42no—
376C2×C4×C59—42no—
377C2×C4×C59—42no—
378C2×C4×C59—42no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—42no—
384C2×C4×C59—42no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—42no—
388C2×C4×C59—42no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—42no—
396C2×C4×C59—42no—
397C2×C4×C59—42no—
398C2×C4×C59—81no—
399C2×C4×C59—81no—
400C2×C4×C59—88no—
401C2×C4×C59#12112yes—
402#24405C5911yesmaximal, characteristic, direct product factor, Sylow
403C22×C59—21no—
404C22×C59—22no—
405C22×C59—21no—
406C22×C59—22no—
407C22×C59—21no—
408C22×C59—21no—
409C22×C59—21no—
410C22×C59—22no—
411C22×C59—22no—
412C22×C59—22no—
413C22×C59—21no—
414C22×C59—21no—
415C22×C59—22no—
416C22×C59—41no—
417C22×C59—41no—
418C22×C59—42no—
419C22×C59—44no—
420C22×C59—44no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59—42no—
424C22×C59—42no—
425C22×C59—41no—
426C22×C59—41no—
427C22×C59—42no—
428C22×C59—41no—
429C22×C59—42no—
430C22×C59—41no—
431C22×C59—42no—
432C22×C59—41no—
433C22×C59—82no—
434C22×C59—81no—
435C22×C59—81no—
436C22×C59—81no—
437C22×C59—82no—
438C22×C59—84no—
439C22×C59—82no—
440C22×C59—82no—
441C22×C59—81no—
442C22×C59—84no—
443C22×C59—162no—
444C22×C59#45812yescomplemented
445C22×C59C2×#12011yescharacteristic
446C22×C59C2×#12111yescharacteristic
447C22×C59#53411yescharacteristic
448C22×C59D4212yes—
449C22×C59#54612yes—
450C4×C59—22no—
451C4×C59—44no—
452C4×C59—41no—
453C4×C59—42no—
454C4×C59—42no—
455C4×C59—42no—
456C4×C59—81no—
457C4×C59—81no—
458C4×C59—82no—
459C4×C59—81no—
460C4×C59—81no—
461#3484C2×C5911yescharacteristic
462C2×#458C2×C5911yescharacteristic, complemented
463C22×#99C2×C5911yescharacteristic, complemented
464#2412C2×C5912yescomplemented
465#2405C2×C5911yescharacteristic, complemented
466#2044C2×C5912yescomplemented
467#2022C2×C5912yescomplemented
468#1898C2×C5912yescomplemented
469#1890C2×C5911yescharacteristic, complemented
470#1867C2×C5911yescharacteristic, complemented
471#1790C2×C5911yescharacteristic, complemented
472C2×C59—22no—
473C2×C59—21no—
474C2×C59—21no—
475C2×C59—22no—
476C2×C59—22no—
477C2×C59—42no—
478C2×C59—41no—
479C2×C59—42no—
480C2×C59—81no—
481C2×C59—82no—
482C2×C59#241011yescharacteristic
483C2×C59C2×#45811yescharacteristic
484C2×C59#302611yescharacteristic
485C2×H(5,𝔽2)C22×C5911yescharacteristic
486C23×D4C22×C5911yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C5912yes—
494#525—21no—
495C2×#123C22×C5911yescharacteristic
496C2×#123C22×C5912yescomplemented
497C2×#123C22×C5911yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C5912yes—
500#518C22×C5911yescharacteristic
501C22×C22⋊C4C22×C5911yescharacteristic, complemented
502C22×C22⋊C4C22×C5912yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C5911yescharacteristic
506C2×#99C22×C5911yescharacteristic
507C2×#99C22×C5912yescomplemented
508C2×#99C22×C5912yescomplemented
509C2×#99C22×C5912yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C5911yescharacteristic
516#386C22×C5911yescharacteristic, complemented
517#386C22×C5912yescomplemented
518#385—21no—
519#385C22×C5912yescomplemented
520#381C22×C5912yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C5911yescharacteristic, complemented
524#342C22×C5912yescomplemented
525#342C22×C5912yescomplemented
526C59#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C5911yescharacteristic
528C25C23×C5911yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C5911yescharacteristic
544C22×D4D4×C5911yescharacteristic
545C22×D4D4×C5912yes—
546C22×D4D4×C5912yes—
547C22×D4C23×C5912yes—
548C22×D4C23×C5911yescharacteristic
549C22×D4C23×C5911yescharacteristic
550C23×C4—22no—
551C23×C4D4×C5911yescharacteristic
552C23×C4C23×C5911yescharacteristic
553C23×C4C23×C5911yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C5912yes—
611C2×C22⋊C4D4×C5912yes—
612C2×C22⋊C4C23×C5912yes—
613C2×C22⋊C4C23×C5911yescharacteristic
614C2×C22⋊C4C23×C5911yescharacteristic
615C2×C22⋊C4C23×C5912yes—
616C2×C22⋊C4C23×C5912yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C5914yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C5911yescharacteristic
641C24C2×D4×C5912yes—
642C24C2×D4×C5911yescharacteristic
643C24C2×D4×C5912yes—
644C24C2×D4×C5912yes—
645C24C2×D4×C5911yescharacteristic
646C24C2×D4×C5911yescharacteristic
647C24C24×C5911yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C5912yes—
692C2×D4#41×C5912yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C5912yes—
717C22×C4C2×D4×C5911yescharacteristic
718C22×C4C2×D4×C5911yescharacteristic
719C22×C4C2×D4×C5912yes—
720C22×C4C2×D4×C5912yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C5914yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C5911yescharacteristic
807C23#120×C5912yes—
808C23#120×C5911yescharacteristic
809C23#121×C5912yes—
810C23C22×D4×C5911yescharacteristic
811C23C22×D4×C5912yes—
812C23C22×D4×C5911yescharacteristic
813C23C2×#41×C5911yescharacteristic
814C23H(5,𝔽2)×C5912yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C5912yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C59×#45812yescomplemented
918C22C2×#120×C5911yescharacteristic
919C22C2×#121×C5911yescharacteristic
920C22C59×#53411yescharacteristic
921C22D42×C5912yes—
922C22C59×#54612yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C59×#241011yescharacteristic
945C2C2×C59×#45811yescharacteristic
946C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC24C24×C59
prime radicalC59×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C25×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#458C2semidirect
3. C22×#99×C59C2semidirect
4. C59×#2412C2semidirect
5. C59×#2405C2semidirect
6. C59×#2044C2semidirect
7. C59×#2022C2semidirect
8. C59×#1898C2semidirect
9. C59×#1890C2semidirect
10. C59×#1867C2semidirect
11. C59×#1790C2semidirect
23. C2×#123×C59C22semidirect
24. C2×#123×C59C22semidirect
28. C22×C22⋊C4×C59C22semidirect
29. C22×C22⋊C4×C59C22semidirect
34. C2×#99×C59C22semidirect
35. C2×#99×C59C22semidirect
36. C2×#99×C59C22semidirect
43. C59×#386C22semidirect
44. C59×#386C22semidirect
46. C59×#385C22semidirect
47. C59×#381C22semidirect
50. C59×#379C22semidirect
51. C59×#342C22semidirect
52. C59×#342C22semidirect
147. #99×C59D4semidirect
284. C22⋊C4×C59C2×D4semidirect
402. #24405C59direct (N × H)
444. C22×C59#458semidirect
462. C2×#458C2×C59semidirect
463. C22×#99C2×C59semidirect
464. #2412C2×C59semidirect
465. #2405C2×C59semidirect
466. #2044C2×C59semidirect
467. #2022C2×C59semidirect
468. #1898C2×C59semidirect
469. #1890C2×C59semidirect
470. #1867C2×C59semidirect
471. #1790C2×C59semidirect
496. C2×#123C22×C59semidirect
497. C2×#123C22×C59semidirect
501. C22×C22⋊C4C22×C59semidirect
502. C22×C22⋊C4C22×C59semidirect
507. C2×#99C22×C59semidirect
508. C2×#99C22×C59semidirect
509. C2×#99C22×C59semidirect
516. #386C22×C59semidirect
517. #386C22×C59semidirect
519. #385C22×C59semidirect
520. #381C22×C59semidirect
523. #379C22×C59semidirect
524. #342C22×C59semidirect
525. #342C22×C59semidirect
526. C59#24405direct (N × H)
621. #99D4×C59semidirect
758. C22⋊C4C2×D4×C59semidirect
917. C22C59×#458semidirect

Maximal subgroups

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

subgroupindex
C59×#34842
C2×C59×#4582
C22×#99×C592
C59×#24122
C59×#24052
C59×#20442
C59×#20222
C59×#18982
C59×#18902
C59×#18672
C59×#17902
#2440559