Finite Group Databasebeta

← C53×#24056 #27231568

Subgroups — C53×#24056 #27231568

Order 13568.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3484C211yesmaximal, characteristic
2C53×#2849C212yesmaximal, complemented
3C2×C53×#386C211yesmaximal, characteristic, complemented
4C53×#2044C214yesmaximal, complemented
5C53×#1898C212yesmaximal, complemented
6C53×#1867C212yesmaximal, complemented
7C53×#1790C212yesmaximal, complemented
8C53×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C53C2211yescharacteristic
10C23×D4×C53C2211yescharacteristic
11C24×C4×C53C2211yescharacteristic, complemented
12C53×#546—22no—
13C53×#546—22no—
14D42×C53—22no—
15D42×C53—22no—
16C53×#535—21no—
17C53×#534—21no—
18C53×#534C2212yes—
19C53×#525—21no—
20C2×#123×C53—22no—
21C2×#120×C53—21no—
22C2×#120×C53C2212yes—
23C53×#518C2211yescharacteristic
24C22×C22⋊C4×C53—21no—
25C22×C22⋊C4×C53C2211yescharacteristic, complemented
26C2×#99×C53C2212yes—
27C2×#99×C53C2212yescomplemented
28C2×#99×C53C2214yescomplemented
29C53×#386—21no—
30C53×#386—21no—
31C53×#386—22no—
32C53×#386C2212yes—
33C53×#386C2212yescomplemented
34C53×#386C2214yescomplemented
35C53×#385—22no—
36C53×#385C2214yescomplemented
37C53×#381—22no—
38C53×#379C2212yescomplemented
39C2×#95×C53—21no—
40C53×#342C2214yescomplemented
41C25×C53D411yescharacteristic
42C25×C53C2311yescharacteristic
43H(5,𝔽2)×C53—24no—
44H(5,𝔽2)×C53—42no—
45C2×#41×C53—21no—
46C2×#41×C53—22no—
47C22×D4×C53—21no—
48C22×D4×C53—22no—
49C22×D4×C53—22no—
50C22×D4×C53—22no—
51C22×D4×C53—21no—
52C22×D4×C53—21no—
53C22×D4×C53—24no—
54C22×D4×C53—42no—
55C22×D4×C53D411yescharacteristic
56C22×D4×C53D411yescharacteristic
57C22×D4×C53D412yes—
58C22×D4×C53D412yes—
59C22×D4×C53C2312yes—
60C22×D4×C53C2311yescharacteristic
61C22×D4×C53C2311yescharacteristic
62C23×C4×C53—21no—
63C23×C4×C53—22no—
64C23×C4×C53—21no—
65C23×C4×C53—22no—
66C23×C4×C53—21no—
67C23×C4×C53—44no—
68C23×C4×C53D411yescharacteristic
69C23×C4×C53C2312yes—
70#127×C53—22no—
71#124×C53—22no—
72#123×C53—22no—
73#123×C53—22no—
74#123×C53—22no—
75#123×C53—48no—
76C22⋊Q8×C53—21no—
77C22⋊Q8×C53—21no—
78#121×C53—21no—
79#121×C53—21no—
80#121×C53—22no—
81#121×C53—22no—
82#121×C53—22no—
83#121×C53—22no—
84#121×C53—22no—
85#121×C53—22no—
86#120×C53—22no—
87#120×C53—22no—
88#120×C53—22no—
89#120×C53—22no—
90#120×C53—22no—
91#120×C53—22no—
92#120×C53—22no—
93#120×C53—22no—
94#120×C53—22no—
95C4×D4×C53—22no—
96C4×D4×C53—22no—
97C4×D4×C53—22no—
98C4×D4×C53—22no—
99#117×C53—21no—
100C2×C4⋊C4×C53—24no—
101C2×C22⋊C4×C53—21no—
102C2×C22⋊C4×C53—21no—
103C2×C22⋊C4×C53—21no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—21no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—24no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—44no—
111C2×C22⋊C4×C53—42no—
112C2×C22⋊C4×C53D412yes—
113C2×C22⋊C4×C53D412yes—
114C2×C22⋊C4×C53C2312yes—
115C2×C22⋊C4×C53C2314yes—
116C2×C22⋊C4×C53C2312yes—
117#99×C53—24no—
118#99×C53—42no—
119#99×C53—44no—
120#95×C53—22no—
121#95×C53—22no—
122#95×C53—24no—
123#95×C53—24no—
124C24×C53—22no—
125C24×C53—22no—
126C24×C53—21no—
127C24×C53—22no—
128C24×C53—21no—
129C24×C53—21no—
130C24×C53—42no—
131C24×C53—42no—
132C24×C53—41no—
133C24×C53—42no—
134C24×C53—42no—
135C24×C53C2×D411yescharacteristic
136C24×C53C2×D412yes—
137C24×C53C2×D412yes—
138C24×C53C2×D411yescharacteristic
139C24×C53C2×D412yes—
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2411yescharacteristic
143#41×C53—48no—
144#41×C53—42no—
145#41×C53—42no—
146C2×Q8×C53—21no—
147C2×D4×C53—22no—
148C2×D4×C53—22no—
149C2×D4×C53—22no—
150C2×D4×C53—21no—
151C2×D4×C53—22no—
152C2×D4×C53—22no—
153C2×D4×C53—22no—
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53—24no—
161C2×D4×C53—22no—
162C2×D4×C53—24no—
163C2×D4×C53—22no—
164C2×D4×C53—22no—
165C2×D4×C53—22no—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—41no—
169C2×D4×C53—41no—
170C2×D4×C53—48no—
171C2×D4×C53—48no—
172C2×D4×C53—48no—
173C2×D4×C53—42no—
174C2×D4×C53—42no—
175C2×D4×C53—44no—
176C2×D4×C53—44no—
177C2×D4×C53—82no—
178C2×D4×C53—82no—
179C2×D4×C53#4114yes—
180C22×C4×C53—21no—
181C22×C4×C53—24no—
182C22×C4×C53—22no—
183C22×C4×C53—28no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—22no—
187C22×C4×C53—24no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—22no—
191C22×C4×C53—24no—
192C22×C4×C53—22no—
193C22×C4×C53—44no—
194C22×C4×C53—41no—
195C22×C4×C53—44no—
196C22×C4×C53—48no—
197C22×C4×C53—42no—
198C22×C4×C53—44no—
199C22×C4×C53—42no—
200C22×C4×C53—41no—
201C22×C4×C53—41no—
202C22×C4×C53—42no—
203C22×C4×C53—42no—
204C22×C4×C53—42no—
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2×D412yes—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53—22no—
213C4⋊C4×C53—22no—
214C4⋊C4×C53—48no—
215C22⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—22no—
224C22⋊C4×C53—22no—
225C22⋊C4×C53—22no—
226C22⋊C4×C53—24no—
227C22⋊C4×C53—24no—
228C22⋊C4×C53—24no—
229C22⋊C4×C53—44no—
230C22⋊C4×C53—44no—
231C22⋊C4×C53—48no—
232C22⋊C4×C53—44no—
233C22⋊C4×C53—42no—
234C22⋊C4×C53—44no—
235C42×C53—22no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53—24no—
246C23×C53—24no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—24no—
253C23×C53—42no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—42no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—42no—
260C23×C53—42no—
261C23×C53—48no—
262C23×C53—48no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—48no—
268C23×C53—42no—
269C23×C53—42no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53—81no—
274C23×C53—81no—
275C23×C53—84no—
276C23×C53—81no—
277C23×C53—81no—
278C23×C53#12012yes—
279C23×C53#12011yescharacteristic
280C23×C53#12011yescharacteristic
281C23×C53#12312yescomplemented
282C23×C53C22×D411yescharacteristic
283C23×C53C22×D412yes—
284C23×C53C2×#4112yes—
285C23×C53H(5,𝔽2)12yes—
286Q8×C53—42no—
287D4×C53—28no—
288D4×C53—44no—
289D4×C53—42no—
290D4×C53—44no—
291D4×C53—44no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—44no—
295D4×C53—44no—
296D4×C53—44no—
297D4×C53—44no—
298D4×C53—82no—
299D4×C53—82no—
300D4×C53—82no—
301D4×C53—82no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—24no—
305C2×C4×C53—28no—
306C2×C4×C53—21no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—24no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—44no—
316C2×C4×C53—44no—
317C2×C4×C53—42no—
318C2×C4×C53—44no—
319C2×C4×C53—48no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—44no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—44no—
328C2×C4×C53—44no—
329C2×C4×C53—42no—
330C2×C4×C53—44no—
331C2×C4×C53—81no—
332C2×C4×C53—81no—
333C2×C4×C53—84no—
334C2×C4×C53#12312yescomplemented
335#24056C5311yesmaximal, characteristic, direct product factor, Sylow
336C22×C53—24no—
337C22×C53—24no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—22no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—22no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—48no—
353C22×C53—48no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—42no—
361C22×C53—41no—
362C22×C53—42no—
363C22×C53—41no—
364C22×C53—42no—
365C22×C53—41no—
366C22×C53—81no—
367C22×C53—84no—
368C22×C53—84no—
369C22×C53—84no—
370C22×C53—81no—
371C22×C53—162no—
372C22×C53B(4,𝔽2)12yes—
373C22×C53#45812yes—
374C22×C53C2×#12011yescharacteristic
375C22×C53C2×#12311yescharacteristic
376C22×C53#53411yescharacteristic
377C22×C53#54614yes—
378C4×C53—22no—
379C4×C53—41no—
380C4×C53—42no—
381C4×C53—44no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—84no—
385C4×C53—82no—
386#3484C2×C5311yescharacteristic
387#2849C2×C5312yescomplemented
388C2×#386C2×C5311yescharacteristic, complemented
389#2044C2×C5314yescomplemented
390#1898C2×C5312yescomplemented
391#1867C2×C5312yescomplemented
392#1790C2×C5312yescomplemented
393#1781C2×C5311yescharacteristic, complemented
394C2×C53—21no—
395C2×C53—24no—
396C2×C53—21no—
397C2×C53—22no—
398C2×C53—22no—
399C2×C53—42no—
400C2×C53—42no—
401C2×C53—81no—
402C2×C53—82no—
403C2×C53#240511yescharacteristic
404C2×C53C2×B(4,𝔽2)11yescharacteristic
405C2×C53C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C5311yescharacteristic
407C23×D4C22×C5311yescharacteristic
408C24×C4C22×C5311yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C5312yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C5312yes—
420#518C22×C5311yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C5311yescharacteristic, complemented
423C2×#99C22×C5312yes—
424C2×#99C22×C5314yescomplemented
425C2×#99C22×C5312yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C5312yes—
430#386C22×C5314yescomplemented
431#386C22×C5312yescomplemented
432#385—22no—
433#385C22×C5314yescomplemented
434#381—22no—
435#379C22×C5312yescomplemented
436C2×#95—21no—
437#342C22×C5314yescomplemented
438C53#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C5311yescharacteristic
440C25C23×C5311yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C5311yescharacteristic
454C22×D4D4×C5311yescharacteristic
455C22×D4D4×C5312yes—
456C22×D4D4×C5312yes—
457C22×D4C23×C5312yes—
458C22×D4C23×C5311yescharacteristic
459C22×D4C23×C5311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C5311yescharacteristic
467C23×C4C23×C5312yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C5312yes—
511C2×C22⋊C4D4×C5312yes—
512C2×C22⋊C4C23×C5312yes—
513C2×C22⋊C4C23×C5314yes—
514C2×C22⋊C4C23×C5312yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C5311yescharacteristic
534C24C2×D4×C5312yes—
535C24C2×D4×C5312yes—
536C24C2×D4×C5311yescharacteristic
537C24C2×D4×C5312yes—
538C24C2×D4×C5311yescharacteristic
539C24C2×D4×C5311yescharacteristic
540C24C24×C5311yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C5314yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C5312yes—
604C22×C4C2×D4×C5311yescharacteristic
605C22×C4C2×D4×C5311yescharacteristic
606C22×C4C2×D4×C5312yes—
607C22×C4C2×D4×C5312yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C5312yes—
677C23#120×C5311yescharacteristic
678C23#120×C5311yescharacteristic
679C23#123×C5312yescomplemented
680C23C22×D4×C5311yescharacteristic
681C23C22×D4×C5312yes—
682C23C2×#41×C5312yes—
683C23H(5,𝔽2)×C5312yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C5312yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C53×B(4,𝔽2)12yes—
770C22C53×#45812yes—
771C22C2×#120×C5311yescharacteristic
772C22C2×#123×C5311yescharacteristic
773C22C53×#53411yescharacteristic
774C22C53×#54614yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C53×#240511yescharacteristic
793C2C2×C53×B(4,𝔽2)11yescharacteristic
794C2C2×C53×#45811yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC24C24×C53
prime radicalC53×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C25×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#2849C2semidirect
3. C2×C53×#386C2semidirect
4. C53×#2044C2semidirect
5. C53×#1898C2semidirect
6. C53×#1867C2semidirect
7. C53×#1790C2semidirect
8. C53×#1781C2semidirect
11. C24×C4×C53C22semidirect
25. C22×C22⋊C4×C53C22semidirect
27. C2×#99×C53C22semidirect
28. C2×#99×C53C22semidirect
33. C53×#386C22semidirect
34. C53×#386C22semidirect
36. C53×#385C22semidirect
38. C53×#379C22semidirect
40. C53×#342C22semidirect
281. C23×C53#123semidirect
334. C2×C4×C53#123semidirect
335. #24056C53direct (N × H)
387. #2849C2×C53semidirect
388. C2×#386C2×C53semidirect
389. #2044C2×C53semidirect
390. #1898C2×C53semidirect
391. #1867C2×C53semidirect
392. #1790C2×C53semidirect
393. #1781C2×C53semidirect
408. C24×C4C22×C53semidirect
422. C22×C22⋊C4C22×C53semidirect
424. C2×#99C22×C53semidirect
425. C2×#99C22×C53semidirect
430. #386C22×C53semidirect
431. #386C22×C53semidirect
433. #385C22×C53semidirect
435. #379C22×C53semidirect
437. #342C22×C53semidirect
438. C53#24056direct (N × H)
679. C23#123×C53semidirect
732. C2×C4#123×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#34842
C53×#28492
C2×C53×#3862
C53×#20442
C53×#18982
C53×#18672
C53×#17902
C53×#17812
#2405653