Finite Group Databasebeta

← C53×#18254 #27225766

Subgroups — C53×#18254 #27225766

Order 13568.

1508 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3537C211yesmaximal, characteristic, complemented
2C53×#3003C211yesmaximal, characteristic, complemented
3C2×C53×#447C211yesmaximal, characteristic, complemented
4C53×#2433C211yesmaximal, characteristic, complemented
5C53×#1600C214yesmaximal, complemented
6C53×#1595C214yesmaximal, complemented
7C53×#1507C211yesmaximal, characteristic, complemented
8C53×#1501C211yesmaximal, characteristic, complemented
9C53×#1471C211yesmaximal, characteristic, complemented
10C23×D4×C53C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C53—21no—
12C22×D8×C53—21no—
13C53×#560—22no—
14C53×#553—21no—
15C53×#553—21no—
16D42×C53—22no—
17D42×C53—21no—
18D42×C53—21no—
19C53×#540—21no—
20C53×#538—21no—
21C53×#538C2212yescomplemented
22C53×#535—21no—
23C53×#534—21no—
24C53×#534C2212yescomplemented
25C2×#127×C53—21no—
26C53×#525C2211yescharacteristic
27C2×#121×C53C2211yescharacteristic
28C2×#121×C53C2211yescharacteristic
29C2×#120×C53—22no—
30C53×#450—21no—
31C53×#450C2212yescomplemented
32C53×#447—22no—
33C53×#447—21no—
34C53×#447C2214yescomplemented
35C53×#447C2212yescomplemented
36C53×#418—21no—
37C2×#102×C53—21no—
38C53×#407C2211yescharacteristic, complemented
39C2×C22⋊C8×C53C2211yescharacteristic, complemented
40C53×#392C2214yescomplemented
41C53×#390—21no—
42C4×C22⋊C4×C53C2211yescharacteristic, complemented
43C53×#328C2212yescomplemented
44C53×#327C2212yescomplemented
45C53×#327C2214yescomplemented
46C53×#323C2214yescomplemented
47C25×C53—21no—
48C2×#41×C53D411yescharacteristic, complemented
49C22×D4×C53—22no—
50C22×D4×C53—21no—
51C22×D4×C53—21no—
52C22×D4×C53—22no—
53C22×D4×C53—24no—
54C22×D4×C53—21no—
55C22×D4×C53—21no—
56C22×D4×C53—21no—
57C22×D4×C53—21no—
58C22×D4×C53—21no—
59C22×D4×C53—44no—
60C22×D4×C53D412yes—
61C22×D4×C53D411yescharacteristic
62C22×D4×C53D411yescharacteristic, complemented
63C22×D4×C53C2312yes—
64C23×C4×C53C2311yescharacteristic
65AGL(1,ℤ/8)×C53—44no—
66C2×SD16×C53—22no—
67C2×D8×C53—24no—
68C2×D8×C53—22no—
69C2×D8×C53—44no—
70C2×M16×C53—21no—
71C22×C8×C53—21no—
72#127×C53—22no—
73#127×C53—21no—
74#127×C53—44no—
75#126×C53—22no—
76#126×C53—22no—
77#125×C53—21no—
78#124×C53—22no—
79#123×C53—22no—
80#123×C53—22no—
81#123×C53—22no—
82#123×C53—22no—
83#123×C53—21no—
84C22⋊Q8×C53D411yescharacteristic, complemented
85C22⋊Q8×C53C2311yescharacteristic
86#121×C53—22no—
87#121×C53—21no—
88#121×C53—21no—
89#121×C53—22no—
90#121×C53—22no—
91#121×C53—22no—
92#121×C53—22no—
93#121×C53—21no—
94#121×C53—21no—
95#121×C53—21no—
96#121×C53—21no—
97#121×C53—21no—
98#121×C53—21no—
99#121×C53—22no—
100#121×C53D412yescomplemented
101#121×C53D411yescharacteristic, complemented
102#121×C53C2312yes—
103#121×C53C2311yescharacteristic
104#120×C53—22no—
105#120×C53—22no—
106#120×C53—22no—
107#120×C53—21no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—22no—
111#120×C53—48no—
112C4×D4×C53—22no—
113C4×D4×C53—21no—
114C4×D4×C53—21no—
115C4×D4×C53—21no—
116C4×D4×C53—21no—
117C4×D4×C53—22no—
118#117×C53—21no—
119#117×C53D411yescharacteristic, complemented
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53D411yescharacteristic, complemented
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—24no—
125C2×C22⋊C4×C53C2312yes—
126C2×C42×C53—21no—
127#102×C53—24no—
128#102×C53—22no—
129#102×C53—22no—
130C22⋊C8×C53—21no—
131C22⋊C8×C53—21no—
132C22⋊C8×C53C2312yes—
133C22⋊C8×C53C2312yes—
134#95×C53C2312yes—
135C24×C53—22no—
136C24×C53—22no—
137C24×C53—21no—
138C24×C53—44no—
139C24×C53—44no—
140C24×C53—41no—
141C24×C53—41no—
142C24×C53—82no—
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D412yes—
145#41×C53—42no—
146C2×Q8×C53C2×D411yescharacteristic
147C2×D4×C53—24no—
148C2×D4×C53—24no—
149C2×D4×C53—24no—
150C2×D4×C53—22no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
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—21no—
160C2×D4×C53—22no—
161C2×D4×C53—22no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—22no—
166C2×D4×C53—22no—
167C2×D4×C53—42no—
168C2×D4×C53—42no—
169C2×D4×C53—42no—
170C2×D4×C53—42no—
171C2×D4×C53—42no—
172C2×D4×C53—48no—
173C2×D4×C53—44no—
174C2×D4×C53—44no—
175C2×D4×C53—44no—
176C2×D4×C53—44no—
177C2×D4×C53—48no—
178C2×D4×C53—41no—
179C2×D4×C53—41no—
180C2×D4×C53—82no—
181C2×D4×C53—84no—
182C2×D4×C53—82no—
183C2×D4×C53—84no—
184C2×D4×C53—84no—
185C2×D4×C53C2×D411yescharacteristic
186C2×D4×C53C2×D412yes—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—42no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200SD16×C53—44no—
201D8×C53—48no—
202D8×C53—44no—
203M16×C53—42no—
204C2×C8×C53—22no—
205C2×C8×C53—22no—
206C2×C8×C53—42no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53C2×D412yes—
215C4⋊C4×C53C2×D411yescharacteristic
216C4⋊C4×C53C2×D411yescharacteristic
217C22⋊C4×C53—24no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—21no—
224C22⋊C4×C53—21no—
225C22⋊C4×C53—21no—
226C22⋊C4×C53—22no—
227C22⋊C4×C53—21no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—21no—
232C22⋊C4×C53—48no—
233C42×C53—22no—
234C42×C53—21no—
235C42×C53—42no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—24no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—21no—
242C23×C53—24no—
243C23×C53—41no—
244C23×C53—44no—
245C23×C53—44no—
246C23×C53—42no—
247C23×C53—44no—
248C23×C53—42no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—44no—
252C23×C53—42no—
253C23×C53—81no—
254C23×C53—81no—
255C23×C53—82no—
256C23×C53—82no—
257C23×C53—82no—
258C23×C53—82no—
259C23×C53—82no—
260C23×C53—82no—
261C23×C53—816no—
262C23×C53—82no—
263C23×C53#12011yescharacteristic
264C23×C53#12011yescharacteristic
265C23×C53C22×D411yescharacteristic
266Q8×C53—41no—
267D4×C53—24no—
268D4×C53—24no—
269D4×C53—42no—
270D4×C53—41no—
271D4×C53—42no—
272D4×C53—42no—
273D4×C53—44no—
274D4×C53—44no—
275D4×C53—42no—
276D4×C53—44no—
277D4×C53—42no—
278D4×C53—44no—
279D4×C53—42no—
280D4×C53—42no—
281D4×C53—81no—
282D4×C53—82no—
283D4×C53—82no—
284D4×C53—81no—
285D4×C53—82no—
286D4×C53—82no—
287D4×C53—82no—
288D4×C53—82no—
289D4×C53—82no—
290D4×C53—816no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—21no—
296C2×C4×C53—22no—
297C2×C4×C53—21no—
298C2×C4×C53—22no—
299C2×C4×C53—21no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—81no—
308C2×C4×C53—82no—
309C2×C4×C53—82no—
310C2×C4×C53#12011yescharacteristic
311C2×C4×C53#12011yescharacteristic
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C22×D411yescharacteristic
314C8×C53—42no—
315C8×C53—42no—
316#18254C5311yesmaximal, characteristic, direct product factor, Sylow
317C22×C53—21no—
318C22×C53—21no—
319C22×C53—21no—
320C22×C53—21no—
321C22×C53—21no—
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—44no—
325C22×C53—48no—
326C22×C53—42no—
327C22×C53—42no—
328C22×C53—41no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—44no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—84no—
337C22×C53—84no—
338C22×C53—88no—
339C22×C53—88no—
340C22×C53—82no—
341C22×C53—82no—
342C22×C53—162no—
343C22×C53—164no—
344C22×C53#45312yes—
345C22×C53C2×#12011yescharacteristic
346C22×C53#57612yes—
347C4×C53—21no—
348C4×C53—21no—
349C4×C53—21no—
350C4×C53—44no—
351C4×C53—42no—
352C4×C53—41no—
353C4×C53—42no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53B(4,𝔽2)12yes—
357#3537C2×C5311yescharacteristic, complemented
358#3003C2×C5311yescharacteristic, complemented
359C2×#447C2×C5311yescharacteristic, complemented
360#2433C2×C5311yescharacteristic, complemented
361#1600C2×C5314yescomplemented
362#1595C2×C5314yescomplemented
363#1507C2×C5311yescharacteristic, complemented
364#1501C2×C5311yescharacteristic, complemented
365#1471C2×C5311yescharacteristic, complemented
366C2×C53—22no—
367C2×C53—22no—
368C2×C53—41no—
369C2×C53—84no—
370C2×C53—82no—
371C2×C53—82no—
372C2×C53—81no—
373C2×C53#300811yescharacteristic
374C2×C53C2×#45311yescharacteristic
375C2×C53C2×B(4,𝔽2)11yescharacteristic
376C23×D4C22×C5311yescharacteristic, complemented
377C2×AGL(1,ℤ/8)—21no—
378C22×D8—21no—
379#560—22no—
380#553—21no—
381#553—21no—
382D42—22no—
383D42—21no—
384D42—21no—
385#540—21no—
386#538—21no—
387#538C22×C5312yescomplemented
388#535—21no—
389#534—21no—
390#534C22×C5312yescomplemented
391C2×#127—21no—
392#525C22×C5311yescharacteristic
393C2×#121C22×C5311yescharacteristic
394C2×#121C22×C5311yescharacteristic
395C2×#120—22no—
396#450—21no—
397#450C22×C5312yescomplemented
398#447—22no—
399#447—21no—
400#447C22×C5312yescomplemented
401#447C22×C5314yescomplemented
402#418—21no—
403C2×#102—21no—
404#407C22×C5311yescharacteristic, complemented
405C2×C22⋊C8C22×C5311yescharacteristic, complemented
406#392C22×C5314yescomplemented
407#390—21no—
408C4×C22⋊C4C22×C5311yescharacteristic, complemented
409#328C22×C5312yescomplemented
410#327C22×C5312yescomplemented
411#327C22×C5314yescomplemented
412#323C22×C5314yescomplemented
413C53#1825411yescharacteristic, direct product factor, Sylow
414C25—21no—
415C2×#41D4×C5311yescharacteristic, complemented
416C22×D4—22no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—24no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—44no—
427C22×D4D4×C5312yes—
428C22×D4D4×C5311yescharacteristic
429C22×D4D4×C5311yescharacteristic, complemented
430C22×D4C23×C5312yes—
431C23×C4C23×C5311yescharacteristic
432AGL(1,ℤ/8)—44no—
433C2×SD16—22no—
434C2×D8—24no—
435C2×D8—22no—
436C2×D8—44no—
437C2×M16—21no—
438C22×C8—21no—
439#127—22no—
440#127—21no—
441#127—44no—
442#126—22no—
443#126—22no—
444#125—21no—
445#124—22no—
446#123—22no—
447#123—21no—
448#123—22no—
449#123—22no—
450#123—22no—
451C22⋊Q8D4×C5311yescharacteristic, complemented
452C22⋊Q8C23×C5311yescharacteristic
453#121—22no—
454#121—21no—
455#121—21no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—22no—
467#121D4×C5312yescomplemented
468#121D4×C5311yescharacteristic, complemented
469#121C23×C5312yes—
470#121C23×C5311yescharacteristic
471#120—22no—
472#120—22no—
473#120—22no—
474#120—21no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—48no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—22no—
485#117—21no—
486#117D4×C5311yescharacteristic, complemented
487C2×C4⋊C4D4×C5311yescharacteristic
488C2×C4⋊C4D4×C5311yescharacteristic, complemented
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4C23×C5312yes—
493C2×C42—21no—
494#102—24no—
495#102—22no—
496#102—22no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499C22⋊C8C23×C5312yes—
500C22⋊C8C23×C5312yes—
501#95C23×C5312yes—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—44no—
506C24—44no—
507C24—41no—
508C24—41no—
509C24—82no—
510C24C2×D4×C5311yescharacteristic
511C24C2×D4×C5312yes—
512#41—42no—
513C2×Q8C2×D4×C5311yescharacteristic
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—82no—
548C2×D4—84no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4C2×D4×C5311yescharacteristic
553C2×D4C2×D4×C5312yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4C2×D4×C5311yescharacteristic
561C22×C4C2×D4×C5311yescharacteristic
562C22×C4C2×D4×C5311yescharacteristic
563C22×C4C2×D4×C5312yes—
564C22×C4C2×D4×C5311yescharacteristic
565C22×C4C2×D4×C5311yescharacteristic
566C22×C4C24×C5311yescharacteristic
567SD16—44no—
568D8—48no—
569D8—44no—
570M16—42no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—42no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×D4×C5312yes—
582C4⋊C4C2×D4×C5311yescharacteristic
583C4⋊C4C2×D4×C5311yescharacteristic
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—22no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—48no—
600C42—22no—
601C42—21no—
602C42—42no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—21no—
609C23—24no—
610C23—41no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—42no—
620C23—81no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—816no—
629C23—82no—
630C23#120×C5311yescharacteristic
631C23#120×C5311yescharacteristic
632C23C22×D4×C5311yescharacteristic
633Q8—41no—
634D4—24no—
635D4—24no—
636D4—42no—
637D4—41no—
638D4—42no—
639D4—42no—
640D4—44no—
641D4—44no—
642D4—42no—
643D4—44no—
644D4—42no—
645D4—44no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—81no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—816no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4#120×C5311yescharacteristic
678C2×C4#120×C5311yescharacteristic
679C2×C4C22×D4×C5311yescharacteristic
680C2×C4C22×D4×C5311yescharacteristic
681C8—42no—
682C8—42no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—44no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—44no—
700C22—42no—
701C22—42no—
702C22—84no—
703C22—84no—
704C22—88no—
705C22—88no—
706C22—82no—
707C22—82no—
708C22—162no—
709C22—164no—
710C22C53×#45312yes—
711C22C2×#120×C5311yescharacteristic
712C22C53×#57612yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—44no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4C53×B(4,𝔽2)12yes—
723C2—22no—
724C2—22no—
725C2—41no—
726C2—84no—
727C2—82no—
728C2—82no—
729C2—81no—
730C2C53×#300811yescharacteristic
731C2C2×C53×#45311yescharacteristic
732C2C2×C53×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3537C2semidirect
2. C53×#3003C2semidirect
3. C2×C53×#447C2semidirect
4. C53×#2433C2semidirect
5. C53×#1600C2semidirect
6. C53×#1595C2semidirect
7. C53×#1507C2semidirect
8. C53×#1501C2semidirect
9. C53×#1471C2semidirect
10. C23×D4×C53C22semidirect
21. C53×#538C22semidirect
24. C53×#534C22semidirect
31. C53×#450C22semidirect
34. C53×#447C22semidirect
35. C53×#447C22semidirect
38. C53×#407C22semidirect
39. C2×C22⋊C8×C53C22semidirect
40. C53×#392C22semidirect
42. C4×C22⋊C4×C53C22semidirect
43. C53×#328C22semidirect
44. C53×#327C22semidirect
45. C53×#327C22semidirect
46. C53×#323C22semidirect
48. C2×#41×C53D4semidirect
62. C22×D4×C53D4semidirect
84. C22⋊Q8×C53D4semidirect
100. #121×C53D4semidirect
101. #121×C53D4semidirect
119. #117×C53D4semidirect
121. C2×C4⋊C4×C53D4semidirect
316. #18254C53direct (N × H)
357. #3537C2×C53semidirect
358. #3003C2×C53semidirect
359. C2×#447C2×C53semidirect
360. #2433C2×C53semidirect
361. #1600C2×C53semidirect
362. #1595C2×C53semidirect
363. #1507C2×C53semidirect
364. #1501C2×C53semidirect
365. #1471C2×C53semidirect
376. C23×D4C22×C53semidirect
387. #538C22×C53semidirect
390. #534C22×C53semidirect
397. #450C22×C53semidirect
400. #447C22×C53semidirect
401. #447C22×C53semidirect
404. #407C22×C53semidirect
405. C2×C22⋊C8C22×C53semidirect
406. #392C22×C53semidirect
408. C4×C22⋊C4C22×C53semidirect
409. #328C22×C53semidirect
410. #327C22×C53semidirect
411. #327C22×C53semidirect
412. #323C22×C53semidirect
413. C53#18254direct (N × H)
415. C2×#41D4×C53semidirect
429. C22×D4D4×C53semidirect
451. C22⋊Q8D4×C53semidirect
467. #121D4×C53semidirect
468. #121D4×C53semidirect
486. #117D4×C53semidirect
488. C2×C4⋊C4D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35372
C53×#30032
C2×C53×#4472
C53×#24332
C53×#16002
C53×#15952
C53×#15072
C53×#15012
C53×#14712
#1825453