Finite Group Databasebeta

← C53×#18450 #27225962

Subgroups — C53×#18450 #27225962

Order 13568.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3537C211yesmaximal, characteristic, complemented
2C53×#3194C211yesmaximal, characteristic, complemented
3C53×#3186C211yesmaximal, characteristic, complemented
4C53×#2815C211yesmaximal, characteristic, complemented
5C53×#1612C212yesmaximal, complemented
6C53×#1607C212yesmaximal, complemented
7C53×#1600C212yesmaximal, complemented
8C53×#1595C212yesmaximal, complemented
9C53×#1516C211yesmaximal, characteristic, complemented
10C53×#1510C211yesmaximal, characteristic, complemented
11C53×#1471C211yesmaximal, characteristic, complemented
12C53×#560—22no—
13C53×#553—21no—
14C53×#553—21no—
15D42×C53—22no—
16D42×C53—21no—
17D42×C53—21no—
18C53×#540—21no—
19C53×#538—21no—
20C53×#538C2212yes—
21C53×#535—21no—
22C53×#534—21no—
23C53×#534C2212yes—
24C53×#525C2211yescharacteristic
25C2×#121×C53C2211yescharacteristic
26C2×#121×C53C2211yescharacteristic
27C2×#121×C53C2211yescharacteristic, complemented
28C53×#483C2211yescharacteristic, complemented
29C53×#482—21no—
30C53×#480—21no—
31C53×#480C2211yescharacteristic, complemented
32C53×#480C2212yescomplemented
33C53×#469—21no—
34C53×#468—21no—
35C53×#466—22no—
36C53×#450C2211yescharacteristic, complemented
37C53×#449—21no—
38C53×#447—21no—
39C53×#447C2211yescharacteristic, complemented
40C53×#447C2212yescomplemented
41C53×#407C2211yescharacteristic, complemented
42C2×C22⋊C8×C53C2211yescharacteristic, complemented
43C53×#397—21no—
44C53×#397C2212yescomplemented
45C53×#392—21no—
46C53×#392—22no—
47C53×#392C2212yescomplemented
48C53×#381C2211yescharacteristic, complemented
49C53×#328C2212yescomplemented
50C53×#327C2212yescomplemented
51C53×#327C2212yescomplemented
52C53×#327C2212yescomplemented
53C53×#323C2212yescomplemented
54C53×#323C2212yescomplemented
55C2×#41×C53D411yescharacteristic, complemented
56C22×D4×C53—22no—
57C22×D4×C53—21no—
58C22×D4×C53—21no—
59C22×D4×C53—22no—
60C22×D4×C53—21no—
61C22×D4×C53—22no—
62C22×D4×C53D412yes—
63C22×D4×C53D411yescharacteristic
64C22×D4×C53D411yescharacteristic, complemented
65C22×D4×C53C2311yescharacteristic
66C23×C4×C53C2311yescharacteristic
67C2×SD16×C53—21no—
68C2×D8×C53—22no—
69C2×D8×C53—21no—
70C2×M16×C53—21no—
71C22×C8×C53—21no—
72#127×C53—22no—
73#127×C53—21no—
74#126×C53—22no—
75#126×C53—22no—
76#125×C53—21no—
77#124×C53—22no—
78#123×C53—22no—
79#123×C53—22no—
80#123×C53—22no—
81#123×C53—22no—
82#123×C53—21no—
83C22⋊Q8×C53D411yescharacteristic, complemented
84C22⋊Q8×C53C2311yescharacteristic
85#121×C53—22no—
86#121×C53—21no—
87#121×C53—21no—
88#121×C53—22no—
89#121×C53—22no—
90#121×C53—22no—
91#121×C53—22no—
92#121×C53—21no—
93#121×C53—21no—
94#121×C53—21no—
95#121×C53—21no—
96#121×C53—21no—
97#121×C53—21no—
98#121×C53—22no—
99#121×C53—21no—
100#121×C53—21no—
101#121×C53—21no—
102#121×C53—21no—
103#121×C53D412yescomplemented
104#121×C53D411yescharacteristic, complemented
105#121×C53C2312yes—
106#121×C53C2311yescharacteristic
107#120×C53—22no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—21no—
111#120×C53—22no—
112#120×C53—22no—
113#120×C53—22no—
114C4×D4×C53—22no—
115C4×D4×C53—21no—
116C4×D4×C53—21no—
117C4×D4×C53—21no—
118C4×D4×C53—21no—
119C4×D4×C53—22no—
120#117×C53—21no—
121#117×C53D411yescharacteristic, complemented
122C2×C4⋊C4×C53D411yescharacteristic
123C2×C4⋊C4×C53D411yescharacteristic, complemented
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—22no—
130C2×C22⋊C4×C53C2312yes—
131#107×C53—22no—
132#107×C53—21no—
133#106×C53—21no—
134#103×C53—21no—
135#102×C53—22no—
136#102×C53—21no—
137#102×C53—21no—
138#102×C53—22no—
139#102×C53—21no—
140C22⋊C8×C53—21no—
141C22⋊C8×C53—21no—
142C22⋊C8×C53C2311yescharacteristic
143C22⋊C8×C53C2311yescharacteristic
144C22⋊C8×C53C2312yes—
145#95×C53—21no—
146#95×C53—22no—
147#95×C53C2312yes—
148C24×C53—22no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53C2×D412yes—
152C24×C53C2×D411yescharacteristic
153#41×C53—81no—
154C2×Q8×C53C2×D411yescharacteristic
155C2×D4×C53—22no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—22no—
162C2×D4×C53—22no—
163C2×D4×C53—22no—
164C2×D4×C53—21no—
165C2×D4×C53—22no—
166C2×D4×C53—22no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—41no—
173C2×D4×C53—41no—
174C2×D4×C53—81no—
175C2×D4×C53—81no—
176C2×D4×C53—82no—
177C2×D4×C53—81no—
178C2×D4×C53—82no—
179C2×D4×C53—82no—
180C2×D4×C53—82no—
181C2×D4×C53—82no—
182C2×D4×C53—82no—
183C2×D4×C53—82no—
184C2×D4×C53—82no—
185C2×D4×C53—82no—
186C2×D4×C53—84no—
187C2×D4×C53C2×D411yescharacteristic
188C2×D4×C53C2×D412yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—81no—
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203SD16×C53—81no—
204D8×C53—82no—
205D8×C53—81no—
206M16×C53—81no—
207C2×C8×C53—22no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—81no—
211C4⋊C4×C53—22no—
212C4⋊C4×C53—22no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53C2×D411yescharacteristic
221C4⋊C4×C53C2×D412yes—
222C4⋊C4×C53C2×D411yescharacteristic
223C22⋊C4×C53—22no—
224C22⋊C4×C53—22no—
225C22⋊C4×C53—22no—
226C22⋊C4×C53—22no—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—21no—
229C22⋊C4×C53—21no—
230C22⋊C4×C53—21no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—21no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—21no—
237C22⋊C4×C53—41no—
238C22⋊C4×C53—41no—
239C22⋊C4×C53—82no—
240C22⋊C4×C53—82no—
241C22⋊C4×C53—81no—
242C42×C53—22no—
243C42×C53—21no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—42no—
253C23×C53—42no—
254C23×C53—42no—
255C23×C53—41no—
256C23×C53—42no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—42no—
260C23×C53—81no—
261C23×C53—81no—
262C23×C53—82no—
263C23×C53—82no—
264C23×C53—82no—
265C23×C53#12011yescharacteristic
266C23×C53#12011yescharacteristic
267C23×C53C22×D411yescharacteristic
268Q8×C53—41no—
269D4×C53—42no—
270D4×C53—41no—
271D4×C53—42no—
272D4×C53—42no—
273D4×C53—42no—
274D4×C53—41no—
275D4×C53—41no—
276D4×C53—44no—
277D4×C53—42no—
278D4×C53—42no—
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—82no—
291D4×C53—82no—
292D4×C53—88no—
293C2×C4×C53—21no—
294C2×C4×C53—22no—
295C2×C4×C53—21no—
296C2×C4×C53—22no—
297C2×C4×C53—21no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—41no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—81no—
312C2×C4×C53—82no—
313C2×C4×C53—82no—
314C2×C4×C53#12011yescharacteristic
315C2×C4×C53#12011yescharacteristic
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C22×D411yescharacteristic
318C8×C53—42no—
319C8×C53—41no—
320C8×C53—41no—
321#18450C5311yesmaximal, characteristic, direct product factor, Sylow
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—21no—
325C22×C53—21no—
326C22×C53—21no—
327C22×C53—21no—
328C22×C53—21no—
329C22×C53—21no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—41no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—82no—
340C22×C53—82no—
341C22×C53—82no—
342C22×C53—82no—
343C22×C53—82no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53—81no—
347C22×C53—162no—
348C22×C53—164no—
349C22×C53C2×#12011yescharacteristic
350C22×C53#57612yes—
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53—42no—
356C4×C53—41no—
357C4×C53—42no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53—82no—
361C4×C53—81no—
362#3537C2×C5311yescharacteristic, complemented
363#3194C2×C5311yescharacteristic, complemented
364#3186C2×C5311yescharacteristic, complemented
365#2815C2×C5311yescharacteristic, complemented
366#1612C2×C5312yescomplemented
367#1607C2×C5312yescomplemented
368#1600C2×C5312yescomplemented
369#1595C2×C5312yescomplemented
370#1516C2×C5311yescharacteristic, complemented
371#1510C2×C5311yescharacteristic, complemented
372#1471C2×C5311yescharacteristic, complemented
373C2×C53—22no—
374C2×C53—41no—
375C2×C53—41no—
376C2×C53—82no—
377C2×C53—82no—
378C2×C53—81no—
379C2×C53—161no—
380C2×C53#300811yescharacteristic
381C2×C53#301911yescharacteristic
382C2×C53#302611yescharacteristic
383#560—22no—
384#553—21no—
385#553—21no—
386D42—22no—
387D42—21no—
388D42—21no—
389#540—21no—
390#538—21no—
391#538C22×C5312yes—
392#535—21no—
393#534—21no—
394#534C22×C5312yes—
395#525C22×C5311yescharacteristic
396C2×#121C22×C5311yescharacteristic
397C2×#121C22×C5311yescharacteristic
398C2×#121C22×C5311yescharacteristic, complemented
399#483C22×C5311yescharacteristic, complemented
400#482—21no—
401#480—21no—
402#480C22×C5311yescharacteristic, complemented
403#480C22×C5312yescomplemented
404#469—21no—
405#468—21no—
406#466—22no—
407#450C22×C5311yescharacteristic, complemented
408#449—21no—
409#447—21no—
410#447C22×C5311yescharacteristic, complemented
411#447C22×C5312yescomplemented
412#407C22×C5311yescharacteristic, complemented
413C2×C22⋊C8C22×C5311yescharacteristic, complemented
414#397—21no—
415#397C22×C5312yescomplemented
416#392—21no—
417#392—22no—
418#392C22×C5312yescomplemented
419#381C22×C5311yescharacteristic, complemented
420#328C22×C5312yescomplemented
421#327C22×C5312yescomplemented
422#327C22×C5312yescomplemented
423#327C22×C5312yescomplemented
424#323C22×C5312yescomplemented
425#323C22×C5312yescomplemented
426C53#1845011yescharacteristic, direct product factor, Sylow
427C2×#41D4×C5311yescharacteristic, complemented
428C22×D4—22no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4D4×C5312yes—
435C22×D4D4×C5311yescharacteristic
436C22×D4D4×C5311yescharacteristic, complemented
437C22×D4C23×C5311yescharacteristic
438C23×C4C23×C5311yescharacteristic
439C2×SD16—21no—
440C2×D8—22no—
441C2×D8—21no—
442C2×M16—21no—
443C22×C8—21no—
444#127—22no—
445#127—21no—
446#126—22no—
447#126—22no—
448#125—21no—
449#124—22no—
450#123—22no—
451#123—21no—
452#123—22no—
453#123—22no—
454#123—22no—
455C22⋊Q8D4×C5311yescharacteristic, complemented
456C22⋊Q8C23×C5311yescharacteristic
457#121—22no—
458#121—21no—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121D4×C5312yescomplemented
476#121D4×C5311yescharacteristic, complemented
477#121C23×C5312yes—
478#121C23×C5311yescharacteristic
479#120—22no—
480#120—22no—
481#120—22no—
482#120—21no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—22no—
492#117—21no—
493#117D4×C5311yescharacteristic, complemented
494C2×C4⋊C4D4×C5311yescharacteristic
495C2×C4⋊C4D4×C5311yescharacteristic, complemented
496C2×C4⋊C4C23×C5311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4C23×C5312yes—
503#107—22no—
504#107—21no—
505#106—21no—
506#103—21no—
507#102—22no—
508#102—21no—
509#102—22no—
510#102—21no—
511#102—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8C23×C5311yescharacteristic
515C22⋊C8C23×C5311yescharacteristic
516C22⋊C8C23×C5312yes—
517#95—21no—
518#95—22no—
519#95C23×C5312yes—
520C24—22no—
521C24—21no—
522C24—21no—
523C24C2×D4×C5312yes—
524C24C2×D4×C5311yescharacteristic
525#41—81no—
526C2×Q8C2×D4×C5311yescharacteristic
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—84no—
559C2×D4C2×D4×C5311yescharacteristic
560C2×D4C2×D4×C5312yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—81no—
568C22×C4C2×D4×C5312yes—
569C22×C4C2×D4×C5311yescharacteristic
570C22×C4C2×D4×C5311yescharacteristic
571C22×C4C2×D4×C5311yescharacteristic
572C22×C4C2×D4×C5311yescharacteristic
573C22×C4C2×D4×C5311yescharacteristic
574C22×C4C24×C5311yescharacteristic
575SD16—81no—
576D8—82no—
577D8—81no—
578M16—81no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C5311yescharacteristic
593C4⋊C4C2×D4×C5312yes—
594C4⋊C4C2×D4×C5311yescharacteristic
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—81no—
614C42—22no—
615C42—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23#120×C5311yescharacteristic
638C23#120×C5311yescharacteristic
639C23C22×D4×C5311yescharacteristic
640Q8—41no—
641D4—42no—
642D4—41no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—81no—
654D4—82no—
655D4—82no—
656D4—81no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664D4—88no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C5311yescharacteristic
687C2×C4#120×C5311yescharacteristic
688C2×C4C22×D4×C5311yescharacteristic
689C2×C4C22×D4×C5311yescharacteristic
690C8—42no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×#120×C5311yescharacteristic
721C22C53×#57612yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C53×#300811yescharacteristic
741C2C53×#301911yescharacteristic
742C2C53×#302611yescharacteristic
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×#3194C2semidirect
3. C53×#3186C2semidirect
4. C53×#2815C2semidirect
5. C53×#1612C2semidirect
6. C53×#1607C2semidirect
7. C53×#1600C2semidirect
8. C53×#1595C2semidirect
9. C53×#1516C2semidirect
10. C53×#1510C2semidirect
11. C53×#1471C2semidirect
27. C2×#121×C53C22semidirect
28. C53×#483C22semidirect
31. C53×#480C22semidirect
32. C53×#480C22semidirect
36. C53×#450C22semidirect
39. C53×#447C22semidirect
40. C53×#447C22semidirect
41. C53×#407C22semidirect
42. C2×C22⋊C8×C53C22semidirect
44. C53×#397C22semidirect
47. C53×#392C22semidirect
48. C53×#381C22semidirect
49. C53×#328C22semidirect
50. C53×#327C22semidirect
51. C53×#327C22semidirect
52. C53×#327C22semidirect
53. C53×#323C22semidirect
54. C53×#323C22semidirect
55. C2×#41×C53D4semidirect
64. C22×D4×C53D4semidirect
83. C22⋊Q8×C53D4semidirect
103. #121×C53D4semidirect
104. #121×C53D4semidirect
121. #117×C53D4semidirect
123. C2×C4⋊C4×C53D4semidirect
321. #18450C53direct (N × H)
362. #3537C2×C53semidirect
363. #3194C2×C53semidirect
364. #3186C2×C53semidirect
365. #2815C2×C53semidirect
366. #1612C2×C53semidirect
367. #1607C2×C53semidirect
368. #1600C2×C53semidirect
369. #1595C2×C53semidirect
370. #1516C2×C53semidirect
371. #1510C2×C53semidirect
372. #1471C2×C53semidirect
398. C2×#121C22×C53semidirect
399. #483C22×C53semidirect
402. #480C22×C53semidirect
403. #480C22×C53semidirect
407. #450C22×C53semidirect
410. #447C22×C53semidirect
411. #447C22×C53semidirect
412. #407C22×C53semidirect
413. C2×C22⋊C8C22×C53semidirect
415. #397C22×C53semidirect
418. #392C22×C53semidirect
419. #381C22×C53semidirect
420. #328C22×C53semidirect
421. #327C22×C53semidirect
422. #327C22×C53semidirect
423. #327C22×C53semidirect
424. #323C22×C53semidirect
425. #323C22×C53semidirect
426. C53#18450direct (N × H)
427. C2×#41D4×C53semidirect
436. C22×D4D4×C53semidirect
455. C22⋊Q8D4×C53semidirect
475. #121D4×C53semidirect
476. #121D4×C53semidirect
493. #117D4×C53semidirect
495. 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×#31942
C53×#31862
C53×#28152
C53×#16122
C53×#16072
C53×#16002
C53×#15952
C53×#15162
C53×#15102
C53×#14712
#1845053