Finite Group Databasebeta

← C53×#18418 #27225930

Subgroups — C53×#18418 #27225930

Order 13568.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3537C211yesmaximal, characteristic, complemented
2C53×#3192C211yesmaximal, characteristic, complemented
3C53×#3188C211yesmaximal, characteristic, complemented
4C53×#2656C211yesmaximal, characteristic, complemented
5C53×#1618C212yesmaximal, complemented
6C53×#1613C212yesmaximal, complemented
7C53×#1600C212yesmaximal, complemented
8C53×#1595C212yesmaximal, complemented
9C53×#1504C211yesmaximal, characteristic, complemented
10C2×C53×#327C211yesmaximal, 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×C53—22no—
26C2×#121×C53C2211yescharacteristic
27C2×#121×C53C2211yescharacteristic
28C2×#121×C53C2211yescharacteristic, complemented
29C53×#484C2211yescharacteristic, complemented
30C53×#482—21no—
31C53×#481—21no—
32C53×#481C2212yescomplemented
33C53×#481C2211yescharacteristic, complemented
34C53×#469—22no—
35C53×#466—21no—
36C53×#465—21no—
37C53×#450C2211yescharacteristic, complemented
38C53×#449—21no—
39C53×#447—21no—
40C53×#447C2212yescomplemented
41C53×#447C2211yescharacteristic, complemented
42C53×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C53C2211yescharacteristic, complemented
44C53×#399—21no—
45C53×#399C2212yescomplemented
46C53×#392—21no—
47C53×#392C2212yescomplemented
48C2×#95×C53C2211yescharacteristic, 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×C53—21no—
67C23×C4×C53C2311yescharacteristic
68C2×SD16×C53—21no—
69C2×D8×C53—22no—
70C2×D8×C53—21no—
71C2×M16×C53—21no—
72C22×C8×C53—21no—
73#127×C53—22no—
74#127×C53—21no—
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×C53—21no—
101#121×C53—21no—
102#121×C53—21no—
103#121×C53—21no—
104#121×C53—48no—
105#121×C53D412yescomplemented
106#121×C53D411yescharacteristic, complemented
107#121×C53C2312yes—
108#121×C53C2311yescharacteristic
109#120×C53—22no—
110#120×C53—22no—
111#120×C53—22no—
112#120×C53—21no—
113#120×C53—22no—
114#120×C53—22no—
115#120×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—21no—
118C4×D4×C53—21no—
119C4×D4×C53—21no—
120C4×D4×C53—21no—
121C4×D4×C53—22no—
122#117×C53—21no—
123#117×C53D411yescharacteristic, complemented
124C2×C4⋊C4×C53—22no—
125C2×C4⋊C4×C53D411yescharacteristic
126C2×C4⋊C4×C53D411yescharacteristic, complemented
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53C2312yes—
133#107×C53—21no—
134#106×C53—21no—
135#106×C53—22no—
136#103×C53—21no—
137#102×C53—21no—
138#102×C53—22no—
139#102×C53—21no—
140#102×C53—22no—
141#102×C53—21no—
142C22⋊C8×C53—21no—
143C22⋊C8×C53—21no—
144C22⋊C8×C53C2311yescharacteristic
145C22⋊C8×C53C2311yescharacteristic
146C22⋊C8×C53C2312yes—
147#95×C53—21no—
148#95×C53C2312yes—
149C24×C53—22no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53C2×D411yescharacteristic
153C24×C53C2×D412yes—
154#41×C53—81no—
155C2×Q8×C53C2×D411yescharacteristic
156C2×D4×C53—22no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—22no—
162C2×D4×C53—22no—
163C2×D4×C53—22no—
164C2×D4×C53—22no—
165C2×D4×C53—21no—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—44no—
174C2×D4×C53—44no—
175C2×D4×C53—44no—
176C2×D4×C53—41no—
177C2×D4×C53—41no—
178C2×D4×C53—81no—
179C2×D4×C53—81no—
180C2×D4×C53—82no—
181C2×D4×C53—81no—
182C2×D4×C53—82no—
183C2×D4×C53—82no—
184C2×D4×C53—81no—
185C2×D4×C53—81no—
186C2×D4×C53—82no—
187C2×D4×C53—82no—
188C2×D4×C53—84no—
189C2×D4×C53C2×D411yescharacteristic
190C2×D4×C53C2×D412yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—24no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—81no—
199C22×C4×C53—81no—
200C22×C4×C53—81no—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2411yescharacteristic
208SD16×C53—81no—
209D8×C53—81no—
210D8×C53—82no—
211M16×C53—81no—
212C2×C8×C53—21no—
213C2×C8×C53—22no—
214C2×C8×C53—21no—
215C2×C8×C53—81no—
216C4⋊C4×C53—22no—
217C4⋊C4×C53—22no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—44no—
226C4⋊C4×C53C2×D412yes—
227C4⋊C4×C53C2×D411yescharacteristic
228C4⋊C4×C53C2×D411yescharacteristic
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—21no—
235C22⋊C4×C53—21no—
236C22⋊C4×C53—21no—
237C22⋊C4×C53—22no—
238C22⋊C4×C53—21no—
239C22⋊C4×C53—22no—
240C22⋊C4×C53—22no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—44no—
244C22⋊C4×C53—44no—
245C22⋊C4×C53—41no—
246C22⋊C4×C53—41no—
247C42×C53—22no—
248C42×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—41no—
258C23×C53—42no—
259C23×C53—42no—
260C23×C53—42no—
261C23×C53—42no—
262C23×C53—42no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—81no—
267C23×C53—81no—
268C23×C53—82no—
269C23×C53—82no—
270C23×C53—82no—
271C23×C53#12011yescharacteristic
272C23×C53#12011yescharacteristic
273C23×C53C22×D411yescharacteristic
274Q8×C53—41no—
275D4×C53—42no—
276D4×C53—41no—
277D4×C53—42no—
278D4×C53—42no—
279D4×C53—42no—
280D4×C53—41no—
281D4×C53—41no—
282D4×C53—42no—
283D4×C53—41no—
284D4×C53—42no—
285D4×C53—41no—
286D4×C53—44no—
287D4×C53—42no—
288D4×C53—81no—
289D4×C53—82no—
290D4×C53—82no—
291D4×C53—81no—
292D4×C53—82no—
293D4×C53—82no—
294D4×C53—82no—
295D4×C53—82no—
296D4×C53—82no—
297D4×C53—88no—
298D4×C53—82no—
299D4×C53—82no—
300C2×C4×C53—24no—
301C2×C4×C53—21no—
302C2×C4×C53—22no—
303C2×C4×C53—21no—
304C2×C4×C53—22no—
305C2×C4×C53—21no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—41no—
318C2×C4×C53—81no—
319C2×C4×C53—84no—
320C2×C4×C53—82no—
321C2×C4×C53—82no—
322C2×C4×C53#12011yescharacteristic
323C2×C4×C53#12011yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C8×C53—41no—
327C8×C53—41no—
328C8×C53—42no—
329#18418C5311yesmaximal, characteristic, direct product factor, Sylow
330C22×C53—21no—
331C22×C53—21no—
332C22×C53—21no—
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—41no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—82no—
349C22×C53—82no—
350C22×C53—82no—
351C22×C53—82no—
352C22×C53—81no—
353C22×C53—81no—
354C22×C53—81no—
355C22×C53—162no—
356C22×C53—164no—
357C22×C53#45312yes—
358C22×C53C2×#12011yescharacteristic
359C22×C53#57611yescharacteristic
360C22×C53#57711yescharacteristic
361C4×C53—21no—
362C4×C53—21no—
363C4×C53—21no—
364C4×C53—21no—
365C4×C53—44no—
366C4×C53—42no—
367C4×C53—41no—
368C4×C53—42no—
369C4×C53—41no—
370C4×C53—41no—
371C4×C53—81no—
372#3537C2×C5311yescharacteristic, complemented
373#3192C2×C5311yescharacteristic, complemented
374#3188C2×C5311yescharacteristic, complemented
375#2656C2×C5311yescharacteristic, complemented
376#1618C2×C5312yescomplemented
377#1613C2×C5312yescomplemented
378#1600C2×C5312yescomplemented
379#1595C2×C5312yescomplemented
380#1504C2×C5311yescharacteristic, complemented
381C2×#327C2×C5311yescharacteristic, complemented
382#1471C2×C5311yescharacteristic, complemented
383C2×C53—21no—
384C2×C53—21no—
385C2×C53—22no—
386C2×C53—41no—
387C2×C53—82no—
388C2×C53—82no—
389C2×C53—81no—
390C2×C53—161no—
391C2×C53#301211yescharacteristic
392C2×C53C2×#45311yescharacteristic
393C2×C53#302611yescharacteristic
394#560—22no—
395#553—21no—
396#553—21no—
397D42—22no—
398D42—21no—
399D42—21no—
400#540—21no—
401#538—21no—
402#538C22×C5312yes—
403#535—21no—
404#534—21no—
405#534C22×C5312yes—
406#525C22×C5311yescharacteristic
407C2×#121—22no—
408C2×#121C22×C5311yescharacteristic
409C2×#121C22×C5311yescharacteristic
410C2×#121C22×C5311yescharacteristic, complemented
411#484C22×C5311yescharacteristic, complemented
412#482—21no—
413#481—21no—
414#481C22×C5311yescharacteristic, complemented
415#481C22×C5312yescomplemented
416#469—22no—
417#466—21no—
418#465—21no—
419#450C22×C5311yescharacteristic, complemented
420#449—21no—
421#447—21no—
422#447C22×C5311yescharacteristic, complemented
423#447C22×C5312yescomplemented
424#407C22×C5311yescharacteristic, complemented
425C2×C22⋊C8C22×C5311yescharacteristic, complemented
426#399—21no—
427#399C22×C5312yescomplemented
428#392—21no—
429#392C22×C5312yescomplemented
430C2×#95C22×C5311yescharacteristic, complemented
431#328C22×C5312yescomplemented
432#327C22×C5312yescomplemented
433#327C22×C5312yescomplemented
434#327C22×C5312yescomplemented
435#323C22×C5312yescomplemented
436#323C22×C5312yescomplemented
437C53#1841811yescharacteristic, direct product factor, Sylow
438C2×#41D4×C5311yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C5312yes—
446C22×D4D4×C5311yescharacteristic
447C22×D4D4×C5311yescharacteristic, complemented
448C22×D4C23×C5311yescharacteristic
449C23×C4—21no—
450C23×C4C23×C5311yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C5311yescharacteristic, complemented
468C22⋊Q8C23×C5311yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C5312yescomplemented
489#121D4×C5311yescharacteristic, complemented
490#121C23×C5312yes—
491#121C23×C5311yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C5311yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C5311yescharacteristic
509C2×C4⋊C4D4×C5311yescharacteristic, complemented
510C2×C4⋊C4C23×C5311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C5312yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C5311yescharacteristic
528C22⋊C8C23×C5311yescharacteristic
529C22⋊C8C23×C5312yes—
530#95—21no—
531#95C23×C5312yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C5311yescharacteristic
536C24C2×D4×C5312yes—
537#41—81no—
538C2×Q8C2×D4×C5311yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C5311yescharacteristic
573C2×D4C2×D4×C5312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C5312yes—
585C22×C4C2×D4×C5311yescharacteristic
586C22×C4C2×D4×C5311yescharacteristic
587C22×C4C2×D4×C5311yescharacteristic
588C22×C4C2×D4×C5311yescharacteristic
589C22×C4C2×D4×C5311yescharacteristic
590C22×C4C24×C5311yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C5312yes—
610C4⋊C4C2×D4×C5311yescharacteristic
611C4⋊C4C2×D4×C5311yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C5311yescharacteristic
655C23#120×C5311yescharacteristic
656C23C22×D4×C5311yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—42no—
666D4—41no—
667D4—42no—
668D4—41no—
669D4—44no—
670D4—42no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C5311yescharacteristic
706C2×C4#120×C5311yescharacteristic
707C2×C4C22×D4×C5311yescharacteristic
708C2×C4C22×D4×C5311yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22C53×#45312yes—
740C22C2×#120×C5311yescharacteristic
741C22C53×#57611yescharacteristic
742C22C53×#57711yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C53×#301211yescharacteristic
763C2C2×C53×#45311yescharacteristic
764C2C53×#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×#3192C2semidirect
3. C53×#3188C2semidirect
4. C53×#2656C2semidirect
5. C53×#1618C2semidirect
6. C53×#1613C2semidirect
7. C53×#1600C2semidirect
8. C53×#1595C2semidirect
9. C53×#1504C2semidirect
10. C2×C53×#327C2semidirect
11. C53×#1471C2semidirect
28. C2×#121×C53C22semidirect
29. C53×#484C22semidirect
32. C53×#481C22semidirect
33. C53×#481C22semidirect
37. C53×#450C22semidirect
40. C53×#447C22semidirect
41. C53×#447C22semidirect
42. C53×#407C22semidirect
43. C2×C22⋊C8×C53C22semidirect
45. C53×#399C22semidirect
47. C53×#392C22semidirect
48. C2×#95×C53C22semidirect
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
84. C22⋊Q8×C53D4semidirect
105. #121×C53D4semidirect
106. #121×C53D4semidirect
123. #117×C53D4semidirect
126. C2×C4⋊C4×C53D4semidirect
329. #18418C53direct (N × H)
372. #3537C2×C53semidirect
373. #3192C2×C53semidirect
374. #3188C2×C53semidirect
375. #2656C2×C53semidirect
376. #1618C2×C53semidirect
377. #1613C2×C53semidirect
378. #1600C2×C53semidirect
379. #1595C2×C53semidirect
380. #1504C2×C53semidirect
381. C2×#327C2×C53semidirect
382. #1471C2×C53semidirect
410. C2×#121C22×C53semidirect
411. #484C22×C53semidirect
414. #481C22×C53semidirect
415. #481C22×C53semidirect
419. #450C22×C53semidirect
422. #447C22×C53semidirect
423. #447C22×C53semidirect
424. #407C22×C53semidirect
425. C2×C22⋊C8C22×C53semidirect
427. #399C22×C53semidirect
429. #392C22×C53semidirect
430. C2×#95C22×C53semidirect
431. #328C22×C53semidirect
432. #327C22×C53semidirect
433. #327C22×C53semidirect
434. #327C22×C53semidirect
435. #323C22×C53semidirect
436. #323C22×C53semidirect
437. C53#18418direct (N × H)
438. C2×#41D4×C53semidirect
447. C22×D4D4×C53semidirect
467. C22⋊Q8D4×C53semidirect
488. #121D4×C53semidirect
489. #121D4×C53semidirect
506. #117D4×C53semidirect
509. 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×#31922
C53×#31882
C53×#26562
C53×#16182
C53×#16132
C53×#16002
C53×#15952
C53×#15042
C2×C53×#3272
C53×#14712
#1841853