Finite Group Databasebeta

← C53×#18228 #27225740

Subgroups — C53×#18228 #27225740

Order 13568.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3537C211yesmaximal, characteristic, complemented
2C53×#3006C211yesmaximal, characteristic, complemented
3C53×#3002C211yesmaximal, characteristic, complemented
4C53×#2615C211yesmaximal, characteristic, complemented
5C53×#1606C212yesmaximal, complemented
6C53×#1601C212yesmaximal, complemented
7C53×#1600C212yesmaximal, complemented
8C53×#1595C212yesmaximal, complemented
9C53×#1519C211yesmaximal, characteristic, complemented
10C53×#1513C211yesmaximal, characteristic, complemented
11C53×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C53C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C53—21no—
14C2×#135×C53—21no—
15C53×#560—22no—
16C53×#553—21no—
17C53×#553—21no—
18D42×C53—22no—
19D42×C53—21no—
20D42×C53—21no—
21C53×#540—21no—
22C53×#538—21no—
23C53×#538C2212yes—
24C53×#535—21no—
25C53×#534—21no—
26C53×#534C2212yes—
27C53×#525C2211yescharacteristic
28C2×#121×C53—21no—
29C2×#121×C53C2211yescharacteristic
30C2×#121×C53C2211yescharacteristic
31C53×#452—21no—
32C53×#451C2211yescharacteristic, complemented
33C53×#450C2211yescharacteristic, complemented
34C53×#449—21no—
35C53×#449—22no—
36C53×#448C2211yescharacteristic, complemented
37C53×#448C2212yescomplemented
38C53×#447C2211yescharacteristic, complemented
39C53×#447C2212yescomplemented
40C53×#417—21no—
41C53×#416—21no—
42C53×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C53C2211yescharacteristic, complemented
44C53×#393C2212yescomplemented
45C53×#392—22no—
46C53×#392C2212yescomplemented
47C53×#380—21no—
48C53×#380C2211yescharacteristic, complemented
49C53×#328C2212yescomplemented
50C53×#327C2212yescomplemented
51C53×#327C2212yescomplemented
52C53×#327C2212yescomplemented
53C53×#323C2212yescomplemented
54C53×#323C2212yescomplemented
55C2×#41×C53—21no—
56C2×#41×C53—21no—
57C2×#41×C53—21no—
58C2×#41×C53—21no—
59C2×#41×C53—44no—
60C2×#41×C53D411yescharacteristic, complemented
61C22×Q8×C53C2311yescharacteristic
62C22×D4×C53—22no—
63C22×D4×C53—21no—
64C22×D4×C53—21no—
65C22×D4×C53—22no—
66C22×D4×C53—21no—
67C22×D4×C53—22no—
68C22×D4×C53D411yescharacteristic
69C22×D4×C53D412yes—
70C22×D4×C53D411yescharacteristic, complemented
71C22×D4×C53C2311yescharacteristic
72C23×C4×C53—21no—
73C23×C4×C53C2311yescharacteristic
74AGL(1,ℤ/8)×C53—44no—
75#135×C53—44no—
76C2×Q16×C53—21no—
77C2×SD16×C53—21no—
78C2×SD16×C53—21no—
79C2×SD16×C53—22no—
80C2×D8×C53—21no—
81C2×D8×C53—22no—
82C2×M16×C53—21no—
83C22×C8×C53—21no—
84#127×C53—22no—
85#127×C53—21no—
86#126×C53—22no—
87#126×C53—22no—
88#125×C53—21no—
89#124×C53—22no—
90#123×C53—22no—
91#123×C53—22no—
92#123×C53—22no—
93#123×C53—22no—
94#123×C53—21no—
95C22⋊Q8×C53D411yescharacteristic, complemented
96C22⋊Q8×C53C2311yescharacteristic
97#121×C53—22no—
98#121×C53—21no—
99#121×C53—21no—
100#121×C53—22no—
101#121×C53—22no—
102#121×C53—22no—
103#121×C53—22no—
104#121×C53—21no—
105#121×C53—21no—
106#121×C53—21no—
107#121×C53—21no—
108#121×C53—21no—
109#121×C53—21no—
110#121×C53—22no—
111#121×C53—44no—
112#121×C53D412yescomplemented
113#121×C53D411yescharacteristic, complemented
114#121×C53C2312yes—
115#121×C53C2311yescharacteristic
116#120×C53—22no—
117#120×C53—22no—
118#120×C53—22no—
119#120×C53—21no—
120#120×C53—22no—
121#120×C53—22no—
122#120×C53—22no—
123C4×D4×C53—22no—
124C4×D4×C53—21no—
125C4×D4×C53—21no—
126C4×D4×C53—21no—
127C4×D4×C53—21no—
128C4×D4×C53—22no—
129#117×C53—21no—
130#117×C53D411yescharacteristic, complemented
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53D411yescharacteristic
133C2×C4⋊C4×C53D411yescharacteristic, complemented
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53C2312yes—
139#103×C53—21no—
140#103×C53—21no—
141#103×C53—22no—
142#102×C53—21no—
143#102×C53—21no—
144#102×C53—22no—
145C22⋊C8×C53—21no—
146C22⋊C8×C53—21no—
147C22⋊C8×C53C2311yescharacteristic
148C22⋊C8×C53C2311yescharacteristic
149C22⋊C8×C53C2312yes—
150#95×C53—22no—
151#95×C53C2312yes—
152C24×C53—22no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53C2×D412yes—
156C24×C53C2×D411yescharacteristic
157#41×C53—24no—
158#41×C53—24no—
159#41×C53—42no—
160#41×C53—42no—
161#41×C53—42no—
162#41×C53—42no—
163#41×C53—42no—
164#41×C53—42no—
165#41×C53—42no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—42no—
169C2×Q8×C53C2×D411yescharacteristic
170C2×D4×C53—22no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—21no—
180C2×D4×C53—22no—
181C2×D4×C53—22no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—42no—
188C2×D4×C53—42no—
189C2×D4×C53—42no—
190C2×D4×C53—42no—
191C2×D4×C53—42no—
192C2×D4×C53—41no—
193C2×D4×C53—41no—
194C2×D4×C53—44no—
195C2×D4×C53—82no—
196C2×D4×C53—82no—
197C2×D4×C53—82no—
198C2×D4×C53—82no—
199C2×D4×C53—81no—
200C2×D4×C53—81no—
201C2×D4×C53—82no—
202C2×D4×C53—82no—
203C2×D4×C53—84no—
204C2×D4×C53C2×D411yescharacteristic
205C2×D4×C53C2×D412yes—
206C22×C4×C53—24no—
207C22×C4×C53—21no—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—22no—
213C22×C4×C53—42no—
214C22×C4×C53—42no—
215C22×C4×C53—41no—
216C22×C4×C53—41no—
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2411yescharacteristic
224Q16×C53—42no—
225SD16×C53—42no—
226SD16×C53—42no—
227SD16×C53—44no—
228D8×C53—42no—
229D8×C53—44no—
230M16×C53—42no—
231C2×C8×C53—21no—
232C2×C8×C53—21no—
233C2×C8×C53—22no—
234C2×C8×C53—42no—
235C4⋊C4×C53—22no—
236C4⋊C4×C53—22no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—42no—
243C4⋊C4×C53C2×D412yes—
244C4⋊C4×C53C2×D411yescharacteristic
245C4⋊C4×C53C2×D411yescharacteristic
246C22⋊C4×C53—22no—
247C22⋊C4×C53—22no—
248C22⋊C4×C53—22no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—22no—
251C22⋊C4×C53—21no—
252C22⋊C4×C53—21no—
253C22⋊C4×C53—21no—
254C22⋊C4×C53—22no—
255C22⋊C4×C53—21no—
256C22⋊C4×C53—22no—
257C22⋊C4×C53—22no—
258C22⋊C4×C53—22no—
259C22⋊C4×C53—21no—
260C22⋊C4×C53—44no—
261C22⋊C4×C53—81no—
262C22⋊C4×C53—82no—
263C42×C53—22no—
264C42×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—21no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—41no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—81no—
285C23×C53—81no—
286C23×C53—82no—
287C23×C53—82no—
288C23×C53—82no—
289C23×C53#12011yescharacteristic
290C23×C53#12011yescharacteristic
291C23×C53C22×D411yescharacteristic
292Q8×C53—22no—
293Q8×C53—22no—
294Q8×C53—41no—
295Q8×C53—41no—
296Q8×C53—41no—
297D4×C53—22no—
298D4×C53—22no—
299D4×C53—42no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53—41no—
303D4×C53—44no—
304D4×C53—42no—
305D4×C53—44no—
306D4×C53—44no—
307D4×C53—42no—
308D4×C53—41no—
309D4×C53—42no—
310D4×C53—41no—
311D4×C53—42no—
312D4×C53—42no—
313D4×C53—81no—
314D4×C53—82no—
315D4×C53—82no—
316D4×C53—81no—
317D4×C53—82no—
318D4×C53—82no—
319D4×C53—82no—
320D4×C53—82no—
321D4×C53—82no—
322D4×C53—88no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—21no—
328C2×C4×C53—22no—
329C2×C4×C53—21no—
330C2×C4×C53—22no—
331C2×C4×C53—21no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—44no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—44no—
339C2×C4×C53—42no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53—42no—
344C2×C4×C53—81no—
345C2×C4×C53—82no—
346C2×C4×C53—82no—
347C2×C4×C53#12011yescharacteristic
348C2×C4×C53#12011yescharacteristic
349C2×C4×C53C22×D411yescharacteristic
350C2×C4×C53C22×D411yescharacteristic
351C8×C53—41no—
352C8×C53—41no—
353C8×C53—42no—
354#18228C5311yesmaximal, characteristic, direct product factor, Sylow
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—21no—
361C22×C53—21no—
362C22×C53—21no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—41no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—41no—
371C22×C53—42no—
372C22×C53—41no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—81no—
376C22×C53—81no—
377C22×C53—82no—
378C22×C53—82no—
379C22×C53—81no—
380C22×C53—81no—
381C22×C53—81no—
382C22×C53—81no—
383C22×C53—162no—
384C22×C53—164no—
385C22×C53C2×#12011yescharacteristic
386C22×C53#57611yescharacteristic
387C22×C53#57711yescharacteristic
388C4×C53—21no—
389C4×C53—21no—
390C4×C53—21no—
391C4×C53—42no—
392C4×C53—41no—
393C4×C53—42no—
394C4×C53—41no—
395C4×C53—42no—
396C4×C53—41no—
397C4×C53—82no—
398C4×C53B(4,𝔽2)12yes—
399#3537C2×C5311yescharacteristic, complemented
400#3006C2×C5311yescharacteristic, complemented
401#3002C2×C5311yescharacteristic, complemented
402#2615C2×C5311yescharacteristic, complemented
403#1606C2×C5312yescomplemented
404#1601C2×C5312yescomplemented
405#1600C2×C5312yescomplemented
406#1595C2×C5312yescomplemented
407#1519C2×C5311yescharacteristic, complemented
408#1513C2×C5311yescharacteristic, complemented
409#1471C2×C5311yescharacteristic, complemented
410C2×C53—21no—
411C2×C53—21no—
412C2×C53—41no—
413C2×C53—41no—
414C2×C53—82no—
415C2×C53—82no—
416C2×C53—82no—
417C2×C53—81no—
418C2×C53#301211yescharacteristic
419C2×C53#301911yescharacteristic
420C2×C53C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C5311yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C5312yes—
433#535—21no—
434#534—21no—
435#534C22×C5312yes—
436#525C22×C5311yescharacteristic
437C2×#121—21no—
438C2×#121C22×C5311yescharacteristic
439C2×#121C22×C5311yescharacteristic
440#452—21no—
441#451C22×C5311yescharacteristic, complemented
442#450C22×C5311yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C5311yescharacteristic, complemented
446#448C22×C5312yescomplemented
447#447C22×C5311yescharacteristic, complemented
448#447C22×C5312yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C5311yescharacteristic, complemented
452C2×C22⋊C8C22×C5311yescharacteristic, complemented
453#393C22×C5312yescomplemented
454#392—22no—
455#392C22×C5312yescomplemented
456#380—21no—
457#380C22×C5311yescharacteristic, complemented
458#328C22×C5312yescomplemented
459#327C22×C5312yescomplemented
460#327C22×C5312yescomplemented
461#327C22×C5312yescomplemented
462#323C22×C5312yescomplemented
463#323C22×C5312yescomplemented
464C53#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C5311yescharacteristic, complemented
471C22×Q8C23×C5311yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C5311yescharacteristic
479C22×D4D4×C5312yes—
480C22×D4D4×C5311yescharacteristic, complemented
481C22×D4C23×C5311yescharacteristic
482C23×C4—21no—
483C23×C4C23×C5311yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C5311yescharacteristic, complemented
506C22⋊Q8C23×C5311yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C5312yescomplemented
523#121D4×C5311yescharacteristic, complemented
524#121C23×C5312yes—
525#121C23×C5311yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C5311yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C5311yescharacteristic
543C2×C4⋊C4D4×C5311yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C5312yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C5311yescharacteristic
558C22⋊C8C23×C5311yescharacteristic
559C22⋊C8C23×C5312yes—
560#95—22no—
561#95C23×C5312yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C5312yes—
566C24C2×D4×C5311yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C5311yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C5311yescharacteristic
615C2×D4C2×D4×C5312yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C5311yescharacteristic
628C22×C4C2×D4×C5311yescharacteristic
629C22×C4C2×D4×C5311yescharacteristic
630C22×C4C2×D4×C5312yes—
631C22×C4C2×D4×C5311yescharacteristic
632C22×C4C2×D4×C5311yescharacteristic
633C22×C4C24×C5311yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C5312yes—
654C4⋊C4C2×D4×C5311yescharacteristic
655C4⋊C4C2×D4×C5311yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C5311yescharacteristic
700C23#120×C5311yescharacteristic
701C23C22×D4×C5311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C5311yescharacteristic
758C2×C4#120×C5311yescharacteristic
759C2×C4C22×D4×C5311yescharacteristic
760C2×C4C22×D4×C5311yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C5311yescharacteristic
795C22C53×#57611yescharacteristic
796C22C53×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C53×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C53×#301211yescharacteristic
817C2C53×#301911yescharacteristic
818C2C2×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×#3006C2semidirect
3. C53×#3002C2semidirect
4. C53×#2615C2semidirect
5. C53×#1606C2semidirect
6. C53×#1601C2semidirect
7. C53×#1600C2semidirect
8. C53×#1595C2semidirect
9. C53×#1519C2semidirect
10. C53×#1513C2semidirect
11. C53×#1471C2semidirect
12. C22×#41×C53C22semidirect
32. C53×#451C22semidirect
33. C53×#450C22semidirect
36. C53×#448C22semidirect
37. C53×#448C22semidirect
38. C53×#447C22semidirect
39. C53×#447C22semidirect
42. C53×#407C22semidirect
43. C2×C22⋊C8×C53C22semidirect
44. C53×#393C22semidirect
46. C53×#392C22semidirect
48. C53×#380C22semidirect
49. C53×#328C22semidirect
50. C53×#327C22semidirect
51. C53×#327C22semidirect
52. C53×#327C22semidirect
53. C53×#323C22semidirect
54. C53×#323C22semidirect
60. C2×#41×C53D4semidirect
70. C22×D4×C53D4semidirect
95. C22⋊Q8×C53D4semidirect
112. #121×C53D4semidirect
113. #121×C53D4semidirect
130. #117×C53D4semidirect
133. C2×C4⋊C4×C53D4semidirect
354. #18228C53direct (N × H)
399. #3537C2×C53semidirect
400. #3006C2×C53semidirect
401. #3002C2×C53semidirect
402. #2615C2×C53semidirect
403. #1606C2×C53semidirect
404. #1601C2×C53semidirect
405. #1600C2×C53semidirect
406. #1595C2×C53semidirect
407. #1519C2×C53semidirect
408. #1513C2×C53semidirect
409. #1471C2×C53semidirect
421. C22×#41C22×C53semidirect
441. #451C22×C53semidirect
442. #450C22×C53semidirect
445. #448C22×C53semidirect
446. #448C22×C53semidirect
447. #447C22×C53semidirect
448. #447C22×C53semidirect
451. #407C22×C53semidirect
452. C2×C22⋊C8C22×C53semidirect
453. #393C22×C53semidirect
455. #392C22×C53semidirect
457. #380C22×C53semidirect
458. #328C22×C53semidirect
459. #327C22×C53semidirect
460. #327C22×C53semidirect
461. #327C22×C53semidirect
462. #323C22×C53semidirect
463. #323C22×C53semidirect
464. C53#18228direct (N × H)
470. C2×#41D4×C53semidirect
480. C22×D4D4×C53semidirect
505. C22⋊Q8D4×C53semidirect
522. #121D4×C53semidirect
523. #121D4×C53semidirect
540. #117D4×C53semidirect
543. 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×#30062
C53×#30022
C53×#26152
C53×#16062
C53×#16012
C53×#16002
C53×#15952
C53×#15192
C53×#15132
C53×#14712
#1822853