Finite Group Databasebeta

← C53×#18126 #27225638

Subgroups — C53×#18126 #27225638

Order 13568.

1034 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3455C211yesmaximal, characteristic, complemented
2C53×#3101C211yesmaximal, characteristic, complemented
3C53×#3100C211yesmaximal, characteristic, complemented
4C53×#2392C211yesmaximal, characteristic, complemented
5C53×#1612C212yesmaximal, complemented
6C53×#1609C212yesmaximal, complemented
7C53×#1600C212yesmaximal, complemented
8C53×#1597C212yesmaximal, complemented
9C53×#1503C211yesmaximal, characteristic, complemented
10C53×#1502C211yesmaximal, characteristic, complemented
11C53×#1458C211yesmaximal, characteristic, complemented
12C53×#542—21no—
13C53×#542—21no—
14C53×#541—21no—
15C53×#540—21no—
16C53×#539—21no—
17C53×#539C2212yes—
18C53×#538—21no—
19C53×#538C2212yes—
20C53×#533C2211yescharacteristic
21C53×#532C2211yescharacteristic
22C53×#529—22no—
23C53×#529—22no—
24C53×#525—21no—
25C4×#41×C53—21no—
26C2×C4×D4×C53—21no—
27C2×C4×D4×C53C2211yescharacteristic
28C2×#117×C53C2211yescharacteristic
29C53×#483C2212yes—
30C53×#480C2212yes—
31C53×#476—21no—
32C53×#474—21no—
33C53×#461—21no—
34C53×#459—21no—
35C53×#450C2212yes—
36C53×#447C2212yes—
37C4×SD16×C53—22no—
38C4×D8×C53—22no—
39C53×#431C2211yescharacteristic
40C53×#431C2211yescharacteristic
41C53×#398C2211yescharacteristic
42C53×#397C2211yescharacteristic
43C53×#396—21no—
44C53×#394—21no—
45C53×#394C2211yescharacteristic
46C53×#392C2211yescharacteristic
47C4×C4⋊C4×C53C2211yescharacteristic
48C4×C22⋊C4×C53—21no—
49C53×#328C2212yes—
50C53×#328C2212yes—
51C53×#327C2212yes—
52C53×#327C2212yes—
53C53×#324C2212yes—
54C53×#323C2212yes—
55C2×#41×C53—21no—
56C22×D4×C53—21no—
57C22×D4×C53C2311yescharacteristic
58C23×C4×C53—21no—
59C23×C4×C53D411yescharacteristic
60C2×SD16×C53—22no—
61C2×D8×C53—22no—
62C4⋊Q8×C53D411yescharacteristic, complemented
63C4⋊Q8×C53D411yescharacteristic, complemented
64C4⋊Q8×C53D411yescharacteristic, complemented
65#127×C53D411yescharacteristic, complemented
66#126×C53—22no—
67#126×C53—22no—
68#126×C53—22no—
69#126×C53—22no—
70#125×C53—22no—
71#125×C53—22no—
72#125×C53—21no—
73#124×C53—22no—
74#124×C53—21no—
75#124×C53—22no—
76#123×C53—22no—
77#123×C53—22no—
78#123×C53—22no—
79#123×C53—22no—
80#123×C53—22no—
81C22⋊Q8×C53—21no—
82C22⋊Q8×C53—21no—
83C22⋊Q8×C53—22no—
84C22⋊Q8×C53—22no—
85C22⋊Q8×C53—21no—
86C22⋊Q8×C53C2312yes—
87#121×C53—21no—
88#121×C53—21no—
89#121×C53—22no—
90#121×C53—22no—
91#121×C53—21no—
92#121×C53C2312yes—
93#120×C53—22no—
94C4×Q8×C53—21no—
95C4×Q8×C53—21no—
96C4×Q8×C53—21no—
97C4×Q8×C53D412yescomplemented
98C4×D4×C53—21no—
99C4×D4×C53—21no—
100C4×D4×C53—22no—
101C4×D4×C53—22no—
102C4×D4×C53—21no—
103C4×D4×C53—22no—
104C4×D4×C53—22no—
105C4×D4×C53—21no—
106C4×D4×C53—21no—
107C4×D4×C53—21no—
108C4×D4×C53—21no—
109C4×D4×C53—44no—
110C4×D4×C53D412yescomplemented
111#117×C53—22no—
112#117×C53—21no—
113#117×C53—21no—
114#117×C53—21no—
115#117×C53—21no—
116#117×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53D411yescharacteristic
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C22⋊C4×C53C2311yescharacteristic
129C2×C42×C53—22no—
130C2×C42×C53—21no—
131C2×C42×C53D411yescharacteristic
132C2×C42×C53C2311yescharacteristic
133#107×C53—22no—
134#106×C53—22no—
135C4⋊C8×C53—21no—
136C4⋊C8×C53—21no—
137#103×C53—22no—
138#102×C53—22no—
139#102×C53—22no—
140#102×C53—22no—
141C22⋊C8×C53C2312yes—
142C22⋊C8×C53C2312yes—
143C4×C8×C53—21no—
144C4×C8×C53—21no—
145#95×C53—21no—
146#95×C53—21no—
147#95×C53C2311yescharacteristic
148#95×C53C2311yescharacteristic
149C24×C53—21no—
150C24×C53C2×D411yescharacteristic
151#41×C53—42no—
152#41×C53—42no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53C2×D412yes—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—22no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
165C2×D4×C53—42no—
166C2×D4×C53—42no—
167C2×D4×C53C2×D412yes—
168C22×C4×C53—21no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—21no—
172C22×C4×C53—22no—
173C22×C4×C53—21no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—41no—
179C22×C4×C53—41no—
180C22×C4×C53—42no—
181C22×C4×C53—42no—
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2411yescharacteristic
188SD16×C53—44no—
189D8×C53—44no—
190C2×C8×C53—22no—
191C2×C8×C53—22no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53—22no—
194C4⋊C4×C53—22no—
195C4⋊C4×C53—22no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—22no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53—42no—
209C4⋊C4×C53—42no—
210C4⋊C4×C53C2×D412yes—
211C4⋊C4×C53C2×D412yes—
212C22⋊C4×C53—22no—
213C22⋊C4×C53—22no—
214C22⋊C4×C53—22no—
215C22⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—21no—
220C22⋊C4×C53—21no—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—21no—
223C22⋊C4×C53—21no—
224C22⋊C4×C53—22no—
225C22⋊C4×C53—42no—
226C22⋊C4×C53—42no—
227C22⋊C4×C53—42no—
228C22⋊C4×C53—42no—
229C22⋊C4×C53—41no—
230C22⋊C4×C53—41no—
231C42×C53—22no—
232C42×C53—22no—
233C42×C53—21no—
234C42×C53—21no—
235C42×C53—22no—
236C42×C53—42no—
237C42×C53C2×D411yescharacteristic
238C42×C53C2×D411yescharacteristic
239C42×C53C2×D411yescharacteristic
240C42×C53C2×D411yescharacteristic
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53C22×D411yescharacteristic
255Q8×C53—42no—
256Q8×C53—42no—
257Q8×C53—81no—
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—42no—
261D4×C53—41no—
262D4×C53—41no—
263D4×C53—48no—
264D4×C53—42no—
265D4×C53—42no—
266D4×C53—42no—
267D4×C53—81no—
268D4×C53—82no—
269D4×C53—82no—
270C2×C4×C53—22no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—44no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—82no—
295C2×C4×C53—82no—
296C2×C4×C53—82no—
297C2×C4×C53—82no—
298C2×C4×C53#12011yescharacteristic
299C2×C4×C53#12011yescharacteristic
300C2×C4×C53#12011yescharacteristic
301C2×C4×C53#12011yescharacteristic
302C2×C4×C53#13512yes—
303C2×C4×C53AGL(1,ℤ/8)12yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×D411yescharacteristic
306C8×C53—42no—
307C8×C53—42no—
308#18126C5311yesmaximal, characteristic, direct product factor, Sylow
309C22×C53—21no—
310C22×C53—21no—
311C22×C53—42no—
312C22×C53—42no—
313C22×C53—42no—
314C22×C53—41no—
315C22×C53—42no—
316C22×C53—42no—
317C22×C53—41no—
318C22×C53—42no—
319C22×C53—42no—
320C22×C53—41no—
321C22×C53—81no—
322C22×C53—81no—
323C22×C53—81no—
324C22×C53—81no—
325C22×C53—81no—
326C22×C53C2×#12011yescharacteristic
327C22×C53C2×#13511yescharacteristic
328C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
329C4×C53—21no—
330C4×C53—21no—
331C4×C53—21no—
332C4×C53—21no—
333C4×C53—42no—
334C4×C53—41no—
335C4×C53—42no—
336C4×C53—41no—
337C4×C53—42no—
338C4×C53—41no—
339C4×C53—42no—
340C4×C53—81no—
341C4×C53—81no—
342C4×C53#44912yes—
343C4×C53#44912yes—
344#3455C2×C5311yescharacteristic, complemented
345#3101C2×C5311yescharacteristic, complemented
346#3100C2×C5311yescharacteristic, complemented
347#2392C2×C5311yescharacteristic, complemented
348#1612C2×C5312yescomplemented
349#1609C2×C5312yescomplemented
350#1600C2×C5312yescomplemented
351#1597C2×C5312yescomplemented
352#1503C2×C5311yescharacteristic, complemented
353#1502C2×C5311yescharacteristic, complemented
354#1458C2×C5311yescharacteristic, complemented
355C2×C53—21no—
356C2×C53—21no—
357C2×C53—82no—
358C2×C53—81no—
359C2×C53—82no—
360C2×C53C2×#44911yescharacteristic
361C2×C53#301811yescharacteristic
362C2×C53#302511yescharacteristic
363#542—21no—
364#542—21no—
365#541—21no—
366#540—21no—
367#539—21no—
368#539C22×C5312yes—
369#538—21no—
370#538C22×C5312yes—
371#533C22×C5311yescharacteristic
372#532C22×C5311yescharacteristic
373#529—22no—
374#529—22no—
375#525—21no—
376C4×#41—21no—
377C2×C4×D4—21no—
378C2×C4×D4C22×C5311yescharacteristic
379C2×#117C22×C5311yescharacteristic
380#483C22×C5312yes—
381#480C22×C5312yes—
382#476—21no—
383#474—21no—
384#461—21no—
385#459—21no—
386#450C22×C5312yes—
387#447C22×C5312yes—
388C4×SD16—22no—
389C4×D8—22no—
390#431C22×C5311yescharacteristic
391#431C22×C5311yescharacteristic
392#398C22×C5311yescharacteristic
393#397C22×C5311yescharacteristic
394#396—21no—
395#394—21no—
396#394C22×C5311yescharacteristic
397#392C22×C5311yescharacteristic
398C4×C4⋊C4C22×C5311yescharacteristic
399C4×C22⋊C4—21no—
400#328C22×C5312yes—
401#328C22×C5312yes—
402#327C22×C5312yes—
403#327C22×C5312yes—
404#324C22×C5312yes—
405#323C22×C5312yes—
406C53#1812611yescharacteristic, direct product factor, Sylow
407C2×#41—21no—
408C22×D4—21no—
409C22×D4C23×C5311yescharacteristic
410C23×C4—21no—
411C23×C4D4×C5311yescharacteristic
412C2×SD16—22no—
413C2×D8—22no—
414C4⋊Q8D4×C5311yescharacteristic, complemented
415C4⋊Q8D4×C5311yescharacteristic, complemented
416C4⋊Q8D4×C5311yescharacteristic, complemented
417#127D4×C5311yescharacteristic, complemented
418#126—22no—
419#126—22no—
420#126—22no—
421#126—22no—
422#125—22no—
423#125—22no—
424#125—21no—
425#124—22no—
426#124—22no—
427#124—21no—
428#123—22no—
429#123—22no—
430#123—22no—
431#123—22no—
432#123—22no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—21no—
438C22⋊Q8C23×C5312yes—
439#121—21no—
440#121—21no—
441#121—22no—
442#121—22no—
443#121—21no—
444#121C23×C5312yes—
445#120—22no—
446C4×Q8—21no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8D4×C5312yescomplemented
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4—44no—
462C4×D4D4×C5312yescomplemented
463#117—22no—
464#117—21no—
465#117—21no—
466#117—21no—
467#117—21no—
468#117—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4D4×C5311yescharacteristic
472C2×C4⋊C4C23×C5311yescharacteristic
473C2×C4⋊C4C23×C5311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4D4×C5311yescharacteristic
480C2×C22⋊C4C23×C5311yescharacteristic
481C2×C42—22no—
482C2×C42—21no—
483C2×C42D4×C5311yescharacteristic
484C2×C42C23×C5311yescharacteristic
485#107—22no—
486#106—22no—
487C4⋊C8—21no—
488C4⋊C8—21no—
489#103—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493C22⋊C8C23×C5312yes—
494C22⋊C8C23×C5312yes—
495C4×C8—21no—
496C4×C8—21no—
497#95—21no—
498#95—21no—
499#95C23×C5311yescharacteristic
500#95C23×C5311yescharacteristic
501C24—21no—
502C24C2×D4×C5311yescharacteristic
503#41—42no—
504#41—42no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8C2×D4×C5312yes—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4C2×D4×C5312yes—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4C2×D4×C5311yescharacteristic
535C22×C4C2×D4×C5311yescharacteristic
536C22×C4C2×D4×C5311yescharacteristic
537C22×C4C2×D4×C5311yescharacteristic
538C22×C4C2×D4×C5311yescharacteristic
539C22×C4C24×C5311yescharacteristic
540SD16—44no—
541D8—44no—
542C2×C8—22no—
543C2×C8—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4C2×D4×C5312yes—
563C4⋊C4C2×D4×C5312yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—22no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C42—22no—
584C42—22no—
585C42—21no—
586C42—22no—
587C42—21no—
588C42—42no—
589C42C2×D4×C5311yescharacteristic
590C42C2×D4×C5311yescharacteristic
591C42C2×D4×C5311yescharacteristic
592C42C2×D4×C5311yescharacteristic
593C23—22no—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×D4×C5311yescharacteristic
607Q8—42no—
608Q8—42no—
609Q8—81no—
610D4—22no—
611D4—22no—
612D4—42no—
613D4—41no—
614D4—41no—
615D4—48no—
616D4—42no—
617D4—42no—
618D4—42no—
619D4—81no—
620D4—82no—
621D4—82no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—82no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4—82no—
650C2×C4#120×C5311yescharacteristic
651C2×C4#120×C5311yescharacteristic
652C2×C4#120×C5311yescharacteristic
653C2×C4#120×C5311yescharacteristic
654C2×C4#135×C5312yes—
655C2×C4AGL(1,ℤ/8)×C5312yes—
656C2×C4C22×D4×C5311yescharacteristic
657C2×C4C22×D4×C5311yescharacteristic
658C8—42no—
659C8—42no—
660C22—21no—
661C22—21no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—42no—
671C22—41no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#120×C5311yescharacteristic
678C22C2×#135×C5311yescharacteristic
679C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4C53×#44912yes—
694C4C53×#44912yes—
695C2—21no—
696C2—21no—
697C2—81no—
698C2—82no—
699C2—82no—
700C2C2×C53×#44911yescharacteristic
701C2C53×#301811yescharacteristic
702C2C53×#302511yescharacteristic
subgroupG/H
centerC2×C4×C53#120
commutator, Frattini, cosocleC22×C4C24×C53
socleC22×C53C2×#120
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3455C2semidirect
2. C53×#3101C2semidirect
3. C53×#3100C2semidirect
4. C53×#2392C2semidirect
5. C53×#1612C2semidirect
6. C53×#1609C2semidirect
7. C53×#1600C2semidirect
8. C53×#1597C2semidirect
9. C53×#1503C2semidirect
10. C53×#1502C2semidirect
11. C53×#1458C2semidirect
62. C4⋊Q8×C53D4semidirect
63. C4⋊Q8×C53D4semidirect
64. C4⋊Q8×C53D4semidirect
65. #127×C53D4semidirect
97. C4×Q8×C53D4semidirect
110. C4×D4×C53D4semidirect
308. #18126C53direct (N × H)
344. #3455C2×C53semidirect
345. #3101C2×C53semidirect
346. #3100C2×C53semidirect
347. #2392C2×C53semidirect
348. #1612C2×C53semidirect
349. #1609C2×C53semidirect
350. #1600C2×C53semidirect
351. #1597C2×C53semidirect
352. #1503C2×C53semidirect
353. #1502C2×C53semidirect
354. #1458C2×C53semidirect
406. C53#18126direct (N × H)
414. C4⋊Q8D4×C53semidirect
415. C4⋊Q8D4×C53semidirect
416. C4⋊Q8D4×C53semidirect
417. #127D4×C53semidirect
449. C4×Q8D4×C53semidirect
462. C4×D4D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#34552
C53×#31012
C53×#31002
C53×#23922
C53×#16122
C53×#16092
C53×#16002
C53×#15972
C53×#15032
C53×#15022
C53×#14582
#1812653