Finite Group Databasebeta

← C53×#26850 #27234362

Subgroups — C53×#26850 #27234362

Order 13568.

776 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3136C211yesmaximal, characteristic, complemented
2C53×#3096C211yesmaximal, characteristic, complemented
3C53×#3081C211yesmaximal, characteristic, complemented
4C53×#2946C211yesmaximal, characteristic, complemented
5C53×#2063C211yesmaximal, characteristic, complemented
6C53×#2060C211yesmaximal, characteristic, complemented
7C53×#2051C211yesmaximal, characteristic, complemented
8C53×#2002C211yesmaximal, characteristic
9C53×#1957C211yesmaximal, characteristic, complemented
10C53×#1937C211yesmaximal, characteristic, complemented
11C53×#1931C211yesmaximal, characteristic, complemented
12C53×#1931C211yesmaximal, characteristic, complemented
13C53×#1887C211yesmaximal, characteristic, complemented
14C53×#1859C211yesmaximal, characteristic, complemented
15C53×#1772C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
17C53×#544C2211yescharacteristic
18C53×#535C2211yescharacteristic
19C2×#127×C53C2211yescharacteristic
20C53×#520C2211yescharacteristic
21C53×#518C2211yescharacteristic
22C53×#490—21no—
23C53×#489—21no—
24C53×#488—21no—
25C53×#486—21no—
26C53×#482—21no—
27C53×#482—21no—
28C53×#481—21no—
29C53×#480—21no—
30C53×#478—21no—
31C53×#478—21no—
32C53×#476—21no—
33C53×#474—21no—
34C53×#442—21no—
35C53×#440—21no—
36C4×SD16×C53—21no—
37C4×D8×C53—21no—
38C2×#108×C53C2211yescharacteristic
39C53×#428C2211yescharacteristic
40C53×#428C2211yescharacteristic
41C53×#428C2211yescharacteristic
42C53×#427C2211yescharacteristic
43C53×#424C2211yescharacteristic
44C2×#104×C53C2211yescharacteristic
45C53×#418C2211yescharacteristic
46C53×#418C2211yescharacteristic
47C53×#418C2211yescharacteristic
48C53×#417C2211yescharacteristic
49C53×#416C2211yescharacteristic
50C2×#102×C53C2211yescharacteristic
51C2×#102×C53C2211yescharacteristic
52C2×#102×C53C2211yescharacteristic
53C2×#102×C53C2211yescharacteristic
54C2×#100×C53C2211yescharacteristic
55C2×#100×C53C2211yescharacteristic
56C53×#408C2211yescharacteristic
57C53×#405C2211yescharacteristic
58C53×#405C2211yescharacteristic
59C2×C4×C8×C53C2211yescharacteristic
60C53×#384C2211yescharacteristic
61C53×#343C2211yescharacteristic
62C53×#343C2211yescharacteristic
63C53×#341C2211yescharacteristic
64C53×#339C2211yescharacteristic
65C53×#339C2211yescharacteristic
66C53×#339C2211yescharacteristic
67C2×#41×C53C2311yescharacteristic
68C22×D4×C53—41no—
69C22×D4×C53C2311yescharacteristic
70C22×D4×C53C2311yescharacteristic
71AGL(1,ℤ/8)×C53—22no—
72AGL(1,ℤ/8)×C53—22no—
73C2×SD16×C53—21no—
74C2×D8×C53—21no—
75C2×M16×C53C2311yescharacteristic
76C2×M16×C53C2311yescharacteristic
77C2×M16×C53C2311yescharacteristic
78C2×M16×C53C2311yescharacteristic
79C22×C8×C53C2311yescharacteristic
80C22×C8×C53C2311yescharacteristic
81C4⋊Q8×C53—21no—
82C4⋊Q8×C53—21no—
83#127×C53—22no—
84#127×C53—21no—
85#127×C53—22no—
86#125×C53—21no—
87#125×C53—21no—
88#124×C53—21no—
89C22⋊Q8×C53—41no—
90#121×C53—21no—
91#121×C53—21no—
92#120×C53—41no—
93C4×Q8×C53—21no—
94C4×D4×C53—21no—
95C4×D4×C53—21no—
96C4×D4×C53—21no—
97C4×D4×C53—21no—
98C4×D4×C53—21no—
99C4×D4×C53—41no—
100#117×C53—21no—
101#117×C53C2311yescharacteristic
102#117×C53C2311yescharacteristic
103#117×C53C2311yescharacteristic
104C2×C4⋊C4×C53—21no—
105C2×C4⋊C4×C53—41no—
106C2×C4⋊C4×C53C2311yescharacteristic
107C2×C4⋊C4×C53C2311yescharacteristic
108C2×C22⋊C4×C53—41no—
109C2×C42×C53C2311yescharacteristic
110#108×C53—22no—
111#107×C53—21no—
112#107×C53—21no—
113#107×C53—21no—
114#107×C53D411yescharacteristic, complemented
115#107×C53D411yescharacteristic, complemented
116#106×C53—21no—
117#106×C53—21no—
118#106×C53—21no—
119#106×C53D411yescharacteristic, complemented
120#106×C53D411yescharacteristic, complemented
121C4⋊C8×C53—21no—
122C4⋊C8×C53—21no—
123#104×C53—22no—
124#103×C53—21no—
125#103×C53D411yescharacteristic, complemented
126#103×C53D411yescharacteristic, complemented
127#102×C53—21no—
128#102×C53—21no—
129#102×C53—21no—
130#102×C53—21no—
131#102×C53—21no—
132#102×C53—21no—
133#102×C53—21no—
134#102×C53—21no—
135#102×C53—21no—
136#102×C53—21no—
137#102×C53—21no—
138#102×C53—21no—
139#102×C53—21no—
140#102×C53—21no—
141#102×C53—21no—
142#102×C53D411yescharacteristic, complemented
143#102×C53D411yescharacteristic, complemented
144#100×C53—22no—
145#100×C53—22no—
146C22⋊C8×C53—21no—
147C22⋊C8×C53—21no—
148#97×C53—21no—
149#97×C53—21no—
150C4×C8×C53—21no—
151C4×C8×C53—21no—
152C4×C8×C53—22no—
153C24×C53—21no—
154C24×C53—21no—
155#41×C53—21no—
156#41×C53—21no—
157#41×C53—21no—
158#41×C53—21no—
159C2×Q8×C53—41no—
160C2×Q8×C53C2×D411yescharacteristic
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
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—41no—
175C2×D4×C53—41no—
176C2×D4×C53—82no—
177C2×D4×C53—82no—
178C2×D4×C53C2×D411yescharacteristic
179C2×D4×C53#4112yes—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—41no—
185C22×C4×C53—41no—
186C22×C4×C53—41no—
187C22×C4×C53C2411yescharacteristic
188SD16×C53—24no—
189D8×C53—24no—
190M16×C53—21no—
191M16×C53—21no—
192M16×C53—21no—
193M16×C53—21no—
194M16×C53—21no—
195M16×C53—21no—
196M16×C53—21no—
197M16×C53#4112yes—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53C2×D411yescharacteristic
207C2×C8×C53C2×D411yescharacteristic
208C2×C8×C53C2×D411yescharacteristic
209C2×C8×C53C2×D411yescharacteristic
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—41no—
215C4⋊C4×C53—41no—
216C4⋊C4×C53—41no—
217C4⋊C4×C53—41no—
218C4⋊C4×C53—82no—
219C4⋊C4×C53C2×D411yescharacteristic
220C4⋊C4×C53C2×D411yescharacteristic
221C4⋊C4×C53C2×D411yescharacteristic
222C4⋊C4×C53C2×D411yescharacteristic
223C4⋊C4×C53C2×D411yescharacteristic
224C4⋊C4×C53C2×D411yescharacteristic
225C22⋊C4×C53—21no—
226C22⋊C4×C53—21no—
227C22⋊C4×C53—21no—
228C22⋊C4×C53—41no—
229C22⋊C4×C53—41no—
230C22⋊C4×C53—41no—
231C22⋊C4×C53—41no—
232C22⋊C4×C53—41no—
233C42×C53—21no—
234C42×C53—21no—
235C42×C53—21no—
236C42×C53—21no—
237C42×C53—41no—
238C42×C53#4112yes—
239C23×C53—21no—
240C23×C53—22no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—81no—
247C23×C53—81no—
248C23×C53—81no—
249C23×C53—81no—
250C23×C53H(5,𝔽2)11yescharacteristic
251Q8×C53—21no—
252Q8×C53—21no—
253Q8×C53—161no—
254D4×C53—22no—
255D4×C53—21no—
256D4×C53—21no—
257D4×C53—22no—
258D4×C53—41no—
259D4×C53—41no—
260D4×C53—41no—
261D4×C53—41no—
262D4×C53—41no—
263D4×C53—41no—
264D4×C53—41no—
265D4×C53—41no—
266D4×C53—88no—
267D4×C53—161no—
268D4×C53—161no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
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—81no—
284C2×C4×C53—81no—
285C2×C4×C53—161no—
286C2×C4×C53—161no—
287C2×C4×C53—161no—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C22×D411yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C532−1+411yescharacteristic
294C8×C53—22no—
295C8×C53—21no—
296C8×C53—21no—
297C8×C53—21no—
298C8×C53—21no—
299C8×C53—41no—
300C8×C53—41no—
301C8×C53—41no—
302#26850C5311yesmaximal, characteristic, direct product factor, Sylow
303C22×C53—21no—
304C22×C53—21no—
305C22×C53—41no—
306C22×C53—42no—
307C22×C53—41no—
308C22×C53—41no—
309C22×C53—82no—
310C22×C53—82no—
311C22×C53—81no—
312C22×C53—81no—
313C22×C53—81no—
314C22×C53—81no—
315C22×C53—81no—
316C22×C53—161no—
317C22×C53—161no—
318C22×C53#54211yescharacteristic
319C22×C53D4211yescharacteristic
320C22×C53#55111yescharacteristic
321C4×C53—24no—
322C4×C53—41no—
323C4×C53—41no—
324C4×C53—41no—
325C4×C53—41no—
326C4×C53—41no—
327C4×C53—41no—
328C4×C53—41no—
329C4×C53—81no—
330C4×C53—81no—
331C4×C53#52511yescharacteristic
332C4×C53#53211yescharacteristic
333C4×C53#54711yescharacteristic
334C4×C53#54811yescharacteristic
335#3136C2×C5311yescharacteristic, complemented
336#3096C2×C5311yescharacteristic, complemented
337#3081C2×C5311yescharacteristic, complemented
338#2946C2×C5311yescharacteristic, complemented
339#2063C2×C5311yescharacteristic, complemented
340#2060C2×C5311yescharacteristic, complemented
341#2051C2×C5311yescharacteristic, complemented
342#2002C2×C5311yescharacteristic
343#1957C2×C5311yescharacteristic, complemented
344#1937C2×C5311yescharacteristic, complemented
345#1931C2×C5311yescharacteristic, complemented
346#1931C2×C5311yescharacteristic, complemented
347#1887C2×C5311yescharacteristic, complemented
348#1859C2×C5311yescharacteristic, complemented
349#1772C2×C5311yescharacteristic, complemented
350C2×C53—21no—
351C2×C53—21no—
352C2×C53—81no—
353C2×C53—82no—
354C2×C53—161no—
355C2×C53#246111yescharacteristic
356C2×C53#329111yescharacteristic
357C2×C53#329211yescharacteristic
358C2×AGL(1,ℤ/8)C22×C5311yescharacteristic
359#544C22×C5311yescharacteristic
360#535C22×C5311yescharacteristic
361C2×#127C22×C5311yescharacteristic
362#520C22×C5311yescharacteristic
363#518C22×C5311yescharacteristic
364#490—21no—
365#489—21no—
366#488—21no—
367#486—21no—
368#482—21no—
369#482—21no—
370#481—21no—
371#480—21no—
372#478—21no—
373#478—21no—
374#476—21no—
375#474—21no—
376#442—21no—
377#440—21no—
378C4×SD16—21no—
379C4×D8—21no—
380C2×#108C22×C5311yescharacteristic
381#428C22×C5311yescharacteristic
382#428C22×C5311yescharacteristic
383#428C22×C5311yescharacteristic
384#427C22×C5311yescharacteristic
385#424C22×C5311yescharacteristic
386C2×#104C22×C5311yescharacteristic
387#418C22×C5311yescharacteristic
388#418C22×C5311yescharacteristic
389#418C22×C5311yescharacteristic
390#417C22×C5311yescharacteristic
391#416C22×C5311yescharacteristic
392C2×#102C22×C5311yescharacteristic
393C2×#102C22×C5311yescharacteristic
394C2×#102C22×C5311yescharacteristic
395C2×#102C22×C5311yescharacteristic
396C2×#100C22×C5311yescharacteristic
397C2×#100C22×C5311yescharacteristic
398#408C22×C5311yescharacteristic
399#405C22×C5311yescharacteristic
400#405C22×C5311yescharacteristic
401C2×C4×C8C22×C5311yescharacteristic
402#384C22×C5311yescharacteristic
403#343C22×C5311yescharacteristic
404#343C22×C5311yescharacteristic
405#341C22×C5311yescharacteristic
406#339C22×C5311yescharacteristic
407#339C22×C5311yescharacteristic
408#339C22×C5311yescharacteristic
409C53#2685011yescharacteristic, direct product factor, Sylow
410C2×#41C23×C5311yescharacteristic
411C22×D4—41no—
412C22×D4C23×C5311yescharacteristic
413C22×D4C23×C5311yescharacteristic
414AGL(1,ℤ/8)—22no—
415AGL(1,ℤ/8)—22no—
416C2×SD16—21no—
417C2×D8—21no—
418C2×M16C23×C5311yescharacteristic
419C2×M16C23×C5311yescharacteristic
420C2×M16C23×C5311yescharacteristic
421C2×M16C23×C5311yescharacteristic
422C22×C8C23×C5311yescharacteristic
423C22×C8C23×C5311yescharacteristic
424C4⋊Q8—21no—
425C4⋊Q8—21no—
426#127—21no—
427#127—22no—
428#127—22no—
429#125—21no—
430#125—21no—
431#124—21no—
432C22⋊Q8—41no—
433#121—21no—
434#121—21no—
435#120—41no—
436C4×Q8—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—41no—
443#117—21no—
444#117C23×C5311yescharacteristic
445#117C23×C5311yescharacteristic
446#117C23×C5311yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4C23×C5311yescharacteristic
450C2×C4⋊C4C23×C5311yescharacteristic
451C2×C22⋊C4—41no—
452C2×C42C23×C5311yescharacteristic
453#108—22no—
454#107—21no—
455#107—21no—
456#107—21no—
457#107D4×C5311yescharacteristic, complemented
458#107D4×C5311yescharacteristic, complemented
459#106—21no—
460#106—21no—
461#106—21no—
462#106D4×C5311yescharacteristic, complemented
463#106D4×C5311yescharacteristic, complemented
464C4⋊C8—21no—
465C4⋊C8—21no—
466#104—22no—
467#103—21no—
468#103D4×C5311yescharacteristic, complemented
469#103D4×C5311yescharacteristic, complemented
470#102—21no—
471#102—21no—
472#102—21no—
473#102—21no—
474#102—21no—
475#102—21no—
476#102—21no—
477#102—21no—
478#102—21no—
479#102—21no—
480#102—21no—
481#102—21no—
482#102—21no—
483#102—21no—
484#102—21no—
485#102D4×C5311yescharacteristic, complemented
486#102D4×C5311yescharacteristic, complemented
487#100—22no—
488#100—22no—
489C22⋊C8—21no—
490C22⋊C8—21no—
491#97—21no—
492#97—21no—
493C4×C8—21no—
494C4×C8—21no—
495C4×C8—22no—
496C24—21no—
497C24—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502C2×Q8—41no—
503C2×Q8C2×D4×C5311yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—44no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—82no—
520C2×D4—82no—
521C2×D4C2×D4×C5311yescharacteristic
522C2×D4#41×C5312yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4C24×C5311yescharacteristic
531SD16—24no—
532D8—24no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16#41×C5312yes—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C2×D4×C5311yescharacteristic
550C2×C8C2×D4×C5311yescharacteristic
551C2×C8C2×D4×C5311yescharacteristic
552C2×C8C2×D4×C5311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—82no—
562C4⋊C4C2×D4×C5311yescharacteristic
563C4⋊C4C2×D4×C5311yescharacteristic
564C4⋊C4C2×D4×C5311yescharacteristic
565C4⋊C4C2×D4×C5311yescharacteristic
566C4⋊C4C2×D4×C5311yescharacteristic
567C4⋊C4C2×D4×C5311yescharacteristic
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—41no—
581C42#41×C5312yes—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—81no—
590C23—81no—
591C23—81no—
592C23—81no—
593C23H(5,𝔽2)×C5311yescharacteristic
594Q8—21no—
595Q8—21no—
596Q8—161no—
597D4—21no—
598D4—22no—
599D4—21no—
600D4—22no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—88no—
610D4—161no—
611D4—161no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—161no—
629C2×C4—161no—
630C2×C4—161no—
631C2×C4C22×D4×C5311yescharacteristic
632C2×C4C22×D4×C5311yescharacteristic
633C2×C4C2×#41×C5311yescharacteristic
634C2×C4C2×#41×C5311yescharacteristic
635C2×C4C2×#41×C5311yescharacteristic
636C2×C42−1+4×C5311yescharacteristic
637C8—22no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—21no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—42no—
649C22—41no—
650C22—41no—
651C22—82no—
652C22—82no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—161no—
659C22—161no—
660C22C53×#54211yescharacteristic
661C22D42×C5311yescharacteristic
662C22C53×#55111yescharacteristic
663C4—24no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—81no—
672C4—81no—
673C4C53×#52511yescharacteristic
674C4C53×#53211yescharacteristic
675C4C53×#54711yescharacteristic
676C4C53×#54811yescharacteristic
677C2—21no—
678C2—21no—
679C2—81no—
680C2—82no—
681C2—161no—
682C2C53×#246111yescharacteristic
683C2C53×#329111yescharacteristic
684C2C53×#329211yescharacteristic
subgroupG/H
center, socleC22×C53D42
commutator, Frattini, cosocleC22×C4C24×C53
prime radicalC53×#2002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3136C2semidirect
2. C53×#3096C2semidirect
3. C53×#3081C2semidirect
4. C53×#2946C2semidirect
5. C53×#2063C2semidirect
6. C53×#2060C2semidirect
7. C53×#2051C2semidirect
9. C53×#1957C2semidirect
10. C53×#1937C2semidirect
11. C53×#1931C2semidirect
12. C53×#1931C2semidirect
13. C53×#1887C2semidirect
14. C53×#1859C2semidirect
15. C53×#1772C2semidirect
114. #107×C53D4semidirect
115. #107×C53D4semidirect
119. #106×C53D4semidirect
120. #106×C53D4semidirect
125. #103×C53D4semidirect
126. #103×C53D4semidirect
142. #102×C53D4semidirect
143. #102×C53D4semidirect
302. #26850C53direct (N × H)
335. #3136C2×C53semidirect
336. #3096C2×C53semidirect
337. #3081C2×C53semidirect
338. #2946C2×C53semidirect
339. #2063C2×C53semidirect
340. #2060C2×C53semidirect
341. #2051C2×C53semidirect
343. #1957C2×C53semidirect
344. #1937C2×C53semidirect
345. #1931C2×C53semidirect
346. #1931C2×C53semidirect
347. #1887C2×C53semidirect
348. #1859C2×C53semidirect
349. #1772C2×C53semidirect
409. C53#26850direct (N × H)
457. #107D4×C53semidirect
458. #107D4×C53semidirect
462. #106D4×C53semidirect
463. #106D4×C53semidirect
468. #103D4×C53semidirect
469. #103D4×C53semidirect
485. #102D4×C53semidirect
486. #102D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#31362
C53×#30962
C53×#30812
C53×#29462
C53×#20632
C53×#20602
C53×#20512
C53×#20022
C53×#19572
C53×#19372
C53×#19312
C53×#18872
C53×#18592
C53×#17722
#2685053