Finite Group Databasebeta

← C53×#24262 #27231774

Subgroups — C53×#24262 #27231774

Order 13568.

1654 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3496C211yesmaximal, characteristic, complemented
2C2×C53×B(4,𝔽2)C212yesmaximal, complemented
3C53×#2617C212yesmaximal, complemented
4C53×#2321C211yesmaximal, characteristic, complemented
5C53×#2044C212yesmaximal, complemented
6C53×#2021C212yesmaximal, complemented
7C53×#1964C212yesmaximal, complemented
8C53×#1799C211yesmaximal, characteristic, complemented
9C53×#1790C212yesmaximal, complemented
10C2×H(5,𝔽2)×C53C2212yes—
11C53×#547—22no—
12C53×#546—24no—
13D42×C53—22no—
14C53×#537—21no—
15C53×#534—21no—
16C53×#534C2212yes—
17C53×#532—21no—
18C2×#121×C53—21no—
19C2×#121×C53C2212yes—
20C2×#120×C53C2211yescharacteristic
21C2×#120×C53C2214yescomplemented
22C2×C4×D4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2211yescharacteristic, complemented
24C53×B(4,𝔽2)—28no—
25C2×#99×C53C2212yes—
26C2×#99×C53C2214yescomplemented
27C2×#99×C53C2214yescomplemented
28C53×#397—22no—
29C53×#394—24no—
30C53×#392—22no—
31C53×#390—21no—
32C53×#388—21no—
33C53×#388—21no—
34C53×#386—21no—
35C53×#386C2211yescharacteristic
36C53×#386C2214yescomplemented
37C53×#385C2211yescharacteristic, complemented
38C53×#380C2212yescomplemented
39C53×#379C2211yescharacteristic, complemented
40C4×C22⋊C4×C53C2211yescharacteristic, complemented
41C53×#342C2212yescomplemented
42C25×C53C2311yescharacteristic
43H(5,𝔽2)×C53—24no—
44H(5,𝔽2)×C53—24no—
45H(5,𝔽2)×C53—44no—
46C2×#41×C53—22no—
47C2×#41×C53—24no—
48C22×D4×C53—22no—
49C22×D4×C53—24no—
50C22×D4×C53—21no—
51C22×D4×C53—21no—
52C22×D4×C53—24no—
53C22×D4×C53D412yescomplemented
54C22×D4×C53C2314yes—
55C22×D4×C53C2311yescharacteristic
56C23×C4×C53D411yescharacteristic, complemented
57C23×C4×C53C2311yescharacteristic
58C23×C4×C53C2311yescharacteristic
59C4⋊Q8×C53—21no—
60#127×C53—21no—
61#124×C53—22no—
62#123×C53—24no—
63#123×C53—24no—
64C22⋊Q8×C53—24no—
65#121×C53—22no—
66#121×C53—22no—
67#121×C53—24no—
68#121×C53—22no—
69#121×C53—22no—
70#121×C53—22no—
71#121×C53—22no—
72#121×C53—22no—
73#121×C53—22no—
74#120×C53—24no—
75#120×C53—24no—
76#120×C53—22no—
77#120×C53—28no—
78#120×C53—44no—
79#120×C53D414yescomplemented
80C4×D4×C53—22no—
81C4×D4×C53—22no—
82C4×D4×C53—22no—
83C4×D4×C53—22no—
84C2×C4⋊C4×C53—21no—
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—21no—
87C2×C4⋊C4×C53D411yescharacteristic, complemented
88C2×C4⋊C4×C53D412yescomplemented
89C2×C22⋊C4×C53—22no—
90C2×C22⋊C4×C53—21no—
91C2×C22⋊C4×C53—24no—
92C2×C22⋊C4×C53—21no—
93C2×C22⋊C4×C53—21no—
94C2×C22⋊C4×C53—21no—
95C2×C22⋊C4×C53—22no—
96C2×C22⋊C4×C53—22no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—21no—
99C2×C22⋊C4×C53—21no—
100C2×C22⋊C4×C53D411yescharacteristic, complemented
101C2×C22⋊C4×C53D414yescomplemented
102C2×C22⋊C4×C53C2314yes—
103C2×C22⋊C4×C53C2311yescharacteristic
104C2×C22⋊C4×C53C2311yescharacteristic
105C2×C22⋊C4×C53C2311yescharacteristic
106C2×C42×C53—21no—
107C2×C42×C53D411yescharacteristic, complemented
108#99×C53—28no—
109#99×C53—24no—
110#99×C53—44no—
111#95×C53—21no—
112#95×C53—22no—
113#95×C53—21no—
114#95×C53—21no—
115#95×C53—24no—
116C24×C53—22no—
117C24×C53—21no—
118C24×C53—22no—
119C24×C53—21no—
120C24×C53—22no—
121C24×C53—81no—
122C24×C53—81no—
123C24×C53C2×D414yes—
124C24×C53C2×D411yescharacteristic
125C24×C53C2×D412yescomplemented
126C24×C53C2411yescharacteristic
127#41×C53—48no—
128#41×C53—48no—
129#41×C53—44no—
130#41×C53—44no—
131C2×Q8×C53—22no—
132C2×D4×C53—22no—
133C2×D4×C53—22no—
134C2×D4×C53—24no—
135C2×D4×C53—22no—
136C2×D4×C53—24no—
137C2×D4×C53—24no—
138C2×D4×C53—24no—
139C2×D4×C53—24no—
140C2×D4×C53—24no—
141C2×D4×C53—24no—
142C2×D4×C53—22no—
143C2×D4×C53—22no—
144C2×D4×C53—24no—
145C2×D4×C53—22no—
146C2×D4×C53—22no—
147C2×D4×C53—48no—
148C2×D4×C53—48no—
149C2×D4×C53—44no—
150C2×D4×C53—44no—
151C2×D4×C53—48no—
152C2×D4×C53—82no—
153C2×D4×C53—82no—
154C2×D4×C53—81no—
155C2×D4×C53—81no—
156C2×D4×C53—84no—
157C2×D4×C53—84no—
158C2×D4×C53C2×D412yes—
159C2×D4×C53#4112yes—
160C22×C4×C53—22no—
161C22×C4×C53—24no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—22no—
167C22×C4×C53—21no—
168C22×C4×C53—24no—
169C22×C4×C53—81no—
170C22×C4×C53—81no—
171C22×C4×C53—81no—
172C22×C4×C53C2×D414yes—
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D412yes—
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D412yes—
180C4⋊C4×C53—22no—
181C4⋊C4×C53—22no—
182C4⋊C4×C53—22no—
183C4⋊C4×C53—22no—
184C4⋊C4×C53—22no—
185C4⋊C4×C53—82no—
186C4⋊C4×C53—81no—
187C22⋊C4×C53—24no—
188C22⋊C4×C53—24no—
189C22⋊C4×C53—22no—
190C22⋊C4×C53—21no—
191C22⋊C4×C53—24no—
192C22⋊C4×C53—22no—
193C22⋊C4×C53—24no—
194C22⋊C4×C53—24no—
195C22⋊C4×C53—24no—
196C22⋊C4×C53—22no—
197C22⋊C4×C53—24no—
198C22⋊C4×C53—48no—
199C22⋊C4×C53—41no—
200C22⋊C4×C53—41no—
201C22⋊C4×C53—42no—
202C22⋊C4×C53—81no—
203C22⋊C4×C53—81no—
204C22⋊C4×C53—84no—
205C22⋊C4×C53—81no—
206C22⋊C4×C53C2×D412yescomplemented
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—81no—
210C23×C53—21no—
211C23×C53—21no—
212C23×C53—24no—
213C23×C53—22no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—41no—
218C23×C53—41no—
219C23×C53—41no—
220C23×C53—41no—
221C23×C53—41no—
222C23×C53—44no—
223C23×C53—41no—
224C23×C53—44no—
225C23×C53—41no—
226C23×C53—41no—
227C23×C53—44no—
228C23×C53—44no—
229C23×C53—44no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—42no—
233C23×C53—82no—
234C23×C53—82no—
235C23×C53—84no—
236C23×C53—82no—
237C23×C53—82no—
238C23×C53#12112yes—
239C23×C53C22×D411yescharacteristic
240C23×C53C22×D412yes—
241C23×C53C22×D411yescharacteristic
242C23×C53C2×#4111yescharacteristic
243C23×C53H(5,𝔽2)12yes—
244Q8×C53—44no—
245D4×C53—24no—
246D4×C53—24no—
247D4×C53—44no—
248D4×C53—44no—
249D4×C53—48no—
250D4×C53—44no—
251D4×C53—44no—
252D4×C53—44no—
253D4×C53—44no—
254D4×C53—82no—
255D4×C53—82no—
256D4×C53—84no—
257D4×C53—82no—
258D4×C53—816no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—24no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—22no—
265C2×C4×C53—24no—
266C2×C4×C53—24no—
267C2×C4×C53—41no—
268C2×C4×C53—42no—
269C2×C4×C53—41no—
270C2×C4×C53—42no—
271C2×C4×C53—42no—
272C2×C4×C53—48no—
273C2×C4×C53—44no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—44no—
280C2×C4×C53—41no—
281C2×C4×C53—44no—
282C2×C4×C53—44no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—44no—
288C2×C4×C53—81no—
289C2×C4×C53#12011yescharacteristic
290C2×C4×C53#12011yescharacteristic
291C2×C4×C53#12012yes—
292C2×C4×C53#12112yes—
293#24262C5311yesmaximal, characteristic, direct product factor, Sylow
294C22×C53—21no—
295C22×C53—22no—
296C22×C53—21no—
297C22×C53—22no—
298C22×C53—22no—
299C22×C53—41no—
300C22×C53—41no—
301C22×C53—42no—
302C22×C53—42no—
303C22×C53—42no—
304C22×C53—48no—
305C22×C53—42no—
306C22×C53—41no—
307C22×C53—41no—
308C22×C53—44no—
309C22×C53—42no—
310C22×C53—44no—
311C22×C53—44no—
312C22×C53—81no—
313C22×C53—84no—
314C22×C53—84no—
315C22×C53—81no—
316C22×C53—81no—
317C22×C53—84no—
318C22×C53—81no—
319C22×C53—81no—
320C22×C53—164no—
321C22×C53C2×#12011yescharacteristic
322C22×C53C2×#12111yescharacteristic
323C22×C53#53511yescharacteristic
324C22×C53D4212yes—
325C22×C53#54612yes—
326C4×C53—22no—
327C4×C53—21no—
328C4×C53—21no—
329C4×C53—22no—
330C4×C53—42no—
331C4×C53—44no—
332C4×C53—41no—
333C4×C53—41no—
334C4×C53—81no—
335C4×C53—84no—
336C4×C53—81no—
337#3496C2×C5311yescharacteristic, complemented
338C2×B(4,𝔽2)C2×C5312yescomplemented
339#2617C2×C5312yescomplemented
340#2321C2×C5311yescharacteristic, complemented
341#2044C2×C5312yescomplemented
342#2021C2×C5312yescomplemented
343#1964C2×C5312yescomplemented
344#1799C2×C5311yescharacteristic, complemented
345#1790C2×C5312yescomplemented
346C2×C53—21no—
347C2×C53—22no—
348C2×C53—21no—
349C2×C53—22no—
350C2×C53—42no—
351C2×C53—82no—
352C2×C53—84no—
353C2×C53#240811yescharacteristic
354C2×C53#302611yescharacteristic
355C2×C53#302711yescharacteristic
356C2×H(5,𝔽2)C22×C5312yes—
357#547—22no—
358#546—24no—
359D42—22no—
360#537—21no—
361#534—21no—
362#534C22×C5312yes—
363#532—21no—
364C2×#121—21no—
365C2×#121C22×C5312yes—
366C2×#120C22×C5311yescharacteristic
367C2×#120C22×C5314yescomplemented
368C2×C4×D4C22×C5311yescharacteristic
369C22×C22⋊C4C22×C5311yescharacteristic, complemented
370B(4,𝔽2)—28no—
371C2×#99C22×C5312yes—
372C2×#99C22×C5314yescomplemented
373C2×#99C22×C5314yescomplemented
374#397—22no—
375#394—24no—
376#392—22no—
377#390—21no—
378#388—21no—
379#388—21no—
380#386—21no—
381#386C22×C5311yescharacteristic
382#386C22×C5314yescomplemented
383#385C22×C5311yescharacteristic, complemented
384#380C22×C5312yescomplemented
385#379C22×C5311yescharacteristic, complemented
386C4×C22⋊C4C22×C5311yescharacteristic, complemented
387#342C22×C5312yescomplemented
388C53#2426211yescharacteristic, direct product factor, Sylow
389C25C23×C5311yescharacteristic
390H(5,𝔽2)—24no—
391H(5,𝔽2)—24no—
392H(5,𝔽2)—44no—
393C2×#41—22no—
394C2×#41—24no—
395C22×D4—22no—
396C22×D4—24no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—24no—
400C22×D4D4×C5312yescomplemented
401C22×D4C23×C5314yes—
402C22×D4C23×C5311yescharacteristic
403C23×C4D4×C5311yescharacteristic, complemented
404C23×C4C23×C5311yescharacteristic
405C23×C4C23×C5311yescharacteristic
406C4⋊Q8—21no—
407#127—21no—
408#124—22no—
409#123—24no—
410#123—24no—
411C22⋊Q8—24no—
412#121—22no—
413#121—22no—
414#121—24no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#120—24no—
422#120—24no—
423#120—22no—
424#120—28no—
425#120—44no—
426#120D4×C5314yescomplemented
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4D4×C5311yescharacteristic, complemented
435C2×C4⋊C4D4×C5312yescomplemented
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C5311yescharacteristic, complemented
448C2×C22⋊C4D4×C5314yescomplemented
449C2×C22⋊C4C23×C5314yes—
450C2×C22⋊C4C23×C5311yescharacteristic
451C2×C22⋊C4C23×C5311yescharacteristic
452C2×C22⋊C4C23×C5311yescharacteristic
453C2×C42—21no—
454C2×C42D4×C5311yescharacteristic, complemented
455#99—24no—
456#99—28no—
457#99—44no—
458#95—21no—
459#95—22no—
460#95—21no—
461#95—21no—
462#95—24no—
463C24—22no—
464C24—21no—
465C24—22no—
466C24—21no—
467C24—22no—
468C24—81no—
469C24—81no—
470C24C2×D4×C5314yes—
471C24C2×D4×C5311yescharacteristic
472C24C2×D4×C5312yescomplemented
473C24C24×C5311yescharacteristic
474#41—48no—
475#41—48no—
476#41—44no—
477#41—44no—
478C2×Q8—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—82no—
500C2×D4—82no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4C2×D4×C5312yes—
506C2×D4#41×C5312yes—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C2×D4×C5314yes—
520C22×C4C2×D4×C5311yescharacteristic
521C22×C4C2×D4×C5311yescharacteristic
522C22×C4C2×D4×C5311yescharacteristic
523C22×C4C2×D4×C5311yescharacteristic
524C22×C4C2×D4×C5312yes—
525C22×C4C2×D4×C5311yescharacteristic
526C22×C4C2×D4×C5312yes—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—82no—
533C4⋊C4—81no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—24no—
539C22⋊C4—22no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—24no—
545C22⋊C4—48no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—84no—
553C22⋊C4C2×D4×C5312yescomplemented
554C42—21no—
555C42—21no—
556C42—81no—
557C23—21no—
558C23—21no—
559C23—24no—
560C23—22no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—44no—
572C23—41no—
573C23—44no—
574C23—44no—
575C23—44no—
576C23—44no—
577C23—41no—
578C23—41no—
579C23—42no—
580C23—82no—
581C23—82no—
582C23—84no—
583C23—82no—
584C23—82no—
585C23#121×C5312yes—
586C23C22×D4×C5311yescharacteristic
587C23C22×D4×C5312yes—
588C23C22×D4×C5311yescharacteristic
589C23C2×#41×C5311yescharacteristic
590C23H(5,𝔽2)×C5312yes—
591Q8—44no—
592D4—24no—
593D4—24no—
594D4—44no—
595D4—44no—
596D4—48no—
597D4—44no—
598D4—44no—
599D4—44no—
600D4—44no—
601D4—82no—
602D4—82no—
603D4—84no—
604D4—82no—
605D4—816no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—48no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—44no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—41no—
631C2×C4—44no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—44no—
635C2×C4—81no—
636C2×C4#120×C5311yescharacteristic
637C2×C4#120×C5311yescharacteristic
638C2×C4#120×C5312yes—
639C2×C4#121×C5312yes—
640C22—21no—
641C22—22no—
642C22—21no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—48no—
651C22—42no—
652C22—41no—
653C22—41no—
654C22—44no—
655C22—44no—
656C22—44no—
657C22—42no—
658C22—81no—
659C22—84no—
660C22—84no—
661C22—81no—
662C22—81no—
663C22—84no—
664C22—81no—
665C22—81no—
666C22—164no—
667C22C2×#120×C5311yescharacteristic
668C22C2×#121×C5311yescharacteristic
669C22C53×#53511yescharacteristic
670C22D42×C5312yes—
671C22C53×#54612yes—
672C4—21no—
673C4—21no—
674C4—22no—
675C4—22no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—44no—
680C4—84no—
681C4—81no—
682C4—81no—
683C2—21no—
684C2—22no—
685C2—21no—
686C2—22no—
687C2—42no—
688C2—82no—
689C2—84no—
690C2C53×#240811yescharacteristic
691C2C53×#302611yescharacteristic
692C2C53×#302711yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC24C24×C53
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3496C2semidirect
2. C2×C53×B(4,𝔽2)C2semidirect
3. C53×#2617C2semidirect
4. C53×#2321C2semidirect
5. C53×#2044C2semidirect
6. C53×#2021C2semidirect
7. C53×#1964C2semidirect
8. C53×#1799C2semidirect
9. C53×#1790C2semidirect
21. C2×#120×C53C22semidirect
23. C22×C22⋊C4×C53C22semidirect
26. C2×#99×C53C22semidirect
27. C2×#99×C53C22semidirect
36. C53×#386C22semidirect
37. C53×#385C22semidirect
38. C53×#380C22semidirect
39. C53×#379C22semidirect
40. C4×C22⋊C4×C53C22semidirect
41. C53×#342C22semidirect
53. C22×D4×C53D4semidirect
56. C23×C4×C53D4semidirect
79. #120×C53D4semidirect
87. C2×C4⋊C4×C53D4semidirect
88. C2×C4⋊C4×C53D4semidirect
100. C2×C22⋊C4×C53D4semidirect
101. C2×C22⋊C4×C53D4semidirect
107. C2×C42×C53D4semidirect
125. C24×C53C2×D4semidirect
206. C22⋊C4×C53C2×D4semidirect
293. #24262C53direct (N × H)
337. #3496C2×C53semidirect
338. C2×B(4,𝔽2)C2×C53semidirect
339. #2617C2×C53semidirect
340. #2321C2×C53semidirect
341. #2044C2×C53semidirect
342. #2021C2×C53semidirect
343. #1964C2×C53semidirect
344. #1799C2×C53semidirect
345. #1790C2×C53semidirect
367. C2×#120C22×C53semidirect
369. C22×C22⋊C4C22×C53semidirect
372. C2×#99C22×C53semidirect
373. C2×#99C22×C53semidirect
382. #386C22×C53semidirect
383. #385C22×C53semidirect
384. #380C22×C53semidirect
385. #379C22×C53semidirect
386. C4×C22⋊C4C22×C53semidirect
387. #342C22×C53semidirect
388. C53#24262direct (N × H)
400. C22×D4D4×C53semidirect
403. C23×C4D4×C53semidirect
426. #120D4×C53semidirect
434. C2×C4⋊C4D4×C53semidirect
435. C2×C4⋊C4D4×C53semidirect
447. C2×C22⋊C4D4×C53semidirect
448. C2×C22⋊C4D4×C53semidirect
454. C2×C42D4×C53semidirect
472. C24C2×D4×C53semidirect
553. C22⋊C4C2×D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#34962
C2×C53×B(4,𝔽2)2
C53×#26172
C53×#23212
C53×#20442
C53×#20212
C53×#19642
C53×#17992
C53×#17902
#2426253