Finite Group Databasebeta

← C53×#21590 #27229102

Subgroups — C53×#21590 #27229102

Order 13568.

900 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#482C211yesmaximal, characteristic
2C53×#2324C211yesmaximal, characteristic
3C53×#2274C211yesmaximal, characteristic, complemented
4C53×#1925C211yesmaximal, characteristic, complemented
5C53×#1925C211yesmaximal, characteristic, complemented
6C53×#1921C211yesmaximal, characteristic, complemented
7C53×#1919C211yesmaximal, characteristic, complemented
8C53×#1874C211yesmaximal, characteristic
9C53×#1852C211yesmaximal, characteristic, complemented
10C53×#1825C211yesmaximal, characteristic, complemented
11C53×#1776C211yesmaximal, characteristic, complemented
12C4×#107×C53C211yesmaximal, characteristic, complemented
13C53×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C53C211yesmaximal, characteristic, complemented
15C53×#1750C211yesmaximal, characteristic, complemented
16C2×#121×C53C2211yescharacteristic
17C2×C4×D4×C53C2211yescharacteristic
18C2×#117×C53C2211yescharacteristic
19C2×#117×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C53×#482C418yescomplemented
22C2×#107×C53C2211yescharacteristic
23C2×#107×C53C2211yescharacteristic
24C2×#107×C53C2211yescharacteristic
25C2×#106×C53C2211yescharacteristic
26C2×#102×C53C2211yescharacteristic
27C2×#102×C53C2211yescharacteristic
28C2×#102×C53C2211yescharacteristic
29C2×#102×C53C2211yescharacteristic
30C2×C22⋊C8×C53C2211yescharacteristic
31C2×C22⋊C8×C53C2211yescharacteristic
32C2×#97×C53C2211yescharacteristic
33C2×C4×C8×C53C2211yescharacteristic
34C53×#390—21no—
35C53×#390C2211yescharacteristic
36C53×#389C2211yescharacteristic
37C53×#388—21no—
38C53×#386—21no—
39C53×#385—21no—
40C53×#380C2211yescharacteristic
41C4×C4⋊C4×C53—21no—
42C4×C4⋊C4×C53—21no—
43C4×C4⋊C4×C53C2211yescharacteristic
44C4×C4⋊C4×C53C2211yescharacteristic
45C4×C4⋊C4×C53C2211yescharacteristic
46C4×C4⋊C4×C53C2211yescharacteristic
47C4×C4⋊C4×C53C2211yescharacteristic
48C4×C22⋊C4×C53—21no—
49C4×C22⋊C4×C53—21no—
50C53×#340C2211yescharacteristic
51C53×#340C2211yescharacteristic
52C53×#340C2211yescharacteristic
53C53×#340C2211yescharacteristic
54C53×#340C2211yescharacteristic
55C53×#340C2211yescharacteristic
56C53×#340C2211yescharacteristic
57C53×#340C2211yescharacteristic
58C53×#336C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C22×D4×C53—21no—
61C22×D4×C53C2311yescharacteristic
62C23×C4×C53—21no—
63C23×C4×C53—21no—
64C23×C4×C53C2311yescharacteristic
65C22×C8×C53C2311yescharacteristic
66C22×C8×C53C2311yescharacteristic
67C22×C8×C53C2311yescharacteristic
68C22×C8×C53C2311yescharacteristic
69#121×C53—22no—
70#121×C53C2×C414yes—
71C4×D4×C53—22no—
72C4×D4×C53—22no—
73#117×C53—22no—
74#117×C53—22no—
75#117×C53—22no—
76#117×C53C2×C414yescomplemented
77C2×C4⋊C4×C53—22no—
78C2×C4⋊C4×C53—22no—
79C2×C4⋊C4×C53—21no—
80C2×C4⋊C4×C53—21no—
81C2×C4⋊C4×C53D411yescharacteristic
82C2×C4⋊C4×C53D411yescharacteristic
83C2×C4⋊C4×C53C2311yescharacteristic
84C2×C4⋊C4×C53C2311yescharacteristic
85C2×C4⋊C4×C53C2311yescharacteristic
86C2×C4⋊C4×C53C2311yescharacteristic
87C2×C4⋊C4×C53C2311yescharacteristic
88C2×C4⋊C4×C53C2311yescharacteristic
89C2×C4⋊C4×C53C2311yescharacteristic
90C2×C22⋊C4×C53—21no—
91C2×C22⋊C4×C53—21no—
92C2×C22⋊C4×C53—21no—
93C2×C22⋊C4×C53—21no—
94C2×C22⋊C4×C53—21no—
95C2×C22⋊C4×C53—21no—
96C2×C22⋊C4×C53D411yescharacteristic
97C2×C22⋊C4×C53D411yescharacteristic
98C2×C42×C53—21no—
99C2×C42×C53—21no—
100C2×C42×C53—21no—
101C2×C42×C53—21no—
102C2×C42×C53—21no—
103C2×C42×C53—21no—
104C2×C42×C53C2311yescharacteristic
105C2×C42×C53C2311yescharacteristic
106#107×C53—22no—
107#107×C53—22no—
108#107×C53C2×C414yescomplemented
109#106×C53C2×C414yescomplemented
110#102×C53—22no—
111#102×C53—22no—
112#102×C53C2×C414yescomplemented
113#102×C53C2×C414yescomplemented
114C22⋊C8×C53—22no—
115C22⋊C8×C53C2×C414yescomplemented
116#97×C53—22no—
117C4×C8×C53—22no—
118#95×C53—21no—
119#95×C53—21no—
120#95×C53—21no—
121#95×C53—21no—
122#95×C53—21no—
123#95×C53—21no—
124#95×C53—21no—
125C24×C53—21no—
126C24×C53C2×D411yescharacteristic
127C2×D4×C53—24no—
128C2×D4×C53—21no—
129C2×D4×C53—21no—
130C2×D4×C53—21no—
131C2×D4×C53—21no—
132C2×D4×C53—21no—
133C2×D4×C53—81no—
134C2×D4×C53—81no—
135C2×D4×C53C22×C412yes—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—24no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—42no—
149C22×C4×C53—81no—
150C22×C4×C53—81no—
151C22×C4×C53—81no—
152C22×C4×C53—81no—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53#4112yes—
160C22×C4×C53C2411yescharacteristic
161C2×C8×C53—21no—
162C2×C8×C53—21no—
163C2×C8×C53—21no—
164C2×C8×C53—21no—
165C2×C8×C53—21no—
166C2×C8×C53—21no—
167C2×C8×C53—21no—
168C2×C8×C53—21no—
169C2×C8×C53—21no—
170C2×C8×C53—21no—
171C2×C8×C53C22×C412yes—
172C2×C8×C53C22×C412yes—
173C4⋊C4×C53—24no—
174C4⋊C4×C53—22no—
175C4⋊C4×C53—22no—
176C4⋊C4×C53—21no—
177C4⋊C4×C53—21no—
178C4⋊C4×C53—21no—
179C4⋊C4×C53—21no—
180C4⋊C4×C53—21no—
181C4⋊C4×C53—21no—
182C4⋊C4×C53—21no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—81no—
186C4⋊C4×C53C22×C412yes—
187C4⋊C4×C53C22×C412yes—
188C4⋊C4×C53C22×C412yes—
189C4⋊C4×C53#4112yes—
190C4⋊C4×C53#4112yes—
191C22⋊C4×C53—24no—
192C22⋊C4×C53—24no—
193C22⋊C4×C53—22no—
194C22⋊C4×C53—22no—
195C22⋊C4×C53—42no—
196C22⋊C4×C53—81no—
197C22⋊C4×C53—81no—
198C22⋊C4×C53—81no—
199C42×C53—24no—
200C42×C53—21no—
201C42×C53—21no—
202C42×C53—81no—
203C42×C53—81no—
204C42×C53—81no—
205C42×C53—81no—
206C42×C53—81no—
207C42×C53#4112yes—
208C42×C53#4112yes—
209C23×C53—21no—
210C23×C53—21no—
211C23×C53—21no—
212C23×C53—21no—
213C23×C53—21no—
214C23×C53—21no—
215C23×C53—22no—
216C23×C53—41no—
217C23×C53—41no—
218C23×C53—41no—
219C23×C53—41no—
220C23×C53—41no—
221C23×C53—41no—
222C23×C53C4×D412yes—
223C23×C53C22×D411yescharacteristic
224D4×C53—22no—
225D4×C53—22no—
226D4×C53—41no—
227D4×C53—41no—
228D4×C53—84no—
229C2×C4×C53—21no—
230C2×C4×C53—21no—
231C2×C4×C53—21no—
232C2×C4×C53—21no—
233C2×C4×C53—21no—
234C2×C4×C53—21no—
235C2×C4×C53—22no—
236C2×C4×C53—22no—
237C2×C4×C53—22no—
238C2×C4×C53—22no—
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—21no—
243C2×C4×C53—21no—
244C2×C4×C53—22no—
245C2×C4×C53—22no—
246C2×C4×C53—21no—
247C2×C4×C53—21no—
248C2×C4×C53—21no—
249C2×C4×C53—21no—
250C2×C4×C53—41no—
251C2×C4×C53—41no—
252C2×C4×C53—41no—
253C2×C4×C53—41no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—84no—
267C2×C4×C53—84no—
268C2×C4×C53C4×D412yes—
269C2×C4×C53#12312yes—
270C2×C4×C53#12312yes—
271C2×C4×C53C23×C411yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C8×C53—22no—
278C8×C53—22no—
279C8×C53—41no—
280C8×C53—41no—
281#21590C5311yesmaximal, characteristic, direct product factor, Sylow
282C22×C53—22no—
283C22×C53—22no—
284C22×C53—22no—
285C22×C53—41no—
286C22×C53—41no—
287C22×C53—41no—
288C22×C53—41no—
289C22×C53—42no—
290C22×C53—42no—
291C22×C53—42no—
292C22×C53—81no—
293C22×C53—81no—
294C22×C53—81no—
295C22×C53—81no—
296C22×C53C2×C4×D411yescharacteristic
297C22×C53C2×#12311yescharacteristic
298C22×C53#52511yescharacteristic
299C22×C53#57611yescharacteristic
300C22×C53#57611yescharacteristic
301C22×C53#57711yescharacteristic
302C22×C53#57811yescharacteristic
303C4×C53—22no—
304C4×C53—22no—
305C4×C53—22no—
306C4×C53—41no—
307C4×C53—41no—
308C4×C53—42no—
309C4×C53—42no—
310C4×C53—42no—
311C4×C53—42no—
312C4×C53—42no—
313C4×C53—81no—
314C4×C53—81no—
315C4×C53C4×#4111yescharacteristic
316C4×C53C4×#4111yescharacteristic
317C4×C53#52911yescharacteristic
318C4×C53#52911yescharacteristic
319C2×#482C2×C5311yescharacteristic
320#2324C2×C5311yescharacteristic
321#2274C2×C5311yescharacteristic, complemented
322#1925C2×C5311yescharacteristic, complemented
323#1925C2×C5311yescharacteristic, complemented
324#1921C2×C5311yescharacteristic, complemented
325#1919C2×C5311yescharacteristic, complemented
326#1874C2×C5311yescharacteristic
327#1852C2×C5311yescharacteristic, complemented
328#1825C2×C5311yescharacteristic, complemented
329#1776C2×C5311yescharacteristic, complemented
330C4×#107C2×C5311yescharacteristic, complemented
331#1762C2×C5311yescharacteristic, complemented
332C4×#102C2×C5311yescharacteristic, complemented
333#1750C2×C5311yescharacteristic, complemented
334C2×C53—42no—
335C2×C53—82no—
336C2×C53C4×#12311yescharacteristic
337C2×C53#294611yescharacteristic
338C2×C53#295111yescharacteristic
339C2×C53#309611yescharacteristic
340C2×C53#309811yescharacteristic
341C2×C53#312111yescharacteristic
342C2×C53#312211yescharacteristic
343C2×#121C22×C5311yescharacteristic
344C2×C4×D4C22×C5311yescharacteristic
345C2×#117C22×C5311yescharacteristic
346C2×#117C22×C5311yescharacteristic
347C22×C4⋊C4C22×C5311yescharacteristic
348#482C4×C5318yescomplemented
349C2×#107C22×C5311yescharacteristic
350C2×#107C22×C5311yescharacteristic
351C2×#107C22×C5311yescharacteristic
352C2×#106C22×C5311yescharacteristic
353C2×#102C22×C5311yescharacteristic
354C2×#102C22×C5311yescharacteristic
355C2×#102C22×C5311yescharacteristic
356C2×#102C22×C5311yescharacteristic
357C2×C22⋊C8C22×C5311yescharacteristic
358C2×C22⋊C8C22×C5311yescharacteristic
359C2×#97C22×C5311yescharacteristic
360C2×C4×C8C22×C5311yescharacteristic
361#390—21no—
362#390C22×C5311yescharacteristic
363#389C22×C5311yescharacteristic
364#388—21no—
365#386—21no—
366#385—21no—
367#380C22×C5311yescharacteristic
368C4×C4⋊C4—21no—
369C4×C4⋊C4—21no—
370C4×C4⋊C4C22×C5311yescharacteristic
371C4×C4⋊C4C22×C5311yescharacteristic
372C4×C4⋊C4C22×C5311yescharacteristic
373C4×C4⋊C4C22×C5311yescharacteristic
374C4×C4⋊C4C22×C5311yescharacteristic
375C4×C22⋊C4—21no—
376C4×C22⋊C4—21no—
377#340C22×C5311yescharacteristic
378#340C22×C5311yescharacteristic
379#340C22×C5311yescharacteristic
380#340C22×C5311yescharacteristic
381#340C22×C5311yescharacteristic
382#340C22×C5311yescharacteristic
383#340C22×C5311yescharacteristic
384#340C22×C5311yescharacteristic
385#336C22×C5311yescharacteristic
386#336C22×C5311yescharacteristic
387C53#2159011yescharacteristic, direct product factor, Sylow
388C22×D4—21no—
389C22×D4C23×C5311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4C23×C5311yescharacteristic
393C22×C8C23×C5311yescharacteristic
394C22×C8C23×C5311yescharacteristic
395C22×C8C23×C5311yescharacteristic
396C22×C8C23×C5311yescharacteristic
397#121—22no—
398#121C2×C4×C5314yes—
399C4×D4—22no—
400C4×D4—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117C2×C4×C5314yescomplemented
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4D4×C5311yescharacteristic
410C2×C4⋊C4D4×C5311yescharacteristic
411C2×C4⋊C4C23×C5311yescharacteristic
412C2×C4⋊C4C23×C5311yescharacteristic
413C2×C4⋊C4C23×C5311yescharacteristic
414C2×C4⋊C4C23×C5311yescharacteristic
415C2×C4⋊C4C23×C5311yescharacteristic
416C2×C4⋊C4C23×C5311yescharacteristic
417C2×C4⋊C4C23×C5311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4D4×C5311yescharacteristic
425C2×C22⋊C4D4×C5311yescharacteristic
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42C23×C5311yescharacteristic
433C2×C42C23×C5311yescharacteristic
434#107—22no—
435#107—22no—
436#107C2×C4×C5314yescomplemented
437#106C2×C4×C5314yescomplemented
438#102—22no—
439#102—22no—
440#102C2×C4×C5314yescomplemented
441#102C2×C4×C5314yescomplemented
442C22⋊C8—22no—
443C22⋊C8C2×C4×C5314yescomplemented
444#97—22no—
445C4×C8—22no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453C24—21no—
454C24C2×D4×C5311yescharacteristic
455C2×D4—24no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4C22×C4×C5312yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4C22×C4×C5312yes—
482C22×C4C2×D4×C5311yescharacteristic
483C22×C4C2×D4×C5311yescharacteristic
484C22×C4C2×D4×C5311yescharacteristic
485C22×C4C2×D4×C5311yescharacteristic
486C22×C4C2×D4×C5311yescharacteristic
487C22×C4#41×C5312yes—
488C22×C4C24×C5311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8C22×C4×C5312yes—
500C2×C8C22×C4×C5312yes—
501C4⋊C4—24no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4C22×C4×C5312yes—
515C4⋊C4C22×C4×C5312yes—
516C4⋊C4C22×C4×C5312yes—
517C4⋊C4#41×C5312yes—
518C4⋊C4#41×C5312yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—81no—
531C42—81no—
532C42—81no—
533C42—81no—
534C42—81no—
535C42#41×C5312yes—
536C42#41×C5312yes—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23C4×D4×C5312yes—
551C23C22×D4×C5311yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—84no—
595C2×C4—84no—
596C2×C4C4×D4×C5312yes—
597C2×C4#123×C5312yes—
598C2×C4#123×C5312yes—
599C2×C4C23×C4×C5311yescharacteristic
600C2×C4C2×#41×C5311yescharacteristic
601C2×C4C2×#41×C5311yescharacteristic
602C2×C4C2×#41×C5311yescharacteristic
603C2×C4C2×#41×C5311yescharacteristic
604C2×C4C2×#41×C5311yescharacteristic
605C8—22no—
606C8—22no—
607C8—41no—
608C8—41no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C2×C4×D4×C5311yescharacteristic
624C22C2×#123×C5311yescharacteristic
625C22C53×#52511yescharacteristic
626C22C53×#57611yescharacteristic
627C22C53×#57611yescharacteristic
628C22C53×#57711yescharacteristic
629C22C53×#57811yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—42no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4C4×#41×C5311yescharacteristic
643C4C4×#41×C5311yescharacteristic
644C4C53×#52911yescharacteristic
645C4C53×#52911yescharacteristic
646C2—42no—
647C2—82no—
648C2C4×#123×C5311yescharacteristic
649C2C53×#294611yescharacteristic
650C2C53×#295111yescharacteristic
651C2C53×#309611yescharacteristic
652C2C53×#309811yescharacteristic
653C2C53×#312111yescharacteristic
654C2C53×#312211yescharacteristic
subgroupG/H
center, socleC23×C53C22×D4
commutatorC2×C4C23×C4×C53
Frattini, cosocleC22×C4C24×C53
prime radicalC2×#121×C53C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×#117×C53 ◁ G

Complements

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

NH ≅ G/Ntype
3. C53×#2274C2semidirect
4. C53×#1925C2semidirect
5. C53×#1925C2semidirect
6. C53×#1921C2semidirect
7. C53×#1919C2semidirect
9. C53×#1852C2semidirect
10. C53×#1825C2semidirect
11. C53×#1776C2semidirect
12. C4×#107×C53C2semidirect
13. C53×#1762C2semidirect
14. C4×#102×C53C2semidirect
15. C53×#1750C2semidirect
21. C53×#482C4semidirect
76. #117×C53C2×C4semidirect
108. #107×C53C2×C4semidirect
109. #106×C53C2×C4semidirect
112. #102×C53C2×C4semidirect
113. #102×C53C2×C4semidirect
115. C22⋊C8×C53C2×C4semidirect
281. #21590C53direct (N × H)
321. #2274C2×C53semidirect
322. #1925C2×C53semidirect
323. #1925C2×C53semidirect
324. #1921C2×C53semidirect
325. #1919C2×C53semidirect
327. #1852C2×C53semidirect
328. #1825C2×C53semidirect
329. #1776C2×C53semidirect
330. C4×#107C2×C53semidirect
331. #1762C2×C53semidirect
332. C4×#102C2×C53semidirect
333. #1750C2×C53semidirect
348. #482C4×C53semidirect
387. C53#21590direct (N × H)
404. #117C2×C4×C53semidirect
436. #107C2×C4×C53semidirect
437. #106C2×C4×C53semidirect
440. #102C2×C4×C53semidirect
441. #102C2×C4×C53semidirect
443. C22⋊C8C2×C4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#4822
C53×#23242
C53×#22742
C53×#19252
C53×#19212
C53×#19192
C53×#18742
C53×#18522
C53×#18252
C53×#17762
C4×#107×C532
C53×#17622
C4×#102×C532
C53×#17502
#2159053