Finite Group Databasebeta

← C53×#18252 #27225764

Subgroups — C53×#18252 #27225764

Order 13568.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3534C211yesmaximal, characteristic, complemented
2C53×#3006C211yesmaximal, characteristic, complemented
3C53×#3002C211yesmaximal, characteristic, complemented
4C53×#2430C211yesmaximal, characteristic, complemented
5C53×#1606C211yesmaximal, characteristic, complemented
6C53×#1604C211yesmaximal, characteristic, complemented
7C53×#1603C211yesmaximal, characteristic, complemented
8C53×#1601C211yesmaximal, characteristic, complemented
9C53×#1600C211yesmaximal, characteristic, complemented
10C53×#1598C211yesmaximal, characteristic, complemented
11C53×#1597C211yesmaximal, characteristic, complemented
12C53×#1595C211yesmaximal, characteristic, complemented
13C53×#1504C211yesmaximal, characteristic, complemented
14C2×C53×#327C211yesmaximal, characteristic, complemented
15C53×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C53C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C53—21no—
18C2×#135×C53—21no—
19C53×#562—21no—
20C53×#560—21no—
21C53×#553—21no—
22C53×#551—21no—
23C53×#546—21no—
24C53×#546—21no—
25C53×#546—21no—
26D42×C53—21no—
27C53×#540—21no—
28C53×#539—21no—
29C53×#539C2211yescharacteristic
30C53×#538—21no—
31C53×#538C2211yescharacteristic
32C53×#537C2211yescharacteristic
33C53×#534—21no—
34C53×#534C2211yescharacteristic
35C53×#525C2211yescharacteristic
36C2×#123×C53C2211yescharacteristic
37C2×#121×C53—21no—
38C2×#121×C53C2211yescharacteristic
39C53×#452—21no—
40C53×#451C2211yescharacteristic, complemented
41C53×#450C2211yescharacteristic, complemented
42C53×#449—21no—
43C53×#449—21no—
44C53×#449—21no—
45C53×#448C2211yescharacteristic
46C53×#448C2211yescharacteristic, complemented
47C53×#448C2211yescharacteristic, complemented
48C53×#447C2211yescharacteristic
49C53×#447C2211yescharacteristic, complemented
50C53×#447C2211yescharacteristic, complemented
51C53×#417—21no—
52C53×#416—21no—
53C53×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C53C2211yescharacteristic, complemented
55C53×#395C2211yescharacteristic, complemented
56C53×#394C2211yescharacteristic, complemented
57C53×#393C2211yescharacteristic, complemented
58C53×#392C2211yescharacteristic, complemented
59C53×#386—21no—
60C53×#386—21no—
61C53×#385—21no—
62C2×#95×C53C2211yescharacteristic, complemented
63C53×#328C2211yescharacteristic, complemented
64C53×#328C2211yescharacteristic, complemented
65C53×#327C2211yescharacteristic
66C53×#327C2211yescharacteristic
67C53×#327C2211yescharacteristic, complemented
68C53×#327C2211yescharacteristic, complemented
69C53×#327C2211yescharacteristic, complemented
70C53×#327C2211yescharacteristic, complemented
71C53×#324C2211yescharacteristic, complemented
72C53×#324C2211yescharacteristic, complemented
73C53×#323C2211yescharacteristic, complemented
74C53×#323C2211yescharacteristic, complemented
75C2×#41×C53—21no—
76C2×#41×C53—21no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—44no—
81C2×#41×C53D411yescharacteristic, complemented
82C22×Q8×C53C2311yescharacteristic
83C22×D4×C53—21no—
84C22×D4×C53—21no—
85C22×D4×C53—21no—
86C22×D4×C53—21no—
87C22×D4×C53—21no—
88C22×D4×C53D411yescharacteristic
89C22×D4×C53D411yescharacteristic, complemented
90C22×D4×C53C2311yescharacteristic
91C23×C4×C53—21no—
92C23×C4×C53—21no—
93C23×C4×C53C2311yescharacteristic
94AGL(1,ℤ/8)×C53—44no—
95#135×C53—44no—
96C2×Q16×C53—21no—
97C2×SD16×C53—21no—
98C2×SD16×C53—21no—
99C2×SD16×C53—21no—
100C2×SD16×C53—21no—
101C2×D8×C53—21no—
102C2×D8×C53—21no—
103C2×D8×C53—21no—
104C2×M16×C53—21no—
105C22×C8×C53—21no—
106#127×C53—21no—
107#126×C53—21no—
108#126×C53—21no—
109#126×C53—21no—
110#126×C53—21no—
111#125×C53—21no—
112#125×C53—21no—
113#124×C53—21no—
114#124×C53—21no—
115#124×C53—21no—
116#123×C53—21no—
117#123×C53—21no—
118#123×C53—21no—
119#123×C53—21no—
120#123×C53—21no—
121#123×C53—21no—
122#123×C53—21no—
123#123×C53—21no—
124#123×C53—21no—
125#123×C53—21no—
126#123×C53—21no—
127#123×C53—21no—
128#123×C53—21no—
129#123×C53—21no—
130C22⋊Q8×C53—21no—
131C22⋊Q8×C53—21no—
132C22⋊Q8×C53—21no—
133C22⋊Q8×C53—21no—
134C22⋊Q8×C53—21no—
135C22⋊Q8×C53D411yescharacteristic, complemented
136C22⋊Q8×C53C2311yescharacteristic
137#121×C53—21no—
138#121×C53—21no—
139#121×C53—21no—
140#121×C53—21no—
141#121×C53—21no—
142#121×C53—21no—
143#121×C53—21no—
144#121×C53—21no—
145#121×C53—21no—
146#121×C53—21no—
147#121×C53—21no—
148#121×C53—21no—
149#121×C53—21no—
150#121×C53—21no—
151#121×C53—21no—
152#121×C53—44no—
153#121×C53D411yescharacteristic, complemented
154#121×C53D411yescharacteristic, complemented
155#121×C53D411yescharacteristic, complemented
156#121×C53C2311yescharacteristic
157#121×C53C2311yescharacteristic
158#121×C53C2311yescharacteristic
159#120×C53—21no—
160#120×C53—21no—
161#120×C53—21no—
162#120×C53—21no—
163#120×C53—21no—
164#120×C53—21no—
165#120×C53—21no—
166#120×C53—21no—
167C4×D4×C53—21no—
168C4×D4×C53—21no—
169C4×D4×C53—21no—
170C4×D4×C53—21no—
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
175#117×C53—21no—
176#117×C53D411yescharacteristic, complemented
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53D411yescharacteristic
179C2×C4⋊C4×C53D411yescharacteristic, complemented
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C22⋊C4×C53—21no—
187C2×C22⋊C4×C53—21no—
188C2×C22⋊C4×C53D411yescharacteristic
189C2×C22⋊C4×C53D411yescharacteristic
190C2×C22⋊C4×C53C2311yescharacteristic
191#103×C53—21no—
192#103×C53—21no—
193#103×C53—21no—
194#103×C53—21no—
195#102×C53—21no—
196#102×C53—21no—
197#102×C53—21no—
198#102×C53—21no—
199C22⋊C8×C53—21no—
200C22⋊C8×C53—21no—
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204C22⋊C8×C53C2311yescharacteristic
205#95×C53—21no—
206#95×C53—21no—
207#95×C53—21no—
208#95×C53C2311yescharacteristic
209#95×C53C2311yescharacteristic
210C24×C53—21no—
211C24×C53—21no—
212C24×C53—21no—
213C24×C53C2×D411yescharacteristic
214C24×C53C2×D411yescharacteristic
215#41×C53—24no—
216#41×C53—24no—
217#41×C53—42no—
218#41×C53—42no—
219#41×C53—42no—
220#41×C53—42no—
221#41×C53—42no—
222#41×C53—42no—
223#41×C53—42no—
224#41×C53—81no—
225#41×C53—81no—
226C2×Q8×C53—21no—
227C2×Q8×C53—21no—
228C2×Q8×C53—21no—
229C2×Q8×C53—42no—
230C2×Q8×C53C2×D411yescharacteristic
231C2×D4×C53—24no—
232C2×D4×C53—21no—
233C2×D4×C53—21no—
234C2×D4×C53—21no—
235C2×D4×C53—21no—
236C2×D4×C53—21no—
237C2×D4×C53—21no—
238C2×D4×C53—21no—
239C2×D4×C53—21no—
240C2×D4×C53—21no—
241C2×D4×C53—21no—
242C2×D4×C53—21no—
243C2×D4×C53—21no—
244C2×D4×C53—21no—
245C2×D4×C53—21no—
246C2×D4×C53—21no—
247C2×D4×C53—21no—
248C2×D4×C53—21no—
249C2×D4×C53—21no—
250C2×D4×C53—21no—
251C2×D4×C53—42no—
252C2×D4×C53—42no—
253C2×D4×C53—42no—
254C2×D4×C53—42no—
255C2×D4×C53—41no—
256C2×D4×C53—41no—
257C2×D4×C53—42no—
258C2×D4×C53—42no—
259C2×D4×C53—81no—
260C2×D4×C53—81no—
261C2×D4×C53—81no—
262C2×D4×C53—81no—
263C2×D4×C53—81no—
264C2×D4×C53—82no—
265C2×D4×C53C2×D411yescharacteristic
266C2×D4×C53C2×D411yescharacteristic
267C2×D4×C53C2×D411yescharacteristic
268C22×C4×C53—21no—
269C22×C4×C53—21no—
270C22×C4×C53—21no—
271C22×C4×C53—21no—
272C22×C4×C53—21no—
273C22×C4×C53—21no—
274C22×C4×C53—21no—
275C22×C4×C53—21no—
276C22×C4×C53—21no—
277C22×C4×C53—21no—
278C22×C4×C53—42no—
279C22×C4×C53—42no—
280C22×C4×C53—42no—
281C22×C4×C53—42no—
282C22×C4×C53—41no—
283C22×C4×C53—41no—
284C22×C4×C53—42no—
285C22×C4×C53—81no—
286C22×C4×C53C2×D411yescharacteristic
287C22×C4×C53C2×D411yescharacteristic
288C22×C4×C53C2×D411yescharacteristic
289C22×C4×C53C2×D411yescharacteristic
290C22×C4×C53C2×D411yescharacteristic
291C22×C4×C53C2×D411yescharacteristic
292C22×C4×C53C2×D411yescharacteristic
293C22×C4×C53C2×D411yescharacteristic
294C22×C4×C53C2411yescharacteristic
295Q16×C53—42no—
296SD16×C53—42no—
297SD16×C53—42no—
298SD16×C53—42no—
299SD16×C53—42no—
300D8×C53—42no—
301D8×C53—42no—
302D8×C53—42no—
303M16×C53—42no—
304C2×C8×C53—21no—
305C2×C8×C53—21no—
306C2×C8×C53—21no—
307C2×C8×C53—21no—
308C2×C8×C53—42no—
309C4⋊C4×C53—21no—
310C4⋊C4×C53—21no—
311C4⋊C4×C53—21no—
312C4⋊C4×C53—21no—
313C4⋊C4×C53—21no—
314C4⋊C4×C53—21no—
315C4⋊C4×C53—21no—
316C4⋊C4×C53—21no—
317C4⋊C4×C53—21no—
318C4⋊C4×C53—21no—
319C4⋊C4×C53—21no—
320C4⋊C4×C53—21no—
321C4⋊C4×C53—21no—
322C4⋊C4×C53—42no—
323C4⋊C4×C53C2×D411yescharacteristic
324C4⋊C4×C53C2×D411yescharacteristic
325C4⋊C4×C53C2×D411yescharacteristic
326C4⋊C4×C53C2×D411yescharacteristic
327C22⋊C4×C53—21no—
328C22⋊C4×C53—21no—
329C22⋊C4×C53—21no—
330C22⋊C4×C53—21no—
331C22⋊C4×C53—21no—
332C22⋊C4×C53—21no—
333C22⋊C4×C53—21no—
334C22⋊C4×C53—21no—
335C22⋊C4×C53—21no—
336C22⋊C4×C53—21no—
337C22⋊C4×C53—21no—
338C22⋊C4×C53—21no—
339C22⋊C4×C53—21no—
340C22⋊C4×C53—21no—
341C22⋊C4×C53—21no—
342C22⋊C4×C53—21no—
343C22⋊C4×C53—21no—
344C22⋊C4×C53—21no—
345C22⋊C4×C53—21no—
346C22⋊C4×C53—21no—
347C22⋊C4×C53—21no—
348C22⋊C4×C53—21no—
349C22⋊C4×C53—21no—
350C22⋊C4×C53—21no—
351C22⋊C4×C53—21no—
352C22⋊C4×C53—42no—
353C22⋊C4×C53—42no—
354C22⋊C4×C53—42no—
355C22⋊C4×C53—81no—
356C42×C53—21no—
357C42×C53—21no—
358C42×C53—21no—
359C23×C53—21no—
360C23×C53—21no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—21no—
364C23×C53—21no—
365C23×C53—21no—
366C23×C53—21no—
367C23×C53—21no—
368C23×C53—21no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—42no—
379C23×C53—81no—
380C23×C53—81no—
381C23×C53—81no—
382C23×C53—81no—
383C23×C53—81no—
384C23×C53#12011yescharacteristic
385C23×C53#12011yescharacteristic
386C23×C53C22×D411yescharacteristic
387Q8×C53—22no—
388Q8×C53—22no—
389Q8×C53—41no—
390Q8×C53—41no—
391Q8×C53—41no—
392Q8×C53—81no—
393D4×C53—22no—
394D4×C53—22no—
395D4×C53—41no—
396D4×C53—41no—
397D4×C53—41no—
398D4×C53—41no—
399D4×C53—41no—
400D4×C53—44no—
401D4×C53—41no—
402D4×C53—41no—
403D4×C53—41no—
404D4×C53—41no—
405D4×C53—41no—
406D4×C53—41no—
407D4×C53—44no—
408D4×C53—42no—
409D4×C53—42no—
410D4×C53—81no—
411D4×C53—81no—
412D4×C53—81no—
413D4×C53—81no—
414D4×C53—81no—
415D4×C53—81no—
416D4×C53—81no—
417D4×C53—81no—
418D4×C53—81no—
419D4×C53—81no—
420D4×C53—81no—
421D4×C53—81no—
422D4×C53—84no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—21no—
428C2×C4×C53—21no—
429C2×C4×C53—21no—
430C2×C4×C53—21no—
431C2×C4×C53—21no—
432C2×C4×C53—21no—
433C2×C4×C53—21no—
434C2×C4×C53—21no—
435C2×C4×C53—21no—
436C2×C4×C53—21no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
441C2×C4×C53—44no—
442C2×C4×C53—44no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—81no—
453C2×C4×C53—81no—
454C2×C4×C53—81no—
455C2×C4×C53—81no—
456C2×C4×C53—81no—
457C2×C4×C53—81no—
458C2×C4×C53—81no—
459C2×C4×C53—84no—
460C2×C4×C53#12011yescharacteristic
461C2×C4×C53#12011yescharacteristic
462C2×C4×C53C22×D411yescharacteristic
463C2×C4×C53C22×D411yescharacteristic
464C8×C53—41no—
465C8×C53—41no—
466C8×C53—41no—
467C8×C53—41no—
468#18252C5311yesmaximal, characteristic, direct product factor, Sylow
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—42no—
477C22×C53—42no—
478C22×C53—42no—
479C22×C53—42no—
480C22×C53—41no—
481C22×C53—41no—
482C22×C53—41no—
483C22×C53—41no—
484C22×C53—41no—
485C22×C53—41no—
486C22×C53—41no—
487C22×C53—41no—
488C22×C53—42no—
489C22×C53—41no—
490C22×C53—41no—
491C22×C53—41no—
492C22×C53—41no—
493C22×C53—81no—
494C22×C53—81no—
495C22×C53—81no—
496C22×C53—81no—
497C22×C53—81no—
498C22×C53—81no—
499C22×C53—162no—
500C22×C53—162no—
501C22×C53B(4,𝔽2)12yes—
502C22×C53C2×#12011yescharacteristic
503C22×C53#57611yescharacteristic
504C22×C53#57711yescharacteristic
505C4×C53—21no—
506C4×C53—21no—
507C4×C53—21no—
508C4×C53—21no—
509C4×C53—42no—
510C4×C53—41no—
511C4×C53—41no—
512C4×C53—41no—
513C4×C53—41no—
514C4×C53—41no—
515C4×C53—41no—
516C4×C53—42no—
517C4×C53—41no—
518C4×C53—41no—
519C4×C53—81no—
520#3534C2×C5311yescharacteristic, complemented
521#3006C2×C5311yescharacteristic, complemented
522#3002C2×C5311yescharacteristic, complemented
523#2430C2×C5311yescharacteristic, complemented
524#1606C2×C5311yescharacteristic, complemented
525#1604C2×C5311yescharacteristic, complemented
526#1603C2×C5311yescharacteristic, complemented
527#1601C2×C5311yescharacteristic, complemented
528#1600C2×C5311yescharacteristic, complemented
529#1598C2×C5311yescharacteristic, complemented
530#1597C2×C5311yescharacteristic, complemented
531#1595C2×C5311yescharacteristic, complemented
532#1504C2×C5311yescharacteristic, complemented
533C2×#327C2×C5311yescharacteristic, complemented
534#1468C2×C5311yescharacteristic, complemented
535C2×C53—21no—
536C2×C53—21no—
537C2×C53—22no—
538C2×C53—41no—
539C2×C53—82no—
540C2×C53—81no—
541C2×C53—81no—
542C2×C53—81no—
543C2×C53—81no—
544C2×C53#301211yescharacteristic
545C2×C53#301811yescharacteristic
546C2×C53C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C5311yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C5311yescharacteristic
561#538—21no—
562#538C22×C5311yescharacteristic
563#537C22×C5311yescharacteristic
564#534—21no—
565#534C22×C5311yescharacteristic
566#525C22×C5311yescharacteristic
567C2×#123C22×C5311yescharacteristic
568C2×#121—21no—
569C2×#121C22×C5311yescharacteristic
570#452—21no—
571#451C22×C5311yescharacteristic, complemented
572#450C22×C5311yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C5311yescharacteristic
577#448C22×C5311yescharacteristic, complemented
578#448C22×C5311yescharacteristic, complemented
579#447C22×C5311yescharacteristic
580#447C22×C5311yescharacteristic, complemented
581#447C22×C5311yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C5311yescharacteristic, complemented
585C2×C22⋊C8C22×C5311yescharacteristic, complemented
586#395C22×C5311yescharacteristic, complemented
587#394C22×C5311yescharacteristic, complemented
588#393C22×C5311yescharacteristic, complemented
589#392C22×C5311yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C5311yescharacteristic, complemented
594#328C22×C5311yescharacteristic, complemented
595#328C22×C5311yescharacteristic, complemented
596#327C22×C5311yescharacteristic
597#327C22×C5311yescharacteristic
598#327C22×C5311yescharacteristic, complemented
599#327C22×C5311yescharacteristic, complemented
600#327C22×C5311yescharacteristic, complemented
601#327C22×C5311yescharacteristic, complemented
602#324C22×C5311yescharacteristic, complemented
603#324C22×C5311yescharacteristic, complemented
604#323C22×C5311yescharacteristic, complemented
605#323C22×C5311yescharacteristic, complemented
606C53#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C5311yescharacteristic, complemented
614C22×Q8C23×C5311yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C5311yescharacteristic
621C22×D4D4×C5311yescharacteristic, complemented
622C22×D4C23×C5311yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C5311yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C5311yescharacteristic, complemented
668C22⋊Q8C23×C5311yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C5311yescharacteristic, complemented
686#121D4×C5311yescharacteristic, complemented
687#121D4×C5311yescharacteristic, complemented
688#121C23×C5311yescharacteristic
689#121C23×C5311yescharacteristic
690#121C23×C5311yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C5311yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C5311yescharacteristic
711C2×C4⋊C4D4×C5311yescharacteristic, complemented
712C2×C4⋊C4C23×C5311yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C5311yescharacteristic
721C2×C22⋊C4D4×C5311yescharacteristic
722C2×C22⋊C4C23×C5311yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C5311yescharacteristic
734C22⋊C8C23×C5311yescharacteristic
735C22⋊C8C23×C5311yescharacteristic
736C22⋊C8C23×C5311yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C5311yescharacteristic
741#95C23×C5311yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C5311yescharacteristic
746C24C2×D4×C5311yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C5311yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C5311yescharacteristic
798C2×D4C2×D4×C5311yescharacteristic
799C2×D4C2×D4×C5311yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C5311yescharacteristic
819C22×C4C2×D4×C5311yescharacteristic
820C22×C4C2×D4×C5311yescharacteristic
821C22×C4C2×D4×C5311yescharacteristic
822C22×C4C2×D4×C5311yescharacteristic
823C22×C4C2×D4×C5311yescharacteristic
824C22×C4C2×D4×C5311yescharacteristic
825C22×C4C2×D4×C5311yescharacteristic
826C22×C4C24×C5311yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C5311yescharacteristic
856C4⋊C4C2×D4×C5311yescharacteristic
857C4⋊C4C2×D4×C5311yescharacteristic
858C4⋊C4C2×D4×C5311yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C5311yescharacteristic
917C23#120×C5311yescharacteristic
918C23C22×D4×C5311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C5311yescharacteristic
993C2×C4#120×C5311yescharacteristic
994C2×C4C22×D4×C5311yescharacteristic
995C2×C4C22×D4×C5311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C53×B(4,𝔽2)12yes—
1033C22C2×#120×C5311yescharacteristic
1034C22C53×#57611yescharacteristic
1035C22C53×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C53×#301211yescharacteristic
1061C2C53×#301811yescharacteristic
1062C2C2×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×#3534C2semidirect
2. C53×#3006C2semidirect
3. C53×#3002C2semidirect
4. C53×#2430C2semidirect
5. C53×#1606C2semidirect
6. C53×#1604C2semidirect
7. C53×#1603C2semidirect
8. C53×#1601C2semidirect
9. C53×#1600C2semidirect
10. C53×#1598C2semidirect
11. C53×#1597C2semidirect
12. C53×#1595C2semidirect
13. C53×#1504C2semidirect
14. C2×C53×#327C2semidirect
15. C53×#1468C2semidirect
16. C22×#41×C53C22semidirect
40. C53×#451C22semidirect
41. C53×#450C22semidirect
46. C53×#448C22semidirect
47. C53×#448C22semidirect
49. C53×#447C22semidirect
50. C53×#447C22semidirect
53. C53×#407C22semidirect
54. C2×C22⋊C8×C53C22semidirect
55. C53×#395C22semidirect
56. C53×#394C22semidirect
57. C53×#393C22semidirect
58. C53×#392C22semidirect
62. C2×#95×C53C22semidirect
63. C53×#328C22semidirect
64. C53×#328C22semidirect
67. C53×#327C22semidirect
68. C53×#327C22semidirect
69. C53×#327C22semidirect
70. C53×#327C22semidirect
71. C53×#324C22semidirect
72. C53×#324C22semidirect
73. C53×#323C22semidirect
74. C53×#323C22semidirect
81. C2×#41×C53D4semidirect
89. C22×D4×C53D4semidirect
135. C22⋊Q8×C53D4semidirect
153. #121×C53D4semidirect
154. #121×C53D4semidirect
155. #121×C53D4semidirect
176. #117×C53D4semidirect
179. C2×C4⋊C4×C53D4semidirect
468. #18252C53direct (N × H)
520. #3534C2×C53semidirect
521. #3006C2×C53semidirect
522. #3002C2×C53semidirect
523. #2430C2×C53semidirect
524. #1606C2×C53semidirect
525. #1604C2×C53semidirect
526. #1603C2×C53semidirect
527. #1601C2×C53semidirect
528. #1600C2×C53semidirect
529. #1598C2×C53semidirect
530. #1597C2×C53semidirect
531. #1595C2×C53semidirect
532. #1504C2×C53semidirect
533. C2×#327C2×C53semidirect
534. #1468C2×C53semidirect
547. C22×#41C22×C53semidirect
571. #451C22×C53semidirect
572. #450C22×C53semidirect
577. #448C22×C53semidirect
578. #448C22×C53semidirect
580. #447C22×C53semidirect
581. #447C22×C53semidirect
584. #407C22×C53semidirect
585. C2×C22⋊C8C22×C53semidirect
586. #395C22×C53semidirect
587. #394C22×C53semidirect
588. #393C22×C53semidirect
589. #392C22×C53semidirect
593. C2×#95C22×C53semidirect
594. #328C22×C53semidirect
595. #328C22×C53semidirect
598. #327C22×C53semidirect
599. #327C22×C53semidirect
600. #327C22×C53semidirect
601. #327C22×C53semidirect
602. #324C22×C53semidirect
603. #324C22×C53semidirect
604. #323C22×C53semidirect
605. #323C22×C53semidirect
606. C53#18252direct (N × H)
613. C2×#41D4×C53semidirect
621. C22×D4D4×C53semidirect
667. C22⋊Q8D4×C53semidirect
685. #121D4×C53semidirect
686. #121D4×C53semidirect
687. #121D4×C53semidirect
708. #117D4×C53semidirect
711. 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×#35342
C53×#30062
C53×#30022
C53×#24302
C53×#16062
C53×#16042
C53×#16032
C53×#16012
C53×#16002
C53×#15982
C53×#15972
C53×#15952
C53×#15042
C2×C53×#3272
C53×#14682
#1825253