Finite Group Databasebeta

← C53×#18446 #27225958

Subgroups — C53×#18446 #27225958

Order 13568.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3534C211yesmaximal, characteristic, complemented
2C53×#3192C211yesmaximal, characteristic, complemented
3C53×#3188C211yesmaximal, characteristic, complemented
4C53×#2813C211yesmaximal, characteristic, complemented
5C53×#1618C211yesmaximal, characteristic, complemented
6C53×#1616C211yesmaximal, characteristic, complemented
7C53×#1615C211yesmaximal, characteristic, complemented
8C53×#1613C211yesmaximal, characteristic, complemented
9C53×#1600C211yesmaximal, characteristic, complemented
10C53×#1598C211yesmaximal, characteristic, complemented
11C53×#1597C211yesmaximal, characteristic, complemented
12C53×#1595C211yesmaximal, characteristic, complemented
13C53×#1519C211yesmaximal, characteristic, complemented
14C53×#1513C211yesmaximal, characteristic, complemented
15C53×#1468C211yesmaximal, characteristic, complemented
16C53×#562—21no—
17C53×#560—21no—
18C53×#553—21no—
19C53×#551—21no—
20C53×#546—21no—
21C53×#546—21no—
22C53×#546—21no—
23D42×C53—21no—
24C53×#540—21no—
25C53×#539—21no—
26C53×#539C2211yescharacteristic
27C53×#538—21no—
28C53×#538C2211yescharacteristic
29C53×#537C2211yescharacteristic
30C53×#534—21no—
31C53×#534C2211yescharacteristic
32C53×#525C2211yescharacteristic
33C2×#123×C53C2211yescharacteristic
34C2×#121×C53C2211yescharacteristic
35C2×#121×C53C2211yescharacteristic, complemented
36C53×#484C2211yescharacteristic, complemented
37C53×#482—21no—
38C53×#481—21no—
39C53×#481C2211yescharacteristic
40C53×#481C2211yescharacteristic, complemented
41C53×#481C2211yescharacteristic, complemented
42C53×#469—21no—
43C53×#469—21no—
44C53×#466—21no—
45C53×#465—21no—
46C53×#450C2211yescharacteristic, complemented
47C53×#449—21no—
48C53×#447—21no—
49C53×#447C2211yescharacteristic
50C53×#447C2211yescharacteristic, complemented
51C53×#447C2211yescharacteristic, complemented
52C53×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C53C2211yescharacteristic, complemented
54C53×#400C2211yescharacteristic, complemented
55C53×#399C2211yescharacteristic, complemented
56C53×#396—21no—
57C53×#394—21no—
58C53×#394—21no—
59C53×#394C2211yescharacteristic, complemented
60C53×#392—21no—
61C53×#392C2211yescharacteristic, complemented
62C53×#380C2211yescharacteristic, 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×C53D411yescharacteristic, complemented
77C22×D4×C53—21no—
78C22×D4×C53—21no—
79C22×D4×C53—21no—
80C22×D4×C53—21no—
81C22×D4×C53—21no—
82C22×D4×C53D411yescharacteristic
83C22×D4×C53D411yescharacteristic, complemented
84C22×D4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C2×SD16×C53—21no—
87C2×D8×C53—21no—
88C2×D8×C53—21no—
89C2×D8×C53—21no—
90C2×M16×C53—21no—
91C22×C8×C53—21no—
92#127×C53—21no—
93#126×C53—21no—
94#126×C53—21no—
95#126×C53—21no—
96#126×C53—21no—
97#125×C53—21no—
98#125×C53—21no—
99#124×C53—21no—
100#124×C53—21no—
101#124×C53—21no—
102#123×C53—21no—
103#123×C53—21no—
104#123×C53—21no—
105#123×C53—21no—
106#123×C53—21no—
107#123×C53—21no—
108#123×C53—21no—
109#123×C53—21no—
110#123×C53—21no—
111#123×C53—21no—
112#123×C53—21no—
113#123×C53—21no—
114#123×C53—21no—
115#123×C53—21no—
116C22⋊Q8×C53—21no—
117C22⋊Q8×C53—21no—
118C22⋊Q8×C53—21no—
119C22⋊Q8×C53—21no—
120C22⋊Q8×C53—21no—
121C22⋊Q8×C53D411yescharacteristic, complemented
122C22⋊Q8×C53C2311yescharacteristic
123#121×C53—21no—
124#121×C53—21no—
125#121×C53—21no—
126#121×C53—21no—
127#121×C53—21no—
128#121×C53—21no—
129#121×C53—21no—
130#121×C53—21no—
131#121×C53—21no—
132#121×C53—21no—
133#121×C53—21no—
134#121×C53—21no—
135#121×C53—21no—
136#121×C53—21no—
137#121×C53—21no—
138#121×C53—21no—
139#121×C53—21no—
140#121×C53—21no—
141#121×C53—21no—
142#121×C53D411yescharacteristic, complemented
143#121×C53D411yescharacteristic, complemented
144#121×C53D411yescharacteristic, complemented
145#121×C53C2311yescharacteristic
146#121×C53C2311yescharacteristic
147#121×C53C2311yescharacteristic
148#120×C53—21no—
149#120×C53—21no—
150#120×C53—21no—
151#120×C53—21no—
152#120×C53—21no—
153#120×C53—21no—
154#120×C53—21no—
155#120×C53—21no—
156C4×D4×C53—21no—
157C4×D4×C53—21no—
158C4×D4×C53—21no—
159C4×D4×C53—21no—
160C4×D4×C53—21no—
161C4×D4×C53—21no—
162C4×D4×C53—21no—
163C4×D4×C53—21no—
164#117×C53—21no—
165#117×C53D411yescharacteristic, complemented
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic, complemented
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C22⋊C4×C53C2311yescharacteristic
184#107×C53—21no—
185#106×C53—21no—
186#106×C53—21no—
187#106×C53—21no—
188#103×C53—21no—
189#102×C53—21no—
190#102×C53—21no—
191#102×C53—21no—
192#102×C53—21no—
193#102×C53—21no—
194#102×C53—21no—
195#102×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53C2311yescharacteristic
199C22⋊C8×C53C2311yescharacteristic
200C22⋊C8×C53C2311yescharacteristic
201C22⋊C8×C53C2311yescharacteristic
202#95×C53—21no—
203#95×C53—21no—
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208C24×C53—21no—
209C24×C53C2×D411yescharacteristic
210C24×C53C2×D411yescharacteristic
211#41×C53—81no—
212#41×C53—81no—
213#41×C53—81no—
214C2×Q8×C53—21no—
215C2×Q8×C53C2×D411yescharacteristic
216C2×D4×C53—21no—
217C2×D4×C53—21no—
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—21no—
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—21no—
232C2×D4×C53—21no—
233C2×D4×C53—21no—
234C2×D4×C53—21no—
235C2×D4×C53—41no—
236C2×D4×C53—41no—
237C2×D4×C53—81no—
238C2×D4×C53—81no—
239C2×D4×C53—81no—
240C2×D4×C53—81no—
241C2×D4×C53—81no—
242C2×D4×C53—81no—
243C2×D4×C53—81no—
244C2×D4×C53—81no—
245C2×D4×C53—81no—
246C2×D4×C53—81no—
247C2×D4×C53—81no—
248C2×D4×C53—81no—
249C2×D4×C53—82no—
250C2×D4×C53C2×D411yescharacteristic
251C2×D4×C53C2×D411yescharacteristic
252C2×D4×C53C2×D411yescharacteristic
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—21no—
259C22×C4×C53—21no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—21no—
263C22×C4×C53—81no—
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2411yescharacteristic
273SD16×C53—81no—
274D8×C53—81no—
275D8×C53—81no—
276D8×C53—81no—
277M16×C53—81no—
278C2×C8×C53—21no—
279C2×C8×C53—21no—
280C2×C8×C53—21no—
281C2×C8×C53—21no—
282C2×C8×C53—81no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53—21no—
293C4⋊C4×C53—21no—
294C4⋊C4×C53—21no—
295C4⋊C4×C53—21no—
296C4⋊C4×C53—21no—
297C4⋊C4×C53—21no—
298C4⋊C4×C53—81no—
299C4⋊C4×C53—81no—
300C4⋊C4×C53C2×D411yescharacteristic
301C4⋊C4×C53C2×D411yescharacteristic
302C4⋊C4×C53C2×D411yescharacteristic
303C4⋊C4×C53C2×D411yescharacteristic
304C22⋊C4×C53—21no—
305C22⋊C4×C53—21no—
306C22⋊C4×C53—21no—
307C22⋊C4×C53—21no—
308C22⋊C4×C53—21no—
309C22⋊C4×C53—21no—
310C22⋊C4×C53—21no—
311C22⋊C4×C53—21no—
312C22⋊C4×C53—21no—
313C22⋊C4×C53—21no—
314C22⋊C4×C53—21no—
315C22⋊C4×C53—21no—
316C22⋊C4×C53—21no—
317C22⋊C4×C53—21no—
318C22⋊C4×C53—21no—
319C22⋊C4×C53—21no—
320C22⋊C4×C53—21no—
321C22⋊C4×C53—21no—
322C22⋊C4×C53—21no—
323C22⋊C4×C53—21no—
324C22⋊C4×C53—21no—
325C22⋊C4×C53—21no—
326C22⋊C4×C53—21no—
327C22⋊C4×C53—21no—
328C22⋊C4×C53—21no—
329C22⋊C4×C53—41no—
330C22⋊C4×C53—41no—
331C22⋊C4×C53—81no—
332C22⋊C4×C53—81no—
333C22⋊C4×C53—81no—
334C22⋊C4×C53—81no—
335C22⋊C4×C53—81no—
336C42×C53—21no—
337C42×C53—21no—
338C42×C53—21no—
339C23×C53—21no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—21no—
343C23×C53—21no—
344C23×C53—21no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—42no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—81no—
360C23×C53—81no—
361C23×C53—81no—
362C23×C53—81no—
363C23×C53—81no—
364C23×C53#12011yescharacteristic
365C23×C53#12011yescharacteristic
366C23×C53C22×D411yescharacteristic
367Q8×C53—41no—
368Q8×C53—81no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—41no—
372D4×C53—41no—
373D4×C53—41no—
374D4×C53—41no—
375D4×C53—41no—
376D4×C53—42no—
377D4×C53—42no—
378D4×C53—41no—
379D4×C53—41no—
380D4×C53—41no—
381D4×C53—41no—
382D4×C53—41no—
383D4×C53—41no—
384D4×C53—81no—
385D4×C53—81no—
386D4×C53—81no—
387D4×C53—81no—
388D4×C53—81no—
389D4×C53—81no—
390D4×C53—81no—
391D4×C53—81no—
392D4×C53—81no—
393D4×C53—81no—
394D4×C53—81no—
395D4×C53—81no—
396D4×C53—82no—
397D4×C53—82no—
398D4×C53—84no—
399C2×C4×C53—21no—
400C2×C4×C53—21no—
401C2×C4×C53—21no—
402C2×C4×C53—21no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—21no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—81no—
427C2×C4×C53—81no—
428C2×C4×C53—81no—
429C2×C4×C53—81no—
430C2×C4×C53—81no—
431C2×C4×C53—81no—
432C2×C4×C53—81no—
433C2×C4×C53#12011yescharacteristic
434C2×C4×C53#12011yescharacteristic
435C2×C4×C53C22×D411yescharacteristic
436C2×C4×C53C22×D411yescharacteristic
437C8×C53—41no—
438C8×C53—41no—
439C8×C53—41no—
440C8×C53—41no—
441#18446C5311yesmaximal, characteristic, direct product factor, Sylow
442C22×C53—21no—
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—41no—
451C22×C53—41no—
452C22×C53—41no—
453C22×C53—41no—
454C22×C53—41no—
455C22×C53—41no—
456C22×C53—41no—
457C22×C53—41no—
458C22×C53—41no—
459C22×C53—41no—
460C22×C53—41no—
461C22×C53—41no—
462C22×C53—81no—
463C22×C53—81no—
464C22×C53—81no—
465C22×C53—81no—
466C22×C53—81no—
467C22×C53—81no—
468C22×C53—81no—
469C22×C53—81no—
470C22×C53—81no—
471C22×C53—81no—
472C22×C53—81no—
473C22×C53—162no—
474C22×C53—162no—
475C22×C53C2×#12011yescharacteristic
476C22×C53#57611yescharacteristic
477C22×C53#57711yescharacteristic
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—41no—
483C4×C53—41no—
484C4×C53—41no—
485C4×C53—41no—
486C4×C53—41no—
487C4×C53—41no—
488C4×C53—41no—
489C4×C53—41no—
490C4×C53—81no—
491C4×C53—81no—
492C4×C53—81no—
493#3534C2×C5311yescharacteristic, complemented
494#3192C2×C5311yescharacteristic, complemented
495#3188C2×C5311yescharacteristic, complemented
496#2813C2×C5311yescharacteristic, complemented
497#1618C2×C5311yescharacteristic, complemented
498#1616C2×C5311yescharacteristic, complemented
499#1615C2×C5311yescharacteristic, complemented
500#1613C2×C5311yescharacteristic, complemented
501#1600C2×C5311yescharacteristic, complemented
502#1598C2×C5311yescharacteristic, complemented
503#1597C2×C5311yescharacteristic, complemented
504#1595C2×C5311yescharacteristic, complemented
505#1519C2×C5311yescharacteristic, complemented
506#1513C2×C5311yescharacteristic, complemented
507#1468C2×C5311yescharacteristic, complemented
508C2×C53—21no—
509C2×C53—21no—
510C2×C53—41no—
511C2×C53—41no—
512C2×C53—81no—
513C2×C53—81no—
514C2×C53—81no—
515C2×C53—81no—
516C2×C53—161no—
517C2×C53#301211yescharacteristic
518C2×C53#302111yescharacteristic
519C2×C53#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C5311yescharacteristic
531#538—21no—
532#538C22×C5311yescharacteristic
533#537C22×C5311yescharacteristic
534#534—21no—
535#534C22×C5311yescharacteristic
536#525C22×C5311yescharacteristic
537C2×#123C22×C5311yescharacteristic
538C2×#121C22×C5311yescharacteristic
539C2×#121C22×C5311yescharacteristic, complemented
540#484C22×C5311yescharacteristic, complemented
541#482—21no—
542#481—21no—
543#481C22×C5311yescharacteristic
544#481C22×C5311yescharacteristic, complemented
545#481C22×C5311yescharacteristic, complemented
546#469—21no—
547#469—21no—
548#466—21no—
549#465—21no—
550#450C22×C5311yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C5311yescharacteristic
554#447C22×C5311yescharacteristic, complemented
555#447C22×C5311yescharacteristic, complemented
556#407C22×C5311yescharacteristic, complemented
557C2×C22⋊C8C22×C5311yescharacteristic, complemented
558#400C22×C5311yescharacteristic, complemented
559#399C22×C5311yescharacteristic, complemented
560#396—21no—
561#394—21no—
562#394—21no—
563#394C22×C5311yescharacteristic, complemented
564#392—21no—
565#392C22×C5311yescharacteristic, complemented
566#380C22×C5311yescharacteristic, complemented
567#328C22×C5311yescharacteristic, complemented
568#328C22×C5311yescharacteristic, complemented
569#327C22×C5311yescharacteristic
570#327C22×C5311yescharacteristic
571#327C22×C5311yescharacteristic, complemented
572#327C22×C5311yescharacteristic, complemented
573#327C22×C5311yescharacteristic, complemented
574#327C22×C5311yescharacteristic, complemented
575#324C22×C5311yescharacteristic, complemented
576#324C22×C5311yescharacteristic, complemented
577#323C22×C5311yescharacteristic, complemented
578#323C22×C5311yescharacteristic, complemented
579C53#1844611yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C5311yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C5311yescharacteristic
588C22×D4D4×C5311yescharacteristic, complemented
589C22×D4C23×C5311yescharacteristic
590C23×C4C23×C5311yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C5311yescharacteristic, complemented
627C22⋊Q8C23×C5311yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C5311yescharacteristic, complemented
648#121D4×C5311yescharacteristic, complemented
649#121D4×C5311yescharacteristic, complemented
650#121C23×C5311yescharacteristic
651#121C23×C5311yescharacteristic
652#121C23×C5311yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C5311yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C5311yescharacteristic
674C2×C4⋊C4D4×C5311yescharacteristic, complemented
675C2×C4⋊C4C23×C5311yescharacteristic
676C2×C4⋊C4C23×C5311yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C5311yescharacteristic
687C2×C22⋊C4D4×C5311yescharacteristic
688C2×C22⋊C4C23×C5311yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C5311yescharacteristic
704C22⋊C8C23×C5311yescharacteristic
705C22⋊C8C23×C5311yescharacteristic
706C22⋊C8C23×C5311yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C5311yescharacteristic
710#95C23×C5311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C5311yescharacteristic
715C24C2×D4×C5311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C5311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C5311yescharacteristic
756C2×D4C2×D4×C5311yescharacteristic
757C2×D4C2×D4×C5311yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C5311yescharacteristic
770C22×C4C2×D4×C5311yescharacteristic
771C22×C4C2×D4×C5311yescharacteristic
772C22×C4C2×D4×C5311yescharacteristic
773C22×C4C2×D4×C5311yescharacteristic
774C22×C4C2×D4×C5311yescharacteristic
775C22×C4C2×D4×C5311yescharacteristic
776C22×C4C2×D4×C5311yescharacteristic
777C22×C4C24×C5311yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C5311yescharacteristic
806C4⋊C4C2×D4×C5311yescharacteristic
807C4⋊C4C2×D4×C5311yescharacteristic
808C4⋊C4C2×D4×C5311yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C5311yescharacteristic
870C23#120×C5311yescharacteristic
871C23C22×D4×C5311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C5311yescharacteristic
939C2×C4#120×C5311yescharacteristic
940C2×C4C22×D4×C5311yescharacteristic
941C2×C4C22×D4×C5311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C5311yescharacteristic
980C22C53×#57611yescharacteristic
981C22C53×#57711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C53×#301211yescharacteristic
1007C2C53×#302111yescharacteristic
1008C2C53×#302611yescharacteristic
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×#3192C2semidirect
3. C53×#3188C2semidirect
4. C53×#2813C2semidirect
5. C53×#1618C2semidirect
6. C53×#1616C2semidirect
7. C53×#1615C2semidirect
8. C53×#1613C2semidirect
9. C53×#1600C2semidirect
10. C53×#1598C2semidirect
11. C53×#1597C2semidirect
12. C53×#1595C2semidirect
13. C53×#1519C2semidirect
14. C53×#1513C2semidirect
15. C53×#1468C2semidirect
35. C2×#121×C53C22semidirect
36. C53×#484C22semidirect
40. C53×#481C22semidirect
41. C53×#481C22semidirect
46. C53×#450C22semidirect
50. C53×#447C22semidirect
51. C53×#447C22semidirect
52. C53×#407C22semidirect
53. C2×C22⋊C8×C53C22semidirect
54. C53×#400C22semidirect
55. C53×#399C22semidirect
59. C53×#394C22semidirect
61. C53×#392C22semidirect
62. C53×#380C22semidirect
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
76. C2×#41×C53D4semidirect
83. C22×D4×C53D4semidirect
121. C22⋊Q8×C53D4semidirect
142. #121×C53D4semidirect
143. #121×C53D4semidirect
144. #121×C53D4semidirect
165. #117×C53D4semidirect
169. C2×C4⋊C4×C53D4semidirect
441. #18446C53direct (N × H)
493. #3534C2×C53semidirect
494. #3192C2×C53semidirect
495. #3188C2×C53semidirect
496. #2813C2×C53semidirect
497. #1618C2×C53semidirect
498. #1616C2×C53semidirect
499. #1615C2×C53semidirect
500. #1613C2×C53semidirect
501. #1600C2×C53semidirect
502. #1598C2×C53semidirect
503. #1597C2×C53semidirect
504. #1595C2×C53semidirect
505. #1519C2×C53semidirect
506. #1513C2×C53semidirect
507. #1468C2×C53semidirect
539. C2×#121C22×C53semidirect
540. #484C22×C53semidirect
544. #481C22×C53semidirect
545. #481C22×C53semidirect
550. #450C22×C53semidirect
554. #447C22×C53semidirect
555. #447C22×C53semidirect
556. #407C22×C53semidirect
557. C2×C22⋊C8C22×C53semidirect
558. #400C22×C53semidirect
559. #399C22×C53semidirect
563. #394C22×C53semidirect
565. #392C22×C53semidirect
566. #380C22×C53semidirect
567. #328C22×C53semidirect
568. #328C22×C53semidirect
571. #327C22×C53semidirect
572. #327C22×C53semidirect
573. #327C22×C53semidirect
574. #327C22×C53semidirect
575. #324C22×C53semidirect
576. #324C22×C53semidirect
577. #323C22×C53semidirect
578. #323C22×C53semidirect
579. C53#18446direct (N × H)
581. C2×#41D4×C53semidirect
588. C22×D4D4×C53semidirect
626. C22⋊Q8D4×C53semidirect
647. #121D4×C53semidirect
648. #121D4×C53semidirect
649. #121D4×C53semidirect
670. #117D4×C53semidirect
674. 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×#31922
C53×#31882
C53×#28132
C53×#16182
C53×#16162
C53×#16152
C53×#16132
C53×#16002
C53×#15982
C53×#15972
C53×#15952
C53×#15192
C53×#15132
C53×#14682
#1844653