Finite Group Databasebeta

← C53×#18224 #27225736

Subgroups — C53×#18224 #27225736

Order 13568.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3534C211yesmaximal, characteristic, complemented
2C53×#3003C211yesmaximal, characteristic, complemented
3C2×C53×#447C211yesmaximal, characteristic, complemented
4C53×#2613C211yesmaximal, characteristic, complemented
5C53×#1600C212yesmaximal, complemented
6C53×#1598C212yesmaximal, complemented
7C53×#1597C212yesmaximal, complemented
8C53×#1595C212yesmaximal, complemented
9C53×#1516C211yesmaximal, characteristic, complemented
10C53×#1510C211yesmaximal, characteristic, complemented
11C53×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C53C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C53—21no—
14C22×D8×C53—21no—
15C53×#562—21no—
16C53×#560—21no—
17C53×#553—21no—
18C53×#551—21no—
19C53×#546—21no—
20C53×#546—21no—
21C53×#546—21no—
22D42×C53—21no—
23C53×#540—21no—
24C53×#539—21no—
25C53×#539C2211yescharacteristic, complemented
26C53×#538—21no—
27C53×#538C2211yescharacteristic, complemented
28C53×#537C2211yescharacteristic, complemented
29C53×#534—21no—
30C53×#534C2211yescharacteristic, complemented
31C53×#525C2211yescharacteristic
32C2×#123×C53C2211yescharacteristic
33C2×#121×C53C2211yescharacteristic
34C2×#120×C53—21no—
35C53×#450—21no—
36C53×#450C2212yescomplemented
37C53×#447—21no—
38C53×#447—21no—
39C53×#447—21no—
40C53×#447C2212yes—
41C53×#447C2212yescomplemented
42C53×#447C2212yescomplemented
43C53×#418—21no—
44C2×#102×C53—21no—
45C53×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C53C2211yescharacteristic, complemented
47C53×#394—21no—
48C53×#394C2212yescomplemented
49C53×#392—21no—
50C53×#392C2212yescomplemented
51C53×#381C2211yescharacteristic, complemented
52C53×#379—21no—
53C53×#328C2212yescomplemented
54C53×#327C2212yescomplemented
55C53×#327C2212yescomplemented
56C53×#327C2212yescomplemented
57C53×#324C2212yescomplemented
58C53×#323C2212yescomplemented
59C25×C53—21no—
60C2×#41×C53—21no—
61C2×#41×C53D411yescharacteristic, complemented
62C22×D4×C53—21no—
63C22×D4×C53—21no—
64C22×D4×C53—21no—
65C22×D4×C53—22no—
66C22×D4×C53—21no—
67C22×D4×C53—21no—
68C22×D4×C53—21no—
69C22×D4×C53—21no—
70C22×D4×C53—21no—
71C22×D4×C53—44no—
72C22×D4×C53D411yescharacteristic
73C22×D4×C53D411yescharacteristic, complemented
74C22×D4×C53C2312yes—
75C23×C4×C53C2311yescharacteristic
76AGL(1,ℤ/8)×C53—44no—
77C2×SD16×C53—22no—
78C2×D8×C53—22no—
79C2×D8×C53—22no—
80C2×D8×C53—22no—
81C2×D8×C53—44no—
82C2×M16×C53—21no—
83C22×C8×C53—21no—
84#127×C53—21no—
85#126×C53—21no—
86#126×C53—21no—
87#126×C53—21no—
88#126×C53—21no—
89#125×C53—21no—
90#125×C53—21no—
91#124×C53—21no—
92#124×C53—21no—
93#124×C53—21no—
94#123×C53—21no—
95#123×C53—21no—
96#123×C53—21no—
97#123×C53—21no—
98#123×C53—21no—
99#123×C53—21no—
100#123×C53—21no—
101#123×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—
108C22⋊Q8×C53—21no—
109C22⋊Q8×C53—21no—
110C22⋊Q8×C53—21no—
111C22⋊Q8×C53—21no—
112C22⋊Q8×C53—21no—
113C22⋊Q8×C53D411yescharacteristic, complemented
114C22⋊Q8×C53C2311yescharacteristic
115#121×C53—21no—
116#121×C53—21no—
117#121×C53—21no—
118#121×C53—21no—
119#121×C53—21no—
120#121×C53—21no—
121#121×C53—21no—
122#121×C53—21no—
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×C53D411yescharacteristic, complemented
131#121×C53D411yescharacteristic, complemented
132#121×C53D411yescharacteristic, complemented
133#121×C53C2311yescharacteristic
134#121×C53C2311yescharacteristic
135#121×C53C2311yescharacteristic
136#120×C53—21no—
137#120×C53—21no—
138#120×C53—21no—
139#120×C53—21no—
140#120×C53—21no—
141#120×C53—21no—
142#120×C53—21no—
143#120×C53—21no—
144#120×C53—44no—
145C4×D4×C53—21no—
146C4×D4×C53—21no—
147C4×D4×C53—21no—
148C4×D4×C53—21no—
149C4×D4×C53—21no—
150C4×D4×C53—21no—
151C4×D4×C53—21no—
152C4×D4×C53—21no—
153#117×C53—21no—
154#117×C53D411yescharacteristic, complemented
155C2×C4⋊C4×C53D411yescharacteristic
156C2×C4⋊C4×C53D411yescharacteristic, complemented
157C2×C4⋊C4×C53C2311yescharacteristic
158C2×C22⋊C4×C53—21no—
159C2×C22⋊C4×C53—21no—
160C2×C22⋊C4×C53—21no—
161C2×C22⋊C4×C53—21no—
162C2×C22⋊C4×C53—22no—
163C2×C22⋊C4×C53—22no—
164C2×C22⋊C4×C53—22no—
165C2×C22⋊C4×C53D411yescharacteristic
166C2×C22⋊C4×C53D411yescharacteristic
167C2×C22⋊C4×C53C2311yescharacteristic
168#102×C53—22no—
169#102×C53—22no—
170#102×C53—22no—
171#102×C53—22no—
172C22⋊C8×C53—21no—
173C22⋊C8×C53—21no—
174C22⋊C8×C53C2312yes—
175C22⋊C8×C53C2312yes—
176#95×C53—21no—
177#95×C53C2312yes—
178C24×C53—24no—
179C24×C53—21no—
180C24×C53—22no—
181C24×C53—21no—
182C24×C53—42no—
183C24×C53—41no—
184C24×C53—41no—
185C24×C53—82no—
186C24×C53—82no—
187C24×C53C2×D411yescharacteristic
188C24×C53C2×D411yescharacteristic
189#41×C53—42no—
190#41×C53—82no—
191C2×Q8×C53—21no—
192C2×Q8×C53C2×D411yescharacteristic
193C2×D4×C53—24no—
194C2×D4×C53—24no—
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—21no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—21no—
204C2×D4×C53—21no—
205C2×D4×C53—21no—
206C2×D4×C53—21no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—21no—
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—22no—
213C2×D4×C53—22no—
214C2×D4×C53—42no—
215C2×D4×C53—42no—
216C2×D4×C53—42no—
217C2×D4×C53—44no—
218C2×D4×C53—44no—
219C2×D4×C53—44no—
220C2×D4×C53—44no—
221C2×D4×C53—42no—
222C2×D4×C53—44no—
223C2×D4×C53—41no—
224C2×D4×C53—41no—
225C2×D4×C53—82no—
226C2×D4×C53—82no—
227C2×D4×C53—82no—
228C2×D4×C53—82no—
229C2×D4×C53—82no—
230C2×D4×C53C2×D411yescharacteristic
231C2×D4×C53C2×D411yescharacteristic
232C2×D4×C53C2×D411yescharacteristic
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—22no—
241C22×C4×C53—42no—
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D411yescharacteristic
244C22×C4×C53C2×D411yescharacteristic
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2411yescharacteristic
251SD16×C53—44no—
252D8×C53—44no—
253D8×C53—44no—
254D8×C53—44no—
255M16×C53—42no—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53—42no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53—21no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53—21no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53C2×D411yescharacteristic
273C4⋊C4×C53C2×D411yescharacteristic
274C4⋊C4×C53C2×D411yescharacteristic
275C4⋊C4×C53C2×D411yescharacteristic
276C22⋊C4×C53—21no—
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C22⋊C4×C53—21no—
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53—21no—
292C22⋊C4×C53—21no—
293C22⋊C4×C53—21no—
294C22⋊C4×C53—21no—
295C22⋊C4×C53—21no—
296C22⋊C4×C53—21no—
297C22⋊C4×C53—21no—
298C22⋊C4×C53—21no—
299C22⋊C4×C53—21no—
300C22⋊C4×C53—21no—
301C22⋊C4×C53—44no—
302C22⋊C4×C53—42no—
303C22⋊C4×C53—82no—
304C22⋊C4×C53—82no—
305C42×C53—21no—
306C42×C53—21no—
307C42×C53—21no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—24no—
311C23×C53—21no—
312C23×C53—21no—
313C23×C53—21no—
314C23×C53—21no—
315C23×C53—22no—
316C23×C53—41no—
317C23×C53—42no—
318C23×C53—44no—
319C23×C53—42no—
320C23×C53—42no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53—42no—
324C23×C53—42no—
325C23×C53—42no—
326C23×C53—44no—
327C23×C53—42no—
328C23×C53—81no—
329C23×C53—81no—
330C23×C53—82no—
331C23×C53—82no—
332C23×C53—82no—
333C23×C53—82no—
334C23×C53—88no—
335C23×C53—81no—
336C23×C53—81no—
337C23×C53—81no—
338C23×C53—88no—
339C23×C53#12011yescharacteristic
340C23×C53#12011yescharacteristic
341C23×C53C22×D411yescharacteristic
342Q8×C53—41no—
343Q8×C53—81no—
344D4×C53—24no—
345D4×C53—24no—
346D4×C53—41no—
347D4×C53—41no—
348D4×C53—41no—
349D4×C53—42no—
350D4×C53—42no—
351D4×C53—44no—
352D4×C53—44no—
353D4×C53—42no—
354D4×C53—42no—
355D4×C53—42no—
356D4×C53—42no—
357D4×C53—42no—
358D4×C53—81no—
359D4×C53—81no—
360D4×C53—81no—
361D4×C53—81no—
362D4×C53—81no—
363D4×C53—81no—
364D4×C53—81no—
365D4×C53—81no—
366D4×C53—81no—
367D4×C53—81no—
368D4×C53—81no—
369D4×C53—81no—
370D4×C53—88no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—21no—
374C2×C4×C53—21no—
375C2×C4×C53—21no—
376C2×C4×C53—21no—
377C2×C4×C53—21no—
378C2×C4×C53—21no—
379C2×C4×C53—21no—
380C2×C4×C53—21no—
381C2×C4×C53—22no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—42no—
389C2×C4×C53—42no—
390C2×C4×C53—42no—
391C2×C4×C53—81no—
392C2×C4×C53—81no—
393C2×C4×C53—81no—
394C2×C4×C53—81no—
395C2×C4×C53—81no—
396C2×C4×C53—81no—
397C2×C4×C53—81no—
398C2×C4×C53#12011yescharacteristic
399C2×C4×C53#12011yescharacteristic
400C2×C4×C53C22×D411yescharacteristic
401C2×C4×C53C22×D411yescharacteristic
402C8×C53—42no—
403C8×C53—42no—
404#18224C5311yesmaximal, characteristic, direct product factor, Sylow
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—21no—
408C22×C53—21no—
409C22×C53—21no—
410C22×C53—21no—
411C22×C53—21no—
412C22×C53—44no—
413C22×C53—44no—
414C22×C53—44no—
415C22×C53—41no—
416C22×C53—41no—
417C22×C53—41no—
418C22×C53—41no—
419C22×C53—41no—
420C22×C53—41no—
421C22×C53—41no—
422C22×C53—41no—
423C22×C53—41no—
424C22×C53—41no—
425C22×C53—44no—
426C22×C53—41no—
427C22×C53—41no—
428C22×C53—82no—
429C22×C53—82no—
430C22×C53—82no—
431C22×C53—88no—
432C22×C53—88no—
433C22×C53—82no—
434C22×C53—82no—
435C22×C53—162no—
436C22×C53—162no—
437C22×C53B(4,𝔽2)12yes—
438C22×C53C2×#12011yescharacteristic
439C22×C53#57612yes—
440C4×C53—21no—
441C4×C53—21no—
442C4×C53—21no—
443C4×C53—21no—
444C4×C53—41no—
445C4×C53—41no—
446C4×C53—41no—
447C4×C53—41no—
448C4×C53—41no—
449C4×C53—41no—
450C4×C53—41no—
451C4×C53—41no—
452C4×C53—82no—
453#3534C2×C5311yescharacteristic, complemented
454#3003C2×C5311yescharacteristic, complemented
455C2×#447C2×C5311yescharacteristic, complemented
456#2613C2×C5311yescharacteristic, complemented
457#1600C2×C5312yescomplemented
458#1598C2×C5312yescomplemented
459#1597C2×C5312yescomplemented
460#1595C2×C5312yescomplemented
461#1516C2×C5311yescharacteristic, complemented
462#1510C2×C5311yescharacteristic, complemented
463#1468C2×C5311yescharacteristic, complemented
464C2×C53—22no—
465C2×C53—22no—
466C2×C53—41no—
467C2×C53—84no—
468C2×C53—81no—
469C2×C53—81no—
470C2×C53—81no—
471C2×C53—81no—
472C2×C53#300811yescharacteristic
473C2×C53#302111yescharacteristic
474C2×C53C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C5311yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C5311yescharacteristic, complemented
489#538—21no—
490#538C22×C5311yescharacteristic, complemented
491#537C22×C5311yescharacteristic, complemented
492#534—21no—
493#534C22×C5311yescharacteristic, complemented
494#525C22×C5311yescharacteristic
495C2×#123C22×C5311yescharacteristic
496C2×#121C22×C5311yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C5312yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C5312yes—
504#447C22×C5312yescomplemented
505#447C22×C5312yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C5311yescharacteristic, complemented
509C2×C22⋊C8C22×C5311yescharacteristic, complemented
510#394—21no—
511#394C22×C5312yescomplemented
512#392—21no—
513#392C22×C5312yescomplemented
514#381C22×C5311yescharacteristic, complemented
515#379—21no—
516#328C22×C5312yescomplemented
517#327C22×C5312yescomplemented
518#327C22×C5312yescomplemented
519#327C22×C5312yescomplemented
520#324C22×C5312yescomplemented
521#323C22×C5312yescomplemented
522C53#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C5311yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C5311yescharacteristic
537C22×D4D4×C5311yescharacteristic, complemented
538C22×D4C23×C5312yes—
539C23×C4C23×C5311yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C5311yescharacteristic, complemented
578C22⋊Q8C23×C5311yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C5311yescharacteristic, complemented
595#121D4×C5311yescharacteristic, complemented
596#121D4×C5311yescharacteristic, complemented
597#121C23×C5311yescharacteristic
598#121C23×C5311yescharacteristic
599#121C23×C5311yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C5311yescharacteristic, complemented
619C2×C4⋊C4D4×C5311yescharacteristic
620C2×C4⋊C4D4×C5311yescharacteristic, complemented
621C2×C4⋊C4C23×C5311yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C5311yescharacteristic
630C2×C22⋊C4D4×C5311yescharacteristic
631C2×C22⋊C4C23×C5311yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C5312yes—
639C22⋊C8C23×C5312yes—
640#95—21no—
641#95C23×C5312yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C5311yescharacteristic
652C24C2×D4×C5311yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C5311yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C5311yescharacteristic
695C2×D4C2×D4×C5311yescharacteristic
696C2×D4C2×D4×C5311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C5311yescharacteristic
707C22×C4C2×D4×C5311yescharacteristic
708C22×C4C2×D4×C5311yescharacteristic
709C22×C4C2×D4×C5311yescharacteristic
710C22×C4C2×D4×C5311yescharacteristic
711C22×C4C2×D4×C5311yescharacteristic
712C22×C4C2×D4×C5311yescharacteristic
713C22×C4C2×D4×C5311yescharacteristic
714C22×C4C24×C5311yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C5311yescharacteristic
737C4⋊C4C2×D4×C5311yescharacteristic
738C4⋊C4C2×D4×C5311yescharacteristic
739C4⋊C4C2×D4×C5311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C5311yescharacteristic
804C23#120×C5311yescharacteristic
805C23C22×D4×C5311yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C5311yescharacteristic
863C2×C4#120×C5311yescharacteristic
864C2×C4C22×D4×C5311yescharacteristic
865C2×C4C22×D4×C5311yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C53×B(4,𝔽2)12yes—
901C22C2×#120×C5311yescharacteristic
902C22C53×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C53×#300811yescharacteristic
925C2C53×#302111yescharacteristic
926C2C2×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×#3003C2semidirect
3. C2×C53×#447C2semidirect
4. C53×#2613C2semidirect
5. C53×#1600C2semidirect
6. C53×#1598C2semidirect
7. C53×#1597C2semidirect
8. C53×#1595C2semidirect
9. C53×#1516C2semidirect
10. C53×#1510C2semidirect
11. C53×#1468C2semidirect
12. C23×D4×C53C22semidirect
25. C53×#539C22semidirect
27. C53×#538C22semidirect
28. C53×#537C22semidirect
30. C53×#534C22semidirect
36. C53×#450C22semidirect
41. C53×#447C22semidirect
42. C53×#447C22semidirect
45. C53×#407C22semidirect
46. C2×C22⋊C8×C53C22semidirect
48. C53×#394C22semidirect
50. C53×#392C22semidirect
51. C53×#381C22semidirect
53. C53×#328C22semidirect
54. C53×#327C22semidirect
55. C53×#327C22semidirect
56. C53×#327C22semidirect
57. C53×#324C22semidirect
58. C53×#323C22semidirect
61. C2×#41×C53D4semidirect
73. C22×D4×C53D4semidirect
113. C22⋊Q8×C53D4semidirect
130. #121×C53D4semidirect
131. #121×C53D4semidirect
132. #121×C53D4semidirect
154. #117×C53D4semidirect
156. C2×C4⋊C4×C53D4semidirect
404. #18224C53direct (N × H)
453. #3534C2×C53semidirect
454. #3003C2×C53semidirect
455. C2×#447C2×C53semidirect
456. #2613C2×C53semidirect
457. #1600C2×C53semidirect
458. #1598C2×C53semidirect
459. #1597C2×C53semidirect
460. #1595C2×C53semidirect
461. #1516C2×C53semidirect
462. #1510C2×C53semidirect
463. #1468C2×C53semidirect
475. C23×D4C22×C53semidirect
488. #539C22×C53semidirect
490. #538C22×C53semidirect
491. #537C22×C53semidirect
493. #534C22×C53semidirect
499. #450C22×C53semidirect
504. #447C22×C53semidirect
505. #447C22×C53semidirect
508. #407C22×C53semidirect
509. C2×C22⋊C8C22×C53semidirect
511. #394C22×C53semidirect
513. #392C22×C53semidirect
514. #381C22×C53semidirect
516. #328C22×C53semidirect
517. #327C22×C53semidirect
518. #327C22×C53semidirect
519. #327C22×C53semidirect
520. #324C22×C53semidirect
521. #323C22×C53semidirect
522. C53#18224direct (N × H)
525. C2×#41D4×C53semidirect
537. C22×D4D4×C53semidirect
577. C22⋊Q8D4×C53semidirect
594. #121D4×C53semidirect
595. #121D4×C53semidirect
596. #121D4×C53semidirect
618. #117D4×C53semidirect
620. 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×#30032
C2×C53×#4472
C53×#26132
C53×#16002
C53×#15982
C53×#15972
C53×#15952
C53×#15162
C53×#15102
C53×#14682
#1822453