Finite Group Databasebeta

← C53×#25563 #27233075

Subgroups — C53×#25563 #27233075

Order 13568.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3490C211yesmaximal, characteristic, complemented
2C53×#2410C212yesmaximal, complemented
3C53×#2405C211yesmaximal, characteristic, complemented
4C53×#2062C211yesmaximal, characteristic, complemented
5C53×#2044C211yesmaximal, characteristic, complemented
6C53×#2029C211yesmaximal, characteristic, complemented
7C53×#2021C211yesmaximal, characteristic, complemented
8C53×#1898C212yesmaximal, complemented
9C53×#1889C212yesmaximal, complemented
10C53×#1867C212yesmaximal, complemented
11C2×C53×#342C211yesmaximal, characteristic, complemented
12C23×D4×C53C2211yescharacteristic
13C53×#551—22no—
14C53×#551—22no—
15C53×#546—22no—
16C53×#546—22no—
17C53×#543C2211yescharacteristic
18C53×#538—21no—
19C53×#538—21no—
20C53×#534C2211yescharacteristic
21C53×#525—21no—
22C53×#525—21no—
23C2×#123×C53—21no—
24C2×#121×C53—22no—
25C2×#120×C53C2212yes—
26C2×#120×C53C2212yes—
27C53×#518C2212yes—
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C22⋊C4×C53C2212yes—
30C2×#99×C53C2212yes—
31C2×#99×C53C2212yes—
32C53×#394—21no—
33C53×#394—21no—
34C53×#394—22no—
35C53×#392—22no—
36C53×#386—21no—
37C53×#386—22no—
38C53×#386C2212yes—
39C53×#385C2211yescharacteristic
40C53×#385C2212yes—
41C53×#385C2211yescharacteristic
42C53×#379C2211yescharacteristic
43C53×#379C2212yes—
44C53×#379C2211yescharacteristic
45C53×#379C2211yescharacteristic
46C53×#342C2211yescharacteristic
47C53×#342C2211yescharacteristic
48C53×#342C2212yes—
49C53×#342C2212yes—
50C53×#342C2212yes—
51C25×C53C2311yescharacteristic
52C25×C53C2311yescharacteristic
53C2×#41×C53—21no—
54C2×#41×C53—21no—
55C22×D4×C53—22no—
56C22×D4×C53—21no—
57C22×D4×C53—22no—
58C22×D4×C53—21no—
59C22×D4×C53—22no—
60C22×D4×C53—44no—
61C22×D4×C53D412yescomplemented
62C22×D4×C53D412yescomplemented
63C22×D4×C53C2312yes—
64C23×C4×C53—22no—
65C23×C4×C53D411yescharacteristic, complemented
66C23×C4×C53D411yescharacteristic, complemented
67C23×C4×C53C2311yescharacteristic
68#126×C53—22no—
69#126×C53—22no—
70#124×C53—22no—
71#124×C53—22no—
72#123×C53—22no—
73#123×C53—22no—
74#123×C53—22no—
75#123×C53—22no—
76#123×C53—22no—
77#123×C53—44no—
78C22⋊Q8×C53—21no—
79C22⋊Q8×C53—21no—
80C22⋊Q8×C53—21no—
81C22⋊Q8×C53—21no—
82C22⋊Q8×C53—22no—
83C22⋊Q8×C53—22no—
84#121×C53—21no—
85#121×C53—21no—
86#121×C53—22no—
87#121×C53—22no—
88#121×C53—21no—
89#121×C53—21no—
90#121×C53—48no—
91#120×C53—22no—
92#120×C53—22no—
93#120×C53—22no—
94#120×C53—22no—
95#120×C53—22no—
96#120×C53—24no—
97#120×C53—42no—
98C4×D4×C53—22no—
99C4×D4×C53—22no—
100C4×D4×C53—22no—
101C4×D4×C53—22no—
102C4×D4×C53—22no—
103C4×D4×C53—22no—
104#117×C53—21no—
105#117×C53—21no—
106#117×C53—22no—
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—21no—
109C2×C4⋊C4×C53—21no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—21no—
116C2×C22⋊C4×C53—21no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—21no—
120C2×C22⋊C4×C53—21no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—24no—
125C2×C22⋊C4×C53—42no—
126C2×C22⋊C4×C53D411yescharacteristic, complemented
127C2×C22⋊C4×C53D411yescharacteristic, complemented
128C2×C22⋊C4×C53D412yescomplemented
129C2×C22⋊C4×C53D412yescomplemented
130C2×C22⋊C4×C53C2312yes—
131C2×C22⋊C4×C53C2311yescharacteristic
132C2×C22⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53C2312yes—
134C2×C22⋊C4×C53C2311yescharacteristic
135C2×C22⋊C4×C53C2311yescharacteristic
136C2×C22⋊C4×C53C2312yes—
137#99×C53—24no—
138#99×C53—42no—
139#95×C53—22no—
140#95×C53—21no—
141#95×C53—21no—
142#95×C53—22no—
143C24×C53—22no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—42no—
152C24×C53—42no—
153C24×C53—81no—
154C24×C53—81no—
155C24×C53C2×D412yes—
156C24×C53C2×D411yescharacteristic
157C24×C53C2×D412yes—
158C24×C53C2×D412yes—
159C24×C53C2×D411yescharacteristic
160C24×C53C2411yescharacteristic
161#41×C53—82no—
162#41×C53—82no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×D4×C53—28no—
166C2×D4×C53—24no—
167C2×D4×C53—22no—
168C2×D4×C53—22no—
169C2×D4×C53—22no—
170C2×D4×C53—22no—
171C2×D4×C53—22no—
172C2×D4×C53—22no—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—44no—
180C2×D4×C53—42no—
181C2×D4×C53—44no—
182C2×D4×C53—44no—
183C2×D4×C53—42no—
184C2×D4×C53—44no—
185C2×D4×C53—42no—
186C2×D4×C53—41no—
187C2×D4×C53—42no—
188C2×D4×C53—41no—
189C2×D4×C53—44no—
190C2×D4×C53—44no—
191C2×D4×C53—82no—
192C2×D4×C53—82no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—22no—
205C22×C4×C53—42no—
206C22×C4×C53—44no—
207C22×C4×C53—42no—
208C22×C4×C53—44no—
209C22×C4×C53—81no—
210C22×C4×C53—82no—
211C22×C4×C53C2×D412yes—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2×D411yescharacteristic
218C4⋊C4×C53—22no—
219C4⋊C4×C53—22no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—44no—
227C4⋊C4×C53—42no—
228C4⋊C4×C53—42no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—22no—
237C22⋊C4×C53—22no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—22no—
240C22⋊C4×C53—22no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—22no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—22no—
248C22⋊C4×C53—21no—
249C22⋊C4×C53—44no—
250C22⋊C4×C53—44no—
251C22⋊C4×C53—44no—
252C22⋊C4×C53—44no—
253C22⋊C4×C53—42no—
254C22⋊C4×C53—42no—
255C22⋊C4×C53—42no—
256C22⋊C4×C53—81no—
257C22⋊C4×C53—81no—
258C22⋊C4×C53—82no—
259C22⋊C4×C53—81no—
260C22⋊C4×C53#4114yescomplemented
261C42×C53—22no—
262C42×C53—22no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—24no—
268C23×C53—22no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—24no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—42no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53—41no—
286C23×C53—41no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—41no—
290C23×C53—41no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—84no—
300C23×C53—84no—
301C23×C53—82no—
302C23×C53—82no—
303C23×C53—82no—
304C23×C53—82no—
305C23×C53#12011yescharacteristic
306C23×C53#12012yes—
307C23×C53#12011yescharacteristic
308C23×C53C22×D411yescharacteristic
309C23×C53C22×D412yes—
310C23×C53C2×#4112yes—
311C23×C53H(5,𝔽2)11yescharacteristic
312C23×C532−1+411yescharacteristic
313Q8×C53—81no—
314Q8×C53—81no—
315D4×C53—44no—
316D4×C53—48no—
317D4×C53—44no—
318D4×C53—42no—
319D4×C53—42no—
320D4×C53—42no—
321D4×C53—42no—
322D4×C53—44no—
323D4×C53—44no—
324D4×C53—82no—
325D4×C53—82no—
326D4×C53—81no—
327D4×C53—81no—
328D4×C53—88no—
329C2×C4×C53—24no—
330C2×C4×C53—22no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—24no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—41no—
342C2×C4×C53—42no—
343C2×C4×C53—42no—
344C2×C4×C53—42no—
345C2×C4×C53—42no—
346C2×C4×C53—41no—
347C2×C4×C53—42no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—42no—
363C2×C4×C53—81no—
364C2×C4×C53—81no—
365C2×C4×C53—82no—
366C2×C4×C53—82no—
367C2×C4×C53—88no—
368#25563C5311yesmaximal, characteristic, direct product factor, Sylow
369C22×C53—21no—
370C22×C53—21no—
371C22×C53—22no—
372C22×C53—21no—
373C22×C53—22no—
374C22×C53—21no—
375C22×C53—21no—
376C22×C53—22no—
377C22×C53—21no—
378C22×C53—22no—
379C22×C53—21no—
380C22×C53—22no—
381C22×C53—42no—
382C22×C53—41no—
383C22×C53—41no—
384C22×C53—44no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—44no—
388C22×C53—44no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—44no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—82no—
397C22×C53—81no—
398C22×C53—81no—
399C22×C53—82no—
400C22×C53—82no—
401C22×C53—82no—
402C22×C53—82no—
403C22×C53—81no—
404C22×C53—81no—
405C22×C53—82no—
406C22×C53—81no—
407C22×C53—81no—
408C22×C53B(4,𝔽2)12yes—
409C22×C53C2×#12011yescharacteristic
410C22×C53#53211yescharacteristic
411C22×C53#53711yescharacteristic
412C22×C53#54612yes—
413C22×C53#54712yes—
414C4×C53—44no—
415C4×C53—42no—
416C4×C53—42no—
417C4×C53—41no—
418C4×C53—41no—
419C4×C53—42no—
420C4×C53—41no—
421C4×C53—41no—
422C4×C53—42no—
423C4×C53—81no—
424C4×C53—81no—
425C4×C53—82no—
426#3490C2×C5311yescharacteristic, complemented
427#2410C2×C5312yescomplemented
428#2405C2×C5311yescharacteristic, complemented
429#2062C2×C5311yescharacteristic, complemented
430#2044C2×C5311yescharacteristic, complemented
431#2029C2×C5311yescharacteristic, complemented
432#2021C2×C5311yescharacteristic, complemented
433#1898C2×C5312yescomplemented
434#1889C2×C5312yescomplemented
435#1867C2×C5312yescomplemented
436C2×#342C2×C5311yescharacteristic, complemented
437C2×C53—22no—
438C2×C53—21no—
439C2×C53—21no—
440C2×C53—22no—
441C2×C53—22no—
442C2×C53—41no—
443C2×C53—42no—
444C2×C53—82no—
445C2×C53—82no—
446C2×C53#243011yescharacteristic
447C2×C53C2×B(4,𝔽2)11yescharacteristic
448C2×C53#302611yescharacteristic
449C23×D4C22×C5311yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C5311yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C5311yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C5312yes—
463C2×#120C22×C5312yes—
464#518C22×C5312yes—
465C22×C22⋊C4C22×C5311yescharacteristic
466C22×C22⋊C4C22×C5312yes—
467C2×#99C22×C5312yes—
468C2×#99C22×C5312yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C5312yes—
476#385C22×C5312yes—
477#385C22×C5311yescharacteristic
478#385C22×C5311yescharacteristic
479#379C22×C5311yescharacteristic
480#379C22×C5312yes—
481#379C22×C5311yescharacteristic
482#379C22×C5311yescharacteristic
483#342C22×C5312yes—
484#342C22×C5311yescharacteristic
485#342C22×C5312yes—
486#342C22×C5312yes—
487#342C22×C5311yescharacteristic
488C53#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C5311yescharacteristic
490C25C23×C5311yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C5312yescomplemented
500C22×D4D4×C5312yescomplemented
501C22×D4C23×C5312yes—
502C23×C4—22no—
503C23×C4D4×C5311yescharacteristic, complemented
504C23×C4D4×C5311yescharacteristic, complemented
505C23×C4C23×C5311yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C5311yescharacteristic, complemented
565C2×C22⋊C4D4×C5311yescharacteristic, complemented
566C2×C22⋊C4D4×C5312yescomplemented
567C2×C22⋊C4D4×C5312yescomplemented
568C2×C22⋊C4C23×C5312yes—
569C2×C22⋊C4C23×C5311yescharacteristic
570C2×C22⋊C4C23×C5311yescharacteristic
571C2×C22⋊C4C23×C5311yescharacteristic
572C2×C22⋊C4C23×C5311yescharacteristic
573C2×C22⋊C4C23×C5312yes—
574C2×C22⋊C4C23×C5312yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C5312yes—
594C24C2×D4×C5311yescharacteristic
595C24C2×D4×C5312yes—
596C24C2×D4×C5312yes—
597C24C2×D4×C5311yescharacteristic
598C24C24×C5311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C5312yes—
650C22×C4C2×D4×C5311yescharacteristic
651C22×C4C2×D4×C5312yes—
652C22×C4C2×D4×C5311yescharacteristic
653C22×C4C2×D4×C5311yescharacteristic
654C22×C4C2×D4×C5312yes—
655C22×C4C2×D4×C5311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C5314yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C5312yes—
744C23#120×C5311yescharacteristic
745C23#120×C5311yescharacteristic
746C23C22×D4×C5311yescharacteristic
747C23C22×D4×C5312yes—
748C23C2×#41×C5312yes—
749C23H(5,𝔽2)×C5311yescharacteristic
750C232−1+4×C5311yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C53×B(4,𝔽2)12yes—
846C22C2×#120×C5311yescharacteristic
847C22C53×#53211yescharacteristic
848C22C53×#53711yescharacteristic
849C22C53×#54612yes—
850C22C53×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C53×#243011yescharacteristic
873C2C2×C53×B(4,𝔽2)11yescharacteristic
874C2C53×#302611yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC24C24×C53
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C25×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3490C2semidirect
2. C53×#2410C2semidirect
3. C53×#2405C2semidirect
4. C53×#2062C2semidirect
5. C53×#2044C2semidirect
6. C53×#2029C2semidirect
7. C53×#2021C2semidirect
8. C53×#1898C2semidirect
9. C53×#1889C2semidirect
10. C53×#1867C2semidirect
11. C2×C53×#342C2semidirect
61. C22×D4×C53D4semidirect
62. C22×D4×C53D4semidirect
65. C23×C4×C53D4semidirect
66. C23×C4×C53D4semidirect
126. C2×C22⋊C4×C53D4semidirect
127. C2×C22⋊C4×C53D4semidirect
128. C2×C22⋊C4×C53D4semidirect
129. C2×C22⋊C4×C53D4semidirect
260. C22⋊C4×C53#41semidirect
368. #25563C53direct (N × H)
426. #3490C2×C53semidirect
427. #2410C2×C53semidirect
428. #2405C2×C53semidirect
429. #2062C2×C53semidirect
430. #2044C2×C53semidirect
431. #2029C2×C53semidirect
432. #2021C2×C53semidirect
433. #1898C2×C53semidirect
434. #1889C2×C53semidirect
435. #1867C2×C53semidirect
436. C2×#342C2×C53semidirect
488. C53#25563direct (N × H)
499. C22×D4D4×C53semidirect
500. C22×D4D4×C53semidirect
503. C23×C4D4×C53semidirect
504. C23×C4D4×C53semidirect
564. C2×C22⋊C4D4×C53semidirect
565. C2×C22⋊C4D4×C53semidirect
566. C2×C22⋊C4D4×C53semidirect
567. C2×C22⋊C4D4×C53semidirect
698. C22⋊C4#41×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#34902
C53×#24102
C53×#24052
C53×#20622
C53×#20442
C53×#20292
C53×#20212
C53×#18982
C53×#18892
C53×#18672
C2×C53×#3422
#2556353