Finite Group Databasebeta

← C53×#25585 #27233097

Subgroups — C53×#25585 #27233097

Order 13568.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3505C211yesmaximal, characteristic, complemented
2C53×#2435C211yesmaximal, characteristic, complemented
3C53×#2433C211yesmaximal, characteristic, complemented
4C53×#2408C211yesmaximal, characteristic, complemented
5C53×#2021C214yesmaximal, complemented
6C53×#1996C211yesmaximal, characteristic, complemented
7C53×#1964C211yesmaximal, characteristic, complemented
8C53×#1889C214yesmaximal, complemented
9C4×#99×C53C211yesmaximal, characteristic, complemented
10C23×D4×C53C2211yescharacteristic
11C53×#553—21no—
12C53×#553—22no—
13C53×#552—21no—
14C53×#551—22no—
15C53×#548—21no—
16C53×#546—21no—
17C53×#539—21no—
18C53×#538—21no—
19C53×#534C2212yes—
20C2×#127×C53—21no—
21C53×#529—21no—
22C2×#124×C53—21no—
23C53×#525—21no—
24C2×C22⋊Q8×C53C2211yescharacteristic
25C2×#121×C53—21no—
26C2×#121×C53C2211yescharacteristic
27C2×#120×C53C2214yes—
28C2×#120×C53C2212yes—
29C53×#518C2212yes—
30C2×C4×D4×C53C2211yescharacteristic
31C2×#99×C53C2212yes—
32C2×#99×C53C2214yes—
33C53×#394—22no—
34C53×#394—21no—
35C53×#392—22no—
36C53×#392—21no—
37C53×#390—21no—
38C53×#390—21no—
39C53×#390—21no—
40C53×#380C2211yescharacteristic
41C53×#379C2214yes—
42C53×#379C2212yes—
43C4×C22⋊C4×C53C2211yescharacteristic
44C4×C22⋊C4×C53C2211yescharacteristic
45C53×#342C2214yes—
46C53×#342C2212yes—
47C25×C53C2312yes—
48C2×#41×C53—21no—
49C22×Q8×C53D411yescharacteristic, complemented
50C22×D4×C53—22no—
51C22×D4×C53—24no—
52C22×D4×C53—21no—
53C22×D4×C53—21no—
54C22×D4×C53—21no—
55C22×D4×C53—21no—
56C22×D4×C53—21no—
57C22×D4×C53—21no—
58C22×D4×C53—44no—
59C22×D4×C53D411yescharacteristic, complemented
60C22×D4×C53C2311yescharacteristic
61C22×D4×C53C2312yes—
62C23×C4×C53D411yescharacteristic, complemented
63C23×C4×C53C2311yescharacteristic
64#127×C53—44no—
65#126×C53—22no—
66#126×C53—22no—
67#126×C53—22no—
68#125×C53—21no—
69#125×C53—22no—
70#124×C53—21no—
71#124×C53—22no—
72#124×C53—44no—
73#123×C53—22no—
74#123×C53—22no—
75#123×C53—22no—
76#123×C53—22no—
77#123×C53—22no—
78C22⋊Q8×C53—21no—
79C22⋊Q8×C53—22no—
80C22⋊Q8×C53—21no—
81C22⋊Q8×C53—21no—
82C22⋊Q8×C53—21no—
83C22⋊Q8×C53—21no—
84#121×C53—21no—
85#121×C53—22no—
86#121×C53—21no—
87#121×C53—21no—
88#121×C53—21no—
89#121×C53—21no—
90#121×C53—22no—
91#121×C53—22no—
92#121×C53—44no—
93#120×C53—22no—
94#120×C53—22no—
95#120×C53—28no—
96#120×C53—44no—
97#120×C53—44no—
98C4×Q8×C53—21no—
99C4×D4×C53—22no—
100C4×D4×C53—21no—
101C4×D4×C53—21no—
102C4×D4×C53—21no—
103C4×D4×C53—21no—
104C4×D4×C53—21no—
105C4×D4×C53—22no—
106C4×D4×C53—22no—
107C4×D4×C53—22no—
108C4×D4×C53—22no—
109#117×C53—21no—
110#117×C53—22no—
111#117×C53—22no—
112C2×C4⋊C4×C53—21no—
113C2×C4⋊C4×C53D411yescharacteristic, complemented
114C2×C4⋊C4×C53D411yescharacteristic, complemented
115C2×C4⋊C4×C53D411yescharacteristic, complemented
116C2×C4⋊C4×C53D412yescomplemented
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—24no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—24no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—24no—
124C2×C22⋊C4×C53D411yescharacteristic, complemented
125C2×C22⋊C4×C53D412yescomplemented
126C2×C22⋊C4×C53C2312yes—
127C2×C22⋊C4×C53C2312yes—
128C2×C22⋊C4×C53C2312yes—
129C2×C22⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53C2312yes—
131C2×C42×C53—21no—
132C2×C42×C53—21no—
133C2×C42×C53D411yescharacteristic, complemented
134#99×C53—24no—
135#99×C53—44no—
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139C24×C53—22no—
140C24×C53—22no—
141C24×C53—22no—
142C24×C53—24no—
143C24×C53—24no—
144C24×C53—44no—
145C24×C53—82no—
146C24×C53C2×D412yes—
147C24×C53C2×D411yescharacteristic
148C24×C53C2411yescharacteristic
149#41×C53—82no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—42no—
153C2×D4×C53—24no—
154C2×D4×C53—24no—
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—22no—
158C2×D4×C53—21no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—24no—
162C2×D4×C53—24no—
163C2×D4×C53—22no—
164C2×D4×C53—22no—
165C2×D4×C53—22no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—42no—
169C2×D4×C53—42no—
170C2×D4×C53—42no—
171C2×D4×C53—42no—
172C2×D4×C53—48no—
173C2×D4×C53—44no—
174C2×D4×C53—44no—
175C2×D4×C53—44no—
176C2×D4×C53—44no—
177C2×D4×C53—44no—
178C2×D4×C53—48no—
179C2×D4×C53—41no—
180C2×D4×C53—41no—
181C2×D4×C53—41no—
182C2×D4×C53—41no—
183C2×D4×C53—84no—
184C2×D4×C53—82no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—42no—
193C22×C4×C53—42no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C4⋊C4×C53—22no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—22no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—22no—
212C4⋊C4×C53—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—22no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—42no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—22no—
224C22⋊C4×C53—22no—
225C22⋊C4×C53—21no—
226C22⋊C4×C53—22no—
227C22⋊C4×C53—21no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—21no—
232C22⋊C4×C53—21no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—48no—
238C22⋊C4×C53—44no—
239C22⋊C4×C53—44no—
240C22⋊C4×C53—48no—
241C22⋊C4×C53—82no—
242C22⋊C4×C53—84no—
243C22⋊C4×C53#4114yescomplemented
244C42×C53—22no—
245C42×C53—22no—
246C42×C53—21no—
247C42×C53—21no—
248C42×C53—42no—
249C42×C53—42no—
250C23×C53—24no—
251C23×C53—24no—
252C23×C53—24no—
253C23×C53—21no—
254C23×C53—22no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—24no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53—42no—
266C23×C53—44no—
267C23×C53—44no—
268C23×C53—42no—
269C23×C53—42no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53—88no—
277C23×C53—88no—
278C23×C53C22×D411yescharacteristic
279C23×C53C22×D411yescharacteristic
280C23×C53C22×D411yescharacteristic
281C23×C53C2×#4112yes—
282C23×C53H(5,𝔽2)12yes—
283Q8×C53—42no—
284Q8×C53—81no—
285D4×C53—44no—
286D4×C53—44no—
287D4×C53—44no—
288D4×C53—42no—
289D4×C53—42no—
290D4×C53—42no—
291D4×C53—42no—
292D4×C53—44no—
293D4×C53—44no—
294D4×C53—42no—
295D4×C53—81no—
296D4×C53—82no—
297D4×C53—82no—
298D4×C53—816no—
299D4×C53—88no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—21no—
308C2×C4×C53—22no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—24no—
312C2×C4×C53—24no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—41no—
320C2×C4×C53—42no—
321C2×C4×C53—41no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—81no—
330C2×C4×C53—82no—
331C2×C4×C53—82no—
332C2×C4×C53#12011yescharacteristic
333C2×C4×C53#12011yescharacteristic
334C2×C4×C53#12011yescharacteristic
335C2×C4×C53#12011yescharacteristic
336#25585C5311yesmaximal, characteristic, direct product factor, Sylow
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—21no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—48no—
347C22×C53—44no—
348C22×C53—48no—
349C22×C53—44no—
350C22×C53—41no—
351C22×C53—42no—
352C22×C53—41no—
353C22×C53—42no—
354C22×C53—44no—
355C22×C53—42no—
356C22×C53—41no—
357C22×C53—84no—
358C22×C53—81no—
359C22×C53—84no—
360C22×C53—82no—
361C22×C53—84no—
362C22×C53—82no—
363C22×C53—82no—
364C22×C53—82no—
365C22×C53C2×#12011yescharacteristic
366C22×C53#53211yescharacteristic
367C22×C53#53511yescharacteristic
368C22×C53#54612yes—
369C22×C53#55012yes—
370C4×C53—21no—
371C4×C53—21no—
372C4×C53—21no—
373C4×C53—44no—
374C4×C53—41no—
375C4×C53—42no—
376C4×C53—41no—
377C4×C53—42no—
378C4×C53—41no—
379C4×C53—42no—
380C4×C53—82no—
381C4×C53—82no—
382C4×C53B(4,𝔽2)12yes—
383#3505C2×C5311yescharacteristic, complemented
384#2435C2×C5311yescharacteristic, complemented
385#2433C2×C5311yescharacteristic, complemented
386#2408C2×C5311yescharacteristic, complemented
387#2021C2×C5314yescomplemented
388#1996C2×C5311yescharacteristic, complemented
389#1964C2×C5311yescharacteristic, complemented
390#1889C2×C5314yescomplemented
391C4×#99C2×C5311yescharacteristic, complemented
392C2×C53—22no—
393C2×C53—21no—
394C2×C53—22no—
395C2×C53—21no—
396C2×C53—84no—
397C2×C53—81no—
398C2×C53—82no—
399C2×C53#243111yescharacteristic
400C2×C53C2×B(4,𝔽2)11yescharacteristic
401C2×C53#302711yescharacteristic
402C23×D4C22×C5311yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C5312yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C5311yescharacteristic
417C2×#121—21no—
418C2×#121C22×C5311yescharacteristic
419C2×#120C22×C5314yes—
420C2×#120C22×C5312yes—
421#518C22×C5312yes—
422C2×C4×D4C22×C5311yescharacteristic
423C2×#99C22×C5312yes—
424C2×#99C22×C5314yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C5311yescharacteristic
433#379C22×C5312yes—
434#379C22×C5314yes—
435C4×C22⋊C4C22×C5311yescharacteristic
436C4×C22⋊C4C22×C5311yescharacteristic
437#342C22×C5312yes—
438#342C22×C5314yes—
439C53#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C5312yes—
441C2×#41—21no—
442C22×Q8D4×C5311yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C5311yescharacteristic, complemented
453C22×D4C23×C5311yescharacteristic
454C22×D4C23×C5312yes—
455C23×C4D4×C5311yescharacteristic, complemented
456C23×C4C23×C5311yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C5311yescharacteristic, complemented
507C2×C4⋊C4D4×C5311yescharacteristic, complemented
508C2×C4⋊C4D4×C5311yescharacteristic, complemented
509C2×C4⋊C4D4×C5312yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C5311yescharacteristic, complemented
518C2×C22⋊C4D4×C5312yescomplemented
519C2×C22⋊C4C23×C5312yes—
520C2×C22⋊C4C23×C5312yes—
521C2×C22⋊C4C23×C5311yescharacteristic
522C2×C22⋊C4C23×C5312yes—
523C2×C22⋊C4C23×C5312yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C5311yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C5312yes—
540C24C2×D4×C5311yescharacteristic
541C24C24×C5311yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C5311yescharacteristic
588C22×C4C2×D4×C5312yes—
589C22×C4C2×D4×C5311yescharacteristic
590C22×C4C2×D4×C5311yescharacteristic
591C22×C4C2×D4×C5311yescharacteristic
592C22×C4C2×D4×C5311yescharacteristic
593C22×C4C2×D4×C5312yes—
594C22×C4C2×D4×C5311yescharacteristic
595C22×C4C2×D4×C5312yes—
596C22×C4C2×D4×C5311yescharacteristic
597C22×C4C2×D4×C5311yescharacteristic
598C22×C4C2×D4×C5311yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C5314yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C5311yescharacteristic
672C23C22×D4×C5311yescharacteristic
673C23C22×D4×C5311yescharacteristic
674C23C2×#41×C5312yes—
675C23H(5,𝔽2)×C5312yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C5311yescharacteristic
726C2×C4#120×C5311yescharacteristic
727C2×C4#120×C5311yescharacteristic
728C2×C4#120×C5311yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C5311yescharacteristic
758C22C53×#53211yescharacteristic
759C22C53×#53511yescharacteristic
760C22C53×#54612yes—
761C22C53×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C53×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C53×#243111yescharacteristic
783C2C2×C53×B(4,𝔽2)11yescharacteristic
784C2C53×#302711yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC24C24×C53
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3505C2semidirect
2. C53×#2435C2semidirect
3. C53×#2433C2semidirect
4. C53×#2408C2semidirect
5. C53×#2021C2semidirect
6. C53×#1996C2semidirect
7. C53×#1964C2semidirect
8. C53×#1889C2semidirect
9. C4×#99×C53C2semidirect
49. C22×Q8×C53D4semidirect
59. C22×D4×C53D4semidirect
62. C23×C4×C53D4semidirect
113. C2×C4⋊C4×C53D4semidirect
114. C2×C4⋊C4×C53D4semidirect
115. C2×C4⋊C4×C53D4semidirect
116. C2×C4⋊C4×C53D4semidirect
124. C2×C22⋊C4×C53D4semidirect
125. C2×C22⋊C4×C53D4semidirect
133. C2×C42×C53D4semidirect
243. C22⋊C4×C53#41semidirect
336. #25585C53direct (N × H)
383. #3505C2×C53semidirect
384. #2435C2×C53semidirect
385. #2433C2×C53semidirect
386. #2408C2×C53semidirect
387. #2021C2×C53semidirect
388. #1996C2×C53semidirect
389. #1964C2×C53semidirect
390. #1889C2×C53semidirect
391. C4×#99C2×C53semidirect
439. C53#25585direct (N × H)
442. C22×Q8D4×C53semidirect
452. C22×D4D4×C53semidirect
455. C23×C4D4×C53semidirect
506. C2×C4⋊C4D4×C53semidirect
507. C2×C4⋊C4D4×C53semidirect
508. C2×C4⋊C4D4×C53semidirect
509. C2×C4⋊C4D4×C53semidirect
517. C2×C22⋊C4D4×C53semidirect
518. C2×C22⋊C4D4×C53semidirect
526. C2×C42D4×C53semidirect
636. 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×#35052
C53×#24352
C53×#24332
C53×#24082
C53×#20212
C53×#19962
C53×#19642
C53×#18892
C4×#99×C532
#2558553