Finite Group Databasebeta

← C53×#25587 #27233099

Subgroups — C53×#25587 #27233099

Order 13568.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3505C211yesmaximal, characteristic, complemented
2C53×#2561C211yesmaximal, characteristic, complemented
3C53×#2539C211yesmaximal, characteristic, complemented
4C53×#2534C211yesmaximal, characteristic, complemented
5C53×#2022C212yesmaximal, complemented
6C53×#2021C212yesmaximal, complemented
7C53×#1996C211yesmaximal, characteristic, complemented
8C53×#1964C211yesmaximal, characteristic, complemented
9C53×#1890C212yesmaximal, complemented
10C53×#1889C212yesmaximal, complemented
11C4×#99×C53C211yesmaximal, characteristic, complemented
12C53×#553—22no—
13C53×#553—21no—
14C53×#552—21no—
15C53×#551—22no—
16C53×#548—21no—
17C53×#546—21no—
18C53×#539—21no—
19C53×#538—21no—
20C53×#534C2212yes—
21C53×#529—21no—
22C53×#525—21no—
23C2×#123×C53C2212yes—
24C2×#123×C53C2211yescharacteristic
25C2×C22⋊Q8×C53C2211yescharacteristic
26C2×#121×C53C2211yescharacteristic
27C2×#120×C53C2212yes—
28C2×#120×C53C2211yescharacteristic
29C53×#518C2212yes—
30C2×C4×D4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C2×#99×C53C2212yes—
33C2×#99×C53C2212yes—
34C2×#99×C53C2212yes—
35C53×#399—21no—
36C53×#397—21no—
37C53×#396—21no—
38C53×#394—21no—
39C53×#393—21no—
40C53×#392—21no—
41C53×#390—22no—
42C53×#388—22no—
43C53×#388—21no—
44C53×#386—21no—
45C53×#381C2212yes—
46C53×#381C2211yescharacteristic
47C53×#380C2211yescharacteristic
48C53×#379C2212yes—
49C53×#379C2211yescharacteristic
50C4×C22⋊C4×C53C2211yescharacteristic
51C4×C22⋊C4×C53C2211yescharacteristic
52C53×#342C2212yes—
53C53×#342C2212yes—
54C53×#342C2212yes—
55C25×C53C2311yescharacteristic
56C2×#41×C53—21no—
57C22×Q8×C53D411yescharacteristic, complemented
58C22×D4×C53—21no—
59C22×D4×C53—22no—
60C22×D4×C53D411yescharacteristic, complemented
61C22×D4×C53C2311yescharacteristic
62C22×D4×C53C2312yes—
63C23×C4×C53D411yescharacteristic, complemented
64C23×C4×C53C2311yescharacteristic
65C23×C4×C53C2311yescharacteristic
66#126×C53—22no—
67#126×C53—22no—
68#126×C53—22no—
69#125×C53—21no—
70#125×C53—22no—
71#124×C53—21no—
72#124×C53—22no—
73#123×C53—22no—
74#123×C53—22no—
75#123×C53—22no—
76#123×C53—24no—
77#123×C53—22no—
78#123×C53—22no—
79#123×C53—42no—
80#123×C53—42no—
81C22⋊Q8×C53—21no—
82C22⋊Q8×C53—22no—
83C22⋊Q8×C53—21no—
84C22⋊Q8×C53—21no—
85C22⋊Q8×C53—21no—
86C22⋊Q8×C53—21no—
87#121×C53—21no—
88#121×C53—22no—
89#121×C53—21no—
90#121×C53—21no—
91#121×C53—21no—
92#121×C53—21no—
93#121×C53—22no—
94#121×C53—22no—
95#120×C53—22no—
96#120×C53—22no—
97#120×C53—24no—
98#120×C53—42no—
99#120×C53—42no—
100C4×Q8×C53—21no—
101C4×D4×C53—22no—
102C4×D4×C53—21no—
103C4×D4×C53—21no—
104C4×D4×C53—21no—
105C4×D4×C53—21no—
106C4×D4×C53—21no—
107C4×D4×C53—22no—
108C4×D4×C53—22no—
109C4×D4×C53—22no—
110C4×D4×C53—22no—
111#117×C53—21no—
112#117×C53—22no—
113#117×C53—22no—
114C2×C4⋊C4×C53—21no—
115C2×C4⋊C4×C53—22no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53D411yescharacteristic, complemented
118C2×C4⋊C4×C53D411yescharacteristic, complemented
119C2×C4⋊C4×C53D412yescomplemented
120C2×C4⋊C4×C53D411yescharacteristic, complemented
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—22no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53D411yescharacteristic, complemented
137C2×C22⋊C4×C53D412yescomplemented
138C2×C22⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53C2312yes—
141C2×C22⋊C4×C53C2312yes—
142C2×C22⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53C2312yes—
144C2×C42×C53—21no—
145C2×C42×C53—21no—
146C2×C42×C53D411yescharacteristic, complemented
147#99×C53—24no—
148#99×C53—42no—
149#99×C53—42no—
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153#95×C53—21no—
154#95×C53—22no—
155#95×C53—21no—
156#95×C53—22no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—42no—
163C24×C53—81no—
164C24×C53C2×D412yes—
165C24×C53C2×D411yescharacteristic
166C24×C53C2411yescharacteristic
167#41×C53—82no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—81no—
171C2×D4×C53—21no—
172C2×D4×C53—22no—
173C2×D4×C53—21no—
174C2×D4×C53—22no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—22no—
182C2×D4×C53—22no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—44no—
186C2×D4×C53—42no—
187C2×D4×C53—44no—
188C2×D4×C53—42no—
189C2×D4×C53—81no—
190C2×D4×C53—82no—
191C2×D4×C53—81no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—81no—
206C22×C4×C53—81no—
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C4⋊C4×C53—22no—
220C4⋊C4×C53—22no—
221C4⋊C4×C53—22no—
222C4⋊C4×C53—22no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—22no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—44no—
232C4⋊C4×C53—42no—
233C4⋊C4×C53—81no—
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—21no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—22no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—21no—
248C22⋊C4×C53—22no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—22no—
251C22⋊C4×C53—22no—
252C22⋊C4×C53—22no—
253C22⋊C4×C53—44no—
254C22⋊C4×C53—44no—
255C22⋊C4×C53—42no—
256C22⋊C4×C53—42no—
257C22⋊C4×C53—44no—
258C22⋊C4×C53—42no—
259C22⋊C4×C53—41no—
260C22⋊C4×C53—41no—
261C22⋊C4×C53—41no—
262C22⋊C4×C53—41no—
263C22⋊C4×C53—81no—
264C22⋊C4×C53—82no—
265C22⋊C4×C53#4114yescomplemented
266C42×C53—22no—
267C42×C53—22no—
268C42×C53—21no—
269C42×C53—21no—
270C42×C53—81no—
271C42×C53—81no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53—41no—
286C23×C53—42no—
287C23×C53—41no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—42no—
291C23×C53—41no—
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×C53C22×D411yescharacteristic
302C23×C53C22×D411yescharacteristic
303C23×C53C22×D411yescharacteristic
304C23×C53C2×#4112yes—
305C23×C53H(5,𝔽2)12yes—
306Q8×C53—42no—
307Q8×C53—81no—
308D4×C53—42no—
309D4×C53—42no—
310D4×C53—42no—
311D4×C53—42no—
312D4×C53—42no—
313D4×C53—42no—
314D4×C53—42no—
315D4×C53—81no—
316D4×C53—82no—
317D4×C53—82no—
318D4×C53—88no—
319D4×C53—84no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—21no—
325C2×C4×C53—22no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—24no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—42no—
338C2×C4×C53—42no—
339C2×C4×C53—42no—
340C2×C4×C53—41no—
341C2×C4×C53—42no—
342C2×C4×C53—41no—
343C2×C4×C53—42no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—42no—
347C2×C4×C53—42no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53—81no—
359C2×C4×C53—82no—
360C2×C4×C53—82no—
361C2×C4×C53#12011yescharacteristic
362C2×C4×C53#12011yescharacteristic
363C2×C4×C53#12011yescharacteristic
364C2×C4×C53#12011yescharacteristic
365#25587C5311yesmaximal, characteristic, direct product factor, Sylow
366C22×C53—21no—
367C22×C53—21no—
368C22×C53—21no—
369C22×C53—21no—
370C22×C53—21no—
371C22×C53—21no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—44no—
376C22×C53—42no—
377C22×C53—44no—
378C22×C53—42no—
379C22×C53—41no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53—41no—
383C22×C53—42no—
384C22×C53—41no—
385C22×C53—42no—
386C22×C53—82no—
387C22×C53—82no—
388C22×C53—81no—
389C22×C53—82no—
390C22×C53—81no—
391C22×C53—82no—
392C22×C53—81no—
393C22×C53—81no—
394C22×C53—81no—
395C22×C53C2×#12011yescharacteristic
396C22×C53#53211yescharacteristic
397C22×C53#53511yescharacteristic
398C22×C53#54612yes—
399C22×C53#55012yes—
400C4×C53—21no—
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—21no—
404C4×C53—44no—
405C4×C53—41no—
406C4×C53—42no—
407C4×C53—41no—
408C4×C53—42no—
409C4×C53—41no—
410C4×C53—42no—
411C4×C53—81no—
412C4×C53—82no—
413C4×C53—81no—
414C4×C53—81no—
415#3505C2×C5311yescharacteristic, complemented
416#2561C2×C5311yescharacteristic, complemented
417#2539C2×C5311yescharacteristic, complemented
418#2534C2×C5311yescharacteristic, complemented
419#2022C2×C5312yescomplemented
420#2021C2×C5312yescomplemented
421#1996C2×C5311yescharacteristic, complemented
422#1964C2×C5311yescharacteristic, complemented
423#1890C2×C5312yescomplemented
424#1889C2×C5312yescomplemented
425C4×#99C2×C5311yescharacteristic, complemented
426C2×C53—22no—
427C2×C53—21no—
428C2×C53—22no—
429C2×C53—21no—
430C2×C53—82no—
431C2×C53—81no—
432C2×C53—82no—
433C2×C53#243111yescharacteristic
434C2×C53#302511yescharacteristic
435C2×C53#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C5312yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C5312yes—
448C2×#123C22×C5311yescharacteristic
449C2×C22⋊Q8C22×C5311yescharacteristic
450C2×#121C22×C5311yescharacteristic
451C2×#120C22×C5312yes—
452C2×#120C22×C5311yescharacteristic
453#518C22×C5312yes—
454C2×C4×D4C22×C5311yescharacteristic
455C22×C22⋊C4C22×C5311yescharacteristic
456C2×#99C22×C5312yes—
457C2×#99C22×C5312yes—
458C2×#99C22×C5312yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C5312yes—
470#381C22×C5311yescharacteristic
471#380C22×C5311yescharacteristic
472#379C22×C5312yes—
473#379C22×C5311yescharacteristic
474C4×C22⋊C4C22×C5311yescharacteristic
475C4×C22⋊C4C22×C5311yescharacteristic
476#342C22×C5312yes—
477#342C22×C5312yes—
478#342C22×C5312yes—
479C53#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C5311yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C5311yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C5311yescharacteristic, complemented
486C22×D4C23×C5311yescharacteristic
487C22×D4C23×C5312yes—
488C23×C4D4×C5311yescharacteristic, complemented
489C23×C4C23×C5311yescharacteristic
490C23×C4C23×C5311yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C5311yescharacteristic, complemented
543C2×C4⋊C4D4×C5311yescharacteristic, complemented
544C2×C4⋊C4D4×C5312yescomplemented
545C2×C4⋊C4D4×C5311yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C5311yescharacteristic, complemented
562C2×C22⋊C4D4×C5312yescomplemented
563C2×C22⋊C4C23×C5311yescharacteristic
564C2×C22⋊C4C23×C5311yescharacteristic
565C2×C22⋊C4C23×C5312yes—
566C2×C22⋊C4C23×C5311yescharacteristic
567C2×C22⋊C4C23×C5312yes—
568C2×C22⋊C4C23×C5312yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C5311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C5312yes—
590C24C2×D4×C5311yescharacteristic
591C24C24×C5311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C5311yescharacteristic
633C22×C4C2×D4×C5312yes—
634C22×C4C2×D4×C5311yescharacteristic
635C22×C4C2×D4×C5312yes—
636C22×C4C2×D4×C5311yescharacteristic
637C22×C4C2×D4×C5312yes—
638C22×C4C2×D4×C5311yescharacteristic
639C22×C4C2×D4×C5311yescharacteristic
640C22×C4C2×D4×C5311yescharacteristic
641C22×C4C2×D4×C5311yescharacteristic
642C22×C4C2×D4×C5311yescharacteristic
643C22×C4C2×D4×C5311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C5314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C5311yescharacteristic
727C23C22×D4×C5311yescharacteristic
728C23C22×D4×C5311yescharacteristic
729C23C2×#41×C5312yes—
730C23H(5,𝔽2)×C5312yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C5311yescharacteristic
787C2×C4#120×C5311yescharacteristic
788C2×C4#120×C5311yescharacteristic
789C2×C4#120×C5311yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C5311yescharacteristic
820C22C53×#53211yescharacteristic
821C22C53×#53511yescharacteristic
822C22C53×#54612yes—
823C22C53×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C53×#243111yescharacteristic
847C2C53×#302511yescharacteristic
848C2C53×#302611yescharacteristic
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×#2561C2semidirect
3. C53×#2539C2semidirect
4. C53×#2534C2semidirect
5. C53×#2022C2semidirect
6. C53×#2021C2semidirect
7. C53×#1996C2semidirect
8. C53×#1964C2semidirect
9. C53×#1890C2semidirect
10. C53×#1889C2semidirect
11. C4×#99×C53C2semidirect
57. C22×Q8×C53D4semidirect
60. C22×D4×C53D4semidirect
63. C23×C4×C53D4semidirect
117. C2×C4⋊C4×C53D4semidirect
118. C2×C4⋊C4×C53D4semidirect
119. C2×C4⋊C4×C53D4semidirect
120. C2×C4⋊C4×C53D4semidirect
136. C2×C22⋊C4×C53D4semidirect
137. C2×C22⋊C4×C53D4semidirect
146. C2×C42×C53D4semidirect
265. C22⋊C4×C53#41semidirect
365. #25587C53direct (N × H)
415. #3505C2×C53semidirect
416. #2561C2×C53semidirect
417. #2539C2×C53semidirect
418. #2534C2×C53semidirect
419. #2022C2×C53semidirect
420. #2021C2×C53semidirect
421. #1996C2×C53semidirect
422. #1964C2×C53semidirect
423. #1890C2×C53semidirect
424. #1889C2×C53semidirect
425. C4×#99C2×C53semidirect
479. C53#25587direct (N × H)
482. C22×Q8D4×C53semidirect
485. C22×D4D4×C53semidirect
488. C23×C4D4×C53semidirect
542. C2×C4⋊C4D4×C53semidirect
543. C2×C4⋊C4D4×C53semidirect
544. C2×C4⋊C4D4×C53semidirect
545. C2×C4⋊C4D4×C53semidirect
561. C2×C22⋊C4D4×C53semidirect
562. C2×C22⋊C4D4×C53semidirect
571. C2×C42D4×C53semidirect
690. 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×#25612
C53×#25392
C53×#25342
C53×#20222
C53×#20212
C53×#19962
C53×#19642
C53×#18902
C53×#18892
C4×#99×C532
#2558753