Finite Group Databasebeta

← C53×#12753 #27220265

Subgroups — C53×#12753 #27220265

Order 13568.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3532C211yesmaximal, characteristic
2C53×#2127C211yesmaximal, characteristic, complemented
3C53×#2121C211yesmaximal, characteristic, complemented
4C2×C53×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C53×#1913C211yesmaximal, characteristic, complemented
6C53×#1911C211yesmaximal, characteristic, complemented
7C53×#1889C211yesmaximal, characteristic, complemented
8C53×H(3,𝔽4)C411yescharacteristic, complemented
9C53×#560—21no—
10C53×#560C411yescharacteristic, complemented
11C53×#551—21no—
12C53×#551C411yescharacteristic, complemented
13C53×#546—21no—
14C53×#546—21no—
15C53×#546—21no—
16D42×C53—21no—
17D42×C53C411yescharacteristic, complemented
18C53×#538—21no—
19C53×#538—21no—
20C53×#538—21no—
21C53×#535—21no—
22C53×#535C2211yescharacteristic
23C53×#534—21no—
24C53×#534C2211yescharacteristic
25C2×#120×C53—21no—
26C2×#120×C53C2211yescharacteristic
27C53×#518C2211yescharacteristic, complemented
28C53×#421—21no—
29C2×#100×C53C2211yescharacteristic, complemented
30C2×#99×C53—21no—
31C2×#99×C53C2211yescharacteristic, complemented
32C2×#99×C53C2211yescharacteristic, complemented
33C53×#379—21no—
34C53×#354—21no—
35C53×#353—21no—
36C53×#352—21no—
37C53×AΣL(1,𝔽16)—21no—
38C53×AΣL(1,𝔽16)—21no—
39C53×AΣL(1,𝔽16)—21no—
40C53×#342—21no—
41C53×#342—21no—
42C53×H(3,ℤ/4)—21no—
43C25×C53D411yescharacteristic
44C2×#41×C53—21no—
45C2×#41×C53D411yescharacteristic
46C22×D4×C53—21no—
47C22×D4×C53—21no—
48C22×D4×C53—21no—
49C22×D4×C53—21no—
50C22×D4×C53—21no—
51C22×D4×C53D411yescharacteristic
52C22×D4×C53C2311yescharacteristic
53C2×M16×C53—21no—
54#127×C53—21no—
55#127×C53C2×C411yescharacteristic
56#127×C53D411yescharacteristic
57#126×C53—21no—
58#126×C53—21no—
59#126×C53—21no—
60#126×C53—21no—
61#124×C53—21no—
62#124×C53—21no—
63#124×C53—21no—
64#124×C53—21no—
65#124×C53—21no—
66#124×C53C2×C411yescharacteristic
67#124×C53D411yescharacteristic
68#123×C53—21no—
69#123×C53—21no—
70#123×C53—21no—
71#123×C53—21no—
72#123×C53—21no—
73#123×C53—21no—
74#123×C53—21no—
75#123×C53—21no—
76#123×C53C2×C411yescharacteristic
77#123×C53D411yescharacteristic
78C22⋊Q8×C53—21no—
79C22⋊Q8×C53—21no—
80C22⋊Q8×C53—21no—
81#121×C53—21no—
82#121×C53—21no—
83#121×C53—21no—
84#121×C53—21no—
85#121×C53—21no—
86#121×C53—21no—
87#121×C53—21no—
88#121×C53—21no—
89#121×C53—21no—
90#121×C53—21no—
91#121×C53—21no—
92#121×C53—21no—
93#121×C53—21no—
94#121×C53—21no—
95#121×C53—21no—
96#120×C53—21no—
97#120×C53—21no—
98#120×C53—21no—
99#120×C53—21no—
100#120×C53—21no—
101#120×C53—21no—
102#120×C53—21no—
103#120×C53—21no—
104#120×C53—21no—
105#120×C53—21no—
106#120×C53—21no—
107#120×C53—21no—
108#120×C53—21no—
109#120×C53—21no—
110#120×C53C2×C411yescharacteristic
111#120×C53C2×C411yescharacteristic
112#120×C53C2×C411yescharacteristic
113#120×C53D411yescharacteristic
114#120×C53D411yescharacteristic
115#120×C53D411yescharacteristic
116C4×D4×C53—21no—
117C4×D4×C53—21no—
118C4×D4×C53—21no—
119C4×D4×C53—21no—
120C4×D4×C53—21no—
121C4×D4×C53—21no—
122C4×D4×C53—42no—
123#117×C53—21no—
124#117×C53—21no—
125#117×C53D411yescharacteristic
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—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—42no—
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C22⋊C4×C53D411yescharacteristic
138#104×C53—42no—
139#100×C53—21no—
140#100×C53—21no—
141#99×C53—21no—
142#99×C53—21no—
143#99×C53—21no—
144#99×C53—21no—
145#99×C53—42no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—41no—
150C24×C53—41no—
151C24×C53—82no—
152C24×C53C22⋊C411yescharacteristic
153C24×C53C22⋊C411yescharacteristic
154C24×C53C22⋊C411yescharacteristic, complemented
155C24×C53C2×D411yescharacteristic
156C24×C53C2×D411yescharacteristic
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—82no—
160C2×Q8×C53—21no—
161C2×Q8×C53C22⋊C411yescharacteristic, complemented
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—41no—
183C2×D4×C53—41no—
184C2×D4×C53—41no—
185C2×D4×C53—41no—
186C2×D4×C53—82no—
187C2×D4×C53—82no—
188C2×D4×C53—82no—
189C2×D4×C53—82no—
190C2×D4×C53—81no—
191C2×D4×C53—81no—
192C2×D4×C53C22⋊C411yescharacteristic, complemented
193C2×D4×C53C22×C411yescharacteristic
194C2×D4×C53C2×D411yescharacteristic
195C2×D4×C53C2×D411yescharacteristic
196C2×D4×C53C2×D411yescharacteristic
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—22no—
206C22×C4×C53—41no—
207C22×C4×C53—41no—
208C22×C4×C53—41no—
209C22×C4×C53C22⋊C411yescharacteristic, complemented
210C22×C4×C53C2×D411yescharacteristic
211M16×C53—41no—
212M16×C53—41no—
213C2×C8×C53—41no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—41no—
224C22⋊C4×C53—21no—
225C22⋊C4×C53—21no—
226C22⋊C4×C53—21no—
227C22⋊C4×C53—21no—
228C22⋊C4×C53—21no—
229C22⋊C4×C53—21no—
230C22⋊C4×C53—21no—
231C22⋊C4×C53—21no—
232C22⋊C4×C53—21no—
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—21no—
241C22⋊C4×C53—21no—
242C22⋊C4×C53—21no—
243C22⋊C4×C53—21no—
244C22⋊C4×C53—21no—
245C22⋊C4×C53—21no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—21no—
248C22⋊C4×C53—21no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—41no—
251C22⋊C4×C53—41no—
252C22⋊C4×C53—41no—
253C22⋊C4×C53—41no—
254C22⋊C4×C53—41no—
255C22⋊C4×C53—41no—
256C22⋊C4×C53—84no—
257C22⋊C4×C53C22⋊C411yescharacteristic
258C22⋊C4×C53C22⋊C411yescharacteristic
259C22⋊C4×C53C22⋊C411yescharacteristic, complemented
260C22⋊C4×C53C22⋊C411yescharacteristic, complemented
261C42×C53—21no—
262C42×C53—21no—
263C42×C53—22no—
264C42×C53C22⋊C411yescharacteristic, complemented
265C42×C53C22⋊C411yescharacteristic, complemented
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—42no—
275C23×C53—41no—
276C23×C53—41no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—41no—
281C23×C53—44no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—81no—
285C23×C53—81no—
286C23×C53—81no—
287C23×C53—81no—
288C23×C53—81no—
289C23×C53—81no—
290C23×C53—81no—
291C23×C53—81no—
292C23×C53—81no—
293C23×C53—82no—
294C23×C53—82no—
295C23×C53—82no—
296C23×C53C2×C22⋊C411yescharacteristic
297C23×C53C2×C22⋊C411yescharacteristic
298C23×C53#12011yescharacteristic
299C23×C53#12011yescharacteristic
300C23×C53#12011yescharacteristic
301Q8×C53—41no—
302Q8×C53—81no—
303D4×C53—41no—
304D4×C53—41no—
305D4×C53—41no—
306D4×C53—41no—
307D4×C53—41no—
308D4×C53—42no—
309D4×C53—42no—
310D4×C53—42no—
311D4×C53—42no—
312D4×C53—41no—
313D4×C53—41no—
314D4×C53—41no—
315D4×C53—41no—
316D4×C53—81no—
317D4×C53—81no—
318D4×C53—81no—
319D4×C53—81no—
320D4×C53—81no—
321D4×C53—81no—
322D4×C53—81no—
323D4×C53—81no—
324D4×C53—81no—
325D4×C53—81no—
326D4×C53—81no—
327D4×C53—81no—
328D4×C53—81no—
329D4×C53—81no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—42no—
341C2×C4×C53—41no—
342C2×C4×C53—42no—
343C2×C4×C53—81no—
344C2×C4×C53—81no—
345C2×C4×C53—81no—
346C2×C4×C53—81no—
347C2×C4×C53—81no—
348C2×C4×C53—81no—
349C2×C4×C53—81no—
350C2×C4×C53—82no—
351C2×C4×C53—81no—
352C2×C4×C53—81no—
353C2×C4×C53—82no—
354C2×C4×C53—161no—
355C2×C4×C53—161no—
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53#12011yescharacteristic
358C8×C53—81no—
359#12753C5311yesmaximal, characteristic, direct product factor, Sylow
360C22×C53—22no—
361C22×C53—21no—
362C22×C53—21no—
363C22×C53—21no—
364C22×C53—21no—
365C22×C53—41no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—41no—
370C22×C53—42no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—42no—
379C22×C53—41no—
380C22×C53—42no—
381C22×C53—41no—
382C22×C53—41no—
383C22×C53—41no—
384C22×C53—81no—
385C22×C53—81no—
386C22×C53—81no—
387C22×C53—82no—
388C22×C53—82no—
389C22×C53—81no—
390C22×C53—84no—
391C22×C53—81no—
392C22×C53—161no—
393C22×C53—162no—
394C22×C53#37911yescharacteristic
395C22×C53B(4,𝔽2)11yescharacteristic
396C22×C53#45811yescharacteristic
397C4×C53—21no—
398C4×C53—21no—
399C4×C53—41no—
400C4×C53—41no—
401C4×C53—41no—
402C4×C53—41no—
403C4×C53—41no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53—41no—
407C4×C53—82no—
408C4×C53—161no—
409C4×C53—161no—
410#3532C2×C5311yescharacteristic
411#2127C2×C5311yescharacteristic, complemented
412#2121C2×C5311yescharacteristic, complemented
413C2×AΣL(1,𝔽16)C2×C5311yescharacteristic, complemented
414#1913C2×C5311yescharacteristic, complemented
415#1911C2×C5311yescharacteristic, complemented
416#1889C2×C5311yescharacteristic, complemented
417C2×C53—21no—
418C2×C53—21no—
419C2×C53—21no—
420C2×C53—41no—
421C2×C53—41no—
422C2×C53—41no—
423C2×C53—42no—
424C2×C53—41no—
425C2×C53—81no—
426C2×C53—81no—
427C2×C53—81no—
428C2×C53#179011yescharacteristic
429H(3,𝔽4)C4×C5311yescharacteristic, complemented
430#560—21no—
431#560C4×C5311yescharacteristic, complemented
432#551—21no—
433#551C4×C5311yescharacteristic, complemented
434#546—21no—
435#546—21no—
436#546—21no—
437D42—21no—
438D42C4×C5311yescharacteristic, complemented
439#538—21no—
440#538—21no—
441#538—21no—
442#535—21no—
443#535C22×C5311yescharacteristic
444#534—21no—
445#534C22×C5311yescharacteristic
446C2×#120—21no—
447C2×#120C22×C5311yescharacteristic
448#518C22×C5311yescharacteristic, complemented
449#421—21no—
450C2×#100C22×C5311yescharacteristic, complemented
451C2×#99—21no—
452C2×#99C22×C5311yescharacteristic, complemented
453C2×#99C22×C5311yescharacteristic, complemented
454#379—21no—
455#354—21no—
456#353—21no—
457#352—21no—
458AΣL(1,𝔽16)—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461#342—21no—
462#342—21no—
463H(3,ℤ/4)—21no—
464C53#1275311yescharacteristic, direct product factor, Sylow
465C25D4×C5311yescharacteristic
466C2×#41—21no—
467C2×#41D4×C5311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C5311yescharacteristic
474C22×D4C23×C5311yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C5311yescharacteristic
478#127D4×C5311yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C5311yescharacteristic
489#124D4×C5311yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C5311yescharacteristic
499#123D4×C5311yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C5311yescharacteristic
533#120C2×C4×C5311yescharacteristic
534#120C2×C4×C5311yescharacteristic
535#120D4×C5311yescharacteristic
536#120D4×C5311yescharacteristic
537#120D4×C5311yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C5311yescharacteristic
548C2×C22⋊C4—21no—
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—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C5311yescharacteristic
559C2×C22⋊C4D4×C5311yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C5311yescharacteristic
575C24C22⋊C4×C5311yescharacteristic
576C24C22⋊C4×C5311yescharacteristic, complemented
577C24C2×D4×C5311yescharacteristic
578C24C2×D4×C5311yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C5311yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C5311yescharacteristic, complemented
615C2×D4C22×C4×C5311yescharacteristic
616C2×D4C2×D4×C5311yescharacteristic
617C2×D4C2×D4×C5311yescharacteristic
618C2×D4C2×D4×C5311yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C5311yescharacteristic, complemented
632C22×C4C2×D4×C5311yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C5311yescharacteristic
680C22⋊C4C22⋊C4×C5311yescharacteristic
681C22⋊C4C22⋊C4×C5311yescharacteristic, complemented
682C22⋊C4C22⋊C4×C5311yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C5311yescharacteristic, complemented
687C42C22⋊C4×C5311yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C5311yescharacteristic
719C23C2×C22⋊C4×C5311yescharacteristic
720C23#120×C5311yescharacteristic
721C23#120×C5311yescharacteristic
722C23#120×C5311yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C5311yescharacteristic
779C2×C4#120×C5311yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22C53×#37911yescharacteristic
816C22C53×B(4,𝔽2)11yescharacteristic
817C22C53×#45811yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C53×#179011yescharacteristic
subgroupG/H
center, socleC2×C53#1790
commutatorC2×D4C22×C4×C53
Frattini, cosocleC22×D4C23×C53
prime radicalC53×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C53 ◁ C23×C53 ◁ C22×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#2127C2semidirect
3. C53×#2121C2semidirect
4. C2×C53×AΣL(1,𝔽16)C2semidirect
5. C53×#1913C2semidirect
6. C53×#1911C2semidirect
7. C53×#1889C2semidirect
8. C53×H(3,𝔽4)C4semidirect
10. C53×#560C4semidirect
12. C53×#551C4semidirect
17. D42×C53C4semidirect
27. C53×#518C22semidirect
29. C2×#100×C53C22semidirect
31. C2×#99×C53C22semidirect
32. C2×#99×C53C22semidirect
154. C24×C53C22⋊C4semidirect
161. C2×Q8×C53C22⋊C4semidirect
192. C2×D4×C53C22⋊C4semidirect
209. C22×C4×C53C22⋊C4semidirect
259. C22⋊C4×C53C22⋊C4semidirect
260. C22⋊C4×C53C22⋊C4semidirect
264. C42×C53C22⋊C4semidirect
265. C42×C53C22⋊C4semidirect
359. #12753C53direct (N × H)
411. #2127C2×C53semidirect
412. #2121C2×C53semidirect
413. C2×AΣL(1,𝔽16)C2×C53semidirect
414. #1913C2×C53semidirect
415. #1911C2×C53semidirect
416. #1889C2×C53semidirect
429. H(3,𝔽4)C4×C53semidirect
431. #560C4×C53semidirect
433. #551C4×C53semidirect
438. D42C4×C53semidirect
448. #518C22×C53semidirect
450. C2×#100C22×C53semidirect
452. C2×#99C22×C53semidirect
453. C2×#99C22×C53semidirect
464. C53#12753direct (N × H)
576. C24C22⋊C4×C53semidirect
583. C2×Q8C22⋊C4×C53semidirect
614. C2×D4C22⋊C4×C53semidirect
631. C22×C4C22⋊C4×C53semidirect
681. C22⋊C4C22⋊C4×C53semidirect
682. C22⋊C4C22⋊C4×C53semidirect
686. C42C22⋊C4×C53semidirect
687. C42C22⋊C4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35322
C53×#21272
C53×#21212
C2×C53×AΣL(1,𝔽16)2
C53×#19132
C53×#19112
C53×#18892
#1275353