Finite Group Databasebeta

← C53×#24404 #27231916

Subgroups — C53×#24404 #27231916

Order 13568.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3484C211yesmaximal, characteristic, complemented
2C2×C53×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C53C211yesmaximal, characteristic, complemented
4C53×#2410C212yesmaximal, complemented
5C53×#2403C211yesmaximal, characteristic, complemented
6C53×#2044C212yesmaximal, complemented
7C53×#2021C212yesmaximal, complemented
8C53×#1898C212yesmaximal, complemented
9C53×#1889C211yesmaximal, characteristic, complemented
10C53×#1867C211yesmaximal, characteristic, complemented
11C53×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C53C2211yescharacteristic
13C23×D4×C53C2211yescharacteristic
14C23×D4×C53C2211yescharacteristic, complemented
15C53×#546—22no—
16C53×#546—22no—
17D42×C53—22no—
18D42×C53—22no—
19C53×#535—21no—
20C53×#534—21no—
21C53×#534C2212yes—
22C53×#525—21no—
23C2×#121×C53—22no—
24C2×#120×C53—21no—
25C2×#120×C53—21no—
26C2×#120×C53C2211yescharacteristic
27C2×#120×C53C2212yes—
28C2×#120×C53C2212yescomplemented
29C2×#120×C53C2211yescharacteristic, complemented
30C53×#518C2211yescharacteristic
31C22×C22⋊C4×C53C2212yescomplemented
32C53×B(4,𝔽2)—24no—
33C2×#99×C53—24no—
34C2×#99×C53C2211yescharacteristic
35C2×#99×C53C2211yescharacteristic
36C2×#99×C53C2212yescomplemented
37C2×#99×C53C2212yescomplemented
38C2×#99×C53C2212yescomplemented
39C53×#394—22no—
40C53×#392—21no—
41C53×#392—21no—
42C53×#392—22no—
43C53×#386—21no—
44C53×#386—22no—
45C53×#386C2211yescharacteristic
46C53×#386C2211yescharacteristic, complemented
47C53×#386C2212yescomplemented
48C53×#385C2212yescomplemented
49C53×#379C2212yescomplemented
50C53×#379C2211yescharacteristic, complemented
51C53×#342C2212yescomplemented
52C53×#342C2212yescomplemented
53C25×C53D411yescharacteristic, complemented
54C25×C53C2311yescharacteristic
55C25×C53C2311yescharacteristic
56H(5,𝔽2)×C53—22no—
57H(5,𝔽2)×C53—22no—
58H(5,𝔽2)×C53—42no—
59C2×#41×C53—21no—
60C2×#41×C53—22no—
61C22×D4×C53—21no—
62C22×D4×C53—21no—
63C22×D4×C53—22no—
64C22×D4×C53—22no—
65C22×D4×C53—22no—
66C22×D4×C53—22no—
67C22×D4×C53—21no—
68C22×D4×C53—21no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
71C22×D4×C53—21no—
72C22×D4×C53—22no—
73C22×D4×C53—21no—
74C22×D4×C53—21no—
75C22×D4×C53—22no—
76C22×D4×C53—44no—
77C22×D4×C53—42no—
78C22×D4×C53D411yescharacteristic, complemented
79C22×D4×C53D411yescharacteristic, complemented
80C22×D4×C53D412yescomplemented
81C22×D4×C53D412yescomplemented
82C22×D4×C53C2312yes—
83C22×D4×C53C2311yescharacteristic
84C22×D4×C53C2311yescharacteristic
85C23×C4×C53—22no—
86C23×C4×C53D411yescharacteristic, complemented
87C23×C4×C53C2311yescharacteristic
88#127×C53—22no—
89#124×C53—22no—
90#123×C53—22no—
91#123×C53—22no—
92#123×C53—22no—
93C22⋊Q8×C53—21no—
94C22⋊Q8×C53—21no—
95#121×C53—21no—
96#121×C53—21no—
97#121×C53—22no—
98#121×C53—22no—
99#121×C53—22no—
100#121×C53—22no—
101#121×C53—22no—
102#121×C53—22no—
103#121×C53—48no—
104#120×C53—22no—
105#120×C53—22no—
106#120×C53—22no—
107#120×C53—22no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—22no—
111#120×C53—22no—
112#120×C53—22no—
113#120×C53—24no—
114#120×C53—22no—
115#120×C53—22no—
116#120×C53—42no—
117#120×C53—42no—
118#120×C53—44no—
119C4×D4×C53—22no—
120C4×D4×C53—22no—
121C4×D4×C53—22no—
122C4×D4×C53—22no—
123#117×C53—21no—
124C2×C4⋊C4×C53—22no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—24no—
140C2×C22⋊C4×C53—42no—
141C2×C22⋊C4×C53D412yescomplemented
142C2×C22⋊C4×C53D412yescomplemented
143C2×C22⋊C4×C53C2312yes—
144C2×C22⋊C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53C2311yescharacteristic
146C2×C22⋊C4×C53C2312yes—
147C2×C22⋊C4×C53C2312yes—
148#99×C53—24no—
149#99×C53—24no—
150#99×C53—22no—
151#99×C53—42no—
152#99×C53D414yescomplemented
153#95×C53—22no—
154#95×C53—21no—
155#95×C53—21no—
156#95×C53—22no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—22no—
160C24×C53—21no—
161C24×C53—22no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—22no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—22no—
169C24×C53—41no—
170C24×C53—42no—
171C24×C53—42no—
172C24×C53—42no—
173C24×C53—81no—
174C24×C53—81no—
175C24×C53—81no—
176C24×C53C2×D411yescharacteristic
177C24×C53C2×D412yes—
178C24×C53C2×D411yescharacteristic
179C24×C53C2×D412yes—
180C24×C53C2×D412yes—
181C24×C53C2×D411yescharacteristic
182C24×C53C2×D411yescharacteristic
183C24×C53C2411yescharacteristic
184#41×C53—44no—
185#41×C53—44no—
186#41×C53—42no—
187#41×C53—42no—
188C2×Q8×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—24no—
193C2×D4×C53—21no—
194C2×D4×C53—28no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53—21no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—22no—
212C2×D4×C53—22no—
213C2×D4×C53—22no—
214C2×D4×C53—22no—
215C2×D4×C53—41no—
216C2×D4×C53—41no—
217C2×D4×C53—42no—
218C2×D4×C53—44no—
219C2×D4×C53—44no—
220C2×D4×C53—44no—
221C2×D4×C53—44no—
222C2×D4×C53—44no—
223C2×D4×C53—44no—
224C2×D4×C53—44no—
225C2×D4×C53—44no—
226C2×D4×C53—42no—
227C2×D4×C53—44no—
228C2×D4×C53—44no—
229C2×D4×C53—42no—
230C2×D4×C53—42no—
231C2×D4×C53—41no—
232C2×D4×C53—42no—
233C2×D4×C53—41no—
234C2×D4×C53—42no—
235C2×D4×C53—44no—
236C2×D4×C53—42no—
237C2×D4×C53—42no—
238C2×D4×C53—42no—
239C2×D4×C53—44no—
240C2×D4×C53—42no—
241C2×D4×C53—82no—
242C2×D4×C53—82no—
243C2×D4×C53—81no—
244C2×D4×C53—81no—
245C2×D4×C53—82no—
246C2×D4×C53—82no—
247C2×D4×C53C2×D412yes—
248C2×D4×C53#4112yes—
249C22×C4×C53—21no—
250C22×C4×C53—22no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—22no—
255C22×C4×C53—22no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—22no—
259C22×C4×C53—22no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—42no—
263C22×C4×C53—41no—
264C22×C4×C53—44no—
265C22×C4×C53—44no—
266C22×C4×C53—82no—
267C22×C4×C53C2×D412yes—
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D412yes—
271C22×C4×C53C2×D412yes—
272C4⋊C4×C53—21no—
273C4⋊C4×C53—21no—
274C4⋊C4×C53—22no—
275C4⋊C4×C53—22no—
276C4⋊C4×C53—44no—
277C22⋊C4×C53—22no—
278C22⋊C4×C53—22no—
279C22⋊C4×C53—22no—
280C22⋊C4×C53—22no—
281C22⋊C4×C53—22no—
282C22⋊C4×C53—22no—
283C22⋊C4×C53—22no—
284C22⋊C4×C53—22no—
285C22⋊C4×C53—22no—
286C22⋊C4×C53—22no—
287C22⋊C4×C53—22no—
288C22⋊C4×C53—22no—
289C22⋊C4×C53—22no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53—21no—
292C22⋊C4×C53—22no—
293C22⋊C4×C53—22no—
294C22⋊C4×C53—44no—
295C22⋊C4×C53—44no—
296C22⋊C4×C53—42no—
297C22⋊C4×C53—42no—
298C22⋊C4×C53—42no—
299C22⋊C4×C53—44no—
300C22⋊C4×C53—42no—
301C22⋊C4×C53—44no—
302C22⋊C4×C53—42no—
303C22⋊C4×C53—82no—
304C22⋊C4×C53—81no—
305C22⋊C4×C53C2×D414yescomplemented
306C42×C53—22no—
307C23×C53—21no—
308C23×C53—21no—
309C23×C53—21no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—24no—
313C23×C53—22no—
314C23×C53—21no—
315C23×C53—21no—
316C23×C53—21no—
317C23×C53—22no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—24no—
321C23×C53—22no—
322C23×C53—21no—
323C23×C53—21no—
324C23×C53—21no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—41no—
328C23×C53—42no—
329C23×C53—41no—
330C23×C53—41no—
331C23×C53—42no—
332C23×C53—41no—
333C23×C53—42no—
334C23×C53—41no—
335C23×C53—42no—
336C23×C53—42no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—42no—
342C23×C53—41no—
343C23×C53—42no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—42no—
347C23×C53—42no—
348C23×C53—42no—
349C23×C53—42no—
350C23×C53—42no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—42no—
355C23×C53—42no—
356C23×C53—42no—
357C23×C53—81no—
358C23×C53—81no—
359C23×C53—82no—
360C23×C53—82no—
361C23×C53—82no—
362C23×C53—82no—
363C23×C53—84no—
364C23×C53—84no—
365C23×C53—81no—
366C23×C53—81no—
367C23×C53—84no—
368C23×C53—84no—
369C23×C53#12011yescharacteristic
370C23×C53#12012yes—
371C23×C53#12011yescharacteristic
372C23×C53#12112yescomplemented
373C23×C53C22×D411yescharacteristic
374C23×C53C22×D412yes—
375C23×C53C22×D411yescharacteristic
376C23×C53C2×#4111yescharacteristic
377C23×C53H(5,𝔽2)12yes—
378Q8×C53—42no—
379D4×C53—24no—
380D4×C53—24no—
381D4×C53—44no—
382D4×C53—42no—
383D4×C53—44no—
384D4×C53—48no—
385D4×C53—44no—
386D4×C53—44no—
387D4×C53—44no—
388D4×C53—42no—
389D4×C53—42no—
390D4×C53—42no—
391D4×C53—42no—
392D4×C53—42no—
393D4×C53—42no—
394D4×C53—44no—
395D4×C53—44no—
396D4×C53—82no—
397D4×C53—82no—
398D4×C53—82no—
399D4×C53—82no—
400D4×C53—88no—
401D4×C53—84no—
402D4×C53—84no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—22no—
406C2×C4×C53—24no—
407C2×C4×C53—21no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—21no—
412C2×C4×C53—21no—
413C2×C4×C53—24no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—42no—
417C2×C4×C53—42no—
418C2×C4×C53—44no—
419C2×C4×C53—42no—
420C2×C4×C53—41no—
421C2×C4×C53—42no—
422C2×C4×C53—42no—
423C2×C4×C53—42no—
424C2×C4×C53—41no—
425C2×C4×C53—42no—
426C2×C4×C53—42no—
427C2×C4×C53—42no—
428C2×C4×C53—42no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—42no—
436C2×C4×C53—81no—
437C2×C4×C53—81no—
438C2×C4×C53—88no—
439C2×C4×C53#12112yescomplemented
440#24404C5311yesmaximal, characteristic, direct product factor, Sylow
441C22×C53—21no—
442C22×C53—22no—
443C22×C53—21no—
444C22×C53—22no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—22no—
449C22×C53—22no—
450C22×C53—22no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—22no—
454C22×C53—41no—
455C22×C53—41no—
456C22×C53—42no—
457C22×C53—44no—
458C22×C53—44no—
459C22×C53—42no—
460C22×C53—42no—
461C22×C53—42no—
462C22×C53—44no—
463C22×C53—42no—
464C22×C53—42no—
465C22×C53—42no—
466C22×C53—44no—
467C22×C53—41no—
468C22×C53—41no—
469C22×C53—42no—
470C22×C53—41no—
471C22×C53—42no—
472C22×C53—42no—
473C22×C53—41no—
474C22×C53—42no—
475C22×C53—41no—
476C22×C53—82no—
477C22×C53—81no—
478C22×C53—81no—
479C22×C53—81no—
480C22×C53—82no—
481C22×C53—84no—
482C22×C53—82no—
483C22×C53—82no—
484C22×C53—81no—
485C22×C53—82no—
486C22×C53—81no—
487C22×C53—81no—
488C22×C53—82no—
489C22×C53—84no—
490C22×C53—81no—
491C22×C53—81no—
492C22×C53—162no—
493C22×C53B(4,𝔽2)12yescomplemented
494C22×C53C2×#12011yescharacteristic
495C22×C53C2×#12111yescharacteristic
496C22×C53#53411yescharacteristic
497C22×C53D4212yes—
498C22×C53#54612yes—
499C4×C53—22no—
500C4×C53—44no—
501C4×C53—41no—
502C4×C53—42no—
503C4×C53—42no—
504C4×C53—42no—
505C4×C53—42no—
506C4×C53—82no—
507C4×C53—81no—
508C4×C53—81no—
509#3484C2×C5311yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C5311yescharacteristic, complemented
511C22×#99C2×C5311yescharacteristic, complemented
512#2410C2×C5312yescomplemented
513#2403C2×C5311yescharacteristic, complemented
514#2044C2×C5312yescomplemented
515#2021C2×C5312yescomplemented
516#1898C2×C5312yescomplemented
517#1889C2×C5311yescharacteristic, complemented
518#1867C2×C5311yescharacteristic, complemented
519#1790C2×C5311yescharacteristic, complemented
520C2×C53—22no—
521C2×C53—21no—
522C2×C53—21no—
523C2×C53—22no—
524C2×C53—22no—
525C2×C53—42no—
526C2×C53—41no—
527C2×C53—42no—
528C2×C53—82no—
529C2×C53—81no—
530C2×C53—82no—
531C2×C53#241011yescharacteristic
532C2×C53C2×B(4,𝔽2)11yescharacteristic
533C2×C53#302611yescharacteristic
534C2×H(5,𝔽2)C22×C5311yescharacteristic
535C23×D4C22×C5311yescharacteristic
536C23×D4C22×C5311yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C5312yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C5311yescharacteristic
549C2×#120C22×C5312yes—
550C2×#120C22×C5312yescomplemented
551C2×#120C22×C5311yescharacteristic, complemented
552#518C22×C5311yescharacteristic
553C22×C22⋊C4C22×C5312yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C5311yescharacteristic
557C2×#99C22×C5311yescharacteristic
558C2×#99C22×C5312yescomplemented
559C2×#99C22×C5312yescomplemented
560C2×#99C22×C5312yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C5311yescharacteristic
568#386C22×C5311yescharacteristic, complemented
569#386C22×C5312yescomplemented
570#385C22×C5312yescomplemented
571#379C22×C5312yescomplemented
572#379C22×C5311yescharacteristic, complemented
573#342C22×C5312yescomplemented
574#342C22×C5312yescomplemented
575C53#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C5311yescharacteristic, complemented
577C25C23×C5311yescharacteristic
578C25C23×C5311yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C5311yescharacteristic, complemented
602C22×D4D4×C5311yescharacteristic, complemented
603C22×D4D4×C5312yescomplemented
604C22×D4D4×C5312yescomplemented
605C22×D4C23×C5312yes—
606C22×D4C23×C5311yescharacteristic
607C22×D4C23×C5311yescharacteristic
608C23×C4—22no—
609C23×C4D4×C5311yescharacteristic, complemented
610C23×C4C23×C5311yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C5312yescomplemented
665C2×C22⋊C4D4×C5312yescomplemented
666C2×C22⋊C4C23×C5312yes—
667C2×C22⋊C4C23×C5311yescharacteristic
668C2×C22⋊C4C23×C5311yescharacteristic
669C2×C22⋊C4C23×C5312yes—
670C2×C22⋊C4C23×C5312yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C5314yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C5311yescharacteristic
700C24C2×D4×C5312yes—
701C24C2×D4×C5311yescharacteristic
702C24C2×D4×C5312yes—
703C24C2×D4×C5312yes—
704C24C2×D4×C5311yescharacteristic
705C24C2×D4×C5311yescharacteristic
706C24C24×C5311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C5312yes—
771C2×D4#41×C5312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C5312yes—
791C22×C4C2×D4×C5311yescharacteristic
792C22×C4C2×D4×C5311yescharacteristic
793C22×C4C2×D4×C5312yes—
794C22×C4C2×D4×C5312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C5314yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C5311yescharacteristic
893C23#120×C5312yes—
894C23#120×C5311yescharacteristic
895C23#121×C5312yescomplemented
896C23C22×D4×C5311yescharacteristic
897C23C22×D4×C5312yes—
898C23C22×D4×C5311yescharacteristic
899C23C2×#41×C5311yescharacteristic
900C23H(5,𝔽2)×C5312yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C5312yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C53×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C5311yescharacteristic
1017C22C2×#121×C5311yescharacteristic
1018C22C53×#53411yescharacteristic
1019C22D42×C5312yes—
1020C22C53×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C53×#241011yescharacteristic
1043C2C2×C53×B(4,𝔽2)11yescharacteristic
1044C2C53×#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×#3484C2semidirect
2. C2×C53×B(4,𝔽2)C2semidirect
3. C22×#99×C53C2semidirect
4. C53×#2410C2semidirect
5. C53×#2403C2semidirect
6. C53×#2044C2semidirect
7. C53×#2021C2semidirect
8. C53×#1898C2semidirect
9. C53×#1889C2semidirect
10. C53×#1867C2semidirect
11. C53×#1790C2semidirect
14. C23×D4×C53C22semidirect
28. C2×#120×C53C22semidirect
29. C2×#120×C53C22semidirect
31. C22×C22⋊C4×C53C22semidirect
36. C2×#99×C53C22semidirect
37. C2×#99×C53C22semidirect
38. C2×#99×C53C22semidirect
46. C53×#386C22semidirect
47. C53×#386C22semidirect
48. C53×#385C22semidirect
49. C53×#379C22semidirect
50. C53×#379C22semidirect
51. C53×#342C22semidirect
52. C53×#342C22semidirect
53. C25×C53D4semidirect
78. C22×D4×C53D4semidirect
79. C22×D4×C53D4semidirect
80. C22×D4×C53D4semidirect
81. C22×D4×C53D4semidirect
86. C23×C4×C53D4semidirect
141. C2×C22⋊C4×C53D4semidirect
142. C2×C22⋊C4×C53D4semidirect
152. #99×C53D4semidirect
305. C22⋊C4×C53C2×D4semidirect
372. C23×C53#121semidirect
439. C2×C4×C53#121semidirect
440. #24404C53direct (N × H)
493. C22×C53B(4,𝔽2)semidirect
509. #3484C2×C53semidirect
510. C2×B(4,𝔽2)C2×C53semidirect
511. C22×#99C2×C53semidirect
512. #2410C2×C53semidirect
513. #2403C2×C53semidirect
514. #2044C2×C53semidirect
515. #2021C2×C53semidirect
516. #1898C2×C53semidirect
517. #1889C2×C53semidirect
518. #1867C2×C53semidirect
519. #1790C2×C53semidirect
536. C23×D4C22×C53semidirect
550. C2×#120C22×C53semidirect
551. C2×#120C22×C53semidirect
553. C22×C22⋊C4C22×C53semidirect
558. C2×#99C22×C53semidirect
559. C2×#99C22×C53semidirect
560. C2×#99C22×C53semidirect
568. #386C22×C53semidirect
569. #386C22×C53semidirect
570. #385C22×C53semidirect
571. #379C22×C53semidirect
572. #379C22×C53semidirect
573. #342C22×C53semidirect
574. #342C22×C53semidirect
575. C53#24404direct (N × H)
576. C25D4×C53semidirect
601. C22×D4D4×C53semidirect
602. C22×D4D4×C53semidirect
603. C22×D4D4×C53semidirect
604. C22×D4D4×C53semidirect
609. C23×C4D4×C53semidirect
664. C2×C22⋊C4D4×C53semidirect
665. C2×C22⋊C4D4×C53semidirect
675. #99D4×C53semidirect
828. C22⋊C4C2×D4×C53semidirect
895. C23#121×C53semidirect
962. C2×C4#121×C53semidirect
1015. C22C53×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C53×#34842
C2×C53×B(4,𝔽2)2
C22×#99×C532
C53×#24102
C53×#24032
C53×#20442
C53×#20212
C53×#18982
C53×#18892
C53×#18672
C53×#17902
#2440453