Finite Group Databasebeta

← C53×#23412 #27230924

Subgroups — C53×#23412 #27230924

Order 13568.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#575C211yesmaximal, characteristic, complemented
2C2×C53×#575C211yesmaximal, characteristic, complemented
3C53×#3449C211yesmaximal, characteristic, complemented
4C2×C53×#421C211yesmaximal, characteristic, complemented
5C53×#2896C211yesmaximal, characteristic, complemented
6C2×C53×#410C211yesmaximal, characteristic, complemented
7C53×#2009C214yesmaximal, complemented
8C53×#2008C214yesmaximal, complemented
9C2×C53×#344C211yesmaximal, characteristic, complemented
10C22×#41×C53C2211yescharacteristic
11C22×#41×C53C2211yescharacteristic
12C22×#41×C53C2211yescharacteristic
13C53×#575—22no—
14C53×#575—22no—
15C53×#575—22no—
16C53×#575—22no—
17C53×#575—22no—
18C53×#575—22no—
19C53×#575—22no—
20C53×#575C2214yes—
21C2×#137×C53—21no—
22C2×#137×C53—21no—
23C2×#137×C53—21no—
24C2×#137×C53C2212yescomplemented
25C2×AGL(1,ℤ/8)×C53—21no—
26C2×AGL(1,ℤ/8)×C53—21no—
27C2×AGL(1,ℤ/8)×C53—21no—
28C2×AGL(1,ℤ/8)×C53C2212yescomplemented
29C2×#135×C53—22no—
30C2×#135×C53—22no—
31C22×M16×C53C2211yescharacteristic
32C22×M16×C53C2211yescharacteristic
33C53×#537—22no—
34C53×#536—21no—
35C53×#536C2212yescomplemented
36C53×#535—21no—
37C53×#535C2212yescomplemented
38C53×#534—22no—
39C53×#532—22no—
40C53×#525—22no—
41C53×#525—22no—
42C2×#117×C53C2211yescharacteristic
43C2×#117×C53C2211yescharacteristic
44C53×#421—22no—
45C53×#421C2214yescomplemented
46C2×#104×C53—22no—
47C53×#419C2212yescomplemented
48C53×#418C2212yescomplemented
49C53×#417—22no—
50C53×#416—22no—
51C53×#410—22no—
52C53×#410C2214yescomplemented
53C2×#99×C53—22no—
54C53×#344C2214yescomplemented
55C2×#41×C53—21no—
56C2×#41×C53—21no—
57C2×#41×C53—21no—
58C2×#41×C53—21no—
59C2×#41×C53—21no—
60C2×#41×C53—21no—
61C2×#41×C53—21no—
62C2×#41×C53—21no—
63C2×#41×C53—21no—
64C2×#41×C53—21no—
65C2×#41×C53—21no—
66C2×#41×C53—21no—
67C2×#41×C53—21no—
68C2×#41×C53—21no—
69C2×#41×C53—21no—
70C2×#41×C53—21no—
71C2×#41×C53—21no—
72C2×#41×C53—21no—
73C2×#41×C53—21no—
74C2×#41×C53—21no—
75C2×#41×C53—21no—
76C2×#41×C53—21no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—21no—
82C2×#41×C53—21no—
83C2×#41×C53—21no—
84C2×#41×C53—21no—
85C2×#41×C53D412yes—
86C2×#41×C53D412yes—
87C2×#41×C53D412yes—
88C2×#41×C53D412yescomplemented
89C2×#41×C53C2312yes—
90C2×#41×C53C2312yes—
91C22×Q8×C53D411yescharacteristic
92C22×Q8×C53D411yescharacteristic, complemented
93C22×Q8×C53C2311yescharacteristic
94C22×D4×C53—21no—
95C22×D4×C53—21no—
96C22×D4×C53—21no—
97C22×D4×C53D411yescharacteristic
98C22×D4×C53D411yescharacteristic, complemented
99C22×D4×C53C2311yescharacteristic
100C23×C4×C53—21no—
101C23×C4×C53—21no—
102C23×C4×C53—21no—
103C23×C4×C53C2311yescharacteristic
104#137×C53—24no—
105#137×C53—24no—
106#137×C53—24no—
107#137×C53—24no—
108#137×C53—24no—
109#137×C53—24no—
110#137×C53—24no—
111#137×C53—24no—
112AGL(1,ℤ/8)×C53—24no—
113AGL(1,ℤ/8)×C53—24no—
114AGL(1,ℤ/8)×C53—24no—
115AGL(1,ℤ/8)×C53—24no—
116AGL(1,ℤ/8)×C53—24no—
117AGL(1,ℤ/8)×C53—24no—
118AGL(1,ℤ/8)×C53—24no—
119AGL(1,ℤ/8)×C53—24no—
120#135×C53—28no—
121#135×C53—28no—
122#135×C53—28no—
123#135×C53—28no—
124C2×Q16×C53—22no—
125C2×Q16×C53—22no—
126C2×SD16×C53—22no—
127C2×SD16×C53—22no—
128C2×SD16×C53—22no—
129C2×SD16×C53—22no—
130C2×D8×C53—22no—
131C2×D8×C53—22no—
132C2×M16×C53—21no—
133C2×M16×C53—21no—
134C2×M16×C53—21no—
135C2×M16×C53—21no—
136C2×M16×C53—21no—
137C2×M16×C53—21no—
138C2×M16×C53—21no—
139C2×M16×C53D412yescomplemented
140C2×M16×C53D412yescomplemented
141C2×M16×C53D412yescomplemented
142C2×M16×C53C2312yes—
143C2×M16×C53C2312yes—
144C22×C8×C53—21no—
145C22×C8×C53D412yescomplemented
146C4⋊Q8×C53—22no—
147#127×C53—22no—
148#124×C53—22no—
149#124×C53—22no—
150#123×C53—24no—
151#123×C53—24no—
152C22⋊Q8×C53—24no—
153C22⋊Q8×C53—24no—
154#121×C53—24no—
155#121×C53—28no—
156#121×C53—24no—
157#120×C53—24no—
158#120×C53—24no—
159C4×D4×C53—28no—
160#117×C53—21no—
161#117×C53—21no—
162#117×C53—21no—
163#117×C53—21no—
164#117×C53—21no—
165#117×C53D412yes—
166#117×C53C2312yes—
167#117×C53C2312yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53D412yes—
172C2×C42×C53—21no—
173C2×C42×C53—21no—
174#104×C53—28no—
175#103×C53—24no—
176#102×C53—24no—
177#99×C53—28no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53C2×D411yescharacteristic
182#41×C53—22no—
183#41×C53—22no—
184#41×C53—22no—
185#41×C53—22no—
186#41×C53—22no—
187#41×C53—22no—
188#41×C53—22no—
189#41×C53—22no—
190#41×C53—22no—
191#41×C53—22no—
192#41×C53—22no—
193#41×C53—22no—
194#41×C53—22no—
195#41×C53—22no—
196#41×C53—22no—
197#41×C53—22no—
198#41×C53—22no—
199#41×C53—22no—
200#41×C53—22no—
201#41×C53—22no—
202#41×C53—22no—
203#41×C53—22no—
204#41×C53—22no—
205#41×C53—22no—
206#41×C53—41no—
207#41×C53—41no—
208#41×C53—41no—
209#41×C53—41no—
210#41×C53—41no—
211#41×C53—41no—
212#41×C53—41no—
213#41×C53—41no—
214#41×C53—41no—
215#41×C53—41no—
216#41×C53—41no—
217#41×C53—41no—
218#41×C53—41no—
219#41×C53—41no—
220#41×C53—41no—
221#41×C53—41no—
222#41×C53—41no—
223#41×C53—41no—
224#41×C53—41no—
225#41×C53—41no—
226#41×C53—41no—
227#41×C53—41no—
228#41×C53—41no—
229#41×C53—41no—
230C2×Q8×C53—21no—
231C2×Q8×C53—21no—
232C2×Q8×C53—21no—
233C2×Q8×C53—21no—
234C2×Q8×C53—21no—
235C2×Q8×C53—21no—
236C2×Q8×C53—21no—
237C2×Q8×C53—21no—
238C2×Q8×C53—21no—
239C2×Q8×C53—21no—
240C2×Q8×C53—21no—
241C2×Q8×C53—21no—
242C2×Q8×C53—21no—
243C2×Q8×C53—21no—
244C2×Q8×C53—21no—
245C2×Q8×C53C2×D412yes—
246C2×Q8×C53C2×D412yes—
247C2×Q8×C53C2×D412yes—
248C2×D4×C53—22no—
249C2×D4×C53—22no—
250C2×D4×C53—22no—
251C2×D4×C53—22no—
252C2×D4×C53—22no—
253C2×D4×C53—22no—
254C2×D4×C53—28no—
255C2×D4×C53—21no—
256C2×D4×C53—21no—
257C2×D4×C53—21no—
258C2×D4×C53—21no—
259C2×D4×C53—21no—
260C2×D4×C53—21no—
261C2×D4×C53—21no—
262C2×D4×C53—21no—
263C2×D4×C53—21no—
264C2×D4×C53—21no—
265C2×D4×C53—21no—
266C2×D4×C53—21no—
267C2×D4×C53—21no—
268C2×D4×C53—21no—
269C2×D4×C53—21no—
270C2×D4×C53—41no—
271C2×D4×C53—41no—
272C2×D4×C53—41no—
273C2×D4×C53—41no—
274C2×D4×C53—41no—
275C2×D4×C53—41no—
276C2×D4×C53—41no—
277C2×D4×C53—41no—
278C2×D4×C53—41no—
279C2×D4×C53—41no—
280C2×D4×C53—41no—
281C2×D4×C53—41no—
282C2×D4×C53C2×D412yes—
283C2×D4×C53C2×D412yes—
284C2×D4×C53C2×D412yes—
285C22×C4×C53—21no—
286C22×C4×C53—21no—
287C22×C4×C53—21no—
288C22×C4×C53—22no—
289C22×C4×C53—22no—
290C22×C4×C53—22no—
291C22×C4×C53—22no—
292C22×C4×C53—22no—
293C22×C4×C53—22no—
294C22×C4×C53—22no—
295C22×C4×C53—41no—
296C22×C4×C53—41no—
297C22×C4×C53—41no—
298C22×C4×C53—41no—
299C22×C4×C53—41no—
300C22×C4×C53—41no—
301C22×C4×C53—41no—
302C22×C4×C53—41no—
303C22×C4×C53—41no—
304C22×C4×C53—41no—
305C22×C4×C53—41no—
306C22×C4×C53—41no—
307C22×C4×C53—41no—
308C22×C4×C53C2×D411yescharacteristic
309C22×C4×C53C2×D411yescharacteristic
310C22×C4×C53C2×D411yescharacteristic
311C22×C4×C53C2×D411yescharacteristic
312C22×C4×C53C2×D411yescharacteristic
313C22×C4×C53C2×D411yescharacteristic
314C22×C4×C53C2×D411yescharacteristic
315C22×C4×C53C2×D411yescharacteristic
316C22×C4×C53C2×D411yescharacteristic
317C22×C4×C53C2×D411yescharacteristic
318C22×C4×C53C2×D411yescharacteristic
319C22×C4×C53#4111yescharacteristic
320C22×C4×C53#4111yescharacteristic
321C22×C4×C53C2411yescharacteristic
322Q16×C53—28no—
323Q16×C53—28no—
324SD16×C53—28no—
325SD16×C53—28no—
326SD16×C53—28no—
327SD16×C53—28no—
328D8×C53—28no—
329D8×C53—28no—
330M16×C53—22no—
331M16×C53—22no—
332M16×C53—22no—
333M16×C53—22no—
334M16×C53—22no—
335M16×C53—22no—
336M16×C53—22no—
337M16×C53C2×D414yes—
338C2×C8×C53—22no—
339C2×C8×C53—22no—
340C2×C8×C53—22no—
341C2×C8×C53—22no—
342C2×C8×C53—22no—
343C2×C8×C53C2×D414yes—
344C4⋊C4×C53—28no—
345C4⋊C4×C53—22no—
346C4⋊C4×C53—22no—
347C4⋊C4×C53—22no—
348C4⋊C4×C53—41no—
349C22⋊C4×C53—28no—
350C22⋊C4×C53—28no—
351C22⋊C4×C53—22no—
352C22⋊C4×C53—22no—
353C22⋊C4×C53—41no—
354C22⋊C4×C53C2×D414yes—
355C42×C53—22no—
356C42×C53—22no—
357C42×C53—22no—
358C42×C53—41no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—81no—
369C23×C53—82no—
370C23×C53—82no—
371C23×C53—82no—
372C23×C53#12011yescharacteristic
373C23×C53#12011yescharacteristic
374C23×C53#12111yescharacteristic
375C23×C53#12111yescharacteristic
376C23×C53#12711yescharacteristic
377C23×C53#12711yescharacteristic
378C23×C53C22×D411yescharacteristic
379Q8×C53—22no—
380Q8×C53—22no—
381Q8×C53—22no—
382Q8×C53—22no—
383Q8×C53—22no—
384Q8×C53—22no—
385Q8×C53—41no—
386Q8×C53—41no—
387Q8×C53—41no—
388Q8×C53—41no—
389Q8×C53—41no—
390Q8×C53—41no—
391D4×C53—22no—
392D4×C53—22no—
393D4×C53—22no—
394D4×C53—22no—
395D4×C53—22no—
396D4×C53—22no—
397D4×C53—42no—
398D4×C53—42no—
399D4×C53—42no—
400D4×C53—42no—
401D4×C53—42no—
402D4×C53—42no—
403D4×C53—42no—
404D4×C53—42no—
405D4×C53—42no—
406D4×C53—42no—
407D4×C53—42no—
408D4×C53—42no—
409D4×C53—41no—
410D4×C53—41no—
411D4×C53—41no—
412D4×C53—41no—
413D4×C53—41no—
414D4×C53—41no—
415D4×C53—88no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—24no—
419C2×C4×C53—22no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—42no—
427C2×C4×C53—42no—
428C2×C4×C53—42no—
429C2×C4×C53—42no—
430C2×C4×C53—42no—
431C2×C4×C53—42no—
432C2×C4×C53—42no—
433C2×C4×C53—42no—
434C2×C4×C53—42no—
435C2×C4×C53—42no—
436C2×C4×C53—42no—
437C2×C4×C53—42no—
438C2×C4×C53—42no—
439C2×C4×C53—82no—
440C2×C4×C53—82no—
441C2×C4×C53#12011yescharacteristic
442C2×C4×C53#12011yescharacteristic
443C2×C4×C53#12011yescharacteristic
444C2×C4×C53#12011yescharacteristic
445C2×C4×C53#12011yescharacteristic
446C2×C4×C53#12011yescharacteristic
447C2×C4×C53#12011yescharacteristic
448C2×C4×C53#12011yescharacteristic
449C2×C4×C53#12011yescharacteristic
450C2×C4×C53#12011yescharacteristic
451C2×C4×C53#12111yescharacteristic
452C2×C4×C53#12111yescharacteristic
453C2×C4×C53#12111yescharacteristic
454C2×C4×C53#12111yescharacteristic
455C2×C4×C53#12111yescharacteristic
456C2×C4×C53#12111yescharacteristic
457C2×C4×C53#12111yescharacteristic
458C2×C4×C53#12111yescharacteristic
459C2×C4×C53#12111yescharacteristic
460C2×C4×C53#12111yescharacteristic
461C2×C4×C53#12711yescharacteristic
462C2×C4×C53#12711yescharacteristic
463C2×C4×C53C22×D411yescharacteristic
464C2×C4×C53C22×D411yescharacteristic
465C2×C4×C53C22×D411yescharacteristic
466C2×C4×C53C22×D411yescharacteristic
467C2×C4×C53C22×D411yescharacteristic
468C2×C4×C53C2×#4111yescharacteristic
469C8×C53—24no—
470C8×C53—24no—
471#23412C5311yesmaximal, characteristic, direct product factor, Sylow
472C22×C53—41no—
473C22×C53—41no—
474C22×C53—41no—
475C22×C53—41no—
476C22×C53—41no—
477C22×C53—41no—
478C22×C53—41no—
479C22×C53—44no—
480C22×C53—44no—
481C22×C53—42no—
482C22×C53—42no—
483C22×C53—42no—
484C22×C53—82no—
485C22×C53—82no—
486C22×C53—82no—
487C22×C53—82no—
488C22×C53—82no—
489C22×C53—82no—
490C22×C53—82no—
491C22×C53#39211yescharacteristic
492C22×C53#39211yescharacteristic
493C22×C53#39211yescharacteristic
494C22×C53#39211yescharacteristic
495C22×C53C2×#12011yescharacteristic
496C22×C53C2×#12111yescharacteristic
497C22×C53C2×#12711yescharacteristic
498C4×C53—44no—
499C4×C53—42no—
500C4×C53—42no—
501C4×C53—42no—
502C4×C53—82no—
503C4×C53#39211yescharacteristic
504C4×C53#39211yescharacteristic
505C4×C53#39211yescharacteristic
506C4×C53#39211yescharacteristic
507C4×C53C2×#12011yescharacteristic
508C4×C53C2×#12011yescharacteristic
509C4×C53C2×#12111yescharacteristic
510C4×C53C2×#12111yescharacteristic
511C2×#575C2×C5311yescharacteristic, complemented
512C2×#575C2×C5311yescharacteristic, complemented
513#3449C2×C5311yescharacteristic, complemented
514C2×#421C2×C5311yescharacteristic, complemented
515#2896C2×C5311yescharacteristic, complemented
516C2×#410C2×C5311yescharacteristic, complemented
517#2009C2×C5314yescomplemented
518#2008C2×C5314yescomplemented
519C2×#344C2×C5311yescharacteristic, complemented
520C2×C53—21no—
521C2×C53—21no—
522C2×C53—21no—
523C2×C53—21no—
524C2×C53—21no—
525C2×C53—21no—
526C2×C53—21no—
527C2×C53—82no—
528C2×C53—82no—
529C2×C53—82no—
530C2×C53C2×#39211yescharacteristic
531C22×#41C22×C5311yescharacteristic
532C22×#41C22×C5311yescharacteristic
533C22×#41C22×C5311yescharacteristic
534#575—22no—
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575C22×C5314yes—
542C2×#137—21no—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137C22×C5312yescomplemented
546C2×AGL(1,ℤ/8)—21no—
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)C22×C5312yescomplemented
550C2×#135—22no—
551C2×#135—22no—
552C22×M16C22×C5311yescharacteristic
553C22×M16C22×C5311yescharacteristic
554#537—22no—
555#536—21no—
556#536C22×C5312yescomplemented
557#535—21no—
558#535C22×C5312yescomplemented
559#534—22no—
560#532—22no—
561#525—22no—
562#525—22no—
563C2×#117C22×C5311yescharacteristic
564C2×#117C22×C5311yescharacteristic
565#421—22no—
566#421C22×C5314yescomplemented
567C2×#104—22no—
568#419C22×C5312yescomplemented
569#418C22×C5312yescomplemented
570#417—22no—
571#416—22no—
572#410—22no—
573#410C22×C5314yescomplemented
574C2×#99—22no—
575#344C22×C5314yescomplemented
576C53#2341211yescharacteristic, direct product factor, Sylow
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C5312yes—
608C2×#41D4×C5312yes—
609C2×#41D4×C5312yes—
610C2×#41D4×C5312yescomplemented
611C2×#41C23×C5312yes—
612C2×#41C23×C5312yes—
613C22×Q8D4×C5311yescharacteristic
614C22×Q8D4×C5311yescharacteristic, complemented
615C22×Q8C23×C5311yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C5311yescharacteristic
620C22×D4D4×C5311yescharacteristic, complemented
621C22×D4C23×C5311yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C5311yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C5312yescomplemented
662C2×M16D4×C5312yescomplemented
663C2×M16D4×C5312yescomplemented
664C2×M16C23×C5312yes—
665C2×M16C23×C5312yes—
666C22×C8—21no—
667C22×C8D4×C5312yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C5312yes—
688#117C23×C5312yes—
689#117C23×C5312yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C5312yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C5311yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C5312yes—
768C2×Q8C2×D4×C5312yes—
769C2×Q8C2×D4×C5312yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C5312yes—
805C2×D4C2×D4×C5312yes—
806C2×D4C2×D4×C5312yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C5311yescharacteristic
831C22×C4C2×D4×C5311yescharacteristic
832C22×C4C2×D4×C5311yescharacteristic
833C22×C4C2×D4×C5311yescharacteristic
834C22×C4C2×D4×C5311yescharacteristic
835C22×C4C2×D4×C5311yescharacteristic
836C22×C4C2×D4×C5311yescharacteristic
837C22×C4C2×D4×C5311yescharacteristic
838C22×C4C2×D4×C5311yescharacteristic
839C22×C4C2×D4×C5311yescharacteristic
840C22×C4C2×D4×C5311yescharacteristic
841C22×C4#41×C5311yescharacteristic
842C22×C4#41×C5311yescharacteristic
843C22×C4C24×C5311yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C5314yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C5314yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C5314yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C5311yescharacteristic
895C23#120×C5311yescharacteristic
896C23#121×C5311yescharacteristic
897C23#121×C5311yescharacteristic
898C23#127×C5311yescharacteristic
899C23#127×C5311yescharacteristic
900C23C22×D4×C5311yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C5311yescharacteristic
964C2×C4#120×C5311yescharacteristic
965C2×C4#120×C5311yescharacteristic
966C2×C4#120×C5311yescharacteristic
967C2×C4#120×C5311yescharacteristic
968C2×C4#120×C5311yescharacteristic
969C2×C4#120×C5311yescharacteristic
970C2×C4#120×C5311yescharacteristic
971C2×C4#120×C5311yescharacteristic
972C2×C4#120×C5311yescharacteristic
973C2×C4#121×C5311yescharacteristic
974C2×C4#121×C5311yescharacteristic
975C2×C4#121×C5311yescharacteristic
976C2×C4#121×C5311yescharacteristic
977C2×C4#121×C5311yescharacteristic
978C2×C4#121×C5311yescharacteristic
979C2×C4#121×C5311yescharacteristic
980C2×C4#121×C5311yescharacteristic
981C2×C4#121×C5311yescharacteristic
982C2×C4#121×C5311yescharacteristic
983C2×C4#127×C5311yescharacteristic
984C2×C4#127×C5311yescharacteristic
985C2×C4C22×D4×C5311yescharacteristic
986C2×C4C22×D4×C5311yescharacteristic
987C2×C4C22×D4×C5311yescharacteristic
988C2×C4C22×D4×C5311yescharacteristic
989C2×C4C22×D4×C5311yescharacteristic
990C2×C4C2×#41×C5311yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22C53×#39211yescharacteristic
1013C22C53×#39211yescharacteristic
1014C22C53×#39211yescharacteristic
1015C22C53×#39211yescharacteristic
1016C22C2×#120×C5311yescharacteristic
1017C22C2×#121×C5311yescharacteristic
1018C22C2×#127×C5311yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4C53×#39211yescharacteristic
1025C4C53×#39211yescharacteristic
1026C4C53×#39211yescharacteristic
1027C4C53×#39211yescharacteristic
1028C4C2×#120×C5311yescharacteristic
1029C4C2×#120×C5311yescharacteristic
1030C4C2×#121×C5311yescharacteristic
1031C4C2×#121×C5311yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×C53×#39211yescharacteristic
subgroupG/H
centerC4×C53#392
commutator, Frattini, cosocleC22×C4C24×C53
socleC2×C53C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#575C2semidirect
2. C2×C53×#575C2semidirect
3. C53×#3449C2semidirect
4. C2×C53×#421C2semidirect
5. C53×#2896C2semidirect
6. C2×C53×#410C2semidirect
7. C53×#2009C2semidirect
8. C53×#2008C2semidirect
9. C2×C53×#344C2semidirect
24. C2×#137×C53C22semidirect
28. C2×AGL(1,ℤ/8)×C53C22semidirect
35. C53×#536C22semidirect
37. C53×#535C22semidirect
45. C53×#421C22semidirect
47. C53×#419C22semidirect
48. C53×#418C22semidirect
52. C53×#410C22semidirect
54. C53×#344C22semidirect
88. C2×#41×C53D4semidirect
92. C22×Q8×C53D4semidirect
98. C22×D4×C53D4semidirect
139. C2×M16×C53D4semidirect
140. C2×M16×C53D4semidirect
141. C2×M16×C53D4semidirect
145. C22×C8×C53D4semidirect
471. #23412C53direct (N × H)
511. C2×#575C2×C53semidirect
512. C2×#575C2×C53semidirect
513. #3449C2×C53semidirect
514. C2×#421C2×C53semidirect
515. #2896C2×C53semidirect
516. C2×#410C2×C53semidirect
517. #2009C2×C53semidirect
518. #2008C2×C53semidirect
519. C2×#344C2×C53semidirect
545. C2×#137C22×C53semidirect
549. C2×AGL(1,ℤ/8)C22×C53semidirect
556. #536C22×C53semidirect
558. #535C22×C53semidirect
566. #421C22×C53semidirect
568. #419C22×C53semidirect
569. #418C22×C53semidirect
573. #410C22×C53semidirect
575. #344C22×C53semidirect
576. C53#23412direct (N × H)
610. C2×#41D4×C53semidirect
614. C22×Q8D4×C53semidirect
620. C22×D4D4×C53semidirect
661. C2×M16D4×C53semidirect
662. C2×M16D4×C53semidirect
663. C2×M16D4×C53semidirect
667. C22×C8D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#5752
C53×#34492
C2×C53×#4212
C53×#28962
C2×C53×#4102
C53×#20092
C53×#20082
C2×C53×#3442
#2341253