Finite Group Databasebeta

← C53×#23894 #27231406

Subgroups — C53×#23894 #27231406

Order 13568.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3586C211yesmaximal, characteristic, complemented
2C53×#3585C211yesmaximal, characteristic, complemented
3C53×#3020C211yesmaximal, characteristic, complemented
4C53×#3019C211yesmaximal, characteristic, complemented
5C53×#3010C211yesmaximal, characteristic, complemented
6C53×#3009C211yesmaximal, characteristic, complemented
7C53×#2019C211yesmaximal, characteristic, complemented
8C53×#2017C211yesmaximal, characteristic, complemented
9C53×#2009C211yesmaximal, characteristic, complemented
10C53×#2008C211yesmaximal, characteristic, complemented
11C53×#1903C211yesmaximal, characteristic, complemented
12C53×#1902C211yesmaximal, characteristic, complemented
13C53×#1881C211yesmaximal, characteristic, complemented
14C53×#1881C211yesmaximal, characteristic, complemented
15C53×#1794C211yesmaximal, characteristic, complemented
16C53×#585C2211yescharacteristic
17C2×2−1+4×C53C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C53C2211yescharacteristic
19C53×#578—22no—
20C53×#578—22no—
21C53×#577—22no—
22C53×#577—22no—
23C53×#577—22no—
24C53×#577—22no—
25C53×#576—22no—
26C53×#576—22no—
27C53×#575—22no—
28C53×#575—22no—
29C53×#575C2211yescharacteristic
30C53×#575C2211yescharacteristic
31C53×#575C2211yescharacteristic
32C53×#575C2211yescharacteristic, complemented
33C53×#575C2211yescharacteristic, complemented
34C2×#137×C53—22no—
35C2×#137×C53C2211yescharacteristic
36C2×#137×C53C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C53—22no—
38C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
40C22×SD16×C53C2211yescharacteristic, complemented
41C53×#568C2211yescharacteristic
42C53×#568C2211yescharacteristic, complemented
43C53×#536C2211yescharacteristic, complemented
44C53×#535C2211yescharacteristic, complemented
45C53×#456—22no—
46C53×#455—22no—
47C53×#454—22no—
48C53×#453—22no—
49C53×#452—22no—
50C53×#450—22no—
51C53×#449—22no—
52C53×#448—22no—
53C53×#421C2211yescharacteristic
54C53×#421C2211yescharacteristic, complemented
55C53×#421C2211yescharacteristic, complemented
56C53×#421C2211yescharacteristic, complemented
57C53×#419C2211yescharacteristic, complemented
58C53×#418C2211yescharacteristic, complemented
59C53×#416C2211yescharacteristic
60C53×#416C2211yescharacteristic, complemented
61C2×#101×C53C2211yescharacteristic, complemented
62C2×#100×C53C2211yescharacteristic, complemented
63C53×#410C2211yescharacteristic, complemented
64C53×#408C2211yescharacteristic, complemented
65C53×#408C2211yescharacteristic, complemented
66C53×#408C2211yescharacteristic, complemented
67C53×#344C2211yescharacteristic, complemented
68C53×#344C2211yescharacteristic, complemented
69C53×#341C2211yescharacteristic, complemented
70C53×#338C2211yescharacteristic, complemented
712−1+4×C53—22no—
722−1+4×C53—21no—
732−1+4×C53—22no—
742−1+4×C53—21no—
752−1+4×C53—22no—
762−1+4×C53—41no—
772−1+4×C53D412yescomplemented
78H(5,𝔽2)×C53—22no—
79H(5,𝔽2)×C53—21no—
80H(5,𝔽2)×C53—22no—
81H(5,𝔽2)×C53—21no—
82H(5,𝔽2)×C53—22no—
83H(5,𝔽2)×C53—41no—
84H(5,𝔽2)×C53—41no—
85H(5,𝔽2)×C53D412yescomplemented
86C2×#41×C53—22no—
87C2×#41×C53—22no—
88C2×#41×C53—21no—
89C2×#41×C53—21no—
90C2×#41×C53—21no—
91C2×#41×C53—21no—
92C2×#41×C53—41no—
93C2×#41×C53—41no—
94C2×#41×C53C2311yescharacteristic
95C2×#41×C53C2311yescharacteristic
96C2×#41×C53C2311yescharacteristic
97C2×#41×C53C2311yescharacteristic
98C2×#41×C53C2311yescharacteristic
99C22×Q8×C53—21no—
100C22×Q8×C53—21no—
101C22×Q8×C53C2311yescharacteristic
102C22×D4×C53—21no—
103C22×D4×C53—21no—
104C22×D4×C53—41no—
105C22×D4×C53C2311yescharacteristic
106#137×C53—24no—
107#137×C53—24no—
108#137×C53—24no—
109#137×C53—24no—
110#137×C53—22no—
111#137×C53—22no—
112#137×C53—22no—
113#137×C53—21no—
114#137×C53—22no—
115#137×C53—21no—
116#137×C53—21no—
117#137×C53—21no—
118#137×C53—21no—
119#137×C53—21no—
120#137×C53—21no—
121#137×C53—21no—
122#137×C53D412yes—
123#137×C53D412yescomplemented
124AGL(1,ℤ/8)×C53—24no—
125AGL(1,ℤ/8)×C53—24no—
126AGL(1,ℤ/8)×C53—24no—
127AGL(1,ℤ/8)×C53—24no—
128AGL(1,ℤ/8)×C53—22no—
129AGL(1,ℤ/8)×C53—22no—
130AGL(1,ℤ/8)×C53—22no—
131AGL(1,ℤ/8)×C53—21no—
132AGL(1,ℤ/8)×C53—22no—
133AGL(1,ℤ/8)×C53—21no—
134AGL(1,ℤ/8)×C53—21no—
135AGL(1,ℤ/8)×C53—21no—
136AGL(1,ℤ/8)×C53—21no—
137AGL(1,ℤ/8)×C53—21no—
138AGL(1,ℤ/8)×C53—21no—
139AGL(1,ℤ/8)×C53—21no—
140AGL(1,ℤ/8)×C53D412yes—
141AGL(1,ℤ/8)×C53D412yescomplemented
142#135×C53—24no—
143#135×C53—24no—
144#135×C53—24no—
145#135×C53—24no—
146#135×C53—22no—
147#135×C53—22no—
148#135×C53—22no—
149#135×C53—22no—
150#135×C53—41no—
151C2×Q16×C53—24no—
152C2×Q16×C53—21no—
153C2×Q16×C53D412yescomplemented
154C2×SD16×C53—24no—
155C2×SD16×C53—24no—
156C2×SD16×C53—21no—
157C2×SD16×C53—22no—
158C2×SD16×C53—21no—
159C2×SD16×C53—22no—
160C2×SD16×C53—41no—
161C2×SD16×C53D412yes—
162C2×SD16×C53D412yescomplemented
163C2×D8×C53—24no—
164C2×D8×C53—21no—
165C2×D8×C53D412yes—
166#131×C53—22no—
167#131×C53—22no—
168#131×C53—22no—
169#131×C53—22no—
170C2×M16×C53—22no—
171C2×M16×C53—22no—
172C2×M16×C53C2311yescharacteristic
173C2×M16×C53C2311yescharacteristic
174C2×M16×C53C2311yescharacteristic
175C2×M16×C53C2311yescharacteristic
176C2×M16×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178C4⋊Q8×C53—21no—
179#127×C53—21no—
180#124×C53—21no—
181#124×C53—21no—
182#123×C53—41no—
183C22⋊Q8×C53—22no—
184#121×C53—22no—
185#120×C53—41no—
186#117×C53C2311yescharacteristic
187#117×C53C2311yescharacteristic
188#104×C53—22no—
189#104×C53—22no—
190#104×C53—22no—
191#104×C53—22no—
192#103×C53—22no—
193#103×C53—21no—
194#103×C53—21no—
195#102×C53—22no—
196#102×C53—21no—
197#102×C53—21no—
198#101×C53—22no—
199#100×C53—22no—
200#99×C53—41no—
201C22⋊C8×C53—22no—
202C22⋊C8×C53—22no—
203C22⋊C8×C53—41no—
204C24×C53—21no—
205C24×C53—41no—
206#41×C53—21no—
207#41×C53—21no—
208#41×C53—21no—
209#41×C53—21no—
210#41×C53—24no—
211#41×C53—24no—
212#41×C53—22no—
213#41×C53—22no—
214#41×C53—22no—
215#41×C53—22no—
216#41×C53—21no—
217#41×C53—21no—
218#41×C53—21no—
219#41×C53—21no—
220#41×C53—21no—
221#41×C53—21no—
222#41×C53—21no—
223#41×C53—21no—
224#41×C53—21no—
225#41×C53—21no—
226#41×C53—21no—
227#41×C53—21no—
228#41×C53—42no—
229#41×C53—42no—
230#41×C53—42no—
231#41×C53—42no—
232#41×C53—42no—
233#41×C53—44no—
234#41×C53—42no—
235#41×C53—42no—
236#41×C53—42no—
237#41×C53—41no—
238#41×C53—41no—
239#41×C53—44no—
240#41×C53—42no—
241#41×C53—42no—
242#41×C53C2×D412yes—
243#41×C53C2×D412yes—
244#41×C53C2×D412yes—
245#41×C53C2×D412yes—
246C2×Q8×C53—21no—
247C2×Q8×C53—24no—
248C2×Q8×C53—22no—
249C2×Q8×C53—22no—
250C2×Q8×C53—21no—
251C2×Q8×C53—21no—
252C2×Q8×C53—21no—
253C2×Q8×C53—21no—
254C2×Q8×C53—41no—
255C2×Q8×C53—42no—
256C2×Q8×C53—42no—
257C2×Q8×C53—41no—
258C2×Q8×C53—42no—
259C2×Q8×C53C2×D412yes—
260C2×Q8×C53C2×D411yescharacteristic
261C2×Q8×C53C2×D411yescharacteristic
262C2×Q8×C53C2×D411yescharacteristic
263C2×Q8×C53C2×D411yescharacteristic
264C2×Q8×C53C2×D411yescharacteristic
265C2×D4×C53—21no—
266C2×D4×C53—21no—
267C2×D4×C53—24no—
268C2×D4×C53—22no—
269C2×D4×C53—22no—
270C2×D4×C53—21no—
271C2×D4×C53—21no—
272C2×D4×C53—21no—
273C2×D4×C53—21no—
274C2×D4×C53—21no—
275C2×D4×C53—21no—
276C2×D4×C53—21no—
277C2×D4×C53—21no—
278C2×D4×C53—42no—
279C2×D4×C53—41no—
280C2×D4×C53—41no—
281C2×D4×C53—42no—
282C2×D4×C53—42no—
283C2×D4×C53—41no—
284C2×D4×C53—44no—
285C2×D4×C53—42no—
286C2×D4×C53—42no—
287C2×D4×C53—44no—
288C2×D4×C53—41no—
289C2×D4×C53—42no—
290C2×D4×C53—42no—
291C2×D4×C53C2×D412yes—
292C2×D4×C53C2×D411yescharacteristic
293C2×D4×C53C2×D411yescharacteristic
294C2×D4×C53C2×D411yescharacteristic
295C2×D4×C53C2×D411yescharacteristic
296C2×D4×C53C2×D411yescharacteristic
297C22×C4×C53—21no—
298C22×C4×C53—21no—
299C22×C4×C53—21no—
300C22×C4×C53—21no—
301C22×C4×C53—21no—
302C22×C4×C53—21no—
303C22×C4×C53—41no—
304C22×C4×C53—42no—
305C22×C4×C53—41no—
306C22×C4×C53—41no—
307C22×C4×C53C2411yescharacteristic
308Q16×C53—24no—
309Q16×C53—22no—
310Q16×C53—22no—
311Q16×C53—22no—
312Q16×C53—24no—
313Q16×C53—22no—
314Q16×C53—41no—
315SD16×C53—24no—
316SD16×C53—22no—
317SD16×C53—24no—
318SD16×C53—22no—
319SD16×C53—22no—
320SD16×C53—22no—
321SD16×C53—22no—
322SD16×C53—24no—
323SD16×C53—22no—
324SD16×C53—22no—
325SD16×C53—24no—
326SD16×C53—22no—
327SD16×C53—44no—
328SD16×C53—41no—
329SD16×C53—41no—
330D8×C53—24no—
331D8×C53—22no—
332D8×C53—22no—
333D8×C53—22no—
334D8×C53—24no—
335D8×C53—22no—
336D8×C53—41no—
337M16×C53—24no—
338M16×C53—24no—
339M16×C53—21no—
340M16×C53—21no—
341M16×C53—21no—
342M16×C53—21no—
343M16×C53—21no—
344M16×C53—21no—
345M16×C53—21no—
346M16×C53—21no—
347M16×C53C2×D412yes—
348M16×C53C2×D412yes—
349C2×C8×C53—24no—
350C2×C8×C53—24no—
351C2×C8×C53—21no—
352C2×C8×C53—21no—
353C2×C8×C53—21no—
354C2×C8×C53—21no—
355C2×C8×C53—21no—
356C2×C8×C53—21no—
357C2×C8×C53C2×D412yes—
358C2×C8×C53C2×D412yes—
359C4⋊C4×C53—21no—
360C4⋊C4×C53—21no—
361C4⋊C4×C53—42no—
362C22⋊C4×C53—21no—
363C22⋊C4×C53—21no—
364C22⋊C4×C53—42no—
365C22⋊C4×C53—42no—
366C42×C53—21no—
367C42×C53—21no—
368C23×C53—21no—
369C23×C53—21no—
370C23×C53—21no—
371C23×C53—21no—
372C23×C53—21no—
373C23×C53—22no—
374C23×C53—42no—
375C23×C53—44no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—161no—
379C23×C53—162no—
380C23×C53H(5,𝔽2)11yescharacteristic
381Q8×C53—21no—
382Q8×C53—21no—
383Q8×C53—21no—
384Q8×C53—22no—
385Q8×C53—21no—
386Q8×C53—21no—
387Q8×C53—21no—
388Q8×C53—22no—
389Q8×C53—21no—
390Q8×C53—21no—
391Q8×C53—42no—
392Q8×C53—44no—
393Q8×C53—41no—
394Q8×C53—41no—
395Q8×C53#12012yes—
396Q8×C53#12012yes—
397D4×C53—22no—
398D4×C53—22no—
399D4×C53—22no—
400D4×C53—22no—
401D4×C53—21no—
402D4×C53—22no—
403D4×C53—21no—
404D4×C53—21no—
405D4×C53—21no—
406D4×C53—21no—
407D4×C53—21no—
408D4×C53—22no—
409D4×C53—21no—
410D4×C53—21no—
411D4×C53—42no—
412D4×C53—42no—
413D4×C53—44no—
414D4×C53—42no—
415D4×C53—44no—
416D4×C53—44no—
417D4×C53—41no—
418D4×C53—41no—
419D4×C53—41no—
420D4×C53—41no—
421D4×C53—41no—
422D4×C53—41no—
423D4×C53—41no—
424D4×C53—41no—
425D4×C53—162no—
426D4×C53#12012yes—
427D4×C53#12012yes—
428C2×C4×C53—21no—
429C2×C4×C53—21no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—21no—
435C2×C4×C53—21no—
436C2×C4×C53—21no—
437C2×C4×C53—22no—
438C2×C4×C53—42no—
439C2×C4×C53—42no—
440C2×C4×C53—42no—
441C2×C4×C53—44no—
442C2×C4×C53—44no—
443C2×C4×C53—44no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53C22×D411yescharacteristic
455C2×C4×C53C22×D411yescharacteristic
456C2×C4×C53C22×D411yescharacteristic
457C2×C4×C53C22×D411yescharacteristic
458C2×C4×C53C22×D411yescharacteristic
459C2×C4×C53H(5,𝔽2)11yescharacteristic
460C8×C53—22no—
461C8×C53—22no—
462C8×C53—22no—
463C8×C53—22no—
464C8×C53—41no—
465C8×C53—41no—
466#23894C5311yesmaximal, characteristic, direct product factor, Sylow
467C22×C53—22no—
468C22×C53—22no—
469C22×C53—41no—
470C22×C53—42no—
471C22×C53—42no—
472C22×C53—41no—
473C22×C53—41no—
474C22×C53—41no—
475C22×C53—42no—
476C22×C53—81no—
477C22×C53—81no—
478C22×C53—82no—
479C22×C53—81no—
480C22×C53—82no—
481C22×C53—161no—
482C22×C53—162no—
483C22×C53—164no—
484C22×C53#53411yescharacteristic
485C22×C53D4211yescharacteristic
486C22×C53D4211yescharacteristic
487C4×C53—22no—
488C4×C53—22no—
489C4×C53—41no—
490C4×C53—41no—
491C4×C53—41no—
492C4×C53—42no—
493C4×C53—81no—
494C4×C53—81no—
495C4×C53C2×#12011yescharacteristic
496C4×C53C2×#12011yescharacteristic
497C4×C53D4211yescharacteristic
498C4×C53D4211yescharacteristic
499#3586C2×C5311yescharacteristic, complemented
500#3585C2×C5311yescharacteristic, complemented
501#3020C2×C5311yescharacteristic, complemented
502#3019C2×C5311yescharacteristic, complemented
503#3010C2×C5311yescharacteristic, complemented
504#3009C2×C5311yescharacteristic, complemented
505#2019C2×C5311yescharacteristic, complemented
506#2017C2×C5311yescharacteristic, complemented
507#2009C2×C5311yescharacteristic, complemented
508#2008C2×C5311yescharacteristic, complemented
509#1903C2×C5311yescharacteristic, complemented
510#1902C2×C5311yescharacteristic, complemented
511#1881C2×C5311yescharacteristic, complemented
512#1881C2×C5311yescharacteristic, complemented
513#1794C2×C5311yescharacteristic, complemented
514C2×C53—21no—
515C2×C53—21no—
516C2×C53—21no—
517C2×C53—42no—
518C2×C53—42no—
519C2×C53—81no—
520C2×C53—81no—
521C2×C53—82no—
522C2×C53—81no—
523C2×C53#240311yescharacteristic
524#585C22×C5311yescharacteristic
525C2×2−1+4C22×C5311yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C5311yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C5311yescharacteristic
538#575C22×C5311yescharacteristic
539#575C22×C5311yescharacteristic
540#575C22×C5311yescharacteristic, complemented
541#575C22×C5311yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C5311yescharacteristic
544C2×#137C22×C5311yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C5311yescharacteristic
547C2×AGL(1,ℤ/8)C22×C5311yescharacteristic
548C22×SD16C22×C5311yescharacteristic, complemented
549#568C22×C5311yescharacteristic
550#568C22×C5311yescharacteristic, complemented
551#536C22×C5311yescharacteristic, complemented
552#535C22×C5311yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C5311yescharacteristic
562#421C22×C5311yescharacteristic, complemented
563#421C22×C5311yescharacteristic, complemented
564#421C22×C5311yescharacteristic, complemented
565#419C22×C5311yescharacteristic, complemented
566#418C22×C5311yescharacteristic, complemented
567#416C22×C5311yescharacteristic
568#416C22×C5311yescharacteristic, complemented
569C2×#101C22×C5311yescharacteristic, complemented
570C2×#100C22×C5311yescharacteristic, complemented
571#410C22×C5311yescharacteristic, complemented
572#408C22×C5311yescharacteristic, complemented
573#408C22×C5311yescharacteristic, complemented
574#408C22×C5311yescharacteristic, complemented
575#344C22×C5311yescharacteristic, complemented
576#344C22×C5311yescharacteristic, complemented
577#341C22×C5311yescharacteristic, complemented
578#338C22×C5311yescharacteristic, complemented
579C53#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C5312yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C5312yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C5311yescharacteristic
604C2×#41C23×C5311yescharacteristic
605C2×#41C23×C5311yescharacteristic
606C2×#41C23×C5311yescharacteristic
607C2×#41C23×C5311yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C5311yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C5311yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C5312yes—
632#137D4×C5312yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C5312yes—
650AGL(1,ℤ/8)D4×C5312yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C5312yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C5312yes—
671C2×SD16D4×C5312yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C5312yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C5311yescharacteristic
682C2×M16C23×C5311yescharacteristic
683C2×M16C23×C5311yescharacteristic
684C2×M16C23×C5311yescharacteristic
685C2×M16C23×C5311yescharacteristic
686C22×C8C23×C5311yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C5311yescharacteristic
696#117C23×C5311yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C5312yes—
752#41C2×D4×C5312yes—
753#41C2×D4×C5312yes—
754#41C2×D4×C5312yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C5312yes—
769C2×Q8C2×D4×C5311yescharacteristic
770C2×Q8C2×D4×C5311yescharacteristic
771C2×Q8C2×D4×C5311yescharacteristic
772C2×Q8C2×D4×C5311yescharacteristic
773C2×Q8C2×D4×C5311yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
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—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C5312yes—
801C2×D4C2×D4×C5311yescharacteristic
802C2×D4C2×D4×C5311yescharacteristic
803C2×D4C2×D4×C5311yescharacteristic
804C2×D4C2×D4×C5311yescharacteristic
805C2×D4C2×D4×C5311yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C5311yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C5312yes—
857M16C2×D4×C5312yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C5312yes—
867C2×C8C2×D4×C5312yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C5311yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C5312yes—
905Q8#120×C5312yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C5312yes—
936D4#120×C5312yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C5311yescharacteristic
964C2×C4C22×D4×C5311yescharacteristic
965C2×C4C22×D4×C5311yescharacteristic
966C2×C4C22×D4×C5311yescharacteristic
967C2×C4C22×D4×C5311yescharacteristic
968C2×C4H(5,𝔽2)×C5311yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C53×#53411yescharacteristic
993C22D42×C5311yescharacteristic
994C22D42×C5311yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C5311yescharacteristic
1004C4C2×#120×C5311yescharacteristic
1005C4D42×C5311yescharacteristic
1006C4D42×C5311yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C53×#240311yescharacteristic
subgroupG/H
center, socleC2×C53#2403
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3586C2semidirect
2. C53×#3585C2semidirect
3. C53×#3020C2semidirect
4. C53×#3019C2semidirect
5. C53×#3010C2semidirect
6. C53×#3009C2semidirect
7. C53×#2019C2semidirect
8. C53×#2017C2semidirect
9. C53×#2009C2semidirect
10. C53×#2008C2semidirect
11. C53×#1903C2semidirect
12. C53×#1902C2semidirect
13. C53×#1881C2semidirect
14. C53×#1881C2semidirect
15. C53×#1794C2semidirect
17. C2×2−1+4×C53C22semidirect
32. C53×#575C22semidirect
33. C53×#575C22semidirect
36. C2×#137×C53C22semidirect
40. C22×SD16×C53C22semidirect
42. C53×#568C22semidirect
43. C53×#536C22semidirect
44. C53×#535C22semidirect
54. C53×#421C22semidirect
55. C53×#421C22semidirect
56. C53×#421C22semidirect
57. C53×#419C22semidirect
58. C53×#418C22semidirect
60. C53×#416C22semidirect
61. C2×#101×C53C22semidirect
62. C2×#100×C53C22semidirect
63. C53×#410C22semidirect
64. C53×#408C22semidirect
65. C53×#408C22semidirect
66. C53×#408C22semidirect
67. C53×#344C22semidirect
68. C53×#344C22semidirect
69. C53×#341C22semidirect
70. C53×#338C22semidirect
77. 2−1+4×C53D4semidirect
85. H(5,𝔽2)×C53D4semidirect
123. #137×C53D4semidirect
141. AGL(1,ℤ/8)×C53D4semidirect
153. C2×Q16×C53D4semidirect
162. C2×SD16×C53D4semidirect
466. #23894C53direct (N × H)
499. #3586C2×C53semidirect
500. #3585C2×C53semidirect
501. #3020C2×C53semidirect
502. #3019C2×C53semidirect
503. #3010C2×C53semidirect
504. #3009C2×C53semidirect
505. #2019C2×C53semidirect
506. #2017C2×C53semidirect
507. #2009C2×C53semidirect
508. #2008C2×C53semidirect
509. #1903C2×C53semidirect
510. #1902C2×C53semidirect
511. #1881C2×C53semidirect
512. #1881C2×C53semidirect
513. #1794C2×C53semidirect
525. C2×2−1+4C22×C53semidirect
540. #575C22×C53semidirect
541. #575C22×C53semidirect
544. C2×#137C22×C53semidirect
548. C22×SD16C22×C53semidirect
550. #568C22×C53semidirect
551. #536C22×C53semidirect
552. #535C22×C53semidirect
562. #421C22×C53semidirect
563. #421C22×C53semidirect
564. #421C22×C53semidirect
565. #419C22×C53semidirect
566. #418C22×C53semidirect
568. #416C22×C53semidirect
569. C2×#101C22×C53semidirect
570. C2×#100C22×C53semidirect
571. #410C22×C53semidirect
572. #408C22×C53semidirect
573. #408C22×C53semidirect
574. #408C22×C53semidirect
575. #344C22×C53semidirect
576. #344C22×C53semidirect
577. #341C22×C53semidirect
578. #338C22×C53semidirect
579. C53#23894direct (N × H)
586. 2−1+4D4×C53semidirect
594. H(5,𝔽2)D4×C53semidirect
632. #137D4×C53semidirect
650. AGL(1,ℤ/8)D4×C53semidirect
662. C2×Q16D4×C53semidirect
671. C2×SD16D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35862
C53×#35852
C53×#30202
C53×#30192
C53×#30102
C53×#30092
C53×#20192
C53×#20172
C53×#20092
C53×#20082
C53×#19032
C53×#19022
C53×#18812
C53×#17942
#2389453