Finite Group Databasebeta

← D53×#2483 #27553012

Subgroups — D53×#2483 #27553012

Order 13568.

4382 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D53C212yesmaximal
2#20278996C211yesmaximal, characteristic, complemented
3#20278995C214yesmaximal, complemented
4#20278994C214yesmaximal, complemented
5#20278993C212yesmaximal, complemented
6#20278992C214yesmaximal, complemented
7#397×D53C214yesmaximal, complemented
8#385×D53C214yesmaximal, complemented
9#381×D53C214yesmaximal, complemented
10#379×D53C211yesmaximal, characteristic
11C53×#2483C211yesmaximal, characteristic, complemented
12C25×D53C2211yescharacteristic
13C23×C4×D53C2212yes—
14C23×C4×D53C2212yes—
15C2×C4⋊C4×D53C2214yescomplemented
16C22×C22⋊Dic53C2212yes—
17C22×#11719921C2212yes—
18C22×#11719921C2212yes—
19C2×C22⋊C4×D53—216no—
20C2×C22⋊C4×D53C2214yes—
21C2×C22⋊C4×D53C2214yes—
22C2×C22⋊C4×D53C2214yes—
23C2×C22⋊C4×D53C2214yes—
24C2×C22⋊C4×D53C2214yes—
25C2×C22⋊C4×D53C2212yes—
26#16810552C2218yescomplemented
27#16810551C2218yescomplemented
28#16810550C2214yescomplemented
29#16810549C2214yescomplemented
30#16810548C2214yescomplemented
31#16810498C2214yescomplemented
32#16810497C2218yescomplemented
33#16810496C2214yescomplemented
34#16810495C2214yescomplemented
35#16810494C2218yescomplemented
36#16810486C2214yescomplemented
37#16810485C2218yescomplemented
38#16810485C2218yescomplemented
39#16810484C2214yescomplemented
40#16810484C2214yescomplemented
41#16810479C2211yescharacteristic
42#16810478C2212yes—
43#16810478C2214yes—
44#95×D53C2214yescomplemented
45#95×D53C2218yescomplemented
46C22×C22⋊C4×C53C2212yes—
47C53×#397C2214yescomplemented
48C53×#385C2214yescomplemented
49C53×#381C2214yescomplemented
50C53×#379C2211yescharacteristic
51C24×D53—216no—
52C24×D53—44no—
53C24×D53D418yes—
54C24×D53C2311yescharacteristic
55C24×D53C2311yescharacteristic
56C24×D53C2312yes—
57C24×D53C2312yes—
58C23×Dic53C2312yes—
59C23×Dic53C2312yes—
60C22×C4×D53—28no—
61C22×C4×D53—28no—
62C22×C4×D53—216no—
63C22×C4×D53—48no—
64C22×C4×D53C2314yes—
65C22×C4×D53C2314yes—
66C22×C4×D53C2314yes—
67C22×C4×D53C2314yes—
68C22×C4×D53C2314yes—
69C2×C4⋊Dic53C2314yescomplemented
70C2×#11719919C2318yescomplemented
71C4⋊C4×D53—48no—
72C2×C22⋊Dic53—28no—
73C2×C22⋊Dic53C2314yes—
74C2×C22⋊Dic53C2314yes—
75C2×C22⋊Dic53C2314yes—
76C2×C22⋊Dic53C2312yes—
77C2×#11719921—28no—
78C2×#11719921—28no—
79C2×#11719921C2314yes—
80C2×#11719921C2318yes—
81C2×#11719921C2314yes—
82C2×#11719921C2314yes—
83C2×#11719921C2314yes—
84C2×#11719921C2314yes—
85C22⋊C4×D53—216no—
86C22⋊C4×D53—216no—
87C22⋊C4×D53—216no—
88C22⋊C4×D53—216no—
89C22⋊C4×D53—216no—
90C22⋊C4×D53—44no—
91#13133124C2318yescomplemented
92#13133124C2318yescomplemented
93#13133124C2318yescomplemented
94#13133124C2314yescomplemented
95#13133124C2318yescomplemented
96C25×C53C2311yescharacteristic
97C23×C4×C53C2312yes—
98C23×C4×C53C2312yes—
99C2×C4⋊C4×C53C2314yescomplemented
100C2×C22⋊C4×C53—28no—
101C2×C22⋊C4×C53C2314yes—
102C2×C22⋊C4×C53C2314yes—
103C2×C22⋊C4×C53C2314yes—
104C2×C22⋊C4×C53C2312yes—
105#95×C53C2318yescomplemented
106#95×C53C2314yescomplemented
107C24×C53—28no—
108C24×C53—42no—
109C24×C53C2×D414yes—
110C24×C53C2411yescharacteristic
111C24×C53C2412yes—
112C23×D53—28no—
113C23×D53—28no—
114C23×D53—28no—
115C23×D53—264no—
116C23×D53—28no—
117C23×D53—28no—
118C23×D53—28no—
119C23×D53—24no—
120C23×D53—416no—
121C23×D53—42no—
122C23×D53—44no—
123C23×D53—464no—
124C23×D53C2×D414yes—
125C23×D53C2×D414yes—
126C23×D53C2×D418yes—
127C23×D53C2×D418yes—
128C23×D53#41116yes—
129C23×D53C2411yescharacteristic
130C23×D53C2412yes—
131C23×D53C2411yescharacteristic
132C22×C4×C53—24no—
133C22×C4×C53—24no—
134C22×C4×C53—28no—
135C22×C4×C53—44no—
136C22×C4×C53C2414yes—
137C22×C4×C53C2414yes—
138C22×C4×C53C2414yes—
139C22×Dic53—24no—
140C22×Dic53—24no—
141C22×Dic53—28no—
142C22×Dic53—44no—
143C22×Dic53C2414yes—
144C22×Dic53C2414yes—
145C22×Dic53C2414yes—
146C2×C4×D53—28no—
147C2×C4×D53—28no—
148C2×C4×D53—28no—
149C2×C4×D53—28no—
150C2×C4×D53—216no—
151C2×C4×D53—216no—
152C2×C4×D53—216no—
153C2×C4×D53—28no—
154C2×C4×D53—216no—
155C2×C4×D53—48no—
156C2×C4×D53—432no—
157C2×C4×D53—432no—
158C4⋊C4×C53—44no—
159C22⋊C4×C53—28no—
160C22⋊C4×C53—28no—
161C22⋊C4×C53—28no—
162C22⋊C4×C53—42no—
163C22⋊Dic53—28no—
164C22⋊Dic53—28no—
165C22⋊Dic53—28no—
166C22⋊Dic53—42no—
167#11719921—28no—
168#11719921—28no—
169#11719921—28no—
170#11719921—28no—
171#11719921—216no—
172#11719921—44no—
173C4⋊Dic53—44no—
174#11719919—48no—
175C23×C53—24no—
176C23×C53—24no—
177C23×C53—216no—
178C23×C53—24no—
179C23×C53—22no—
180C23×C53—44no—
181C23×C53—416no—
182C23×C53C22×D412yes—
183C23×C53C22×D414yes—
184C23×C53C2×#4118yes—
185C23×C53C2511yescharacteristic
186C22×D53—24no—
187C22×D53—24no—
188C22×D53—216no—
189C22×D53—216no—
190C22×D53—264no—
191C22×D53—216no—
192C22×D53—24no—
193C22×D53—22no—
194C22×D53—216no—
195C22×D53—216no—
196C22×D53—216no—
197C22×D53—28no—
198C22×D53—44no—
199C22×D53—48no—
200C22×D53—416no—
201C22×D53—4128no—
202C22×D53—432no—
203C22×D53—416no—
204C22×D53#123132yes—
205C22×D53C22×D412yes—
206C22×D53C22×D414yes—
207C22×D53C22×D412yes—
208C22×D53C2×#4118yes—
209C22×D53C2×#4118yes—
210C22×D53H(5,𝔽2)14yes—
211C2×C4×C53—24no—
212C2×C4×C53—24no—
213C2×C4×C53—28no—
214C2×C4×C53—28no—
215C2×C4×C53—28no—
216C2×C4×C53—24no—
217C2×C4×C53—48no—
218C2×C4×C53—48no—
219C2×Dic53—24no—
220C2×Dic53—24no—
221C2×Dic53—28no—
222C2×Dic53—28no—
223C2×Dic53—28no—
224C2×Dic53—24no—
225C2×Dic53—48no—
226C2×Dic53—48no—
227C4×D53—416no—
228C4×D53—416no—
229C4×D53—416no—
230C4×D53—416no—
231C4×D53—416no—
232C2×#2483—531nomaximal, Sylow
233C22×C53—24no—
234C22×C53—24no—
235C22×C53—216no—
236C22×C53—24no—
237C22×C53—22no—
238C22×C53—416no—
239C22×C53—44no—
240C22×C53C2×#12318yes—
241C22×C53C23×D411yescharacteristic
242C22×C53C22×#4114yes—
243C22×C53C2×H(5,𝔽2)12yes—
244C2×D53—24no—
245C2×D53—24no—
246C2×D53—216no—
247C2×D53—264no—
248C2×D53—24no—
249C2×D53—22no—
250C2×D53—416no—
251C2×D53—432no—
252C2×D53—44no—
253C2×D53—416no—
254C2×D53C2×#12318yes—
255C2×D53C2×#12318yes—
256C2×D53#53414yes—
257C2×D53#551116yes—
258C4×C53—44no—
259C4×C53—44no—
260C4×C53—44no—
261Dic53—44no—
262Dic53—44no—
263Dic53—44no—
264C23×C22⋊C4—532no—
265#2483—534no—
266#2483—534no—
267#2483—534no—
268#2483—531no—
269#2483—532no—
270#2483D5311yescharacteristic, direct product factor
271C2×#397—534no—
272C2×#385—534no—
273C2×#381—534no—
274C2×#379—531no—
275C2×C53—28no—
276C2×C53—42no—
277C2×C53C22×#12312yes—
278C2×C53C2×#53411yescharacteristic
279C2×C53C2×#55114yes—
280D53—28no—
281D53—42no—
282D53#248318yesdirect product factor
283C26—531no—
284C24×C4—532no—
285C24×C4—532no—
286C22×C4⋊C4—534no—
287C22×C22⋊C4—532no—
288C22×C22⋊C4—532no—
289C22×C22⋊C4—532no—
290C22×C22⋊C4—534no—
291C22×C22⋊C4—534no—
292C22×C22⋊C4—534no—
293C22×C22⋊C4—534no—
294C22×C22⋊C4—534no—
295C22×C22⋊C4—532no—
296C22×C22⋊C4—10616no—
297C22×C22⋊C4C2×D5312yes—
298#397—534no—
299#397—534no—
300#397—538no—
301#397—534no—
302#397—538no—
303#397C2×D5314yescomplemented
304#385—534no—
305#385—538no—
306#385—534no—
307#385—534no—
308#385—538no—
309#385C2×D5314yescomplemented
310#381—534no—
311#381—534no—
312#381—534no—
313#381—538no—
314#381—538no—
315#381C2×D5314yescomplemented
316#379—531no—
317#379—534no—
318#379—532no—
319#379C2×D5311yescharacteristic
320C2×#95—534no—
321C2×#95—538no—
322C53C2×#248311yescharacteristic, complemented, Sylow
323C25—532no—
324C25—531no—
325C25—538no—
326C25—531no—
327C25—532no—
328C25—10616no—
329C25—2124no—
330C25C22×D5311yescharacteristic
331C23×C4—532no—
332C23×C4—532no—
333C23×C4—534no—
334C23×C4—534no—
335C23×C4—534no—
336C23×C4—534no—
337C23×C4—534no—
338C23×C4—1068no—
339C23×C4—1068no—
340C23×C4—10616no—
341C23×C4—2128no—
342C23×C4C22×D5312yes—
343C23×C4C22×D5312yes—
344C2×C4⋊C4—538no—
345C2×C4⋊C4—534no—
346C2×C4⋊C4—2128no—
347C2×C4⋊C4C22×D5314yescomplemented
348C2×C22⋊C4—28no—
349C2×C22⋊C4—534no—
350C2×C22⋊C4—534no—
351C2×C22⋊C4—534no—
352C2×C22⋊C4—534no—
353C2×C22⋊C4—534no—
354C2×C22⋊C4—534no—
355C2×C22⋊C4—534no—
356C2×C22⋊C4—538no—
357C2×C22⋊C4—532no—
358C2×C22⋊C4—534no—
359C2×C22⋊C4—10616no—
360C2×C22⋊C4—10616no—
361C2×C22⋊C4—10616no—
362C2×C22⋊C4—10616no—
363C2×C22⋊C4—10616no—
364C2×C22⋊C4—1068no—
365C2×C22⋊C4—1068no—
366C2×C22⋊C4—1068no—
367C2×C22⋊C4—2124no—
368C2×C22⋊C4C22×D5314yes—
369C2×C22⋊C4C22×D5314yes—
370C2×C22⋊C4C22×D5314yes—
371C2×C22⋊C4C22×D5312yes—
372#95—534no—
373#95—538no—
374#95—538no—
375#95—538no—
376#95—538no—
377#95C22×D5314yescomplemented
378#95C22×D5318yescomplemented
379C24—28no—
380C24—42no—
381C24—531no—
382C24—538no—
383C24—5316no—
384C24—532no—
385C24—534no—
386C24—531no—
387C24—534no—
388C24—538no—
389C24—1068no—
390C24—1068no—
391C24—1064no—
392C24—1068no—
393C24—10664no—
394C24—1068no—
395C24—1068no—
396C24—1068no—
397C24—2124no—
398C24—2122no—
399C24—21216no—
400C24—21264no—
401C24D4×D5314yes—
402C24C23×D5311yescharacteristic
403C24C23×D5312yes—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—28no—
407C22×C4—44no—
408C22×C4—534no—
409C22×C4—534no—
410C22×C4—534no—
411C22×C4—1068no—
412C22×C4—1068no—
413C22×C4—1068no—
414C22×C4—1068no—
415C22×C4—10616no—
416C22×C4—1068no—
417C22×C4—10616no—
418C22×C4—10616no—
419C22×C4—10616no—
420C22×C4—1064no—
421C22×C4—1064no—
422C22×C4—1068no—
423C22×C4—2128no—
424C22×C4—21232no—
425C22×C4—21232no—
426C22×C4—2124no—
427C22×C4C23×D5314yes—
428C22×C4C23×D5314yes—
429C22×C4C23×D5314yes—
430C4⋊C4—44no—
431C4⋊C4—2128no—
432C4⋊C4—2124no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—42no—
437C22⋊C4—1068no—
438C22⋊C4—1068no—
439C22⋊C4—1068no—
440C22⋊C4—1068no—
441C22⋊C4—10616no—
442C22⋊C4—1068no—
443C22⋊C4—1068no—
444C22⋊C4—1068no—
445C22⋊C4—2124no—
446C22⋊C4—2122no—
447C23—24no—
448C23—24no—
449C23—216no—
450C23—24no—
451C23—22no—
452C23—44no—
453C23—416no—
454C23—532no—
455C23—538no—
456C23—534no—
457C23—5332no—
458C23—534no—
459C23—538no—
460C23—532no—
461C23—10616no—
462C23—10616no—
463C23—10664no—
464C23—10616no—
465C23—10616no—
466C23—10616no—
467C23—1068no—
468C23—1064no—
469C23—1064no—
470C23—10616no—
471C23—1064no—
472C23—1062no—
473C23—2128no—
474C23—2124no—
475C23—21232no—
476C23—21216no—
477C23—212128no—
478C23—21216no—
479C23C2×D4×D5312yes—
480C23C2×D4×D5314yes—
481C23#41×D5318yes—
482C23C24×D5311yescharacteristic
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—1064no—
492C2×C4—1064no—
493C2×C4—1068no—
494C2×C4—1068no—
495C2×C4—1064no—
496C2×C4—1068no—
497C2×C4—21216no—
498C2×C4—21216no—
499C2×C4—21216no—
500C2×C4—21216no—
501C2×C4—21216no—
502C2×C4—2128no—
503C2×C4—2128no—
504C22—24no—
505C22—24no—
506C22—216no—
507C22—22no—
508C22—24no—
509C22—416no—
510C22—44no—
511C22—534no—
512C22—538no—
513C22—5316no—
514C22—538no—
515C22—10664no—
516C22—1064no—
517C22—1064no—
518C22—10616no—
519C22—1062no—
520C22—1064no—
521C22—21232no—
522C22—21216no—
523C22—21216no—
524C22—2124no—
525C22#123×D5318yes—
526C22C22×D4×D5311yescharacteristic
527C22C2×#41×D5314yes—
528C22H(5,𝔽2)×D5312yes—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—2124no—
533C4—2124no—
534C4—2124no—
535C2—28no—
536C2—42no—
537C2—538no—
538C2—1068no—
539C2—2122no—
540C2C2×#123×D5312yes—
541C2#534×D5311yescharacteristic
542C2#551×D5314yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2483C2
prime radicalC25×D53C22
hypercenter#2483D53
hypocenterC53C2×#2483
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. #20278996C2semidirect
3. #20278995C2semidirect
4. #20278994C2semidirect
5. #20278993C2semidirect
6. #20278992C2semidirect
7. #397×D53C2semidirect
8. #385×D53C2semidirect
9. #381×D53C2semidirect
11. C53×#2483C2semidirect
15. C2×C4⋊C4×D53C22semidirect
26. #16810552C22semidirect
27. #16810551C22semidirect
28. #16810550C22semidirect
29. #16810549C22semidirect
30. #16810548C22semidirect
31. #16810498C22semidirect
32. #16810497C22semidirect
33. #16810496C22semidirect
34. #16810495C22semidirect
35. #16810494C22semidirect
36. #16810486C22semidirect
37. #16810485C22semidirect
38. #16810485C22semidirect
39. #16810484C22semidirect
40. #16810484C22semidirect
44. #95×D53C22semidirect
45. #95×D53C22semidirect
47. C53×#397C22semidirect
48. C53×#385C22semidirect
49. C53×#381C22semidirect
69. C2×C4⋊Dic53C23semidirect
70. C2×#11719919C23semidirect
91. #13133124C23semidirect
92. #13133124C23semidirect
93. #13133124C23semidirect
94. #13133124C23semidirect
95. #13133124C23semidirect
99. C2×C4⋊C4×C53C23semidirect
105. #95×C53C23semidirect
106. #95×C53C23semidirect
270. #2483D53direct (N × H)
282. D53#2483direct (N × H)
303. #397C2×D53semidirect
309. #385C2×D53semidirect
315. #381C2×D53semidirect
322. C53C2×#2483semidirect
347. C2×C4⋊C4C22×D53semidirect
377. #95C22×D53semidirect
378. #95C22×D53semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D532
#202789962
#202789952
#202789942
#202789932
#202789922
#397×D532
#385×D532
#381×D532
#379×D532
C53×#24832
C2×#248353