Finite Group Databasebeta

← #14458558

Subgroups — #14458558

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752737C211yesmaximal, characteristic
2#11752645C211yesmaximal, characteristic, complemented
3#11750935C211yesmaximal, characteristic, complemented
4C5×#4848C211yesmaximal, characteristic, complemented
5C3×#65131C211yesmaximal, characteristic, complemented
6#11748118C212yesmaximal, complemented
7#11748108C212yesmaximal, complemented
8#11747931C212yesmaximal, complemented
9#11747635C212yesmaximal, complemented
10C4×#6655C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10612126—31nomaximal, Hall
13C2×#6777C2212yes—
14C2×D5×D12—21no—
15C2×C8×D15C2212yescomplemented
16C4×D60C2211yescharacteristic
17C2×C5×#204C2212yescomplemented
18C5×#874C2211yescharacteristic
19C4×C5×Dic6C2211yescharacteristic, complemented
20C3×C4×D20C2211yescharacteristic
21C3×#4015C2211yescharacteristic, complemented
22#91475—22no—
23#91466C2212yes—
24#91449—21no—
25#91437C2212yescomplemented
26#91428—21no—
27#91411—22no—
28#91383C2212yescomplemented
29#91381—21no—
30C2×#6655C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic, complemented
32#91104C2212yescomplemented
33C4×C3⋊#168C2211yescharacteristic, complemented
34C5×#821C2212yescomplemented
35C3×#3953C2212yes—
36C3×#3949C2212yescomplemented
37#90986C2211yescharacteristic, complemented
38#90972C2211yescharacteristic, complemented
39#90966C2212yescomplemented
40#90966C2212yescomplemented
41#90964C2211yescharacteristic
42#81075—51nomaximal, Hall
43#66051—31no—
44#65913—31no—
45C5×#460—31no—
46#65460—32no—
47#65458—32no—
48#65359—31no—
49C4×#688—31no—
50#65131D311yescharacteristic, complemented
51#65123—31no—
52#65066—32no—
53D5×#102—32no—
54C22×D3×D5—22no—
55C2×D60D411yescharacteristic
56C2×C4×D15C2312yes—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10—21no—
64C2×#1203—22no—
65C2×#1201—22no—
66C2×#1200—22no—
67#6777—24no—
68#6777—42no—
69D5×D12—44no—
70C2×C3×C5×C8C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6714D412yes—
73C4⋊Dic15D411yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C8×D15—42no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×Dic3⋊C4—21no—
79C4×C5×Dic3—21no—
80C5×#204—42no—
81C3×#685—21no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4⋊Dic5C2311yescharacteristic
85#6669—22no—
86#6668—22no—
87#6667—22no—
88(C2×D3)⋊Dic5—22no—
89#6655—22no—
90#5730—51no—
91D4×D12—51no—
92C3×#476—51no—
93#5088—51no—
94C4×#214—51no—
95#4864—52no—
96#4863—52no—
97#4848D511yescharacteristic, complemented
98#4834—51no—
99#4776—52no—
100D3×#102—52no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C2×C5×SD16—32no—
104C5×#127—31no—
105C4×C5×Q8—31no—
106#4092—32no—
107C2×#688—31no—
108#4084—32no—
109#4084—61no—
110#4083—62no—
111C2×C8×D5—32no—
112#4042—62no—
113D5×C4⋊C4—32no—
114C4×D20—31no—
115C4×D20—61no—
116C4×D20C2×D311yescharacteristic
117#4016—61no—
118#4015C2×D311yescharacteristic, complemented
119C5×C4⋊C8C2×D311yescharacteristic, complemented
120C5×#102—32no—
121#3967—31no—
122#3964—32no—
123#3964—32no—
124#3953C2×D312yes—
125#3952—32no—
126#3949C2×D312yescomplemented
127#3941—31no—
128#3940—31no—
129C4×#168—31no—
130#3295—151noSylow
131C22×D15C2×D412yes—
132C22×C5×D3—22no—
133C22×C3×D5—21no—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15C2×D412yes—
141D60SD1614yescomplemented
142C4×D15—22no—
143C4×D15—22no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C5×D12—22no—
147C5×D12—22no—
148C5×D12—42no—
149C5×D12—81no—
150C5×Dic6—21no—
151C5×Dic6—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—22no—
154C3×D20—21no—
155C3×D20#4112yes—
156C3×C4×D5—42no—
157C3×Dic10—81no—
158#1203—44no—
159#1201—44no—
160#1200—82no—
161C3×C5×C8—22no—
162C3⋊#168—21no—
163C3⋊#168—21no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C3×C4⋊Q8—51no—
167C3×C4×D4—51no—
168#946—102no—
169C2×#214—51no—
170#930—101no—
171C2×#204C2×D512yescomplemented
172C2×D3×C8—52no—
173#897—52no—
174#895—52no—
175#893—101no—
176D3×C4⋊C4—52no—
177#890—101no—
178#882—102no—
179#874C2×D511yescharacteristic
180C4×D12—51no—
181C4×Dic6C2×D511yescharacteristic, complemented
182C3×#106—52no—
183C3×C4⋊C8C2×D511yescharacteristic, complemented
184C3×#102—52no—
185#832—51no—
186#821C2×D512yescomplemented
187(C2×D3)⋊C8—52no—
188#810—51no—
189#809—52no—
190#809—52no—
191#808—51no—
192C4×C3⋊C8—51no—
193C23×D5—62no—
194C2×C5×Q8—31no—
195C2×C5×D4—32no—
196C2×C5×D4—61no—
197C2×C5×D4—61no—
198C2×C22⋊D5—62no—
199C2×C22⋊D5—62no—
200D4×D5—64no—
201D4×D5—124no—
202D4×D5—122no—
203C2×D20—31no—
204C2×D20C22×D311yescharacteristic
205C2×C4×D5—21no—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×Dic10—21no—
209C5×SD16—122no—
210C2×C5×C8C22×D312yes—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—61no—
213C42×C5—61no—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#688—62no—
217#685—21no—
218#685—32no—
219#685—62no—
220C4⋊Dic5—21no—
221C4⋊Dic5—31no—
222C4⋊Dic5C22×D311yescharacteristic
223C4⋊Dic5C22×D312yes—
224#683—62no—
225#683—62no—
226C2×#168—31no—
227C2×#168—31no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—51no—
234#465—152no—
235#460—31no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—22no—
242C2×D15—22no—
243C2×D15C2×SD1614yes—
244C2×C5×D3—42no—
245C2×C5×D3—42no—
246C2×C5×D3—42no—
247C2×C3×D5—22no—
248C2×C3×D5—41no—
249C2×C3×D5—41no—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5C2×SD1612yes—
253C3×C4×C5C2×#4111yescharacteristic
254C3×C4×C5H(5,𝔽2)11yescharacteristic
255Dic15—22no—
256C3×Dic5—41no—
257C3×Dic5—42no—
258C5×Dic3—41no—
259C5×Dic3—41no—
260C23×D3—102no—
261C2×C3×Q8—101no—
262C2×C3×D4—51no—
263C22×C3×C4—101no—
264C2×#67—102no—
265D3×D4—104no—
266D3×D4—202no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—51no—
270C2×D12—102no—
271C2×D12—204no—
272C2×D12C22×D512yes—
273C2×C4×D3—52no—
274C2×C4×D3—102no—
275C2×Dic6C22×D511yescharacteristic
276C2×C3×C8C22×D512yes—
277C3×C4⋊C4—51no—
278C3×C4⋊C4—52no—
279C3×C4⋊C4—101no—
280C3×C22⋊C4—101no—
281C3×C42C22×D511yescharacteristic
282#214—102no—
283(C2×D3)⋊C4—52no—
284(C2×D3)⋊C4—102no—
285(C2×D3)⋊C4—102no—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—102no—
291C4×Dic3—21no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294#204—42no—
295D3×C8—202no—
296C23×C5—62no—
297C22×D5—21no—
298C22×D5—32no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—61no—
303C5×Q8—61no—
304C5×D4—62no—
305C5×D4—62no—
306C5×D4—122no—
307C5×D4—241no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—124no—
314C22⋊D5—124no—
315C2×Dic5—22no—
316C2×Dic5—21no—
317C2×Dic5—32no—
318D20—21no—
319D20—34no—
320D20#23912yes—
321C4×D5—42no—
322C4×D5—62no—
323C4×D5—62no—
324C4×D5—242no—
325Dic10—81no—
326C5×C8—22no—
327#168—61no—
328#168—61no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—32no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8—51no—
335#127—31no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—31no—
343C4×D4—51no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—52no—
348#106—151no—
349C4⋊C8D3×D511yescharacteristic, complemented
350#103—151no—
351#102—32no—
352#102—52no—
353#102—151no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5C22×SD1611yescharacteristic
360C2×C3×C5#57611yescharacteristic
361D15—24no—
362C3×D5—42no—
363C5×D3—82no—
364C23×C3—101no—
365C22×D3—22no—
366C22×D3—52no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—401no—
371C3×D4—52no—
372C3×D4—101no—
373C2×C3×C4—102no—
374C2×C3×C4—101no—
375C2×C3×C4—202no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—204no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—52no—
383D12—22no—
384D12—22no—
385D12—42no—
386D12—54no—
387D12—81no—
388D12—204no—
389C4×D3—102no—
390C4×D3—102no—
391C4×D3—402no—
392Dic6—21no—
393Dic6—21no—
394C3×C8—22no—
395C3⋊C8—101no—
396C3⋊C8—101no—
397C22×C5—122no—
398C22×C5—122no—
399C22×C5—122no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—22no—
402C2×D5—34no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—62no—
406C2×D5—62no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—121no—
410C4×C5—121no—
411C4×C5D3×SD1612yes—
412C4×C5C2×#23911yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—41no—
415Dic5—42no—
416Dic5—62no—
417C24—302no—
418C2×Q8—31no—
419C2×Q8—101no—
420C2×D4—32no—
421C2×D4—51no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—151no—
425C2×D4—302no—
426C2×D4—302no—
427C2×D4—304no—
428C2×D4—604no—
429C2×D4—602no—
430C22×C4—101no—
431C22×C4—152no—
432C22×C4—302no—
433SD16—122no—
434SD16—302no—
435C2×C8—151no—
436C2×C8—151no—
437C2×C8—602no—
438C2×C8C2×D3×D512yes—
439C4⋊C4—31no—
440C4⋊C4—52no—
441C4⋊C4—51no—
442C4⋊C4—61no—
443C4⋊C4—101no—
444C4⋊C4—151no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—101no—
448C22⋊C4—152no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—61no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—102no—
455C22×C3—201no—
456C22×C3—201no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—54no—
462C2×D3—102no—
463C2×D3—102no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—201no—
467C3×C4—202no—
468C3×C4D5×SD1612yes—
469C3×C4#414411yescharacteristic
470C3×C4D5×#4111yescharacteristic
471Dic3—41no—
472Dic3—41no—
473Dic3—102no—
474C2×C5—242no—
475C2×C5#563011yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#577411yescharacteristic
478D5—42no—
479D5—64no—
480C23—62no—
481C23—101no—
482C23—152no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—61no—
487Q8—61no—
488Q8—401no—
489D4—52no—
490D4—62no—
491D4—62no—
492D4—101no—
493D4—122no—
494D4—154no—
495D4—241no—
496D4—604no—
497D4—604no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—101no—
501C2×C4—102no—
502C2×C4—152no—
503C2×C4—202no—
504C2×C4—302no—
505C2×C4—302no—
506C2×C4—1202no—
507C2×C4#677711yescharacteristic
508C2×C4#677711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—22no—
511C8—301no—
512C8—301no—
513C2×C3—202no—
514C2×C3#6594611yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—82no—
518D3—104no—
519C5#8107511yescharacteristic, complemented, Sylow
520C22—102no—
521C22—122no—
522C22—122no—
523C22—122no—
524C22—154no—
525C22—201no—
526C22—201no—
527C22—302no—
528C22—302no—
529C22—1208no—
530C22C2×#677711yescharacteristic
531C4—21no—
532C4—121no—
533C4—121no—
534C4—202no—
535C4—201no—
536C4—302no—
537C4#9125512yes—
538C4#9202711yescharacteristic
539C4D5×#23911yescharacteristic
540C3#1061212611yescharacteristic, complemented, Sylow
541C2—202no—
542C2—242no—
543C2—304no—
544C2#1175388711yescharacteristic
545C2C2×#9125511yescharacteristic
546C2#1175403811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752737C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752645C2semidirect
3. #11750935C2semidirect
4. C5×#4848C2semidirect
5. C3×#65131C2semidirect
6. #11748118C2semidirect
7. #11748108C2semidirect
8. #11747931C2semidirect
9. #11747635C2semidirect
10. C4×#6655C2semidirect
11. #11746901C2semidirect
15. C2×C8×D15C22semidirect
17. C2×C5×#204C22semidirect
19. C4×C5×Dic6C22semidirect
21. C3×#4015C22semidirect
25. #91437C22semidirect
28. #91383C22semidirect
31. C3×C5×C4⋊C8C22semidirect
32. #91104C22semidirect
33. C4×C3⋊#168C22semidirect
34. C5×#821C22semidirect
36. C3×#3949C22semidirect
37. #90986C22semidirect
38. #90972C22semidirect
39. #90966C22semidirect
40. #90966C22semidirect
50. #65131D3semidirect
97. #4848D5semidirect
118. #4015C2×D3semidirect
119. C5×C4⋊C8C2×D3semidirect
126. #3949C2×D3semidirect
141. D60SD16semidirect
171. C2×#204C2×D5semidirect
181. C4×Dic6C2×D5semidirect
183. C3×C4⋊C8C2×D5semidirect
186. #821C2×D5semidirect
349. C4⋊C8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#81075semidirect
540. C3#10612126semidirect

Maximal subgroups

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

subgroupindex
#117527372
#117526452
#117509352
C5×#48482
C3×#651312
#117481182
#117481082
#117479312
#117476352
C4×#66552
#117469012
#106121263
#810755