Finite Group Databasebeta

← #14458552

Subgroups — #14458552

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#11756489C211yesmaximal, characteristic, complemented
2#11752737C211yesmaximal, characteristic
3C5×#5088C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11747484C212yesmaximal, complemented
6#11747478C212yesmaximal, complemented
7#11747333C212yesmaximal, complemented
8#11747315C212yesmaximal, complemented
9#11747086C211yesmaximal, characteristic, complemented
10C4×#6657C211yesmaximal, characteristic, complemented
11#11746994C211yesmaximal, characteristic, complemented
12#10613308—31nomaximal, Hall
13C2×#6777C2212yes—
14C2×D5×D12—21no—
15C3×C5×C4⋊Q8C2211yescharacteristic, complemented
16#91835—22no—
17#91786C2212yescomplemented
18#91782—21no—
19C4⋊C4×D15C2212yescomplemented
20#91779—21no—
21C4×D60C2211yescharacteristic
22C4×Dic30C2211yescharacteristic, complemented
23C5×#874C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91475—22no—
26#91466C2212yes—
27#91449—21no—
28C2×#6659C2212yescomplemented
29C2×#6657C2211yescharacteristic
30C2×#6648C2212yescomplemented
31C5×#809C2212yescomplemented
32C5×#809C2212yescomplemented
33C4×C5×C3⋊C8C2211yescharacteristic, complemented
34C3×#3941C2212yes—
35C3×#3940C2212yescomplemented
36C3×C4⋊#168C2211yescharacteristic, complemented
37#90987C2211yescharacteristic, complemented
38#90974C2211yescharacteristic, complemented
39#90967C2212yescomplemented
40#90965C2211yescharacteristic
41#90957C2212yescomplemented
42#81075—51nomaximal, Hall
43#66064—31no—
44#66051—31no—
45C5×#486—31no—
46#65373D311yescharacteristic, complemented
47#65364—31no—
48#65067—32no—
49#65066—32no—
50#65065—32no—
51D5×#102—32no—
52C4×#677—31no—
53C8×D20—31no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8—21no—
56C2×D60D411yescharacteristic
57C2×C4×D15—22no—
58C2×C4×D15C2312yes—
59C2×Dic30C2311yescharacteristic
60C2×C5×D12—21no—
61C2×C5×D12—21no—
62C2×C5×D12C2312yes—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×#1203—22no—
66C2×#1201—22no—
67#6777—24no—
68#6777—42no—
69D5×D12—44no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C42×C5C2311yescharacteristic
73#6714—22no—
74#6714D412yes—
75C4⋊Dic15—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2311yescharacteristic
78#6712—21no—
79#6712—22no—
80C4×Dic15—21no—
81C2×C5×C3⋊C8C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C3×#685—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C2×C3×#168C2312yes—
86(C2×D3)⋊Dic5—22no—
87#6659—42no—
88#6657—22no—
89#6648—42no—
90#5730—51no—
91D4×D12—51no—
92C3×#476—51no—
93#5088D511yescharacteristic, complemented
94C4×#214—51no—
95#4864—52no—
96#4863—52no—
97#4848—51no—
98#4834—51no—
99#4776—52no—
100D3×#102—52no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C5×C4⋊Q8C2×D311yescharacteristic, complemented
104C5×#127—31no—
105#4092—62no—
106#4084—32no—
107#4084—61no—
108#4083—62no—
109C2×#687—32no—
110C2×#677—31no—
111C2×C8×D5—32no—
112#4043—32no—
113#4039—61no—
114D5×C4⋊C4—32no—
115#4036—61no—
116C4×D20—31no—
117C4×D20C2×D311yescharacteristic
118C4×Dic10—31no—
119C5×#102—32no—
120C5×#102—32no—
121C4×C5×C8—31no—
122#3964—32no—
123#3953—31no—
124#3952—32no—
125#3949—31no—
126#3948—31no—
127#3941C2×D312yes—
128#3940C2×D312yescomplemented
129C4⋊#168C2×D311yescharacteristic, complemented
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—
137C3×C5×Q8—81no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15C2×D412yes—
145D60SD1614yescomplemented
146C4×D15—22no—
147C4×D15—22no—
148C4×D15—82no—
149Dic30—21no—
150Dic30—21no—
151C5×D12—22no—
152C5×D12—22no—
153C5×D12—42no—
154C5×D12—81no—
155C2×C3×Dic5—21no—
156C3×D20—21no—
157C3×D20#4112yes—
158C3×C4×D5—42no—
159#1203—44no—
160#1201—44no—
161C3×#168—22no—
162C5×C3⋊C8—21no—
163C5×C3⋊C8—21no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C3×C4⋊Q8C2×D511yescharacteristic, complemented
167C3×C4×D4—51no—
168#946—102no—
169C2×#214—51no—
170#930—101no—
171C2×#204—52no—
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×Dic6—51no—
182C3×#106—52no—
183C3×C4⋊C8—51no—
184C3×#102—52no—
185#832—51no—
186#821—52no—
187(C2×D3)⋊C8—52no—
188#810—51no—
189#809C2×D512yescomplemented
190#809C2×D512yescomplemented
191#808—51no—
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×Q8—21no—
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—31no—
209C2×C5×C8—31no—
210C2×C5×C8—31no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4C22×D312yes—
213C42×C5C22×D311yescharacteristic
214C22⋊Dic5—62no—
215#687—122no—
216#685—21no—
217#685—32no—
218#685—62no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D311yescharacteristic
223#683—62no—
224#683—61no—
225C4×Dic5—61no—
226C2×#168C22×D312yes—
227#677—62no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—31no—
232#481—152no—
233#476—51no—
234#465—152no—
235#460—151no—
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×C5—42no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—22no—
257Dic15—41no—
258Dic15—41no—
259C3×Dic5—41no—
260C23×D3—102no—
261C2×C3×Q8—21no—
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×Dic6—51no—
276C2×C3×C8—52no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—51no—
279C3×C4⋊C4C22×D512yes—
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—51no—
288C4⋊Dic3—102no—
289Dic3⋊C4—102no—
290Dic3⋊C4—101no—
291C4×Dic3—101no—
292C2×C3⋊C8C22×D511yescharacteristic
293C2×C3⋊C8C22×D511yescharacteristic
294#204—202no—
295D3×C8—202no—
296C23×C5—62no—
297C22×D5—21no—
298C22×D5—32no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—81no—
303C5×D4—62no—
304C5×D4—62no—
305C5×D4—122no—
306C5×D4—241no—
307C2×C4×C5—22no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C22⋊D5—124no—
313C2×Dic5—21no—
314C2×Dic5—32no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317D20—21no—
318D20—34no—
319D20#23912yes—
320C4×D5—42no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5—242no—
324Dic10—61no—
325Dic10—61no—
326C5×C8—61no—
327C5×C8—61no—
328#168—22no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8D3×D511yescharacteristic, complemented
335#127—31no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—151no—
343C4×D4—51no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—52no—
348#106—151no—
349C4⋊C8—51no—
350#103—151no—
351#102—32no—
352#102—32no—
353#102—52no—
354#102—151no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—31no—
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—81no—
371C3×D4—52no—
372C3×D4—101no—
373C2×C3×C4—22no—
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—52no—
381C2×Dic3—101no—
382C2×Dic3—101no—
383D12—22no—
384D12—22no—
385D12—42no—
386D12—54no—
387D12—81no—
388D12—204no—
389C4×D3—102no—
390C4×D3—102no—
391C4×D3—402no—
392Dic6—101no—
393Dic6—101no—
394C3×C8—102no—
395C3⋊C8—21no—
396C3⋊C8—21no—
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—42no—
410C4×C5D3×SD1612yes—
411C4×C5C2×#23911yescharacteristic
412C4×C5#100911yescharacteristic
413Dic5—41no—
414Dic5—62no—
415Dic5—121no—
416Dic5—121no—
417C24—302no—
418C2×Q8—21no—
419C2×Q8—151no—
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—302no—
434SD16—602no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—52no—
438C2×C8—602no—
439C4⋊C4—21no—
440C4⋊C4—51no—
441C4⋊C4—151no—
442C4⋊C4—151no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—101no—
448C22⋊C4—152no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—301no—
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—42no—
467C3×C4—201no—
468C3×C4D5×SD1612yes—
469C3×C4D5×#4111yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—102no—
472Dic3—201no—
473Dic3—201no—
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—81no—
487Q8—301no—
488Q8—301no—
489D4—52no—
490D4—62no—
491D4—62no—
492D4—101no—
493D4—122no—
494D4—154no—
495D4—241no—
496D4—604no—
497D4—604no—
498C2×C4—22no—
499C2×C4—101no—
500C2×C4—152no—
501C2×C4—202no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—301no—
505C2×C4—301no—
506C2×C4—1202no—
507C2×C4#679011yescharacteristic
508C2×C4#679011yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—102no—
513C2×C3—202no—
514C2×C3#6601011yescharacteristic
515C2×C3#6609111yescharacteristic
516C2×C3C2×D5×SD1611yescharacteristic
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×#679011yescharacteristic
531C4—21no—
532C4—42no—
533C4—201no—
534C4—302no—
535C4—601no—
536C4—601no—
537C4#9150512yes—
538C4D5×#23911yescharacteristic
539C4#9203511yescharacteristic
540C3#1061330811yescharacteristic, complemented, Sylow
541C2—202no—
542C2—242no—
543C2—304no—
544C2#1175470411yescharacteristic
545C2C2×#9150511yescharacteristic
546C2#1175528311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752737C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
3. C5×#5088C2semidirect
4. C3×#65373C2semidirect
5. #11747484C2semidirect
6. #11747478C2semidirect
7. #11747333C2semidirect
8. #11747315C2semidirect
9. #11747086C2semidirect
10. C4×#6657C2semidirect
11. #11746994C2semidirect
15. C3×C5×C4⋊Q8C22semidirect
17. #91786C22semidirect
19. C4⋊C4×D15C22semidirect
22. C4×Dic30C22semidirect
28. C2×#6659C22semidirect
30. C2×#6648C22semidirect
31. C5×#809C22semidirect
32. C5×#809C22semidirect
33. C4×C5×C3⋊C8C22semidirect
35. C3×#3940C22semidirect
36. C3×C4⋊#168C22semidirect
37. #90987C22semidirect
38. #90974C22semidirect
39. #90967C22semidirect
41. #90957C22semidirect
46. #65373D3semidirect
93. #5088D5semidirect
103. C5×C4⋊Q8C2×D3semidirect
128. #3940C2×D3semidirect
129. C4⋊#168C2×D3semidirect
145. D60SD16semidirect
166. C3×C4⋊Q8C2×D5semidirect
189. #809C2×D5semidirect
190. #809C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
334. C4⋊Q8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#81075semidirect
540. C3#10613308semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117527372
C5×#50882
C3×#653732
#117474842
#117474782
#117473332
#117473152
#117470862
C4×#66572
#117469942
#106133083
#810755