Finite Group Databasebeta

← #14458565

Subgroups — #14458565

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
1C3×#65913C211yesmaximal, characteristic, complemented
2#11752737C211yesmaximal, characteristic
3C4×#6717C211yesmaximal, characteristic, complemented
4C5×#5027C211yesmaximal, characteristic, complemented
5#11749397C212yesmaximal, complemented
6#11749365C212yesmaximal, complemented
7D5×#809C212yesmaximal, complemented
8#11747308C212yesmaximal, complemented
9#11746996C211yesmaximal, characteristic, complemented
10#11746942C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10612126—31nomaximal, Hall
13C2×#6777—21no—
14C2×D5×D12C2212yes—
15C3×C4×C5×Q8C2211yescharacteristic, complemented
16C2×#6717C2211yescharacteristic
17C4×D60C2211yescharacteristic
18C2×C5×#215C2212yescomplemented
19C5×#874C2211yescharacteristic
20C3×#4092C2212yescomplemented
21C3×#4042—22no—
22C3×D5×C4⋊C4C2212yescomplemented
23C3×C4×D20—21no—
24C3×C4×D20C2211yescharacteristic
25C3×#4016—21no—
26C3×#4015C2211yescharacteristic, complemented
27#91475—22no—
28#91466—21no—
29#91449C2212yes—
30C2×D5×C3⋊C8C2212yescomplemented
31#91119C2211yescharacteristic, complemented
32#91093C2211yescharacteristic
33#91092C2211yescharacteristic, complemented
34C4×C3⋊#168C2211yescharacteristic, complemented
35C5×#809C2212yescomplemented
36C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37#90987C2212yescomplemented
38#90968C2212yes—
39#90966C2212yescomplemented
40#90966C2212yescomplemented
41#90955C2212yescomplemented
42#83634—51nomaximal, Hall
43#66051—31no—
44#65913D311yescharacteristic, complemented
45C5×#460—31no—
46#65460—32no—
47#65458—32no—
48#65359—31no—
49C4×#688—31no—
50#65131—31no—
51#65123—31no—
52#65066—32no—
53D5×#102—32no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×D12—21no—
59C2×C5×D12—21no—
60C2×C5×D12C2312yes—
61C2×C3×D20D411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5C2312yes—
64C2×C3×Dic10—21no—
65C2×#1203—22no—
66C2×#1201—22no—
67#6777—44no—
68D5×D12—24no—
69D5×D12—42no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C42×C5—21no—
73C3×C42×C5C2311yescharacteristic
74#6717—22no—
75#6714—21no—
76C4⋊Dic15C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C5×#215—42no—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—22no—
82C3×#685D412yes—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5D411yescharacteristic
85C3×C4⋊Dic5C2312yes—
86C3×#683—22no—
87C3×#683—22no—
88(C2×D3)⋊Dic5—22no—
89D5×C3⋊C8—42no—
90C3×#554—51no—
91D4×D12—51no—
92#5088—51no—
93#5084—51no—
94#5048—52no—
95#5046—52no—
96#5027D511yescharacteristic, complemented
97C4×#215—51no—
98D4×C3⋊C8—51no—
99#4968—52no—
100C2×#809—52no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C2×C5×SD16—32no—
104C5×#127—31no—
105C4×C5×Q8C2×D311yescharacteristic, complemented
106#4092C2×D312yescomplemented
107C2×#688—31no—
108#4084—32no—
109#4084—61no—
110#4083—62no—
111C2×C8×D5—32no—
112#4042—22no—
113D5×C4⋊C4C2×D312yescomplemented
114C4×D20—21no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117#4016—21no—
118#4015C2×D311yescharacteristic, complemented
119C5×C4⋊C8—31no—
120C5×#102—32no—
121#3967—31no—
122#3964—32no—
123#3964—32no—
124#3953—32no—
125#3952—32no—
126#3949—32no—
127#3941—31no—
128#3940—31no—
129C4×#168—31no—
130#3295—151noSylow
131C22×D15—21no—
132C22×C5×D3—22no—
133C22×C3×D5C2×D412yes—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C3×C5×Q8—21no—
138C3×C5×Q8—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145D60—21no—
146D60#4112yes—
147C4×D15—42no—
148C5×D12—22no—
149C5×D12—22no—
150C5×D12—42no—
151C5×D12—81no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C2×D412yes—
154C3×D20SD1614yescomplemented
155C3×C4×D5—22no—
156C3×C4×D5—22no—
157C3×C4×D5—82no—
158C3×Dic10—81no—
159#1203—44no—
160#1201—44no—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C5×C3⋊C8—22no—
164C2×D3×D4—101no—
165C22×D12—52no—
166C3×C4⋊Q8—51no—
167C3×#125—101no—
168C3×C22⋊Q8—52no—
169C3×C22⋊Q8—102no—
170C3×C4×Q8C2×D511yescharacteristic, complemented
171C3×C4×D4—51no—
172C3×C4×D4—101no—
173C2×C3×C4⋊C4—52no—
174C2×#215—51no—
175C2×#215C2×D512yescomplemented
176#930—52no—
177C22×C3⋊C8—52no—
178#895—101no—
179#882—102no—
180#874C2×D511yescharacteristic
181C4×D12—51no—
182#835—51no—
183#830—52no—
184#809—52no—
185#809—52no—
186#809—51no—
187#809—52no—
188#809C2×D512yescomplemented
189#808—51no—
190#808—52no—
191C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
192C4×C3⋊C8—51no—
193C23×D5—62no—
194C2×C5×Q8C22×D311yescharacteristic
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—122no—
202D4×D5—124no—
203C2×D20—31no—
204C2×D20#6711yescharacteristic
205C2×C4×D5—22no—
206C2×C4×D5—61no—
207C2×C4×D5C22×D312yes—
208C2×Dic10—21no—
209C5×SD16—122no—
210C2×C5×C8—32no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4C22×D311yescharacteristic
213C42×C5—21no—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#688—62no—
217#685—22no—
218#685—61no—
219#685#6712yes—
220C4⋊Dic5—21no—
221C4⋊Dic5—31no—
222C4⋊Dic5#6711yescharacteristic
223C4⋊Dic5C22×D312yes—
224#683—22no—
225#683—22no—
226C2×#168—31no—
227C2×#168—31no—
228C8×D5—122no—
229#554—51no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—151no—
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—41no—
243C2×D15—41no—
244C2×C5×D3—42no—
245C2×C5×D3—42no—
246C2×C5×D3—42no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5C2×SD1614yes—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5C2×SD1612yes—
255C3×C4×C5C2×#4111yescharacteristic
256C3×C4×C5H(5,𝔽2)11yescharacteristic
257Dic15—41no—
258C3×Dic5—22no—
259C3×Dic5—42no—
260C23×D3—102no—
261C2×C3×Q8—101no—
262C2×C3×Q8C22×D511yescharacteristic
263C2×C3×D4—51no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C2×#67—102no—
267D3×D4—204no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—51no—
271C2×D12—104no—
272C2×D12—102no—
273C2×D12—202no—
274C2×D12C22×D512yes—
275C2×C4×D3—101no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—51no—
278C3×C4⋊C4—52no—
279C3×C4⋊C4—102no—
280C3×C4⋊C4—102no—
281C3×C4⋊C4—101no—
282C3×C4⋊C4C22×D511yescharacteristic
283C3×C22⋊C4—52no—
284C3×C22⋊C4—102no—
285C3×C42—21no—
286C3×C42C22×D511yescharacteristic
287#215—42no—
288#215—102no—
289(C2×D3)⋊C4—102no—
290(C2×D3)⋊C4—101no—
291C4⋊Dic3—51no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—202no—
295C2×C3⋊C8C22×D512yes—
296C23×C5—62no—
297C22×D5—61no—
298C22×D5—124no—
299C22×D5—124no—
300C22×D5—242no—
301C22×D5C2×#6712yes—
302C5×Q8—21no—
303C5×Q8—21no—
304C5×D4—62no—
305C5×D4—62no—
306C5×D4—122no—
307C5×D4—241no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5C2×#6711yescharacteristic
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—124no—
314C22⋊D5—124no—
315C2×Dic5—22no—
316C2×Dic5—61no—
317C2×Dic5C2×#6712yes—
318D20—32no—
319D20—61no—
320D20#21514yescomplemented
321C4×D5—22no—
322C4×D5—22no—
323C4×D5—82no—
324C4×D5—122no—
325Dic10—81no—
326C5×C8—62no—
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—101no—
337C22⋊Q8—52no—
338C22⋊Q8—102no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8D3×D511yescharacteristic, complemented
343C4×D4—51no—
344C4×D4—101no—
345C4×D4—151no—
346C2×C4⋊C4—52no—
347#106—152no—
348#106—151no—
349C4⋊C8—31no—
350#103—151no—
351#102—32no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—151no—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5C22×SD1611yescharacteristic
360C2×C3×C5#57611yescharacteristic
361D15—42no—
362C3×D5—24no—
363C5×D3—82no—
364C23×C3—52no—
365C22×D3—22no—
366C22×D3—101no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—21no—
371C3×Q8—21no—
372C3×Q8—401no—
373C3×D4—54no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—52no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—402no—
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4D4×D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—204no—
385C2×Dic3—101no—
386D12—22no—
387D12—22no—
388D12—42no—
389D12—52no—
390D12—81no—
391D12—101no—
392D12—204no—
393C4×D3—202no—
394C3⋊C8—22no—
395C3⋊C8—101no—
396C3⋊C8—101no—
397C22×C5—122no—
398C22×C5—122no—
399C22×C5—122no—
400C22×C5C22×#6711yescharacteristic
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—62no—
404C2×D5—121no—
405C2×D5—121no—
406C2×D5—248no—
407C2×D5C2×#21514yes—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5C2×#21512yes—
412C4×C5D3×#4111yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—22no—
415Dic5—42no—
416Dic5—121no—
417C24—302no—
418C2×Q8—101no—
419C2×Q8C2×D3×D511yescharacteristic
420C2×D4—32no—
421C2×D4—51no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—151no—
425C2×D4—302no—
426C2×D4—304no—
427C2×D4—302no—
428C2×D4—602no—
429C2×D4—604no—
430C22×C4—52no—
431C22×C4—102no—
432C22×C4—301no—
433SD16—122no—
434SD16—302no—
435C2×C8—32no—
436C2×C8—151no—
437C2×C8—151no—
438C2×C8—602no—
439C4⋊C4—21no—
440C4⋊C4—51no—
441C4⋊C4—52no—
442C4⋊C4—102no—
443C4⋊C4—102no—
444C4⋊C4—101no—
445C4⋊C4—151no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—52no—
448C22⋊C4—102no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—21no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—54no—
455C22×C3—102no—
456C22×C3—102no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—102no—
462C2×D3—201no—
463C2×D3—201no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—102no—
469C3×C4—202no—
470C3×C4D5×SD1612yes—
471C3×C4#414411yescharacteristic
472C3×C4D5×#4111yescharacteristic
473Dic3—201no—
474C2×C5—242no—
475C2×C5C22×#21511yescharacteristic
476C2×C5#582911yescharacteristic
477C2×C5#583511yescharacteristic
478D5—24no—
479D5—122no—
480C23—52no—
481C23—62no—
482C23—301no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—21no—
487Q8—21no—
488Q8—401no—
489D4—54no—
490D4—62no—
491D4—62no—
492D4—122no—
493D4—152no—
494D4—241no—
495D4—301no—
496D4—604no—
497D4—604no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—52no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—301no—
505C2×C4—402no—
506C2×C4—602no—
507C2×C4D5×#6711yescharacteristic
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—301no—
512C8—301no—
513C2×C3—104no—
514C2×C3#6594611yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—82no—
518D3—202no—
519C5#8363411yescharacteristic, complemented, Sylow
520C22—54no—
521C22—102no—
522C22—102no—
523C22—122no—
524C22—122no—
525C22—122no—
526C22—302no—
527C22—601no—
528C22—601no—
529C22—1208no—
530C22C2×D5×#6711yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—102no—
535C4—202no—
536C4—601no—
537C4D5×#21512yes—
538C4#9201611yescharacteristic
539C4#9201811yescharacteristic
540C3#1061212611yescharacteristic, complemented, Sylow
541C2—104no—
542C2—242no—
543C2—602no—
544C2#1175464111yescharacteristic
545C2C2×D5×#21511yescharacteristic
546C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. C3×#65913C2semidirect
3. C4×#6717C2semidirect
4. C5×#5027C2semidirect
5. #11749397C2semidirect
6. #11749365C2semidirect
7. D5×#809C2semidirect
8. #11747308C2semidirect
9. #11746996C2semidirect
10. #11746942C2semidirect
11. #11746901C2semidirect
15. C3×C4×C5×Q8C22semidirect
18. C2×C5×#215C22semidirect
20. C3×#4092C22semidirect
22. C3×D5×C4⋊C4C22semidirect
26. C3×#4015C22semidirect
30. C2×D5×C3⋊C8C22semidirect
31. #91119C22semidirect
33. #91092C22semidirect
34. C4×C3⋊#168C22semidirect
35. C5×#809C22semidirect
36. C5×C4⋊(C3⋊C8)C22semidirect
37. #90987C22semidirect
39. #90966C22semidirect
40. #90966C22semidirect
41. #90955C22semidirect
44. #65913D3semidirect
96. #5027D5semidirect
105. C4×C5×Q8C2×D3semidirect
106. #4092C2×D3semidirect
113. D5×C4⋊C4C2×D3semidirect
118. #4015C2×D3semidirect
154. C3×D20SD16semidirect
170. C3×C4×Q8C2×D5semidirect
175. C2×#215C2×D5semidirect
188. #809C2×D5semidirect
191. C4⋊(C3⋊C8)C2×D5semidirect
320. D20#215semidirect
342. C4×Q8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#83634semidirect
540. C3#10612126semidirect

Maximal subgroups

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

subgroupindex
C3×#659132
#117527372
C4×#67172
C5×#50272
#117493972
#117493652
D5×#8092
#117473082
#117469962
#117469422
#117469012
#106121263
#836345