Finite Group Databasebeta

← #14458445

Subgroups — #14458445

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
2D4×D60C211yesmaximal, characteristic
3C3×C5×#476C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5C4×#6716C211yesmaximal, characteristic, complemented
6#11750965C212yesmaximal, complemented
7#11750964C212yesmaximal, complemented
8#11750949C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750877C212yesmaximal, complemented
11D15×#102C212yesmaximal, complemented
12#10612806—31nomaximal, Hall
13C2×D4×D15C2212yes—
14C22×D60—21no—
15C3×C5×C4⋊Q8C2211yescharacteristic, complemented
16C3×C4×C5×D4C2211yescharacteristic
17#91835—22no—
18C2×#6716C2211yescharacteristic
19#91819—21no—
20C2×#6706C2212yescomplemented
21C2×C8×D15C2212yescomplemented
22#91786C2212yescomplemented
23#91784C2212yes—
24#91782—21no—
25C4⋊C4×D15C2212yescomplemented
26#91779—21no—
27#91771—22no—
28#91763C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C4×Dic30C2211yescharacteristic, complemented
31C3×C5×#106C2212yescomplemented
32C3×C5×C4⋊C8C2211yescharacteristic, complemented
33C3×C5×#102C2212yes—
34#91116C2211yescharacteristic
35#91105C2212yescomplemented
36#91104C2212yescomplemented
37#91094C2211yescharacteristic, complemented
38#91093C2212yescomplemented
39#91093C2212yescomplemented
40#91092C2211yescharacteristic, complemented
41C4×C3⋊#168C2211yescharacteristic, complemented
42#81075—51nomaximal, Hall
43#66064—31no—
44D4×D20—31no—
45C5×#476D311yescharacteristic, complemented
46#65377—31no—
47C4×#687—31no—
48#65153—32no—
49#65152—32no—
50#65137—31no—
51#65123—31no—
52#65065—32no—
53D5×#102—32no—
54C23×D15—22no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C2×#1220—22no—
59D4×D15—24no—
60D4×D15—42no—
61C2×D60—22no—
62C2×D60—21no—
63C2×D60—21no—
64C2×D60—44no—
65C2×D60D411yescharacteristic
66C2×D60C2312yes—
67C2×C4×D15—22no—
68C2×C4×D15C2312yes—
69C2×Dic30C2311yescharacteristic
70C2×C3×C5×C8C2312yes—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76#6716—22no—
77#6714—22no—
78#6714—22no—
79#6714D412yes—
80C4⋊Dic15—22no—
81C4⋊Dic15D411yescharacteristic
82C4⋊Dic15C2311yescharacteristic
83#6712—21no—
84#6712—22no—
85C4×Dic15—21no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88#6706—42no—
89C8×D15—42no—
90#5730—51no—
91D4×D12—51no—
92C3×#476D511yescharacteristic, complemented
93#5088—51no—
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—
102C22×D20—61no—
103C5×C4⋊Q8C2×D311yescharacteristic, complemented
104C4×C5×D4C2×D311yescharacteristic
105#4092—62no—
106C2×#687—31no—
107#4076—61no—
108C2×#677—32no—
109C2×C8×D5—32no—
110#4043—32no—
111#4041—32no—
112#4039—61no—
113D5×C4⋊C4—32no—
114#4036—61no—
115#4028—62no—
116#4020—31no—
117C4×D20—31no—
118C4×Dic10—31no—
119C5×#106C2×D312yescomplemented
120C5×C4⋊C8C2×D311yescharacteristic, complemented
121C5×#102C2×D312yes—
122#3964—31no—
123#3953—32no—
124#3952—32no—
125#3942—31no—
126#3941—32no—
127#3941—32no—
128#3940—31no—
129C4×#168—31no—
130#3295—151noSylow
131C23×C3×C5—21no—
132C22×D15—22no—
133C22×D15—44no—
134C22×D15—44no—
135C22×D15—82no—
136C22×D15C2×D412yes—
137C3×C5×Q8—81no—
138C3×C5×D4—21no—
139C3×C5×D4#4112yes—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147C2×Dic15—21no—
148C2×Dic15—21no—
149C2×Dic15C2×D412yes—
150D60—22no—
151D60—22no—
152D60—44no—
153D60—42no—
154D60—81no—
155D60SD1614yescomplemented
156C4×D15—22no—
157C4×D15—22no—
158C4×D15—82no—
159Dic30—21no—
160Dic30—21no—
161C3×C5×C8—22no—
162C3⋊#168—21no—
163C3⋊#168—21no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C3×C4⋊Q8C2×D511yescharacteristic, complemented
167C3×C4×D4C2×D511yescharacteristic
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#874—51no—
180C4×D12—51no—
181C4×Dic6—51no—
182C3×#106C2×D512yescomplemented
183C3×C4⋊C8C2×D511yescharacteristic, complemented
184C3×#102C2×D512yes—
185#832—51no—
186#821—52no—
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—21no—
195C2×C5×D4C22×D311yescharacteristic
196C22×C4×C5—21no—
197C2×C22⋊D5—62no—
198D4×D5—64no—
199D4×D5—122no—
200C2×D20—31no—
201C2×D20—32no—
202C2×D20—62no—
203C2×D20—61no—
204C2×D20—61no—
205C2×D20—124no—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×Dic10—31no—
209C2×C5×C8C22×D312yes—
210C5×C4⋊C4—21no—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C4⋊C4C22×D312yes—
213C5×C22⋊C4—21no—
214C42×C5C22×D311yescharacteristic
215#687—62no—
216#685—32no—
217#685—62no—
218#685—62no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222#683—62no—
223#683—61no—
224C4×Dic5—61no—
225C2×#168—31no—
226C2×#168—31no—
227#677—122no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476D1511yescharacteristic, complemented
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—41no—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—42no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—88no—
250C2×D15C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—42no—
254C3×C4×C5C2×SD1612yes—
255C3×C4×C5C2×#4111yescharacteristic
256C3×C4×C5H(5,𝔽2)11yescharacteristic
257Dic15—22no—
258Dic15—41no—
259Dic15—41no—
260C23×D3—102no—
261C2×C3×Q8—21no—
262C2×C3×D4C22×D511yescharacteristic
263C22×C3×C4—21no—
264C2×#67—102no—
265D3×D4—104no—
266D3×D4—202no—
267C2×D12—51no—
268C2×D12—52no—
269C2×D12—102no—
270C2×D12—101no—
271C2×D12—101no—
272C2×D12—204no—
273C2×C4×D3—52no—
274C2×C4×D3—102no—
275C2×Dic6—51no—
276C2×C3×C8C22×D512yes—
277C3×C4⋊C4—21no—
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C4⋊C4C22×D512yes—
280C3×C22⋊C4—21no—
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⋊C8—51no—
293C2×C3⋊C8—51no—
294#204—202no—
295D3×C8—202no—
296C23×C5—21no—
297C22×D5—32no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—81no—
303C5×D4—21no—
304C5×D4#23912yes—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—42no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C2×Dic5—32no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315D20—34no—
316D20—62no—
317D20—62no—
318D20—124no—
319D20—122no—
320D20—241no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5—242no—
324Dic10—61no—
325Dic10—61no—
326C5×C8—22no—
327#168—61no—
328#168—61no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8C2×D1511yescharacteristic, complemented
335#127—151no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—151no—
343C4×D4—151no—
344C4×D4—301no—
345C4×D4C2×D1511yescharacteristic
346C2×C4⋊C4—152no—
347#106—151no—
348#106C2×D1512yescomplemented
349C4⋊C8C2×D1511yescharacteristic, complemented
350#103—151no—
351#102—151no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102C2×D1512yes—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5—42no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—24no—
363D15—82no—
364C23×C3—21no—
365C22×D3—52no—
366C22×D3—102no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—81no—
371C3×D4—21no—
372C3×D4#71312yes—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—42no—
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—54no—
384D12—102no—
385D12—102no—
386D12—204no—
387D12—202no—
388D12—401no—
389C4×D3—102no—
390C4×D3—102no—
391C4×D3—402no—
392Dic6—101no—
393Dic6—101no—
394C3×C8—22no—
395C3⋊C8—101no—
396C3⋊C8—101no—
397C22×C5—22no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—34no—
402C2×D5—62no—
403C2×D5—62no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—42no—
411C4×C5D3×SD1612yes—
412C4×C5C2×#23911yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—62no—
415Dic5—121no—
416Dic5—121no—
417C24—302no—
418C2×Q8—21no—
419C2×Q8—151no—
420C2×D4—151no—
421C2×D4—152no—
422C2×D4—302no—
423C2×D4—302no—
424C2×D4—304no—
425C2×D4—301no—
426C2×D4—301no—
427C2×D4—604no—
428C2×D4—602no—
429C2×D4C22×D1511yescharacteristic
430C22×C4—21no—
431C22×C4—152no—
432C22×C4—302no—
433SD16—302no—
434SD16—602no—
435C2×C8—151no—
436C2×C8—151no—
437C2×C8—602no—
438C2×C8C22×D1512yes—
439C4⋊C4—21no—
440C4⋊C4—151no—
441C4⋊C4—151no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—301no—
445C4⋊C4C22×D1512yes—
446C4⋊C4C22×D1511yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—152no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—301no—
452C42C22×D1511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—54no—
459C2×D3—102no—
460C2×D3—102no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—202no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—42no—
468C3×C4D5×SD1612yes—
469C3×C4C2×#71311yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—102no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—42no—
475C2×C5#563011yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#577411yescharacteristic
478D5—64no—
479D5—242no—
480C23—21no—
481C23—152no—
482C23—302no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—81no—
487Q8—301no—
488Q8—301no—
489D4—21no—
490D4—154no—
491D4—302no—
492D4—302no—
493D4—604no—
494D4—604no—
495D4—602no—
496D4—1201no—
497D4#682112yes—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—152no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—301no—
505C2×C4—301no—
506C2×C4—1202no—
507C2×C4D4×D1511yescharacteristic
508C2×C4D4×D1511yescharacteristic
509C2×C4C23×D1511yescharacteristic
510C8—22no—
511C8—301no—
512C8—301no—
513C2×C3—42no—
514C2×C3#6596411yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—104no—
518D3—402no—
519C5#8107511yescharacteristic, complemented, Sylow
520C22—22no—
521C22—41no—
522C22—41no—
523C22—154no—
524C22—302no—
525C22—302no—
526C22—602no—
527C22—602no—
528C22—602no—
529C22—1208no—
530C22C2×D4×D1511yescharacteristic
531C4—21no—
532C4—41no—
533C4—42no—
534C4—302no—
535C4—601no—
536C4—601no—
537C4SD16×D1512yes—
538C4C2×#682111yescharacteristic
539C4#9210011yescharacteristic
540C3#1061280611yescharacteristic, complemented, Sylow
541C2—42no—
542C2—304no—
543C2—1202no—
544C2#1175638911yescharacteristic
545C2C2×SD16×D1511yescharacteristic
546C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#476C2
socleC22×C3×C5C22×D4
prime radicalD4×D60C2
hypercenter#476D15
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
3. C3×C5×#476C2semidirect
4. #11751189C2semidirect
5. C4×#6716C2semidirect
6. #11750965C2semidirect
7. #11750964C2semidirect
8. #11750949C2semidirect
9. #11750935C2semidirect
10. #11750877C2semidirect
11. D15×#102C2semidirect
15. C3×C5×C4⋊Q8C22semidirect
20. C2×#6706C22semidirect
21. C2×C8×D15C22semidirect
22. #91786C22semidirect
25. C4⋊C4×D15C22semidirect
30. C4×Dic30C22semidirect
31. C3×C5×#106C22semidirect
32. C3×C5×C4⋊C8C22semidirect
35. #91105C22semidirect
36. #91104C22semidirect
37. #91094C22semidirect
38. #91093C22semidirect
39. #91093C22semidirect
40. #91092C22semidirect
41. C4×C3⋊#168C22semidirect
45. C5×#476D3semidirect
92. C3×#476D5semidirect
103. C5×C4⋊Q8C2×D3semidirect
119. C5×#106C2×D3semidirect
120. C5×C4⋊C8C2×D3semidirect
155. D60SD16semidirect
166. C3×C4⋊Q8C2×D5semidirect
182. C3×#106C2×D5semidirect
183. C3×C4⋊C8C2×D5semidirect
233. #476D15semidirect
334. C4⋊Q8C2×D15semidirect
348. #106C2×D15semidirect
349. C4⋊C8C2×D15semidirect
453. C3×C5#3295semidirect
519. C5#81075semidirect
540. C3#10612806semidirect

Maximal subgroups

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

subgroupindex
#117564892
D4×D602
C3×C5×#4762
#117511892
C4×#67162
#117509652
#117509642
#117509492
#117509352
#117508772
D15×#1022
#106128063
#810755