Finite Group Databasebeta

← #14458508

Subgroups — #14458508

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
1C5×D4×D12C211yesmaximal, characteristic
2#11752641C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749056C212yesmaximal, complemented
6D3×#3964C212yesmaximal, complemented
7#11747448C212yesmaximal, complemented
8#11747199C212yesmaximal, complemented
9#11747086C211yesmaximal, characteristic, complemented
10#11746998C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10615214—31nomaximal, Hall
13C2×C5×D3×D4C2212yes—
14C22×C5×D12—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C2×#6716C2211yescharacteristic
17C4×Dic30C2211yescharacteristic, complemented
18C5×#930—21no—
19C5×#895C2212yes—
20C5×#882—22no—
21C5×#874C2211yescharacteristic
22C4×C5×D12C2211yescharacteristic
23C3×#4015C2211yescharacteristic, complemented
24#91435—21no—
25D3×C4⋊Dic5C2212yescomplemented
26#91410—22no—
27#91384—21no—
28#91365C2212yescomplemented
29C2×#6659C2212yescomplemented
30C2×D3×#168C2212yescomplemented
31#91116C2211yescharacteristic
32#91094C2211yescharacteristic, complemented
33#91092C2211yescharacteristic, complemented
34C4×C3⋊#168C2211yescharacteristic, complemented
35C3×#3964C2212yes—
36C3×#3940C2212yescomplemented
37C3×C4⋊#168C2211yescharacteristic, complemented
38#90967C2212yescomplemented
39#90966C2212yescomplemented
40#90966C2212yescomplemented
41(C2×D3)⋊#168C2212yescomplemented
42#81075—51nomaximal, Hall
43C5×D42—31no—
44#65877—31no—
45#65507—32no—
46C2×#3964—32no—
47#65364—31no—
48#65359—31no—
49#65330—32no—
50#65323—32no—
51C4×#687—31no—
52D4×#168—31no—
53#65297D311yescharacteristic, complemented
54C23×C5×D3—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×Dic30C2311yescharacteristic
58C2×C5×#67—22no—
59C5×D3×D4—24no—
60C5×D3×D4—42no—
61C2×C5×D12—22no—
62C2×C5×D12—21no—
63C2×C5×D12—21no—
64C2×C5×D12—44no—
65C2×C5×D12D411yescharacteristic
66C2×C5×D12C2312yes—
67C2×C4×C5×D3C2312yes—
68C2×C3×Dic10—21no—
69C2×D3×Dic5—22no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6716—22no—
74C4⋊Dic15C2311yescharacteristic
75#6712—21no—
76C4×Dic15—21no—
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C5×(C2×D3)⋊C4—22no—
80C5×(C2×D3)⋊C4D412yes—
81C5×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C2×C3×#168C2312yes—
85Dic3⋊Dic5—22no—
86#6668—22no—
87(C2×D3)⋊Dic5—22no—
88#6659—42no—
89D3×#168—42no—
90#5730—51no—
91D4×D12D511yescharacteristic
92C3×#476—51no—
93#5088—51no—
94C4×#214—51no—
95#4864—52no—
96#4863—52no—
97#4848—51no—
98#4834—51no—
99#4776—52no—
100D3×#102—52no—
101C22×C5×D4—32no—
102C22×C5×D4—61no—
103C5×#127—31no—
104C5×#121—32no—
105C5×#121—61no—
106C5×#120—62no—
107C4×C5×D4—31no—
108C4×C5×D4C2×D311yescharacteristic
109D4×Dic5—61no—
110C2×#687—31no—
111C2×#687—32no—
112C2×C4⋊Dic5—32no—
113#4070—32no—
114C22×#168—32no—
115#4036—61no—
116#4024—62no—
117#4015C2×D311yescharacteristic, complemented
118C4×Dic10—31no—
119#3964—31no—
120#3964—32no—
121#3964—32no—
122#3964—32no—
123#3964C2×D312yes—
124C22⋊#168—32no—
125#3942—31no—
126#3940—31no—
127#3940C2×D312yescomplemented
128C4⋊#168C2×D311yescharacteristic, complemented
129C4×#168—31no—
130#3295—151noSylow
131C23×C3×C5—21no—
132C22×C5×D3—22no—
133C22×C5×D3—44no—
134C22×C5×D3—44no—
135C22×C5×D3—82no—
136C22×C5×D3C2×D412yes—
137C3×C5×D4—21no—
138C3×C5×D4#4112yes—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—42no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146Dic30—21no—
147Dic30—21no—
148C5×#67—44no—
149C2×C5×Dic3C2×D412yes—
150C5×D12—22no—
151C5×D12—22no—
152C5×D12—44no—
153C5×D12—42no—
154C5×D12—81no—
155C5×D12SD1614yescomplemented
156C4×C5×D3—22no—
157C4×C5×D3—22no—
158C2×C3×Dic5—22no—
159C3×Dic10—81no—
160D3×Dic5—82no—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C3×#168—22no—
164C2×D3×D4C2×D512yes—
165C22×D12—21no—
166C3×C4⋊Q8—51no—
167C3×C4×D4C2×D511yescharacteristic
168#946—102no—
169C2×#214—51no—
170#930—21no—
171C2×#204—52no—
172C2×D3×C8—52no—
173#897—52no—
174#895C2×D512yes—
175#893—101no—
176D3×C4⋊C4—52no—
177#890—101no—
178#882—22no—
179#874C2×D511yescharacteristic
180C4×D12C2×D511yescharacteristic
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#809—52no—
190#809—52no—
191#808—51no—
192C4×C3⋊C8—51no—
193C24×C5—62no—
194C2×C5×D4—31no—
195C2×C5×D4—32no—
196C2×C5×D4—62no—
197C2×C5×D4—62no—
198C2×C5×D4—64no—
199C2×C5×D4—61no—
200C2×C5×D4—61no—
201C2×C5×D4—124no—
202C2×C5×D4—122no—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5—32no—
206C22×Dic5—62no—
207C2×Dic10—21no—
208C2×Dic10—31no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C22⋊C4—21no—
212C5×C22⋊C4—32no—
213C5×C22⋊C4—62no—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#687—62no—
217#687—122no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5—62no—
221C4⋊Dic5C22×D312yes—
222#683—62no—
223#683—61no—
224C4×Dic5—61no—
225C2×#168—31no—
226C2×#168—31no—
227C2×#168—122no—
228C2×#168C22×D312yes—
229#554—151no—
230D42—31no—
231#486—151no—
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×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—41no—
243C22×C3×C5C22×D411yescharacteristic
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3—42no—
247C2×C5×D3—42no—
248C2×C5×D3—42no—
249C2×C5×D3—88no—
250C2×C5×D3C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—41no—
257Dic15—41no—
258C3×Dic5—42no—
259C5×Dic3—22no—
260C23×D3—22no—
261C2×C3×Q8—101no—
262C2×C3×D4C22×D511yescharacteristic
263C22×C3×C4—21no—
264C2×#67—22no—
265D3×D4—24no—
266D3×D4—42no—
267C2×D12—22no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—44no—
271C2×D12C22⋊D511yescharacteristic
272C2×D12C22×D512yes—
273C2×C4×D3—102no—
274C2×C4×D3C22×D512yes—
275C2×Dic6—51no—
276C2×C3×C8—52no—
277C3×C4⋊C4—52no—
278C3×C4⋊C4—101no—
279C3×C4⋊C4C22×D511yescharacteristic
280C3×C22⋊C4—21no—
281C3×C42C22×D511yescharacteristic
282#214—102no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—102no—
285(C2×D3)⋊C4C22⋊D512yes—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22⋊D511yescharacteristic
289Dic3⋊C4—101no—
290Dic3⋊C4—102no—
291C4×Dic3—101no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294#204—202no—
295D3×C8—202no—
296C23×C5—21no—
297C23×C5—32no—
298C23×C5—62no—
299C23×C5—124no—
300C23×C5—124no—
301C23×C5—242no—
302C5×D4—21no—
303C5×D4—34no—
304C5×D4—62no—
305C5×D4—62no—
306C5×D4—124no—
307C5×D4—124no—
308C5×D4—122no—
309C5×D4—241no—
310C5×D4#23912yes—
311C2×C4×C5—21no—
312C2×C4×C5—32no—
313C2×C4×C5—42no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C2×Dic5—22no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322C2×Dic5—242no—
323Dic10—61no—
324Dic10—61no—
325Dic10—81no—
326#168—22no—
327#168—61no—
328#168—61no—
329C22×D4—32no—
330C22×D4—61no—
331C2×SD16—152no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8—51no—
335#127—31no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—32no—
340#121—61no—
341#120—62no—
342C4×Q8—151no—
343C4×D4—31no—
344C4×D4—301no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—152no—
347#106—52no—
348#106—151no—
349C4⋊C8—51no—
350#103—151no—
351#102—52no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—151no—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5—42no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362C5×D3—24no—
363C5×D3—82no—
364C23×C3—21no—
365C22×D3—22no—
366C22×D3—44no—
367C22×D3—44no—
368C22×D3—82no—
369C22×D3C2×C22⋊D512yes—
370C3×Q8—401no—
371C3×D4—21no—
372C3×D4#71112yes—
373C2×C3×C4—21no—
374C2×C3×C4—42no—
375C2×C3×C4—102no—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—44no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382C2×Dic3C2×C22⋊D512yes—
383D12—22no—
384D12—22no—
385D12—44no—
386D12—42no—
387D12—81no—
388D12#68714yescomplemented
389C4×D3—22no—
390C4×D3—22no—
391C4×D3—402no—
392Dic6—101no—
393Dic6—101no—
394C3×C8—102no—
395C3⋊C8—101no—
396C3⋊C8—101no—
397C22×C5—22no—
398C22×C5—34no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—62no—
402C22×C5—62no—
403C22×C5—122no—
404C22×C5—122no—
405C22×C5—122no—
406C22×C5—248no—
407C22×C5C2×D3×D411yescharacteristic
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—62no—
411C4×C5D3×SD1612yes—
412C4×C5C2×#23911yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—42no—
415Dic5—121no—
416Dic5—121no—
417C24—62no—
418C2×Q8—101no—
419C2×Q8—151no—
420C2×D4—31no—
421C2×D4—32no—
422C2×D4—62no—
423C2×D4—62no—
424C2×D4—64no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—124no—
428C2×D4—122no—
429C2×D4C2×D3×D511yescharacteristic
430C22×C4—21no—
431C22×C4—32no—
432C22×C4—302no—
433SD16—302no—
434SD16—602no—
435C2×C8—52no—
436C2×C8—151no—
437C2×C8—151no—
438C2×C8—602no—
439C4⋊C4—31no—
440C4⋊C4—52no—
441C4⋊C4—101no—
442C4⋊C4—151no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—32no—
449C22⋊C4—62no—
450C22⋊C4—302no—
451C42—301no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3C22×C22⋊D511yescharacteristic
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—88no—
464C2×D3C2×#68714yes—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—202no—
468C3×C4C2×#68712yes—
469C3×C4C2×#71111yescharacteristic
470C3×C4#414411yescharacteristic
471Dic3—22no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—42no—
475C2×C5—64no—
476C2×C5—242no—
477C2×C5#563011yescharacteristic
478C2×C5C2×D3×SD1611yescharacteristic
479C2×C5#577411yescharacteristic
480C23—21no—
481C23—32no—
482C23—62no—
483C23—124no—
484C23—124no—
485C23—242no—
486Q8—301no—
487Q8—301no—
488Q8—401no—
489D4—21no—
490D4—34no—
491D4—62no—
492D4—62no—
493D4—124no—
494D4—124no—
495D4—122no—
496D4—241no—
497D4#676812yes—
498C2×C4—21no—
499C2×C4—32no—
500C2×C4—42no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—102no—
504C2×C4—301no—
505C2×C4—301no—
506C2×C4—1202no—
507C2×C4D3×C22⋊D511yescharacteristic
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—102no—
511C8—301no—
512C8—301no—
513C2×C3—42no—
514C2×C3C22×#68711yescharacteristic
515C2×C3#6614011yescharacteristic
516C2×C3#6616911yescharacteristic
517D3—24no—
518D3—82no—
519C5#8107511yescharacteristic, complemented, Sylow
520C22—22no—
521C22—34no—
522C22—41no—
523C22—41no—
524C22—62no—
525C22—62no—
526C22—122no—
527C22—122no—
528C22—122no—
529C22—248no—
530C22C2×D3×C22⋊D511yescharacteristic
531C4—21no—
532C4—41no—
533C4—62no—
534C4—202no—
535C4—601no—
536C4—601no—
537C4D3×#68712yes—
538C4C2×#676811yescharacteristic
539C4#9201811yescharacteristic
540C3#1061521411yescharacteristic, complemented, Sylow
541C2—42no—
542C2—64no—
543C2—242no—
544C2#1175434911yescharacteristic
545C2C2×D3×#68711yescharacteristic
546C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×D4×D12C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752641C2semidirect
3. C4×#6716C2semidirect
4. C3×#65297C2semidirect
5. #11749056C2semidirect
6. D3×#3964C2semidirect
7. #11747448C2semidirect
8. #11747199C2semidirect
9. #11747086C2semidirect
10. #11746998C2semidirect
11. #11746901C2semidirect
17. C4×Dic30C22semidirect
23. C3×#4015C22semidirect
25. D3×C4⋊Dic5C22semidirect
28. #91365C22semidirect
29. C2×#6659C22semidirect
30. C2×D3×#168C22semidirect
32. #91094C22semidirect
33. #91092C22semidirect
34. C4×C3⋊#168C22semidirect
36. C3×#3940C22semidirect
37. C3×C4⋊#168C22semidirect
38. #90967C22semidirect
39. #90966C22semidirect
40. #90966C22semidirect
41. (C2×D3)⋊#168C22semidirect
53. #65297D3semidirect
117. #4015C2×D3semidirect
127. #3940C2×D3semidirect
128. C4⋊#168C2×D3semidirect
155. C5×D12SD16semidirect
388. D12#687semidirect
453. C3×C5#3295semidirect
519. C5#81075semidirect
540. C3#10615214semidirect

Maximal subgroups

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

subgroupindex
C5×D4×D122
#117526412
C4×#67162
C3×#652972
#117490562
D3×#39642
#117474482
#117471992
#117470862
#117469982
#117469012
#106152143
#810755