Finite Group Databasebeta

← #14458570

Subgroups — #14458570

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#11752654C211yesmaximal, characteristic, complemented
3C8×D60C211yesmaximal, characteristic, complemented
4C5×#4694C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11748111C212yesmaximal, complemented
7#11748108C212yesmaximal, complemented
8#11747928C212yesmaximal, complemented
9#11747635C212yesmaximal, complemented
10#11747060C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10613308—31nomaximal, Hall
13C2×#6777C2212yes—
14C2×D5×D12—21no—
15C2×C8×D15C2212yescomplemented
16C4×D60C2211yescharacteristic
17C5×#874C2211yescharacteristic
18C5×#869C2211yescharacteristic, complemented
19C2×C3×#677C2211yescharacteristic
20C3×C4×D20C2211yescharacteristic
21C3×C4×Dic10C2211yescharacteristic, complemented
22#91475—22no—
23#91466C2212yes—
24#91449—21no—
25#91437C2212yescomplemented
26#91424—22no—
27#91418—21no—
28#91390C2212yescomplemented
29#91388—21no—
30C2×#6656C2212yescomplemented
31C3×C4×C5×C8C2211yescharacteristic, complemented
32#91104C2212yescomplemented
33C4⋊(C3⋊#168)C2211yescharacteristic, complemented
34C5×#821C2212yescomplemented
35C5×#821C2212yescomplemented
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic, complemented
38C3×#3948C2211yescharacteristic, complemented
39#90986C2212yescomplemented
40#90966C2212yescomplemented
41#90964C2212yes—
42#79676—51nomaximal, Hall
43#66064—31no—
44#66051—31no—
45C5×#486—31no—
46#65373—31no—
47#65364—31no—
48#65067—32no—
49#65066—32no—
50#65065—32no—
51D5×#102—32no—
52C4×#677D311yescharacteristic, complemented
53C8×D20—31no—
54C22×D3×D5—22no—
55C2×D60D411yescharacteristic
56C2×C4×D15C2312yes—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C5×Dic6—21no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10C2311yescharacteristic
64C2×#1203—22no—
65C2×#1201—22no—
66C2×#1200—22no—
67#6777—24no—
68#6777—42no—
69D5×D12—44no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C3×C42×C5C2311yescharacteristic
73#6714D412yes—
74C4⋊Dic15D411yescharacteristic
75C2×C3⋊#168C2312yes—
76C8×D15—42no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—21no—
83C3×C4×Dic5—21no—
84C3×#677—22no—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6667—22no—
88(C2×D3)⋊Dic5—22no—
89#6656—42no—
90#5579—51no—
91D4×D12—51no—
92C3×C4×SD16—51no—
93#5169—52no—
94#5027—51no—
95#5008—51no—
96#4863—52no—
97#4807—52no—
98D3×#102—52no—
99#4694D511yescharacteristic, complemented
100C8×D12—51no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C5×C4⋊Q8—31no—
104C5×#127—31no—
105#4092—62no—
106#4084—32no—
107#4084—61no—
108#4083—62no—
109C2×#687—32no—
110C2×#677C2×D311yescharacteristic
111C2×C8×D5—32no—
112#4043—32no—
113#4039—61no—
114D5×C4⋊C4—32no—
115#4036—61no—
116C4×D20—31no—
117C4×D20C2×D311yescharacteristic
118C4×Dic10C2×D311yescharacteristic, complemented
119C5×#102—32no—
120C5×#102—32no—
121C4×C5×C8C2×D311yescharacteristic, complemented
122#3964—32no—
123#3953C2×D311yescharacteristic
124#3952—32no—
125#3949C2×D311yescharacteristic, complemented
126#3948C2×D311yescharacteristic, complemented
127#3941—32no—
128#3940—32no—
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—22no—
145C5×D12—22no—
146C5×D12—22no—
147C5×D12—42no—
148C5×D12—81no—
149C5×Dic6—81no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C3×D20—21no—
154C3×D20#4112yes—
155C3×C4×D5—42no—
156C3×Dic10—21no—
157C3×Dic10—21no—
158#1203—44no—
159#1201—44no—
160#1200—82no—
161C3×C5×C8—21no—
162C3×C5×C8—21no—
163C3⋊#168—22no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C2×C3×SD16—51no—
167C3×C4×Q8—51no—
168C3×C4×D4—51no—
169#946—52no—
170C2×#215—52no—
171#930—101no—
172C2×D3×C8—52no—
173#896—102no—
174#895—52no—
175D3×C4⋊C4—52no—
176#882—102no—
177#874C2×D511yescharacteristic
178C4×D12—51no—
179C4×D12—101no—
180#870—101no—
181#869C2×D511yescharacteristic, complemented
182C3×#106—51no—
183C3×#103—51no—
184C3×#102—51no—
185C3×C4×C8C2×D511yescharacteristic, complemented
186#832—52no—
187#821C2×D512yescomplemented
188#821C2×D512yescomplemented
189(C2×D3)⋊C8—52no—
190#809—52no—
191#808—52no—
192C4⋊(C3⋊C8)—51no—
193C23×D5—62no—
194C2×C5×Q8—61no—
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×Dic10C22×D311yescharacteristic
209C2×C5×C8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C42×C5C22×D311yescharacteristic
214C22⋊Dic5—62no—
215#687—122no—
216#685—21no—
217#685—32no—
218#685—62no—
219C4⋊Dic5—31no—
220C4⋊Dic5—62no—
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D311yescharacteristic
223#683—21no—
224#683—62no—
225C4×Dic5—21no—
226C2×#168—32no—
227#677—22no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—31no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—51no—
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—41no—
258C3×Dic5—41no—
259C5×Dic3—42no—
260C23×D3—102no—
261C2×C3×Q8—51no—
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—21no—
276C3×SD16—102no—
277C2×C3×C8C22×D511yescharacteristic
278C2×C3×C8C22×D511yescharacteristic
279C3×C4⋊C4—51no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4—101no—
282C3×C22⋊C4—101no—
283C3×C42—101no—
284C3×C42C22×D511yescharacteristic
285#215—202no—
286(C2×D3)⋊C4—52no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—102no—
289C4⋊Dic3—21no—
290C4⋊Dic3—51no—
291C4⋊Dic3C22×D512yes—
292Dic3⋊C4—102no—
293Dic3⋊C4—102no—
294C2×C3⋊C8—52no—
295D3×C8—202no—
296C23×C5—62no—
297C22×D5—21no—
298C22×D5—32no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—241no—
303C5×D4—62no—
304C5×D4—62no—
305C5×D4—122no—
306C5×D4—241no—
307C2×C4×C5—62no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C22⋊D5—124no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—32no—
317D20—21no—
318D20—34no—
319D20#23512yes—
320C4×D5—42no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5—242no—
324Dic10—21no—
325Dic10—21no—
326C5×C8—21no—
327C5×C8—21no—
328#168—62no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—51no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8—31no—
335#127—31no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—51no—
343C4×D4—51no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—51no—
348#106—152no—
349C4⋊C8—151no—
350#103—51no—
351#102—32no—
352#102—32no—
353#102—51no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8D3×D511yescharacteristic, complemented
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—101no—
371C3×Q8—101no—
372C3×D4—52no—
373C3×D4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—202no—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—204no—
382C2×Dic3—22no—
383C2×Dic3—52no—
384D12—22no—
385D12—22no—
386D12—42no—
387D12—54no—
388D12—81no—
389D12—204no—
390C4×D3—102no—
391C4×D3—102no—
392C4×D3—402no—
393Dic6—81no—
394C3×C8—21no—
395C3×C8—21no—
396C3⋊C8—102no—
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—122no—
410C4×C5D3×SD1612yes—
411C4×C5C2×#23511yescharacteristic
412C4×C5#100911yescharacteristic
413Dic5—41no—
414Dic5—41no—
415Dic5—41no—
416Dic5—62no—
417C24—302no—
418C2×Q8—51no—
419C2×Q8—61no—
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—102no—
434SD16—602no—
435C2×C8—152no—
436C2×C8—602no—
437C2×C8C2×D3×D511yescharacteristic
438C2×C8C2×D3×D511yescharacteristic
439C4⋊C4—32no—
440C4⋊C4—51no—
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—101no—
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—201no—
468C3×C4—201no—
469C3×C4D5×SD1612yes—
470C3×C4D5×#4111yescharacteristic
471C3×C4#414911yescharacteristic
472Dic3—42no—
473Dic3—102no—
474C2×C5—242no—
475C2×C5#555011yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#576911yescharacteristic
478D5—42no—
479D5—64no—
480C23—62no—
481C23—101no—
482C23—152no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—101no—
487Q8—101no—
488Q8—241no—
489D4—52no—
490D4—62no—
491D4—62no—
492D4—101no—
493D4—122no—
494D4—154no—
495D4—241no—
496D4—604no—
497D4—604no—
498C2×C4—62no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—101no—
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—21no—
511C8—21no—
512C8—302no—
513C2×C3—202no—
514C2×C3#6601011yescharacteristic
515C2×C3#6609111yescharacteristic
516C2×C3C2×D5×SD1611yescharacteristic
517D3—82no—
518D3—104no—
519C5#7967611yescharacteristic, 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—122no—
533C4—201no—
534C4—201no—
535C4—201no—
536C4—302no—
537C4#9125512yes—
538C4D5×#23511yescharacteristic
539C4#9201911yescharacteristic
540C3#1061330811yescharacteristic, complemented, Sylow
541C2—202no—
542C2—242no—
543C2—304no—
544C2#1175274811yescharacteristic
545C2C2×#9125511yescharacteristic
546C2#1175398311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. #11752654C2semidirect
3. C8×D60C2semidirect
4. C5×#4694C2semidirect
5. C3×C4×#677C2semidirect
6. #11748111C2semidirect
7. #11748108C2semidirect
8. #11747928C2semidirect
9. #11747635C2semidirect
10. #11747060C2semidirect
11. #11746880C2semidirect
15. C2×C8×D15C22semidirect
18. C5×#869C22semidirect
21. C3×C4×Dic10C22semidirect
25. #91437C22semidirect
28. #91390C22semidirect
30. C2×#6656C22semidirect
31. C3×C4×C5×C8C22semidirect
32. #91104C22semidirect
33. C4⋊(C3⋊#168)C22semidirect
34. C5×#821C22semidirect
35. C5×#821C22semidirect
37. C3×#3949C22semidirect
38. C3×#3948C22semidirect
39. #90986C22semidirect
40. #90966C22semidirect
52. C4×#677D3semidirect
99. #4694D5semidirect
118. C4×Dic10C2×D3semidirect
121. C4×C5×C8C2×D3semidirect
125. #3949C2×D3semidirect
126. #3948C2×D3semidirect
141. D60SD16semidirect
181. #869C2×D5semidirect
185. C3×C4×C8C2×D5semidirect
187. #821C2×D5semidirect
188. #821C2×D5semidirect
357. C4×C8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#79676semidirect
540. C3#10613308semidirect

Maximal subgroups

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

subgroupindex
#117527372
#117526542
C8×D602
C5×#46942
C3×C4×#6772
#117481112
#117481082
#117479282
#117476352
#117470602
#117468802
#106133083
#796765