Finite Group Databasebeta

← #14478496

Subgroups — #14478496

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756528C211yesmaximal, characteristic, complemented
2#11756516C211yesmaximal, characteristic, complemented
3C3×C5×#509C211yesmaximal, characteristic, complemented
4#11751295C211yesmaximal, characteristic, complemented
5C2×#91110C211yesmaximal, characteristic, complemented
6#11751017C212yesmaximal, complemented
7#11751015C212yesmaximal, complemented
8#11751012C212yesmaximal, complemented
9D15×D16C212yesmaximal, complemented
10#11751009C211yesmaximal, characteristic, complemented
11#11751008C211yesmaximal, characteristic, complemented
12#10613767—31nomaximal, Hall
13#92100—21no—
14#92095—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16C2×C3×C5×D8C2211yescharacteristic, complemented
17#91838—21no—
18#91821—21no—
19#91808C2212yescomplemented
20#91803—22no—
21#91801C2212yescomplemented
22#91800—22no—
23D8×D15C2212yescomplemented
24D8×D15C2212yescomplemented
25#91793C2211yescharacteristic, complemented
26C2×D120C2211yescharacteristic, complemented
27#91790C2211yescharacteristic
28C3×C5×SD32C2212yescomplemented
29C3×C5×D16C2212yescomplemented
30C3×C5×M32C2211yescharacteristic, complemented
31#91113C2211yescharacteristic, complemented
32#91112C2211yescharacteristic, complemented
33#91111C2211yescharacteristic, complemented
34#91110C2212yescomplemented
35#91110C2212yescomplemented
36#91110C2211yescharacteristic, complemented
37C2×C3⋊#672C2211yescharacteristic, complemented
38#91084C2212yescomplemented
39D240C2212yescomplemented
40#91082C2212yescomplemented
41C16×D15C2212yescomplemented
42#82036—51nomaximal, Hall
43#66103—31no—
44#66091—31no—
45C5×#509D311yescharacteristic, complemented
46#65483—31no—
47C2×#3958—31no—
48#65205—32no—
49#65203—32no—
50#65200—32no—
51D5×D16—32no—
52#65197—31no—
53#65196—31no—
54C3×C5×#41—21no—
55C2×C3×C5×D4—21no—
56C2×#1220—42no—
57#6821—22no—
58#6819—22no—
59#6819—41no—
60D4×D15—22no—
61D4×D15—22no—
62D4×D15—42no—
63D4×D15—41no—
64#6817—21no—
65#6817—41no—
66#6817D411yescharacteristic
67C2×D60—21no—
68C2×D60—41no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8—21no—
72C3×C5×D8C2311yescharacteristic
73C3×C5×D8C2312yes—
74C2×C3×C5×C8C2311yescharacteristic
75#6717—22no—
76#6716—22no—
77#6715—22no—
78#6715—22no—
79#6710D411yescharacteristic
80Dic60C2311yescharacteristic
81D120—21no—
82D120C2312yes—
83D120C2311yescharacteristic
84#6706—21no—
85#6705D412yes—
86C8×D15C2312yes—
87C3×C5×C16C2312yes—
88C3⋊#672C2311yescharacteristic
89C3⋊#672C2311yescharacteristic
90#5769—51no—
91#5757—51no—
92C3×#509D511yescharacteristic, complemented
93#5194—51no—
94C2×#826—51no—
95#4916—52no—
96#4914—52no—
97#4911—52no—
98D3×D16—52no—
99#4908—51no—
100#4907—51no—
101#4149—61no—
102#4144—61no—
103C5×#135C2×D311yescharacteristic, complemented
104C2×C5×D8C2×D311yescharacteristic, complemented
105#4095—61no—
106#4078—61no—
107#4065—32no—
108#4060—62no—
109#4058—32no—
110#4057—62no—
111D5×D8—32no—
112D5×D8—32no—
113#4050—31no—
114C2×D40—31no—
115#4047—31no—
116C5×SD32C2×D312yescomplemented
117C5×D16C2×D312yescomplemented
118C5×M32C2×D311yescharacteristic, complemented
119#3961—31no—
120#3960—31no—
121#3959—31no—
122#3958—32no—
123#3958—32no—
124#3958—31no—
125C2×#672—31no—
126#3932—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3415—151noSylow
131C23×C3×C5—41no—
132C22×D15—41no—
133C22×D15—42no—
134C22×D15—42no—
135C3×C5×Q8—21no—
136C3×C5×D4—21no—
137C3×C5×D4—22no—
138C3×C5×D4—41no—
139C3×C5×D4—41no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5C2×D411yescharacteristic
142#1220—41no—
143#1220—42no—
144#1220—42no—
145#1220—42no—
146#1220D812yes—
147C2×Dic15—42no—
148D60—21no—
149D60—22no—
150D60—42no—
151D60—41no—
152D60D811yescharacteristic
153C4×D15—41no—
154C4×D15—42no—
155C4×D15C2×D412yes—
156Dic30—21no—
157Dic30D811yescharacteristic
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1009—101no—
162#1004—101no—
163C3×#135C2×D511yescharacteristic, complemented
164C2×C3×D8C2×D511yescharacteristic, complemented
165#949—101no—
166#932—101no—
167#919—52no—
168#914—102no—
169#912—52no—
170#911—102no—
171D3×D8—52no—
172D3×D8—52no—
173#904—51no—
174C2×D24—51no—
175#901—51no—
176C3×SD32C2×D512yescomplemented
177C3×D16C2×D512yescomplemented
178C3×M32C2×D511yescharacteristic, complemented
179#829—51no—
180#828—51no—
181#827—51no—
182#826—52no—
183#826—52no—
184#826—51no—
185C2×C3⋊C16—51no—
186#800—52no—
187D48—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C2×C5×D4—21no—
192C2×C22⋊D5—122no—
193#713—62no—
194#711—62no—
195#711—121no—
196D4×D5—62no—
197D4×D5—62no—
198D4×D5—121no—
199D4×D5—122no—
200#709—31no—
201#709—61no—
202#709—121no—
203C2×D20—61no—
204C2×D20—121no—
205C5×Q16C22×D311yescharacteristic
206C5×SD16—21no—
207C5×D8—21no—
208C5×D8C22×D312yes—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#688—62no—
212#687—62no—
213#686—62no—
214#686—62no—
215#681—31no—
216Dic20—31no—
217D40—31no—
218D40—32no—
219D40—61no—
220#677—61no—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D312yes—
224#672—31no—
225#672—31no—
226#576—151no—
227#576—151no—
228#509—152no—
229#509—152no—
230#509—151no—
231#509D1511yescharacteristic, complemented
232#508—151no—
233#508—152no—
234C2×D16—151no—
235C2×D16—152no—
236#504—151no—
237C22×C3×C5—42no—
238C22×C3×C5—41no—
239C22×C3×C5—161no—
240C22×C3×C5C2×D811yescharacteristic
241C2×D15—42no—
242C2×D15—41no—
243C2×D15—162no—
244C2×D15—162no—
245C2×D15—161no—
246C2×D15C2×D812yes—
247C3×C4×C5—41no—
248C3×C4×C5C2×D811yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—41no—
251Dic15C2×D812yes—
252C3×#41—21no—
253C2×C3×D4—21no—
254C2×#67—202no—
255#239—102no—
256#237—102no—
257#237—201no—
258D3×D4—102no—
259D3×D4—102no—
260D3×D4—201no—
261D3×D4—202no—
262#235—51no—
263#235—101no—
264#235—201no—
265C2×D12—101no—
266C2×D12—201no—
267C3×Q16C22×D511yescharacteristic
268C3×SD16—21no—
269C3×D8—21no—
270C3×D8C22×D512yes—
271C3×D8C22×D511yescharacteristic
272C2×C3×C8C22×D511yescharacteristic
273#215—102no—
274#214—102no—
275#213—102no—
276#213—102no—
277#208—51no—
278Dic12—51no—
279D24—51no—
280D24—52no—
281D24—101no—
282#204—101no—
283ΓL(1,𝔽25)—52no—
284D3×C8—52no—
285C3×C16C22×D512yes—
286C3⋊C16—51no—
287C3⋊C16—51no—
288C23×C5—41no—
289C22×D5—122no—
290C22×D5—122no—
291C22×D5—121no—
292C5×Q8—21no—
293C5×D4—21no—
294C5×D4—22no—
295C5×D4—41no—
296C5×D4—41no—
297C2×C4×C5—41no—
298C2×C4×C5D3×D411yescharacteristic
299C22⋊D5—32no—
300C22⋊D5—122no—
301C22⋊D5—122no—
302C22⋊D5—122no—
303C22⋊D5—121no—
304C2×Dic5—122no—
305D20—31no—
306D20—61no—
307D20—62no—
308D20—122no—
309D20—121no—
310C4×D5—32no—
311C4×D5—122no—
312C4×D5—121no—
313Dic10—31no—
314Dic10—61no—
315C5×C8D3×D411yescharacteristic
316C5×C8C23×D311yescharacteristic
317#168—32no—
318H(5,𝔽2)—301no—
319H(5,𝔽2)—301no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—302no—
322AGL(1,ℤ/8)—301no—
323AGL(1,ℤ/8)—301no—
324#135—152no—
325#135—152no—
326#135—151no—
327#135C2×D1511yescharacteristic, complemented
328C2×D8—152no—
329C2×D8—152no—
330C2×D8—151no—
331C2×D8C2×D1511yescharacteristic, complemented
332#131—151no—
333Q32—151no—
334SD32—151no—
335SD32—151no—
336SD32—152no—
337SD32C2×D1512yescomplemented
338D16—152no—
339D16—151no—
340D16—152no—
341D16—152no—
342D16C2×D1512yescomplemented
343M32—152no—
344M32C2×D1511yescharacteristic, complemented
345C2×C16—151no—
346C2×C16—152no—
347C2×C3×C5—21no—
348C2×C3×C5—81no—
349C2×C3×C5—82no—
350C2×C3×C5C22×D811yescharacteristic
351D15—22no—
352D15—82no—
353D15—81no—
354C23×C3—41no—
355C22×D3—202no—
356C22×D3—202no—
357C22×D3—201no—
358C3×Q8—21no—
359C3×D4—21no—
360C3×D4—22no—
361C3×D4—41no—
362C3×D4—41no—
363C2×C3×C4—41no—
364C2×C3×C4D4×D511yescharacteristic
365#67—52no—
366#67—202no—
367#67—202no—
368#67—202no—
369#67—201no—
370C2×Dic3—202no—
371D12—51no—
372D12—101no—
373D12—102no—
374D12—202no—
375D12—201no—
376C4×D3—52no—
377C4×D3—202no—
378C4×D3—201no—
379Dic6—51no—
380Dic6—101no—
381C3×C8D4×D511yescharacteristic
382C3×C8C23×D511yescharacteristic
383C3⋊C8—52no—
384C22×C5—42no—
385C22×C5—41no—
386C22×C5—161no—
387C22×C5D3×D811yescharacteristic
388C2×D5—32no—
389C2×D5—122no—
390C2×D5—121no—
391C2×D5—482no—
392C2×D5—482no—
393C2×D5—481no—
394C4×C5—41no—
395C4×C5D3×D811yescharacteristic
396C4×C5C2×D3×D411yescharacteristic
397Dic5—32no—
398Dic5—121no—
399#41—21no—
400#41—151no—
401#41—302no—
402#41—302no—
403#41—301no—
404#41—601no—
405#41—601no—
406C2×D4—21no—
407C2×D4—302no—
408C2×D4—302no—
409C2×D4—301no—
410C2×D4—601no—
411C2×D4—602no—
412C2×D4—601no—
413C2×D4—602no—
414Q16—151no—
415Q16C22×D1511yescharacteristic
416SD16—21no—
417SD16—302no—
418SD16—302no—
419SD16—301no—
420D8—21no—
421D8—152no—
422D8—151no—
423D8—302no—
424D8—302no—
425D8—301no—
426D8C22×D1512yes—
427D8C22×D1511yescharacteristic
428M16—151no—
429M16—152no—
430C2×C8—152no—
431C2×C8C22×D1511yescharacteristic
432C16—151no—
433C16—151no—
434C16C22×D1512yes—
435C3×C5#341511yescharacteristic, complemented, Hall
436C22×C3—42no—
437C22×C3—41no—
438C22×C3—161no—
439C22×C3D5×D811yescharacteristic
440C2×D3—52no—
441C2×D3—202no—
442C2×D3—201no—
443C2×D3—802no—
444C2×D3—802no—
445C2×D3—801no—
446C3×C4—41no—
447C3×C4D5×D811yescharacteristic
448C3×C4C2×D4×D511yescharacteristic
449Dic3—52no—
450Dic3—201no—
451C2×C5—21no—
452C2×C5—81no—
453C2×C5—82no—
454C2×C5C2×D3×D811yescharacteristic
455D5—62no—
456D5—242no—
457D5—241no—
458C23—41no—
459C23—602no—
460C23—602no—
461C23—601no—
462Q8—21no—
463Q8—151no—
464Q8—301no—
465D4—22no—
466D4—21no—
467D4—41no—
468D4—41no—
469D4—152no—
470D4—151no—
471D4—301no—
472D4—302no—
473D4—602no—
474D4—602no—
475D4—602no—
476D4—602no—
477D4—601no—
478D4—601no—
479C2×C4—41no—
480C2×C4—152no—
481C2×C4—602no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C4D4×D1511yescharacteristic
485C8—152no—
486C8D4×D1511yescharacteristic
487C8C23×D1511yescharacteristic
488C2×C3—21no—
489C2×C3—81no—
490C2×C3—82no—
491C2×C3C2×D5×D811yescharacteristic
492D3—102no—
493D3—402no—
494D3—401no—
495C5#8203611yescharacteristic, complemented, Sylow
496C22—41no—
497C22—42no—
498C22—152no—
499C22—161no—
500C22—602no—
501C22—601no—
502C22—2401no—
503C22—2402no—
504C22—2402no—
505C22D8×D1511yescharacteristic
506C4—41no—
507C4—152no—
508C4—601no—
509C4D8×D1511yescharacteristic
510C4C2×D4×D1511yescharacteristic
511C3#1061376711yescharacteristic, complemented, Sylow
512C2—21no—
513C2—82no—
514C2—81no—
515C2—302no—
516C2—1202no—
517C2—1201no—
518C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC2C2×D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC3×C5×#509C2
socleC2×C3×C5C22×D8
hypercenter#509D15
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #11756528C2semidirect
2. #11756516C2semidirect
3. C3×C5×#509C2semidirect
4. #11751295C2semidirect
5. C2×#91110C2semidirect
6. #11751017C2semidirect
7. #11751015C2semidirect
8. #11751012C2semidirect
9. D15×D16C2semidirect
10. #11751009C2semidirect
11. #11751008C2semidirect
15. C3×C5×#135C22semidirect
16. C2×C3×C5×D8C22semidirect
19. #91808C22semidirect
21. #91801C22semidirect
23. D8×D15C22semidirect
24. D8×D15C22semidirect
25. #91793C22semidirect
26. C2×D120C22semidirect
28. C3×C5×SD32C22semidirect
29. C3×C5×D16C22semidirect
30. C3×C5×M32C22semidirect
31. #91113C22semidirect
32. #91112C22semidirect
33. #91111C22semidirect
34. #91110C22semidirect
35. #91110C22semidirect
36. #91110C22semidirect
37. C2×C3⋊#672C22semidirect
38. #91084C22semidirect
39. D240C22semidirect
40. #91082C22semidirect
41. C16×D15C22semidirect
45. C5×#509D3semidirect
92. C3×#509D5semidirect
103. C5×#135C2×D3semidirect
104. C2×C5×D8C2×D3semidirect
116. C5×SD32C2×D3semidirect
117. C5×D16C2×D3semidirect
118. C5×M32C2×D3semidirect
163. C3×#135C2×D5semidirect
164. C2×C3×D8C2×D5semidirect
176. C3×SD32C2×D5semidirect
177. C3×D16C2×D5semidirect
178. C3×M32C2×D5semidirect
231. #509D15semidirect
327. #135C2×D15semidirect
331. C2×D8C2×D15semidirect
337. SD32C2×D15semidirect
342. D16C2×D15semidirect
344. M32C2×D15semidirect
435. C3×C5#3415semidirect
495. C5#82036semidirect
511. C3#10613767semidirect

Maximal subgroups

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

subgroupindex
#117565282
#117565162
C3×C5×#5092
#117512952
C2×#911102
#117510172
#117510152
#117510122
D15×D162
#117510092
#117510082
#106137673
#820365