Finite Group Databasebeta

← #14478525

Subgroups — #14478525

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#11753981C211yesmaximal, characteristic, complemented
3C5×#5194C211yesmaximal, characteristic, complemented
4C3×#65482C211yesmaximal, characteristic, complemented
5#11748308C212yesmaximal, complemented
6#11748293C212yesmaximal, complemented
7#11748285C212yesmaximal, complemented
8#11748268C212yesmaximal, complemented
9#11747548C211yesmaximal, characteristic, complemented
10C2×#90938C211yesmaximal, characteristic, complemented
11#11747532C211yesmaximal, characteristic, complemented
12#10613762—31nomaximal, Hall
13#92100—21no—
14#92017—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16#91838—21no—
17#91808C2212yescomplemented
18#91803—22no—
19D8×D15C2212yescomplemented
20C2×D120C2211yescharacteristic, complemented
21#91790C2211yescharacteristic
22C5×#904C2211yescharacteristic, complemented
23C2×C3×D40C2211yescharacteristic, complemented
24#91298—21no—
25#91277C2212yescomplemented
26#91258—22no—
27#91256C2212yescomplemented
28C5×#829C2211yescharacteristic, complemented
29C5×#828C2211yescharacteristic, complemented
30C5×#827C2211yescharacteristic, complemented
31C5×#826C2211yescharacteristic, complemented
32C2×C5×C3⋊C16C2211yescharacteristic, complemented
33C3×#3960C2212yescomplemented
34C3×#3958C2212yescomplemented
35C3×#3944C2211yescharacteristic, complemented
36#90945C2212yescomplemented
37#90939C2212yescomplemented
38#90938C2212yescomplemented
39#90938C2212yescomplemented
40#90936C2212yescomplemented
41#90933C2212yescomplemented
42#82036—51nomaximal, Hall
43#66103—31no—
44#66103—31no—
45C5×#508—31no—
46#65482—31no—
47#65482D311yescharacteristic, complemented
48#65208—32no—
49#65203—32no—
50#65203—32no—
51D5×D16—32no—
52C2×D80—31no—
53#65190—31no—
54C3×C5×#41—21no—
55#6821—22no—
56D4×D15—22no—
57D4×D15—42no—
58#6817—41no—
59#6817D411yescharacteristic
60C2×D60—21no—
61C2×D60—41no—
62C5×#235—21no—
63C2×C3×D20—21no—
64D5×#67—42no—
65#6777—22no—
66D3×D20—41no—
67#6766—22no—
68#6765—41no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73#6717—22no—
74#6715—22no—
75#6710D411yescharacteristic
76D120—21no—
77D120C2312yes—
78#6705D412yes—
79C8×D15C2312yes—
80C5×Dic12C2311yescharacteristic
81C5×D24C2311yescharacteristic
82C5×#204—21no—
83C3×D40—21no—
84C3×D40C2312yes—
85#6655—22no—
86#6652—22no—
87C3×#672C2312yes—
88C5×C3⋊C16C2311yescharacteristic
89C5×C3⋊C16C2311yescharacteristic
90#5769—51no—
91#5757—51no—
92C3×#509—51no—
93#5194D511yescharacteristic, complemented
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#4149—61no—
103C5×#135—31no—
104C5×#135C2×D311yescharacteristic, complemented
105#4095—61no—
106#4095—61no—
107#4065—32no—
108#4065—32no—
109#4060—62no—
110#4060—62no—
111D5×D8—32no—
112D5×D8—32no—
113C2×D40—31no—
114C2×D40C2×D311yescharacteristic, complemented
115#4047—31no—
116C5×Q32—31no—
117C5×SD32—31no—
118C5×SD32—31no—
119C5×D16—31no—
120C2×C5×C16—31no—
121#3960—32no—
122#3960C2×D312yescomplemented
123#3958—32no—
124#3958C2×D312yescomplemented
125#3944C2×D311yescharacteristic, complemented
126D80—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3415—151noSylow
131C22×D15—41no—
132C22×D15—42no—
133C22×C3×D5—41no—
134C2×D3×D5—42no—
135C3×C5×Q8—21no—
136C3×C5×D4—21no—
137C3×C5×D4—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5C2×D411yescharacteristic
140#1220—42no—
141#1220D812yes—
142D60—22no—
143D60—42no—
144D60—41no—
145D60D811yescharacteristic
146C4×D15—42no—
147C4×D15C2×D412yes—
148Dic30D811yescharacteristic
149C5×#67—41no—
150C5×D12—21no—
151C4×C5×D3—41no—
152C5×Dic6—21no—
153C3×D20—22no—
154C3×D20—41no—
155#1202—42no—
156#1201—42no—
157D5×Dic3—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1009—101no—
162#1004—101no—
163C3×#135C2×D511yescharacteristic, complemented
164C2×C3×D8—51no—
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#904C2×D511yescharacteristic, complemented
174C2×D24—51no—
175#901—51no—
176C3×SD32—52no—
177C3×D16—52no—
178C3×M32—51no—
179#829C2×D511yescharacteristic, complemented
180#828C2×D511yescharacteristic, complemented
181#827C2×D511yescharacteristic, complemented
182#826—52no—
183#826—52no—
184#826C2×D511yescharacteristic, complemented
185C2×C3⋊C16C2×D511yescharacteristic, complemented
186#800—52no—
187D48—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C5×#41—61no—
192#713—62no—
193#713—62no—
194D4×D5—62no—
195D4×D5—62no—
196D4×D5—122no—
197D4×D5—122no—
198#709—31no—
199#709—121no—
200#709—121no—
201C2×D20—21no—
202C2×D20—61no—
203C2×D20—121no—
204C2×D20—121no—
205C5×Q16—31no—
206C5×Q16C22×D311yescharacteristic
207C5×SD16—21no—
208C5×SD16—61no—
209C5×D8—31no—
210C5×D8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212#688—62no—
213#688—62no—
214#686—62no—
215#686—62no—
216#681—31no—
217D40—21no—
218D40—32no—
219D40—61no—
220D40C22×D312yes—
221#676—32no—
222C8×D5—32no—
223C5×C16—31no—
224C5×C16—31no—
225#672C22×D312yes—
226#576—151no—
227#576—151no—
228#509—51no—
229#509—151no—
230#509—152no—
231#509—152no—
232#508—31no—
233#508—152no—
234C2×D16—151no—
235C2×D16—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15—42no—
240C2×D15—162no—
241C2×D15—161no—
242C2×D15C2×D812yes—
243C2×C5×D3—41no—
244C2×C3×D5—42no—
245C2×C3×D5—161no—
246D3×D5—162no—
247C3×C4×C5—41no—
248C3×C4×C5C2×D811yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15C2×D812yes—
251C5×Dic3—41no—
252C3×#41—21no—
253C2×C3×D4—101no—
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—21no—
263#235—51no—
264#235—201no—
265C2×D12—101no—
266C2×D12—201no—
267C3×Q16C22×D511yescharacteristic
268C3×SD16—21no—
269C3×D8—52no—
270C3×D8—101no—
271C3×D8C22×D511yescharacteristic
272C2×C3×C8C22×D511yescharacteristic
273#215—102no—
274#214—102no—
275#213—102no—
276#213—102no—
277#208—51no—
278Dic12C22×D511yescharacteristic
279D24—52no—
280D24—101no—
281D24C22×D511yescharacteristic
282#204—21no—
283ΓL(1,𝔽25)—52no—
284D3×C8—52no—
285C3×C16—52no—
286C3⋊C16C22×D511yescharacteristic
287C3⋊C16C22×D511yescharacteristic
288C22×D5—41no—
289C22×D5—122no—
290C22×D5—122no—
291C22×D5—121no—
292C5×Q8—21no—
293C5×Q8—61no—
294C5×D4—21no—
295C5×D4—41no—
296C5×D4—61no—
297C5×D4—121no—
298C2×C4×C5—41no—
299C2×C4×C5—121no—
300C2×C4×C5D3×D411yescharacteristic
301C22⋊D5—32no—
302C22⋊D5—122no—
303C22⋊D5—122no—
304D20—22no—
305D20—31no—
306D20—41no—
307D20—62no—
308D20—122no—
309D20—122no—
310D20—121no—
311C4×D5—32no—
312C4×D5—122no—
313C4×D5—122no—
314Dic10—31no—
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—31no—
325#135—152no—
326#135—152no—
327#135D3×D511yescharacteristic, complemented
328C2×D8—51no—
329C2×D8—152no—
330C2×D8—152no—
331C2×D8—151no—
332#131—151no—
333Q32—31no—
334SD32—31no—
335SD32—31no—
336SD32—52no—
337SD32—152no—
338D16—31no—
339D16—52no—
340D16—152no—
341D16—152no—
342D16—152no—
343M32—51no—
344M32—152no—
345C2×C16—31no—
346C2×C16—152no—
347C2×C3×C5—21no—
348C2×C3×C5—81no—
349C2×C3×C5C22×D811yescharacteristic
350D15—22no—
351D15—82no—
352C3×D5—82no—
353C5×D3—81no—
354C23×C3—201no—
355C22×D3—202no—
356C22×D3—202no—
357C22×D3—201no—
358C3×Q8—21no—
359C3×D4—21no—
360C3×D4—41no—
361C3×D4—102no—
362C3×D4—201no—
363C2×C3×C4—41no—
364C2×C3×C4D4×D511yescharacteristic
365#67—41no—
366#67—52no—
367#67—202no—
368#67—202no—
369#67—202no—
370C2×Dic3—202no—
371D12—21no—
372D12—51no—
373D12—102no—
374D12—202no—
375D12—201no—
376C4×D3—41no—
377C4×D3—52no—
378C4×D3—202no—
379Dic6—21no—
380Dic6—51no—
381C3×C8D4×D511yescharacteristic
382C3×C8C23×D511yescharacteristic
383C3⋊C8—52no—
384C22×C5—41no—
385C22×C5—121no—
386C22×C5D3×D811yescharacteristic
387C2×D5—32no—
388C2×D5—42no—
389C2×D5—122no—
390C2×D5—161no—
391C2×D5—482no—
392C2×D5—482no—
393C2×D5—481no—
394C4×C5—41no—
395C4×C5—121no—
396C4×C5D3×D811yescharacteristic
397C4×C5C2×D3×D411yescharacteristic
398Dic5—32no—
399#41—21no—
400#41—61no—
401#41—151no—
402#41—302no—
403#41—302no—
404#41—601no—
405#41—601no—
406C2×D4—101no—
407C2×D4—302no—
408C2×D4—302no—
409C2×D4—301no—
410C2×D4—601no—
411C2×D4—601no—
412C2×D4—602no—
413C2×D4—602no—
414Q16—31no—
415Q16C2×D3×D511yescharacteristic
416SD16—21no—
417SD16—61no—
418SD16—302no—
419SD16—302no—
420D8—31no—
421D8—52no—
422D8—101no—
423D8—152no—
424D8—302no—
425D8—302no—
426D8—301no—
427D8C2×D3×D511yescharacteristic
428M16—151no—
429M16—152no—
430C2×C8—152no—
431C2×C8C2×D3×D511yescharacteristic
432C16—31no—
433C16—31no—
434C16—52no—
435C3×C5#341511yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—202no—
438C22×C3—801no—
439C22×C3D5×D811yescharacteristic
440C2×D3—41no—
441C2×D3—52no—
442C2×D3—202no—
443C2×D3—802no—
444C2×D3—802no—
445C2×D3—801no—
446C3×C4—41no—
447C3×C4D5×D811yescharacteristic
448C3×C4C2×D4×D511yescharacteristic
449Dic3—41no—
450Dic3—52no—
451C2×C5—21no—
452C2×C5—81no—
453C2×C5—241no—
454C2×C5C2×D3×D811yescharacteristic
455D5—62no—
456D5—82no—
457D5—242no—
458C23—201no—
459C23—602no—
460C23—602no—
461C23—601no—
462Q8—21no—
463Q8—61no—
464Q8—151no—
465D4—21no—
466D4—41no—
467D4—61no—
468D4—102no—
469D4—121no—
470D4—152no—
471D4—151no—
472D4—201no—
473D4—302no—
474D4—602no—
475D4—602no—
476D4—602no—
477D4—602no—
478D4—601no—
479C2×C4—41no—
480C2×C4—121no—
481C2×C4—152no—
482C2×C4—602no—
483C2×C4—602no—
484C2×C4#679011yescharacteristic
485C8—152no—
486C8#679011yescharacteristic
487C8C22×D3×D511yescharacteristic
488C2×C3—21no—
489C2×C3—81no—
490C2×C3—402no—
491C2×C3C2×D5×D811yescharacteristic
492D3—81no—
493D3—102no—
494D3—402no—
495C5#8203611yescharacteristic, complemented, Sylow
496C22—41no—
497C22—121no—
498C22—152no—
499C22—202no—
500C22—602no—
501C22—801no—
502C22—2401no—
503C22—2402no—
504C22—2402no—
505C22#9148111yescharacteristic
506C4—41no—
507C4—121no—
508C4—152no—
509C4#9148111yescharacteristic
510C4C2×#679011yescharacteristic
511C3#1061376211yescharacteristic, complemented, Sylow
512C2—21no—
513C2—81no—
514C2—241no—
515C2—302no—
516C2—402no—
517C2—1202no—
518C2C2×#9148111yescharacteristic
subgroupG/H
centerC2C2×#91481
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C22×D8
hypercenter#135D3×D5
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11756528C2semidirect
2. #11753981C2semidirect
3. C5×#5194C2semidirect
4. C3×#65482C2semidirect
5. #11748308C2semidirect
6. #11748293C2semidirect
7. #11748285C2semidirect
8. #11748268C2semidirect
9. #11747548C2semidirect
10. C2×#90938C2semidirect
11. #11747532C2semidirect
15. C3×C5×#135C22semidirect
17. #91808C22semidirect
19. D8×D15C22semidirect
20. C2×D120C22semidirect
22. C5×#904C22semidirect
23. C2×C3×D40C22semidirect
25. #91277C22semidirect
27. #91256C22semidirect
28. C5×#829C22semidirect
29. C5×#828C22semidirect
30. C5×#827C22semidirect
31. C5×#826C22semidirect
32. C2×C5×C3⋊C16C22semidirect
33. C3×#3960C22semidirect
34. C3×#3958C22semidirect
35. C3×#3944C22semidirect
36. #90945C22semidirect
37. #90939C22semidirect
38. #90938C22semidirect
39. #90938C22semidirect
40. #90936C22semidirect
41. #90933C22semidirect
47. #65482D3semidirect
93. #5194D5semidirect
104. C5×#135C2×D3semidirect
114. C2×D40C2×D3semidirect
122. #3960C2×D3semidirect
124. #3958C2×D3semidirect
125. #3944C2×D3semidirect
163. C3×#135C2×D5semidirect
173. #904C2×D5semidirect
179. #829C2×D5semidirect
180. #828C2×D5semidirect
181. #827C2×D5semidirect
184. #826C2×D5semidirect
185. C2×C3⋊C16C2×D5semidirect
327. #135D3×D5semidirect
435. C3×C5#3415semidirect
495. C5#82036semidirect
511. C3#10613762semidirect

Maximal subgroups

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

subgroupindex
#117565282
#117539812
C5×#51942
C3×#654822
#117483082
#117482932
#117482852
#117482682
#117475482
C2×#909382
#117475322
#106137623
#820365