Finite Group Databasebeta

← #14478595

Subgroups — #14478595

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756528C211yesmaximal, characteristic, complemented
2#11754011C211yesmaximal, characteristic, complemented
3C5×#5194C211yesmaximal, characteristic, complemented
4C3×#65484C211yesmaximal, characteristic, complemented
5#11748310C212yesmaximal, complemented
6#11748299C212yesmaximal, complemented
7#11748287C212yesmaximal, complemented
8#11748274C212yesmaximal, complemented
9C2×#90943C211yesmaximal, characteristic, complemented
10#11747548C211yesmaximal, characteristic, complemented
11#11747532C211yesmaximal, characteristic, complemented
12#10613763—31nomaximal, Hall
13#92100—21no—
14#92004—21no—
15C3×C5×#135C2211yescharacteristic
16#91838—21no—
17#91808C2212yes—
18#91803—22no—
19D8×D15C2212yes—
20C2×D120C2211yescharacteristic
21#91790C2211yescharacteristic
22C5×#904C2211yescharacteristic, complemented
23C2×C3×Dic20C2211yescharacteristic, complemented
24#91309—21no—
25#91280—22no—
26#91279C2212yescomplemented
27#91264C2212yescomplemented
28C5×#829C2211yescharacteristic, complemented
29C5×#828C2211yescharacteristic, complemented
30C5×#827C2211yescharacteristic, complemented
31C5×#826C2211yescharacteristic, complemented
32C2×C5×C3⋊C16C2211yescharacteristic, complemented
33C3×#3961C2212yescomplemented
34C3×#3959C2212yescomplemented
35C3×#3944C2211yescharacteristic, complemented
36#90945C2212yescomplemented
37#90943C2212yescomplemented
38#90943C2212yescomplemented
39#90939C2212yescomplemented
40#90936C2212yescomplemented
41#90933C2212yescomplemented
42#82040—51nomaximal, Hall
43#66105—31no—
44#66103—31no—
45C5×#508—31no—
46#65484D311yescharacteristic, complemented
47#65482—31no—
48#65207—32no—
49#65205—32no—
50D5×SD32—32no—
51#65200—32no—
52C2×#3932—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×Dic10—21no—
64#6782—42no—
65D15⋊Q8—22no—
66#6769—41no—
67#6768—22no—
68D3×Dic10—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×Dic20—21no—
84C3×Dic20C2312yes—
85#6661—22no—
86#6656—22no—
87C3×#672C2312yes—
88C5×C3⋊C16C2311yescharacteristic
89C5×C3⋊C16C2311yescharacteristic
90#5769—51no—
91#5766—51no—
92C3×#510—51no—
93#5194D511yescharacteristic, complemented
94C2×#828—51no—
95#4919—52no—
96#4918—52no—
97#4914—52no—
98D3×SD32—52no—
99#4908—51no—
100#4907—51no—
101#4150—61no—
102#4149—61no—
103C5×#135—31no—
104C5×#135C2×D311yescharacteristic
105#4097—61no—
106#4095—61no—
107#4065—32no—
108D5×Q16—32no—
109#4061—62no—
110#4060—62no—
111#4058—32no—
112D5×D8—32no—
113C2×Dic20C2×D311yescharacteristic, complemented
114C2×D40—31no—
115#4047—31no—
116C5×Q32—31no—
117C5×SD32—31no—
118C5×SD32—31no—
119C5×D16—31no—
120C2×C5×C16—31no—
121#3961C2×D312yescomplemented
122#3960—32no—
123#3959C2×D312yescomplemented
124#3958—32no—
125#3944C2×D311yescharacteristic, complemented
126#3932—32no—
127#3932—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×D15—41no—
132C22×D15—42no—
133C3×C5×Q8—21no—
134C3×C5×D4—21no—
135C3×C5×D4—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5C2×D411yescharacteristic
138#1220—42no—
139#1220D812yes—
140D60—22no—
141D60—42no—
142D60—41no—
143D60D811yescharacteristic
144C4×D15—42no—
145C4×D15C2×D412yes—
146Dic30D811yescharacteristic
147C5×#67—41no—
148C5×D12—21no—
149C4×C5×D3—41no—
150C5×Dic6—21no—
151C2×C3×Dic5—41no—
152C3×Dic10—22no—
153C3×Dic10—41no—
154#1204—42no—
155#1203—42no—
156#1200—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1009—101no—
162#1007—101no—
163C3×#135C2×D511yescharacteristic
164C2×C3×Q16—51no—
165#949—101no—
166#942—101no—
167#919—52no—
168#919—52no—
169#918—102no—
170D3×Q16—52no—
171#914—102no—
172D3×D8—52no—
173#904C2×D511yescharacteristic, complemented
174C2×D24—51no—
175#901—51no—
176C3×Q32—52no—
177C3×SD32—52no—
178C3×M32—51no—
179#829C2×D511yescharacteristic, complemented
180#828—52no—
181#828—52no—
182#828C2×D511yescharacteristic, complemented
183#827C2×D511yescharacteristic, complemented
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—
193Q8×D5—62no—
194#711—62no—
195#711—122no—
196D4×D5—62no—
197D4×D5—122no—
198#709—31no—
199#709—121no—
200#709—121no—
201C2×D20—61no—
202C2×D20—121no—
203C2×Dic10—21no—
204C2×Dic10—121no—
205C5×Q16—31no—
206C5×Q16C22×D311yescharacteristic
207C5×SD16—21no—
208C5×SD16—61no—
209C5×D8—31no—
210C5×D8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212#689—62no—
213#688—62no—
214#687—62no—
215#686—62no—
216#681—31no—
217Dic20—21no—
218Dic20C22×D312yes—
219D40—32no—
220D40—61no—
221#676—32no—
222C8×D5—32no—
223C5×C16—31no—
224C5×C16—31no—
225#672C22×D312yes—
226#578—151no—
227#576—151no—
228#510—51no—
229#510—152no—
230#509—151no—
231#509—152no—
232#508—31no—
233#508—152no—
234C2×SD32—151no—
235C2×SD32—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—
244C3×C4×C5—41no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247Dic15C2×D812yes—
248C3×Dic5—42no—
249C5×Dic3—41no—
250C3×#41—21no—
251C2×C3×Q8—101no—
252#239—102no—
253#239—102no—
254#239—201no—
255D3×Q8—102no—
256D3×Q8—201no—
257D3×D4—102no—
258D3×D4—202no—
259#235—21no—
260#235—51no—
261#235—201no—
262#235—202no—
263C2×D12—101no—
264C2×D12—201no—
265C3×Q16—52no—
266C3×Q16—101no—
267C3×Q16C22×D511yescharacteristic
268C3×SD16—21no—
269C3×D8C22×D511yescharacteristic
270C2×C3×C8C22×D511yescharacteristic
271#216—102no—
272#215—102no—
273#215—102no—
274#213—102no—
275#208—51no—
276Dic12C22×D511yescharacteristic
277D24—52no—
278D24—101no—
279D24C22×D511yescharacteristic
280#204—21no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16—52no—
284C3⋊C16C22×D511yescharacteristic
285C3⋊C16C22×D511yescharacteristic
286C22×D5—122no—
287C22×D5—121no—
288C5×Q8—21no—
289C5×Q8—61no—
290C5×D4—21no—
291C5×D4—41no—
292C5×D4—61no—
293C5×D4—121no—
294C2×C4×C5—41no—
295C2×C4×C5—121no—
296C2×C4×C5D3×D411yescharacteristic
297C22⋊D5—32no—
298C22⋊D5—122no—
299C22⋊D5—122no—
300C2×Dic5—41no—
301C2×Dic5—122no—
302D20—31no—
303D20—62no—
304D20—122no—
305D20—121no—
306C4×D5—32no—
307C4×D5—122no—
308C4×D5—122no—
309Dic10—22no—
310Dic10—31no—
311Dic10—41no—
312Dic10—122no—
313C5×C8D3×D411yescharacteristic
314C5×C8C23×D311yescharacteristic
315#168—32no—
3162−1+4—301no—
317H(5,𝔽2)—301no—
318#137—302no—
319#137—301no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—301no—
322#135—31no—
323#135—152no—
324#135—152no—
325#135D3×D511yescharacteristic
326C2×Q16—51no—
327C2×Q16—152no—
328C2×D8—152no—
329C2×D8—151no—
330#131—151no—
331Q32—31no—
332Q32—52no—
333SD32—31no—
334SD32—31no—
335SD32—52no—
336SD32—152no—
337SD32—152no—
338SD32—152no—
339D16—31no—
340D16—152no—
341M32—51no—
342M32—152no—
343C2×C16—31no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5C22×D811yescharacteristic
348D15—22no—
349D15—82no—
350C5×D3—81no—
351C22×D3—202no—
352C22×D3—201no—
353C3×Q8—21no—
354C3×Q8—102no—
355C3×Q8—201no—
356C3×D4—21no—
357C3×D4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—201no—
360C2×C3×C4D4×D511yescharacteristic
361#67—41no—
362#67—52no—
363#67—202no—
364D12—21no—
365D12—51no—
366D12—102no—
367D12—202no—
368D12—202no—
369D12—201no—
370C4×D3—41no—
371C4×D3—52no—
372C4×D3—202no—
373C4×D3—202no—
374C4×D3—202no—
375Dic6—21no—
376Dic6—51no—
377Dic6—202no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—41no—
382C22×C5—121no—
383C22×C5D3×D811yescharacteristic
384C2×D5—32no—
385C2×D5—122no—
386C2×D5—482no—
387C2×D5—481no—
388C4×C5—41no—
389C4×C5—121no—
390C4×C5D3×D811yescharacteristic
391C4×C5C2×D3×D411yescharacteristic
392Dic5—32no—
393Dic5—42no—
394#41—21no—
395#41—61no—
396#41—151no—
397#41—302no—
398#41—302no—
399#41—601no—
400#41—601no—
401#41—602no—
402C2×Q8—101no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—302no—
406C2×D4—301no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—31no—
410Q16—52no—
411Q16—101no—
412Q16—302no—
413Q16C2×D3×D511yescharacteristic
414SD16—21no—
415SD16—61no—
416SD16—302no—
417SD16—302no—
418D8—31no—
419D8—152no—
420D8—302no—
421D8—301no—
422D8C2×D3×D511yescharacteristic
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C2×D3×D511yescharacteristic
427C16—31no—
428C16—31no—
429C16—52no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—41no—
432C22×C3D5×D811yescharacteristic
433C2×D3—41no—
434C2×D3—52no—
435C2×D3—202no—
436C2×D3—802no—
437C2×D3—801no—
438C3×C4—41no—
439C3×C4—202no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—41no—
443Dic3—52no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5—241no—
447C2×C5C2×D3×D811yescharacteristic
448D5—62no—
449D5—242no—
450C23—602no—
451C23—601no—
452Q8—21no—
453Q8—61no—
454Q8—102no—
455Q8—151no—
456Q8—201no—
457Q8—602no—
458D4—21no—
459D4—41no—
460D4—61no—
461D4—121no—
462D4—152no—
463D4—151no—
464D4—302no—
465D4—602no—
466D4—602no—
467D4—602no—
468D4—601no—
469C2×C4—41no—
470C2×C4—121no—
471C2×C4—152no—
472C2×C4—201no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—602no—
476C2×C4#679011yescharacteristic
477C8—152no—
478C8#679011yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—81no—
482C2×C3C2×D5×D811yescharacteristic
483D3—81no—
484D3—102no—
485D3—402no—
486C5#8204011yescharacteristic, complemented, Sylow
487C22—41no—
488C22—121no—
489C22—152no—
490C22—602no—
491C22—2401no—
492C22—2402no—
493C22#9148111yescharacteristic
494C4—41no—
495C4—121no—
496C4—152no—
497C4—202no—
498C4#9148111yescharacteristic
499C4C2×#679011yescharacteristic
500C3#1061376311yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—241no—
504C2—302no—
505C2—1202no—
506C2C2×#9148111yescharacteristic
subgroupG/H
centerC2C2×#91481
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C22×D8
hypercenter#135D3×D5
hypocenterC3×C5#3416
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. #11754011C2semidirect
3. C5×#5194C2semidirect
4. C3×#65484C2semidirect
5. #11748310C2semidirect
6. #11748299C2semidirect
7. #11748287C2semidirect
8. #11748274C2semidirect
9. C2×#90943C2semidirect
10. #11747548C2semidirect
11. #11747532C2semidirect
22. C5×#904C22semidirect
23. C2×C3×Dic20C22semidirect
26. #91279C22semidirect
27. #91264C22semidirect
28. C5×#829C22semidirect
29. C5×#828C22semidirect
30. C5×#827C22semidirect
31. C5×#826C22semidirect
32. C2×C5×C3⋊C16C22semidirect
33. C3×#3961C22semidirect
34. C3×#3959C22semidirect
35. C3×#3944C22semidirect
36. #90945C22semidirect
37. #90943C22semidirect
38. #90943C22semidirect
39. #90939C22semidirect
40. #90936C22semidirect
41. #90933C22semidirect
46. #65484D3semidirect
93. #5194D5semidirect
113. C2×Dic20C2×D3semidirect
121. #3961C2×D3semidirect
123. #3959C2×D3semidirect
125. #3944C2×D3semidirect
173. #904C2×D5semidirect
179. #829C2×D5semidirect
182. #828C2×D5semidirect
183. #827C2×D5semidirect
184. #826C2×D5semidirect
185. C2×C3⋊C16C2×D5semidirect
430. C3×C5#3416semidirect
486. C5#82040semidirect
500. C3#10613763semidirect

Maximal subgroups

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

subgroupindex
#117565282
#117540112
C5×#51942
C3×#654842
#117483102
#117482992
#117482872
#117482742
C2×#909432
#117475482
#117475322
#106137633
#820405