Finite Group Databasebeta

← #14478581

Subgroups — #14478581

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#11753991C211yesmaximal, characteristic, complemented
2#11753971C211yesmaximal, characteristic, complemented
3#11751005C211yesmaximal, characteristic, complemented
4C5×#4901C211yesmaximal, characteristic, complemented
5C2×C3×#3932C211yesmaximal, characteristic, complemented
6#11747560C211yesmaximal, characteristic, complemented
7#11747543C211yesmaximal, characteristic, complemented
8#11746837C212yesmaximal, complemented
9#11746836C212yesmaximal, complemented
10#11746821C212yesmaximal, complemented
11D3×#3932C212yesmaximal, complemented
12#10613745—31nomaximal, Hall
13#92017—21no—
14#92004—21no—
15#91793C2211yescharacteristic
16#91793C2211yescharacteristic, complemented
17C5×#901C2211yescharacteristic
18C2×C3×Dic20C2211yescharacteristic, complemented
19C2×C3×D40C2211yescharacteristic
20#91315—21no—
21#91312—21no—
22#91275C2212yescomplemented
23#91273C2212yes—
24#91263—22no—
25D3×Dic20C2212yescomplemented
26#91254—22no—
27D3×D40C2212yes—
28C2×C3×C5×C16C2211yescharacteristic, complemented
29Dic120C2211yescharacteristic, complemented
30#91084C2211yescharacteristic, complemented
31#91084C2211yescharacteristic, complemented
32D240C2211yescharacteristic, complemented
33C5×#812C2211yescharacteristic, complemented
34C5×#798C2212yescomplemented
35C5×D3×C16C2212yescomplemented
36C3×#3932C2212yescomplemented
37C3×#3932C2212yescomplemented
38#90947C2212yescomplemented
39#90943C2212yescomplemented
40#90942C2212yescomplemented
41#90938C2212yescomplemented
42#82024—51nomaximal, Hall
43#66087—31no—
44#66086—31no—
45C5×#504—31no—
46#65198—31no—
47#65198—32no—
48#65197—31no—
49#65197—32no—
50#65193—31no—
51#65193—32no—
52C2×#3932—32no—
53C2×#3932D311yescharacteristic, complemented
54#6817—21no—
55#6817—21no—
56C5×#235D411yescharacteristic
57C2×C3×D20—21no—
58C2×C3×Dic10—21no—
59D5×#67—42no—
60#6782—42no—
61#6777—41no—
62D3×D20—22no—
63D15⋊Q8—41no—
64#6769—22no—
65#6768—41no—
66D3×Dic10—22no—
67#6766—41no—
68#6765—22no—
69C2×C3×C5×C8C2311yescharacteristic
70Dic60C2311yescharacteristic
71Dic60C2311yescharacteristic
72D120C2311yescharacteristic
73D120C2311yescharacteristic
74#6706—21no—
75#6706—21no—
76C5×#208D411yescharacteristic
77C5×ΓL(1,𝔽25)D412yes—
78C5×D3×C8C2312yes—
79C3×Dic20—21no—
80C3×Dic20C2312yes—
81C3×D40—21no—
82C3×D40C2312yes—
83#6662—22no—
84#6658—22no—
85#6657—22no—
86#6653—22no—
87C3×C5×C16C2311yescharacteristic
88C3×C5×C16C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90#5766—51no—
91#5757—51no—
92C2×C3×SD32—51no—
93#5179—51no—
94#5147—51no—
95#4916—52no—
96#4915—52no—
97#4914—52no—
98D3×SD32—52no—
99#4904—51no—
100#4901D511yescharacteristic, complemented
101#4150—61no—
102#4149—61no—
103C5×#131—31no—
104#4055—62no—
105#4055—61no—
106#4054—62no—
107#4054—61no—
108C2×Dic20—32no—
109C2×Dic20C2×D311yescharacteristic, complemented
110#4050—31no—
111#4050—31no—
112#4050—32no—
113#4050—32no—
114C2×D40—32no—
115C2×D40C2×D311yescharacteristic
116C5×M32—31no—
117C5×M32—32no—
118C2×C5×C16—32no—
119C2×C5×C16C2×D311yescharacteristic, complemented
120Dic40—32no—
121Dic40—31no—
122#3932—32no—
123#3932—32no—
124#3932—31no—
125#3932—31no—
126#3932C2×D312yescomplemented
127#3932C2×D312yescomplemented
128D80—32no—
129D80—31no—
130#3416—151noSylow
131C22×C3×D5—41no—
132C2×D3×D5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134#1220—41no—
135#1220—41no—
136D60—21no—
137D60—21no—
138C4×D15—41no—
139C4×D15—41no—
140Dic30—21no—
141Dic30—21no—
142C5×#67D812yes—
143C5×D12D811yescharacteristic
144C4×C5×D3C2×D412yes—
145C5×Dic6D811yescharacteristic
146C2×C3×Dic5—41no—
147C3×D20—22no—
148C3×D20—41no—
149C3×Dic10—22no—
150C3×Dic10—41no—
151#1204—42no—
152#1203—42no—
153#1202—42no—
154#1201—42no—
155#1200—42no—
156D3×Dic5—42no—
157D5×Dic3—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C5×C3⋊C8C2×D412yes—
161#1007—101no—
162#1004—101no—
163C2×C3×Q16—51no—
164C2×C3×D8—51no—
165#942—101no—
166#932—101no—
167#919—52no—
168#918—102no—
169D3×Q16—52no—
170#912—52no—
171#911—102no—
172D3×D8—52no—
173#904—51no—
174#904—51no—
175#901C2×D511yescharacteristic
176C3×SD32—52no—
177C3×SD32—52no—
178C2×C3×C16C2×D511yescharacteristic, complemented
179#829—52no—
180#828—52no—
181#827—52no—
182#826—52no—
183#812C2×D511yescharacteristic, complemented
184Dic24—51no—
185#800—51no—
186#800—51no—
187D48—51no—
188#798C2×D512yescomplemented
189D3×C16C2×D512yescomplemented
190C5×#41—31no—
191#713—121no—
192Q8×D5—121no—
193#711—121no—
194#711—122no—
195D4×D5—121no—
196D4×D5—122no—
197#709—62no—
198#709—62no—
199#709—61no—
200#709—61no—
201C2×D20—21no—
202C2×D20—62no—
203C2×Dic10—21no—
204C2×Dic10—62no—
205C5×M16—31no—
206C5×M16—32no—
207C2×C5×C8—32no—
208C2×C5×C8C22×D311yescharacteristic
209Dic20—21no—
210Dic20—31no—
211Dic20—31no—
212Dic20—62no—
213Dic20C22×D312yes—
214D40—21no—
215D40—31no—
216D40—31no—
217D40—62no—
218D40C22×D312yes—
219#677—62no—
220#677—62no—
221#677—61no—
222#677—61no—
223C5×C16—32no—
224C5×C16C22×D311yescharacteristic
225C5×C16C22×D311yescharacteristic
226#578—151no—
227#576—151no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509—151no—
232#508—152no—
233#508—151no—
234C2×SD32—51no—
235C2×SD32—152no—
236#504—31no—
237C22×C3×C5C2×D811yescharacteristic
238C2×D15—41no—
239C2×D15—41no—
240C2×C5×D3C2×D812yes—
241C2×C3×D5—42no—
242C2×C3×D5—161no—
243D3×D5—162no—
244C3×C4×C5C2×D811yescharacteristic
245C3×C4×C5C22×D411yescharacteristic
246Dic15—41no—
247Dic15—41no—
248C3×Dic5—42no—
249C5×Dic3C2×D812yes—
250C2×C3×Q8—101no—
251C2×C3×D4—101no—
252C2×#67—202no—
253#239—102no—
254#239—201no—
255D3×Q8—102no—
256D3×Q8—201no—
257#237—102no—
258#237—201no—
259D3×D4—102no—
260D3×D4—201no—
261#235—101no—
262#235—101no—
263#235—202no—
264#235D2011yescharacteristic
265C3×Q16—52no—
266C3×Q16—101no—
267C3×D8—52no—
268C3×D8—101no—
269C2×C3×C8C22×D511yescharacteristic
270#216—102no—
271#215—102no—
272#214—102no—
273#213—102no—
274#208D2011yescharacteristic
275Dic12—51no—
276Dic12—51no—
277D24—51no—
278D24—51no—
279#204—101no—
280#204—101no—
281ΓL(1,𝔽25)D2012yes—
282D3×C8C22×D512yes—
283C3×C16C22×D511yescharacteristic
284C3×C16C22×D511yescharacteristic
285C3⋊C16C22×D512yes—
286C22×D5—41no—
287C22×D5—122no—
288C5×Q8—31no—
289C5×D4—32no—
290C5×D4—31no—
291C2×C4×C5—32no—
292C2×C4×C5D3×D411yescharacteristic
293C22⋊D5—122no—
294C22⋊D5—122no—
295C22⋊D5—121no—
296C22⋊D5—121no—
297C2×Dic5—41no—
298C2×Dic5—122no—
299D20—22no—
300D20—41no—
301D20—61no—
302D20—61no—
303D20—122no—
304C4×D5—122no—
305C4×D5—122no—
306C4×D5—121no—
307C4×D5—121no—
308Dic10—22no—
309Dic10—41no—
310Dic10—61no—
311Dic10—61no—
312Dic10—122no—
313C5×C8—32no—
314C5×C8D3×D411yescharacteristic
315C5×C8C23×D311yescharacteristic
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—152no—
323#135—152no—
324#135—151no—
325#135—151no—
326C2×Q16—51no—
327C2×Q16—152no—
328C2×D8—51no—
329C2×D8—152no—
330#131—31no—
331Q32—152no—
332Q32—151no—
333SD32—52no—
334SD32—52no—
335SD32—152no—
336SD32—152no—
337SD32—151no—
338SD32—151no—
339D16—152no—
340D16—151no—
341M32—31no—
342M32—32no—
343C2×C16—32no—
344C2×C16D3×D511yescharacteristic, complemented
345C2×C3×C5—21no—
346C2×C3×C5C22×D811yescharacteristic
347D15—81no—
348D15—81no—
349C3×D5—82no—
350C5×D3—22no—
351C23×C3—201no—
352C22×D3—202no—
353C3×Q8—102no—
354C3×Q8—201no—
355C3×D4—102no—
356C3×D4—201no—
357C2×C3×C4—201no—
358C2×C3×C4C2×D2011yescharacteristic
359#67—201no—
360#67—201no—
361#67—202no—
362#67—202no—
363#67D4012yes—
364C2×Dic3—202no—
365D12—101no—
366D12—101no—
367D12—202no—
368D12D4011yescharacteristic
369C4×D3—202no—
370C4×D3—201no—
371C4×D3—201no—
372C4×D3—202no—
373C4×D3C2×D2012yes—
374Dic6—101no—
375Dic6—101no—
376Dic6—202no—
377Dic6D4011yescharacteristic
378C3×C8C2×D2011yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8C2×D2012yes—
381C22×C5—32no—
382C22×C5D3×D811yescharacteristic
383C2×D5—42no—
384C2×D5—121no—
385C2×D5—121no—
386C2×D5—161no—
387C2×D5—482no—
388C4×C5—32no—
389C4×C5D3×D811yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—42no—
392Dic5—121no—
393Dic5—121no—
394#41—31no—
395#41—302no—
396#41—302no—
397#41—301no—
398#41—301no—
399#41—602no—
400#41—601no—
401#41—601no—
402C2×Q8—101no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—101no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—52no—
410Q16—101no—
411Q16—151no—
412Q16—151no—
413Q16—302no—
414SD16—302no—
415SD16—302no—
416SD16—301no—
417SD16—301no—
418D8—52no—
419D8—101no—
420D8—151no—
421D8—151no—
422D8—302no—
423M16—31no—
424M16—32no—
425C2×C8—32no—
426C2×C8C2×D3×D511yescharacteristic
427C16—32no—
428C16C2×D3×D511yescharacteristic
429C16C2×D3×D511yescharacteristic
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—202no—
432C22×C3—801no—
433C22×C3C2×D4011yescharacteristic
434C2×D3—201no—
435C2×D3—201no—
436C2×D3—802no—
437C2×D3C2×D4012yes—
438C3×C4—202no—
439C3×C4C2×D4011yescharacteristic
440C3×C4C22×D2011yescharacteristic
441Dic3—201no—
442Dic3—201no—
443Dic3C2×D4012yes—
444C2×C5—21no—
445C2×C5—62no—
446C2×C5C2×D3×D811yescharacteristic
447D5—82no—
448D5—241no—
449D5—241no—
450C23—201no—
451C23—602no—
452Q8—31no—
453Q8—102no—
454Q8—201no—
455Q8—301no—
456Q8—301no—
457Q8—602no—
458D4—32no—
459D4—31no—
460D4—102no—
461D4—201no—
462D4—301no—
463D4—301no—
464D4—602no—
465D4—602no—
466D4—602no—
467D4—601no—
468D4—601no—
469C2×C4—32no—
470C2×C4—201no—
471C2×C4—602no—
472C2×C4—602no—
473C2×C4—602no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4D3×D2011yescharacteristic
477C8—32no—
478C8D3×D2011yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—402no—
482C2×C3C22×D4011yescharacteristic
483D3—22no—
484D3—401no—
485D3—401no—
486C5#8202411yescharacteristic, complemented, Sylow
487C22—32no—
488C22—202no—
489C22—601no—
490C22—601no—
491C22—801no—
492C22—2402no—
493C22D3×D4011yescharacteristic
494C4—32no—
495C4—202no—
496C4—601no—
497C4—601no—
498C4D3×D4011yescharacteristic
499C4C2×D3×D2011yescharacteristic
500C3#1061374511yescharacteristic, complemented, Sylow
501C2—21no—
502C2—62no—
503C2—402no—
504C2—1201no—
505C2—1201no—
506C2C2×D3×D4011yescharacteristic
subgroupG/H
centerC2C2×D3×D40
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC2×C3×C5C22×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #11753991C2semidirect
2. #11753971C2semidirect
3. #11751005C2semidirect
4. C5×#4901C2semidirect
5. C2×C3×#3932C2semidirect
6. #11747560C2semidirect
7. #11747543C2semidirect
8. #11746837C2semidirect
9. #11746836C2semidirect
10. #11746821C2semidirect
11. D3×#3932C2semidirect
16. #91793C22semidirect
18. C2×C3×Dic20C22semidirect
22. #91275C22semidirect
25. D3×Dic20C22semidirect
28. C2×C3×C5×C16C22semidirect
29. Dic120C22semidirect
30. #91084C22semidirect
31. #91084C22semidirect
32. D240C22semidirect
33. C5×#812C22semidirect
34. C5×#798C22semidirect
35. C5×D3×C16C22semidirect
36. C3×#3932C22semidirect
37. C3×#3932C22semidirect
38. #90947C22semidirect
39. #90943C22semidirect
40. #90942C22semidirect
41. #90938C22semidirect
53. C2×#3932D3semidirect
100. #4901D5semidirect
109. C2×Dic20C2×D3semidirect
119. C2×C5×C16C2×D3semidirect
126. #3932C2×D3semidirect
127. #3932C2×D3semidirect
178. C2×C3×C16C2×D5semidirect
183. #812C2×D5semidirect
188. #798C2×D5semidirect
189. D3×C16C2×D5semidirect
344. C2×C16D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#82024semidirect
500. C3#10613745semidirect

Maximal subgroups

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

subgroupindex
#117539912
#117539712
#117510052
C5×#49012
C2×C3×#39322
#117475602
#117475432
#117468372
#117468362
#117468212
D3×#39322
#106137453
#820245