Finite Group Databasebeta

← #14478536

Subgroups — #14478536

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#11756525C211yesmaximal, characteristic, complemented
2#11756516C211yesmaximal, characteristic, complemented
3C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
4#11751280C211yesmaximal, characteristic, complemented
5#11751248C211yesmaximal, characteristic, complemented
6#11751017C212yesmaximal, complemented
7#11751016C212yesmaximal, complemented
8#11751015C212yesmaximal, complemented
9D15×SD32C212yesmaximal, complemented
10#11751005C211yesmaximal, characteristic, complemented
11#11751002C211yesmaximal, characteristic, complemented
12#10613755—31nomaximal, Hall
13#92098—21no—
14#92095—21no—
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16C2×C3×C5×D8C2211yescharacteristic
17#91831—21no—
18#91821—21no—
19#91808C2212yescomplemented
20#91807—22no—
21Q16×D15C2212yescomplemented
22#91801C2212yes—
23#91800—22no—
24D8×D15C2212yes—
25#91793C2211yescharacteristic
26#91793C2211yescharacteristic, complemented
27#91790C2211yescharacteristic
28C3×C5×SD32C2212yescomplemented
29C3×C5×SD32C2212yescomplemented
30C2×C3×C5×C16C2211yescharacteristic, complemented
31#91113C2212yescomplemented
32#91112C2212yescomplemented
33#91111C2212yescomplemented
34#91110C2212yescomplemented
35#91096C2211yescharacteristic, complemented
36Dic120C2211yescharacteristic, complemented
37#91084C2211yescharacteristic, complemented
38#91084C2211yescharacteristic, complemented
39D240C2211yescharacteristic, complemented
40#91082C2212yescomplemented
41C16×D15C2212yescomplemented
42#82024—51nomaximal, Hall
43#66100—31no—
44#66091—31no—
45C2×C5×SD32D311yescharacteristic, complemented
46#65468—31no—
47#65436—31no—
48#65205—32no—
49#65204—32no—
50#65203—32no—
51D5×SD32—32no—
52#65193—31no—
53#65190—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4—21no—
56C2×#1220—42no—
57#6821—22no—
58#6821—41no—
59Q8×D15—22no—
60Q8×D15—41no—
61#6819—22no—
62#6819—41no—
63D4×D15—22no—
64D4×D15—41no—
65#6817—21no—
66#6817—21no—
67#6817—42no—
68#6817D411yescharacteristic
69C3×C5×Q16—21no—
70C3×C5×Q16C2312yes—
71C3×C5×D8—21no—
72C3×C5×D8C2312yes—
73C2×C3×C5×C8C2311yescharacteristic
74#6718—22no—
75#6717—22no—
76#6716—22no—
77#6715—22no—
78#6710D411yescharacteristic
79Dic60C2311yescharacteristic
80Dic60C2311yescharacteristic
81D120C2311yescharacteristic
82D120C2311yescharacteristic
83#6706—21no—
84#6706—21no—
85#6705D412yes—
86C8×D15C2312yes—
87C3×C5×C16C2311yescharacteristic
88C3×C5×C16C2311yescharacteristic
89C3⋊#672C2312yes—
90#5766—51no—
91#5757—51no—
92C2×C3×SD32D511yescharacteristic, complemented
93#5179—51no—
94#5147—51no—
95#4916—52no—
96#4915—52no—
97#4914—52no—
98D3×SD32—52no—
99#4904—51no—
100#4901—51no—
101#4147—61no—
102#4144—61no—
103C2×C5×Q16C2×D311yescharacteristic, complemented
104C2×C5×D8C2×D311yescharacteristic
105#4088—61no—
106#4078—61no—
107#4065—32no—
108#4064—62no—
109D5×Q16—32no—
110#4058—32no—
111#4057—62no—
112D5×D8—32no—
113#4050—31no—
114#4050—31no—
115#4047—31no—
116C5×SD32C2×D312yescomplemented
117C5×SD32C2×D312yescomplemented
118C2×C5×C16C2×D311yescharacteristic, complemented
119#3961—32no—
120#3960—32no—
121#3959—32no—
122#3958—32no—
123#3944—31no—
124Dic40—31no—
125#3932—31no—
126#3932—31no—
127D80—31no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C23×C3×C5—41no—
132C22×D15—42no—
133C3×C5×Q8—22no—
134C3×C5×Q8—41no—
135C3×C5×D4—22no—
136C3×C5×D4—41no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5C2×D411yescharacteristic
139#1220—41no—
140#1220—41no—
141#1220—42no—
142#1220—42no—
143#1220D812yes—
144C2×Dic15—42no—
145D60—21no—
146D60—21no—
147D60—42no—
148D60D811yescharacteristic
149C4×D15—42no—
150C4×D15—41no—
151C4×D15—41no—
152C4×D15—42no—
153C4×D15C2×D412yes—
154Dic30—21no—
155Dic30—21no—
156Dic30—42no—
157Dic30D811yescharacteristic
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1007—101no—
162#1004—101no—
163C2×C3×Q16C2×D511yescharacteristic, complemented
164C2×C3×D8C2×D511yescharacteristic
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#901—51no—
176C3×SD32C2×D512yescomplemented
177C3×SD32C2×D512yescomplemented
178C2×C3×C16C2×D511yescharacteristic, complemented
179#829—52no—
180#828—52no—
181#827—52no—
182#826—52no—
183#812—51no—
184Dic24—51no—
185#800—51no—
186#800—51no—
187D48—51no—
188#798—52no—
189D3×C16—52no—
190C2×C5×Q8—21no—
191C2×C5×D4—21no—
192C2×C22⋊D5—122no—
193#713—62no—
194#713—121no—
195Q8×D5—62no—
196Q8×D5—121no—
197#711—62no—
198#711—121no—
199D4×D5—62no—
200D4×D5—121no—
201#709—31no—
202#709—61no—
203#709—61no—
204#709—122no—
205C5×Q16—21no—
206C5×Q16C22×D312yes—
207C5×D8—21no—
208C5×D8C22×D312yes—
209C2×C5×C8C22×D311yescharacteristic
210#689—62no—
211#688—62no—
212#687—62no—
213#686—62no—
214#681—31no—
215Dic20—31no—
216Dic20—31no—
217D40—31no—
218D40—31no—
219#677—61no—
220#677—61no—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D311yescharacteristic
224C5×C16C22×D311yescharacteristic
225#672—32no—
226#578—151no—
227#576—151no—
228#510—151no—
229#510—152no—
230#509—151no—
231#509—152no—
232#508—152no—
233#508—151no—
234C2×SD32—152no—
235C2×SD32D1511yescharacteristic, complemented
236#504—151no—
237C22×C3×C5—42no—
238C22×C3×C5—161no—
239C22×C3×C5C2×D811yescharacteristic
240C2×D15—41no—
241C2×D15—41no—
242C2×D15—162no—
243C2×D15C2×D812yes—
244C3×C4×C5—42no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247Dic15—41no—
248Dic15—41no—
249Dic15C2×D812yes—
250C2×C3×Q8—21no—
251C2×C3×D4—21no—
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—51no—
262#235—101no—
263#235—101no—
264#235—202no—
265C3×Q16—21no—
266C3×Q16C22×D512yes—
267C3×D8—21no—
268C3×D8C22×D512yes—
269C2×C3×C8C22×D511yescharacteristic
270#216—102no—
271#215—102no—
272#214—102no—
273#213—102no—
274#208—51no—
275Dic12—51no—
276Dic12—51no—
277D24—51no—
278D24—51no—
279#204—101no—
280#204—101no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D511yescharacteristic
284C3×C16C22×D511yescharacteristic
285C3⋊C16—52no—
286C23×C5—41no—
287C22×D5—122no—
288C5×Q8—22no—
289C5×Q8—41no—
290C5×D4—22no—
291C5×D4—41no—
292C2×C4×C5—41no—
293C2×C4×C5D3×D411yescharacteristic
294C22⋊D5—32no—
295C22⋊D5—122no—
296C22⋊D5—122no—
297C22⋊D5—121no—
298C22⋊D5—121no—
299C2×Dic5—122no—
300D20—31no—
301D20—61no—
302D20—61no—
303D20—122no—
304C4×D5—32no—
305C4×D5—122no—
306C4×D5—122no—
307C4×D5—121no—
308C4×D5—121no—
309Dic10—31no—
310Dic10—61no—
311Dic10—61no—
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—152no—
323#135—152no—
324#135—151no—
325#135—151no—
326C2×Q16—152no—
327C2×Q16C2×D1511yescharacteristic, complemented
328C2×D8—152no—
329C2×D8C2×D1511yescharacteristic
330#131—151no—
331Q32—152no—
332Q32—151no—
333SD32—152no—
334SD32—152no—
335SD32—151no—
336SD32—151no—
337SD32C2×D1512yescomplemented
338SD32C2×D1512yescomplemented
339D16—152no—
340D16—151no—
341M32—151no—
342M32—152no—
343C2×C16—152no—
344C2×C16C2×D1511yescharacteristic, complemented
345C2×C3×C5—21no—
346C2×C3×C5—82no—
347C2×C3×C5C22×D811yescharacteristic
348D15—22no—
349D15—81no—
350D15—81no—
351C23×C3—41no—
352C22×D3—202no—
353C3×Q8—22no—
354C3×Q8—41no—
355C3×D4—22no—
356C3×D4—41no—
357C2×C3×C4—41no—
358C2×C3×C4D4×D511yescharacteristic
359#67—52no—
360#67—202no—
361#67—202no—
362#67—201no—
363#67—201no—
364C2×Dic3—202no—
365D12—51no—
366D12—101no—
367D12—101no—
368D12—202no—
369C4×D3—52no—
370C4×D3—202no—
371C4×D3—202no—
372C4×D3—201no—
373C4×D3—201no—
374Dic6—51no—
375Dic6—101no—
376Dic6—101no—
377Dic6—202no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—42no—
382C22×C5—161no—
383C22×C5D3×D811yescharacteristic
384C2×D5—32no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—482no—
388C4×C5—42no—
389C4×C5D3×D811yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—32no—
392Dic5—121no—
393Dic5—121no—
394#41—151no—
395#41—302no—
396#41—302no—
397#41—301no—
398#41—301no—
399#41—602no—
400#41—601no—
401#41—601no—
402C2×Q8—21no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—21no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—21no—
410Q16—151no—
411Q16—151no—
412Q16—302no—
413Q16C22×D1512yes—
414SD16—302no—
415SD16—302no—
416SD16—301no—
417SD16—301no—
418D8—21no—
419D8—151no—
420D8—151no—
421D8—302no—
422D8C22×D1512yes—
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C22×D1511yescharacteristic
427C16—152no—
428C16C22×D1511yescharacteristic
429C16C22×D1511yescharacteristic
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—42no—
432C22×C3—161no—
433C22×C3D5×D811yescharacteristic
434C2×D3—52no—
435C2×D3—201no—
436C2×D3—201no—
437C2×D3—802no—
438C3×C4—42no—
439C3×C4D5×D811yescharacteristic
440C3×C4C2×D4×D511yescharacteristic
441Dic3—52no—
442Dic3—201no—
443Dic3—201no—
444C2×C5—21no—
445C2×C5—82no—
446C2×C5C2×D3×D811yescharacteristic
447D5—62no—
448D5—241no—
449D5—241no—
450C23—41no—
451C23—602no—
452Q8—22no—
453Q8—41no—
454Q8—151no—
455Q8—301no—
456Q8—301no—
457Q8—602no—
458D4—22no—
459D4—41no—
460D4—152no—
461D4—151no—
462D4—301no—
463D4—301no—
464D4—602no—
465D4—602no—
466D4—602no—
467D4—601no—
468D4—601no—
469C2×C4—41no—
470C2×C4—152no—
471C2×C4—602no—
472C2×C4—602no—
473C2×C4—602no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4D4×D1511yescharacteristic
477C8—152no—
478C8D4×D1511yescharacteristic
479C8C23×D1511yescharacteristic
480C2×C3—21no—
481C2×C3—82no—
482C2×C3C2×D5×D811yescharacteristic
483D3—102no—
484D3—401no—
485D3—401no—
486C5#8202411yescharacteristic, complemented, Sylow
487C22—42no—
488C22—152no—
489C22—161no—
490C22—601no—
491C22—601no—
492C22—2402no—
493C22D8×D1511yescharacteristic
494C4—42no—
495C4—152no—
496C4—601no—
497C4—601no—
498C4D8×D1511yescharacteristic
499C4C2×D4×D1511yescharacteristic
500C3#1061375511yescharacteristic, complemented, Sylow
501C2—21no—
502C2—82no—
503C2—302no—
504C2—1201no—
505C2—1201no—
506C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC2C2×D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC2×C3×C5×SD32C2
socleC2×C3×C5C22×D8
hypercenterC2×SD32D15
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #11756525C2semidirect
2. #11756516C2semidirect
3. C2×C3×C5×SD32C2semidirect
4. #11751280C2semidirect
5. #11751248C2semidirect
6. #11751017C2semidirect
7. #11751016C2semidirect
8. #11751015C2semidirect
9. D15×SD32C2semidirect
10. #11751005C2semidirect
11. #11751002C2semidirect
15. C2×C3×C5×Q16C22semidirect
19. #91808C22semidirect
21. Q16×D15C22semidirect
26. #91793C22semidirect
28. C3×C5×SD32C22semidirect
29. C3×C5×SD32C22semidirect
30. C2×C3×C5×C16C22semidirect
31. #91113C22semidirect
32. #91112C22semidirect
33. #91111C22semidirect
34. #91110C22semidirect
35. #91096C22semidirect
36. Dic120C22semidirect
37. #91084C22semidirect
38. #91084C22semidirect
39. D240C22semidirect
40. #91082C22semidirect
41. C16×D15C22semidirect
45. C2×C5×SD32D3semidirect
92. C2×C3×SD32D5semidirect
103. C2×C5×Q16C2×D3semidirect
116. C5×SD32C2×D3semidirect
117. C5×SD32C2×D3semidirect
118. C2×C5×C16C2×D3semidirect
163. C2×C3×Q16C2×D5semidirect
176. C3×SD32C2×D5semidirect
177. C3×SD32C2×D5semidirect
178. C2×C3×C16C2×D5semidirect
235. C2×SD32D15semidirect
327. C2×Q16C2×D15semidirect
337. SD32C2×D15semidirect
338. SD32C2×D15semidirect
344. C2×C16C2×D15semidirect
430. C3×C5#3416semidirect
486. C5#82024semidirect
500. C3#10613755semidirect

Maximal subgroups

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

subgroupindex
#117565252
#117565162
C2×C3×C5×SD322
#117512802
#117512482
#117510172
#117510162
#117510152
D15×SD322
#117510052
#117510022
#106137553
#820245