Finite Group Databasebeta

← #14478509

Subgroups — #14478509

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
1C3×#66091C211yesmaximal, characteristic, complemented
2#11753961C211yesmaximal, characteristic, complemented
3#11751248C211yesmaximal, characteristic, complemented
4C2×C5×#826C211yesmaximal, characteristic, complemented
5#11748277C212yesmaximal, complemented
6#11748276C212yesmaximal, complemented
7#11748265C212yesmaximal, complemented
8D5×#826C212yesmaximal, complemented
9#11747542C211yesmaximal, characteristic, complemented
10#11747540C211yesmaximal, characteristic, complemented
11#11747524C211yesmaximal, characteristic, complemented
12#10613750—31nomaximal, Hall
13C3×#4144—21no—
14#92018—21no—
15C2×C3×C5×D8C2211yescharacteristic, complemented
16#91793C2211yescharacteristic, complemented
17C2×C5×D24C2211yescharacteristic, complemented
18C3×#4078—21no—
19C3×#4058C2212yescomplemented
20C3×#4057—22no—
21C3×D5×D8C2212yescomplemented
22C3×#4050C2211yescharacteristic, complemented
23C3×#4047C2211yescharacteristic
24#91304—21no—
25#91270C2212yescomplemented
26#91250—22no—
27D5×D24C2212yescomplemented
28#91111C2212yescomplemented
29#91110C2212yescomplemented
30#91096C2211yescharacteristic, complemented
31C5×#826C2212yescomplemented
32C5×#826C2212yescomplemented
33C2×C5×C3⋊C16C2211yescharacteristic, complemented
34#90947C2211yescharacteristic, complemented
35#90943C2211yescharacteristic, complemented
36#90942C2211yescharacteristic, complemented
37#90941C2212yescomplemented
38#90938C2211yescharacteristic, complemented
39#90937C2212yescomplemented
40#90934C2212yescomplemented
41D5×C3⋊C16C2212yescomplemented
42#84007—51nomaximal, Hall
43#66091—31no—
44#66091D311yescharacteristic, complemented
45C2×C5×D16—31no—
46#65436—31no—
47#65436—31no—
48#65201—32no—
49#65200—32no—
50#65200—32no—
51D5×D16—32no—
52#65193—31no—
53#65190—31no—
54C2×C3×C5×D4—21no—
55#6817—21no—
56C2×C5×D12—21no—
57C2×C3×C22⋊D5—42no—
58C3×#711—22no—
59C3×#711—41no—
60C3×D4×D5—22no—
61C3×D4×D5—41no—
62C3×#709—21no—
63C3×#709D411yescharacteristic
64D3×C22⋊D5—42no—
65#6777—41no—
66D5×D12—22no—
67#6772—22no—
68#6768—41no—
69C3×C5×D8—21no—
70C3×C5×D8C2312yes—
71C2×C3×C5×C8C2311yescharacteristic
72Dic60C2311yescharacteristic
73D120C2311yescharacteristic
74#6706—21no—
75C5×D24—21no—
76C5×D24C2312yes—
77C3×#687—22no—
78C3×#686—22no—
79C3×#681D411yescharacteristic
80C3×Dic20C2311yescharacteristic
81C3×D40C2311yescharacteristic
82C3×#677—21no—
83C3×#676D412yes—
84C3×C8×D5C2312yes—
85#6659—22no—
86#6654—22no—
87C3⋊#672C2312yes—
88C5×C3⋊C16C2311yescharacteristic
89C5×C3⋊C16C2311yescharacteristic
90C3×#576—51no—
91#5752—51no—
92#5194—52no—
93#5194—51no—
94#5193—51no—
95#5193—52no—
96#5147—51no—
97#5147—52no—
98C2×#826—52no—
99C2×#826D511yescharacteristic, complemented
100#5140—51no—
101#4144—21no—
102#4144—61no—
103C2×C5×D8—31no—
104C2×C5×D8C2×D311yescharacteristic, complemented
105#4078—21no—
106#4078—61no—
107#4058—32no—
108#4058C2×D312yescomplemented
109#4057—22no—
110#4057—62no—
111D5×D8—32no—
112D5×D8C2×D312yescomplemented
113#4050—31no—
114#4050C2×D311yescharacteristic, complemented
115#4047C2×D311yescharacteristic
116C5×D16—32no—
117C5×D16—32no—
118C2×C5×C16—31no—
119#3959—32no—
120#3959—32no—
121#3958—32no—
122#3958—32no—
123#3944—31no—
124Dic40—31no—
125#3932—31no—
126#3932—31no—
127D80—31no—
128#3930—32no—
129D5×C16—32no—
130#3415—151noSylow
131C23×C3×C5—41no—
132C22×C5×D3—41no—
133C22×C3×D5—42no—
134C2×D3×D5—42no—
135C3×C5×D4—22no—
136C3×C5×D4—41no—
137C2×C3×C4×C5C2×D411yescharacteristic
138#1220—41no—
139D60—21no—
140C4×D15—41no—
141Dic30—21no—
142C5×D12—22no—
143C5×D12—41no—
144C3×C22⋊D5—41no—
145C3×C22⋊D5—42no—
146C3×C22⋊D5—42no—
147C3×C22⋊D5D812yes—
148C2×C3×Dic5—42no—
149C3×D20—21no—
150C3×D20D811yescharacteristic
151C3×C4×D5—41no—
152C3×C4×D5C2×D412yes—
153C3×Dic10—21no—
154C3×Dic10D811yescharacteristic
155#1203—42no—
156#1201—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3×#168C2×D412yes—
161C3×H(5,𝔽2)—101no—
162#1009—101no—
163C3×AGL(1,ℤ/8)—102no—
164C3×AGL(1,ℤ/8)—101no—
165C3×#135—52no—
166C3×#135—51no—
167C2×C3×D8—52no—
168C2×C3×D8C2×D511yescharacteristic, complemented
169C3×#131—51no—
170#908—102no—
171#908—101no—
172#904—51no—
173#904—52no—
174C2×D24—52no—
175C2×D24C2×D511yescharacteristic, complemented
176#829—51no—
177#828—52no—
178#828—51no—
179#827—52no—
180#827—51no—
181#826—52no—
182#826—52no—
183#826—51no—
184#826C2×D512yescomplemented
185#826C2×D512yescomplemented
186#812—51no—
187#812—52no—
188C2×C3⋊C16—52no—
189C2×C3⋊C16C2×D511yescharacteristic, complemented
190C2×C5×D4—21no—
191C2×C5×D4—61no—
192C2×C22⋊D5—42no—
193C2×C22⋊D5—122no—
194#711—22no—
195#711—41no—
196#711—62no—
197#711—121no—
198D4×D5—22no—
199D4×D5—41no—
200D4×D5—62no—
201D4×D5—121no—
202#709—21no—
203#709—61no—
204#709#6711yescharacteristic
205C5×D8—21no—
206C5×D8—32no—
207C5×D8—61no—
208C5×D8C22×D312yes—
209C2×C5×C8C22×D311yescharacteristic
210#687—22no—
211#687—62no—
212#686—22no—
213#686—62no—
214#681#6711yescharacteristic
215Dic20—31no—
216Dic20C22×D311yescharacteristic
217D40—31no—
218D40C22×D311yescharacteristic
219#677—21no—
220#677—61no—
221#676#6712yes—
222C8×D5C22×D312yes—
223C5×C16—31no—
224C5×C16—31no—
225#672—32no—
226#576—51no—
227#576—151no—
228#509—152no—
229#509—152no—
230#509—151no—
231#509—151no—
232#508—151no—
233#508—152no—
234C2×D16—31no—
235C2×D16—152no—
236#504—151no—
237C22×C3×C5—42no—
238C22×C3×C5—161no—
239C22×C3×C5C2×D811yescharacteristic
240C2×D15—41no—
241C2×C5×D3—42no—
242C2×C5×D3—161no—
243C2×C3×D5—41no—
244C2×C3×D5—162no—
245C2×C3×D5C2×D812yes—
246D3×D5—162no—
247C3×C4×C5C2×D811yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249Dic15—41no—
250C3×Dic5—41no—
251C3×Dic5C2×D812yes—
252C3×#41—51no—
253C3×#41—102no—
254C3×#41—101no—
255C3×#41—201no—
256C2×C3×D4—21no—
257C2×C3×D4—102no—
258C2×C3×D4—201no—
259C2×C3×D4—202no—
260#239—201no—
261D3×D4—201no—
262D3×D4—202no—
263#235—102no—
264#235—101no—
265C2×D12—21no—
266C2×D12—102no—
267C3×Q16—51no—
268C3×SD16—102no—
269C3×SD16—101no—
270C3×D8—21no—
271C3×D8—51no—
272C3×D8—102no—
273C3×D8C22×D512yes—
274C3×M16—51no—
275C3×M16—52no—
276C2×C3×C8—52no—
277C2×C3×C8C22×D511yescharacteristic
278Dic12—51no—
279D24—21no—
280D24—51no—
281D24—102no—
282D24C22×D512yes—
283#204—102no—
284#204—101no—
285C3⋊C16—52no—
286C3⋊C16C22×D511yescharacteristic
287C3⋊C16C22×D511yescharacteristic
288C23×C5—41no—
289C23×C5—121no—
290C22×D5—42no—
291C22×D5—122no—
292C5×D4—22no—
293C5×D4—41no—
294C5×D4—62no—
295C5×D4—121no—
296C2×C4×C5C2×#6711yescharacteristic
297C22⋊D5—41no—
298C22⋊D5—42no—
299C22⋊D5—42no—
300C22⋊D5—121no—
301C22⋊D5—122no—
302C22⋊D5—122no—
303C22⋊D5#21312yes—
304C2×Dic5—42no—
305C2×Dic5—122no—
306D20—21no—
307D20—61no—
308D20#21311yescharacteristic
309C4×D5—41no—
310C4×D5—121no—
311C4×D5C2×#6712yes—
312Dic10—21no—
313Dic10—61no—
314Dic10#21311yescharacteristic
315C5×C8C2×#6711yescharacteristic
316C5×C8C23×D311yescharacteristic
317#168C2×#6712yes—
318H(5,𝔽2)—101no—
319H(5,𝔽2)—301no—
320AGL(1,ℤ/8)—102no—
321AGL(1,ℤ/8)—101no—
322AGL(1,ℤ/8)—302no—
323AGL(1,ℤ/8)—301no—
324#135—52no—
325#135—51no—
326#135—152no—
327#135—151no—
328C2×D8—31no—
329C2×D8—52no—
330C2×D8—152no—
331C2×D8D3×D511yescharacteristic, complemented
332#131—51no—
333Q32—151no—
334SD32—151no—
335SD32—151no—
336SD32—152no—
337SD32—152no—
338D16—32no—
339D16—32no—
340D16—151no—
341D16—152no—
342D16—152no—
343M32—152no—
344M32—151no—
345C2×C16—31no—
346C2×C16—152no—
347C2×C3×C5—21no—
348C2×C3×C5—82no—
349C2×C3×C5C22×D811yescharacteristic
350D15—81no—
351C3×D5—22no—
352C3×D5—81no—
353C5×D3—82no—
354C23×C3—41no—
355C23×C3—202no—
356C22×D3—41no—
357C22×D3—202no—
358C3×Q8—51no—
359C3×Q8—101no—
360C3×D4—22no—
361C3×D4—41no—
362C3×D4—52no—
363C3×D4—51no—
364C3×D4—101no—
365C3×D4—202no—
366C3×D4—202no—
367C3×D4—201no—
368C2×C3×C4—52no—
369C2×C3×C4—202no—
370C2×C3×C4—201no—
371C2×C3×C4D4×D511yescharacteristic
372#67—202no—
373#67—201no—
374D12—22no—
375D12—41no—
376D12—101no—
377D12—202no—
378C4×D3—202no—
379C4×D3—201no—
380Dic6—101no—
381C3×C8—52no—
382C3×C8D4×D511yescharacteristic
383C3×C8C23×D511yescharacteristic
384C22×C5—42no—
385C22×C5—122no—
386C22×C5—161no—
387C22×C5—481no—
388C22×C5C2×#21311yescharacteristic
389C2×D5—41no—
390C2×D5—121no—
391C2×D5—162no—
392C2×D5—482no—
393C2×D5C2×#21312yes—
394C4×C5C2×#21311yescharacteristic
395C4×C5C22×#6711yescharacteristic
396Dic5—41no—
397Dic5—121no—
398Dic5C2×#21312yes—
399#41—51no—
400#41—102no—
401#41—101no—
402#41—201no—
403#41—302no—
404#41—301no—
405#41—601no—
406C2×D4—21no—
407C2×D4—61no—
408C2×D4—102no—
409C2×D4—201no—
410C2×D4—202no—
411C2×D4—302no—
412C2×D4—601no—
413C2×D4—602no—
414Q16—51no—
415Q16—151no—
416SD16—102no—
417SD16—101no—
418SD16—302no—
419SD16—301no—
420D8—21no—
421D8—32no—
422D8—51no—
423D8—61no—
424D8—102no—
425D8—151no—
426D8—302no—
427D8C2×D3×D512yes—
428M16—51no—
429M16—52no—
430C2×C8—52no—
431C2×C8C2×D3×D511yescharacteristic
432C16—31no—
433C16—31no—
434C16—152no—
435C3×C5#341511yescharacteristic, complemented, Hall
436C22×C3—42no—
437C22×C3—52no—
438C22×C3—161no—
439C22×C3—201no—
440C22×C3—802no—
441C22×C3D5×D811yescharacteristic
442C2×D3—42no—
443C2×D3—161no—
444C2×D3—201no—
445C2×D3—802no—
446C3×C4—52no—
447C3×C4—201no—
448C3×C4D5×D811yescharacteristic
449C3×C4C2×D4×D511yescharacteristic
450Dic3—201no—
451C2×C5—21no—
452C2×C5—82no—
453C2×C5—242no—
454C2×C5C22×#21311yescharacteristic
455D5—22no—
456D5—81no—
457D5—241no—
458C23—41no—
459C23—121no—
460C23—202no—
461C23—602no—
462Q8—51no—
463Q8—101no—
464Q8—301no—
465D4—22no—
466D4—41no—
467D4—52no—
468D4—51no—
469D4—62no—
470D4—101no—
471D4—121no—
472D4—202no—
473D4—202no—
474D4—201no—
475D4—301no—
476D4—602no—
477D4—602no—
478D4—601no—
479C2×C4—52no—
480C2×C4—202no—
481C2×C4—201no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C4D5×#6711yescharacteristic
485C8—52no—
486C8D5×#6711yescharacteristic
487C8C22×D3×D511yescharacteristic
488C2×C3—21no—
489C2×C3—82no—
490C2×C3—102no—
491C2×C3—401no—
492C2×C3C2×D5×D811yescharacteristic
493D3—82no—
494D3—401no—
495C5#8400711yescharacteristic, complemented, Sylow
496C22—42no—
497C22—52no—
498C22—122no—
499C22—161no—
500C22—201no—
501C22—481no—
502C22—601no—
503C22—802no—
504C22—2402no—
505C22D5×#21311yescharacteristic
506C4—52no—
507C4—201no—
508C4—601no—
509C4D5×#21311yescharacteristic
510C4C2×D5×#6711yescharacteristic
511C3#1061375011yescharacteristic, complemented, Sylow
512C2—21no—
513C2—82no—
514C2—102no—
515C2—242no—
516C2—401no—
517C2—1201no—
518C2C2×D5×#21311yescharacteristic
subgroupG/H
centerC2C2×D5×#213
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5C22×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#66091C2semidirect
2. #11753961C2semidirect
3. #11751248C2semidirect
4. C2×C5×#826C2semidirect
5. #11748277C2semidirect
6. #11748276C2semidirect
7. #11748265C2semidirect
8. D5×#826C2semidirect
9. #11747542C2semidirect
10. #11747540C2semidirect
11. #11747524C2semidirect
15. C2×C3×C5×D8C22semidirect
16. #91793C22semidirect
17. C2×C5×D24C22semidirect
19. C3×#4058C22semidirect
21. C3×D5×D8C22semidirect
22. C3×#4050C22semidirect
25. #91270C22semidirect
27. D5×D24C22semidirect
28. #91111C22semidirect
29. #91110C22semidirect
30. #91096C22semidirect
31. C5×#826C22semidirect
32. C5×#826C22semidirect
33. C2×C5×C3⋊C16C22semidirect
34. #90947C22semidirect
35. #90943C22semidirect
36. #90942C22semidirect
37. #90941C22semidirect
38. #90938C22semidirect
39. #90937C22semidirect
40. #90934C22semidirect
41. D5×C3⋊C16C22semidirect
44. #66091D3semidirect
99. C2×#826D5semidirect
104. C2×C5×D8C2×D3semidirect
108. #4058C2×D3semidirect
112. D5×D8C2×D3semidirect
114. #4050C2×D3semidirect
168. C2×C3×D8C2×D5semidirect
175. C2×D24C2×D5semidirect
184. #826C2×D5semidirect
185. #826C2×D5semidirect
189. C2×C3⋊C16C2×D5semidirect
331. C2×D8D3×D5semidirect
435. C3×C5#3415semidirect
495. C5#84007semidirect
511. C3#10613750semidirect

Maximal subgroups

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

subgroupindex
C3×#660912
#117539612
#117512482
C2×C5×#8262
#117482772
#117482762
#117482652
D5×#8262
#117475422
#117475402
#117475242
#106137503
#840075