Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×D5⋊AGL(1,𝔽5) #72213871
Order 4000.
536 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C2×C42 |
| prime radical | D53 | C22 |
| cosocle | D5×C5⋊D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14522937 | C2 | semidirect |
| 5. #14522936 | C2 | semidirect |
| 6. AGL(1,𝔽5)×#1044 | C2 | semidirect |
| 7. AGL(1,𝔽5)×#1043 | C2 | semidirect |
| 10. D5×#1042 | C4 | semidirect |
| 12. #11758789 | C4 | semidirect |
| 13. #11758788 | C4 | semidirect |
| 14. D5⋊#1042 | C4 | semidirect |
| 16. D5⋊#1044 | C4 | semidirect |
| 19. D5⋊#1043 | C4 | semidirect |
| 21. C5×D5×AGL(1,𝔽5) | C4 | semidirect |
| 22. C5×D5⋊AGL(1,𝔽5) | C4 | semidirect |
| 30. #92563 | C2×C4 | semidirect |
| 31. #92563 | C2×C4 | semidirect |
| 32. #92562 | C2×C4 | semidirect |
| 33. #92561 | C2×C4 | semidirect |
| 34. #92560 | C2×C4 | semidirect |
| 35. #92559 | C2×C4 | semidirect |
| 36. C5×#1044 | C2×C4 | semidirect |
| 37. C5×#1043 | C2×C4 | semidirect |
| 38. C5×#1042 | C2×C4 | semidirect |
| 39. C52×AGL(1,𝔽5) | C2×C4 | semidirect |
| 56. C5×C5⋊D5 | C42 | semidirect |
| 58. C52×D5 | C42 | semidirect |
| 83. D5⋊AGL(1,𝔽5) | AGL(1,𝔽5) | direct (N × H) |
| 93. D5×AGL(1,𝔽5) | AGL(1,𝔽5) | semidirect |
| 100. C53 | C2×C42 | semidirect |
| 121. #1044 | C2×AGL(1,𝔽5) | semidirect |
| 130. #1043 | C2×AGL(1,𝔽5) | semidirect |
| 136. #1042 | C2×AGL(1,𝔽5) | semidirect |
| 142. C5×AGL(1,𝔽5) | C2×AGL(1,𝔽5) | semidirect |
| 168. C5⋊D5 | C4×AGL(1,𝔽5) | semidirect |
| 177. C5×D5 | C4×AGL(1,𝔽5) | semidirect |
| 178. C5×D5 | C4×AGL(1,𝔽5) | semidirect |
| 222. C52 | C2×C4×AGL(1,𝔽5) | semidirect |
| 223. C52 | C2×C4×AGL(1,𝔽5) | semidirect |
| 258. AGL(1,𝔽5) | D5⋊AGL(1,𝔽5) | direct (N × H) |
| 293. D5 | AGL(1,𝔽5)2 | semidirect |
| 313. C5 | C4×D5⋊AGL(1,𝔽5) | semidirect |
| 314. C5 | C2×AGL(1,𝔽5)2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D52×AGL(1,𝔽5) | 2 |
| D5×D5⋊AGL(1,𝔽5) | 2 |
| D5⋊(D5⋊AGL(1,𝔽5)) | 2 |
| #14522937 | 2 |
| #14522936 | 2 |
| AGL(1,𝔽5)×#1044 | 2 |
| AGL(1,𝔽5)×#1043 | 2 |
| C2×AGL(1,𝔽5)2 | 5 |
| C4×D5⋊AGL(1,𝔽5) | 5 |