Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
404 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#4149 | C2 | semidirect |
| 2. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C5×#4086 | C2 | semidirect |
| 4. C5×#4078 | C2 | semidirect |
| 5. C5×#3969 | C2 | semidirect |
| 6. C5×#3957 | C2 | semidirect |
| 7. C5×#3955 | C2 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 20. C52×M16 | C22 | semidirect |
| 23. C4×C5×Dic5 | C22 | semidirect |
| 24. C5×#681 | C22 | semidirect |
| 26. #65487 | C5 | direct (N × H) |
| 30. C52×Q8 | D4 | semidirect |
| 34. C52×D4 | D4 | semidirect |
| 44. C5×D20 | D4 | semidirect |
| 47. C5×Dic10 | D4 | semidirect |
| 51. #4149 | C2×C5 | semidirect |
| 54. C5×AGL(1,ℤ/8) | D5 | semidirect |
| 55. C5×AGL(1,ℤ/8) | C2×C5 | semidirect |
| 57. #4086 | C2×C5 | semidirect |
| 58. #4078 | C2×C5 | semidirect |
| 62. #3969 | C2×C5 | semidirect |
| 63. #3957 | C2×C5 | semidirect |
| 64. #3955 | C2×C5 | semidirect |
| 90. C2×C5×D4 | C2×D5 | semidirect |
| 91. C2×C5×D4 | C22×C5 | semidirect |
| 110. C5×M16 | C2×D5 | semidirect |
| 111. C5×M16 | C22×C5 | semidirect |
| 115. C4×Dic5 | C22×C5 | semidirect |
| 116. #681 | C22×C5 | semidirect |
| 133. C5×Q8 | C22⋊D5 | semidirect |
| 134. C5×Q8 | C5×D4 | semidirect |
| 152. C5×D4 | C22⋊D5 | semidirect |
| 153. C5×D4 | C5×D4 | semidirect |
| 170. D20 | C5×D4 | semidirect |
| 173. Dic10 | C5×D4 | semidirect |
| 181. AGL(1,ℤ/8) | C5×D5 | semidirect |
| 186. C52 | #453 | semidirect |
| 229. C2×D4 | C2×C5×D5 | semidirect |
| 235. M16 | C2×C5×D5 | semidirect |
| 257. Q8 | C5×C22⋊D5 | semidirect |
| 268. D4 | C5×C22⋊D5 | semidirect |
| 277. C5 | #65487 | direct (N × H) |
| 278. C5 | C5×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4149 | 2 |
| C52×AGL(1,ℤ/8) | 2 |
| C5×#4086 | 2 |
| C5×#4078 | 2 |
| C5×#3969 | 2 |
| C5×#3957 | 2 |
| C5×#3955 | 2 |
| C5×#453 | 5 |
| #65487 | 5 |