Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
274 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. C5×#4094 | C2 | semidirect |
| 3. C5×#3969 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 7. C52×Q16 | C4 | semidirect |
| 8. C52×SD16 | C4 | semidirect |
| 9. C52×D8 | C4 | semidirect |
| 17. #65485 | C5 | direct (N × H) |
| 33. #4094 | C2×C5 | semidirect |
| 37. #3969 | C2×C5 | semidirect |
| 38. #3951 | C2×C5 | semidirect |
| 39. C8×Dic5 | C2×C5 | semidirect |
| 50. C5×Q16 | Dic5 | semidirect |
| 51. C5×Q16 | C4×C5 | semidirect |
| 53. C5×SD16 | Dic5 | semidirect |
| 54. C5×SD16 | C4×C5 | semidirect |
| 56. C5×D8 | Dic5 | semidirect |
| 57. C5×D8 | C4×C5 | semidirect |
| 109. C52 | #443 | semidirect |
| 128. Q16 | C5×Dic5 | semidirect |
| 129. SD16 | C5×Dic5 | semidirect |
| 130. D8 | C5×Dic5 | semidirect |
| 158. C5 | #65485 | direct (N × H) |
| 159. C5 | C5×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C5×#4094 | 2 |
| C5×#3969 | 2 |
| C5×#3951 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#443 | 5 |
| #65485 | 5 |