Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4047 | C2 | semidirect |
| 3. C4×C52×C8 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. C5×#3937 | C2 | semidirect |
| 11. C5×Dic20 | C4 | semidirect |
| 12. C5×D40 | C4 | semidirect |
| 13. C5×#677 | C4 | semidirect |
| 17. #64989 | C5 | direct (N × H) |
| 32. #4047 | C2×C5 | semidirect |
| 36. C4×C5×C8 | D5 | semidirect |
| 37. C4×C5×C8 | C2×C5 | semidirect |
| 38. #3951 | C2×C5 | semidirect |
| 39. #3937 | C2×C5 | semidirect |
| 64. Dic20 | C4×C5 | semidirect |
| 65. D40 | C4×C5 | semidirect |
| 66. #677 | C4×C5 | semidirect |
| 105. C4×C8 | C5×D5 | semidirect |
| 106. C52 | #443 | semidirect |
| 153. C5 | #64989 | direct (N × H) |
| 154. C5 | C5×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4050 | 2 |
| C5×#4047 | 2 |
| C4×C52×C8 | 2 |
| C5×#3951 | 2 |
| C5×#3937 | 2 |
| C5×#443 | 5 |
| #64989 | 5 |