Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C5×#3947 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 6. #11716595 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 11. #87799 | C4 | semidirect |
| 18. #87767 | C4 | semidirect |
| 42. #3947 | D5 | semidirect |
| 44. C8×Dic5 | D5 | semidirect |
| 121. C52 | #405 | semidirect |
| 176. C5 | #64978 | semidirect |
| 177. C5 | #64997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| #11716992 | 2 |
| C2×#87767 | 2 |
| C5×#3947 | 2 |
| C5×C8×Dic5 | 2 |
| #11716595 | 2 |
| Dic5×#168 | 2 |
| #64997 | 5 |
| #64978 | 5 |