Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11716410 | C2 | semidirect |
| 5. C8×#1035 | C2 | semidirect |
| 8. C2×#6016 | C4 | semidirect |
| 11. D25⋊C8 | C4 | semidirect |
| 14. M16×C25 | C4 | semidirect |
| 15. #87716 | C4 | semidirect |
| 16. #87712 | C4 | semidirect |
| 79. C25 | #405 | semidirect |
| 92. M16 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716549 | 2 |
| C2×D25⋊C8 | 2 |
| M16×D25 | 2 |
| #11716410 | 2 |
| C8×#1035 | 2 |
| #65728 | 5 |