Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #11716887 | C2 | semidirect |
| 4. #11716886 | C2 | semidirect |
| 9. C2×C52×C8 | C4 | semidirect |
| 10. C2×#6029 | C4 | semidirect |
| 11. C8×C5⋊D5 | C4 | semidirect |
| 12. C8×C5⋊D5 | C4 | semidirect |
| 48. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 91. C52 | #427 | semidirect |
| 115. C2×C8 | #1044 | semidirect |
| 140. C5 | #65721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717451 | 2 |
| C2×C8×C5⋊D5 | 2 |
| #11716887 | 2 |
| #11716886 | 2 |
| #65721 | 5 |