Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 6. C2×#6032 | C4 | semidirect |
| 11. C52×M16 | C4 | semidirect |
| 12. C5×#681 | C4 | semidirect |
| 54. C5×M16 | Dic5 | semidirect |
| 55. C5×M16 | AGL(1,𝔽5) | semidirect |
| 62. #681 | Dic5 | semidirect |
| 98. C52 | #344 | semidirect |
| 125. M16 | #1042 | semidirect |
| 153. C5 | #64779 | semidirect |
| 154. C5 | #64902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C2×#87849 | 2 |
| C5×D5×M16 | 2 |
| #64902 | 5 |
| #64779 | 5 |