Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 1. C2×#87812 | C2 | semidirect |
| 5. C5×#3968 | C2 | semidirect |
| 6. #11716619 | C2 | semidirect |
| 7. #11716602 | C2 | semidirect |
| 51. #3968 | D5 | semidirect |
| 150. C52 | #473 | semidirect |
| 210. C5 | #65044 | semidirect |
| 211. C5 | #65493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87812 | 2 |
| C5×#4088 | 2 |
| #11716949 | 2 |
| #11716933 | 2 |
| C5×#3968 | 2 |
| #11716619 | 2 |
| #11716602 | 2 |
| #65493 | 5 |
| #65044 | 5 |