Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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. C5×#4047 | C2 | semidirect |
| 3. #11716682 | C2 | semidirect |
| 4. #11716619 | C2 | semidirect |
| 5. #11716609 | C2 | semidirect |
| 13. #87775 | C4 | semidirect |
| 14. #87772 | C4 | semidirect |
| 15. #87770 | C4 | semidirect |
| 29. #4047 | D5 | semidirect |
| 89. C52 | #444 | semidirect |
| 129. C5 | #65434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4047 | 2 |
| #11716940 | 2 |
| #11716682 | 2 |
| #11716619 | 2 |
| #11716609 | 2 |
| #65434 | 5 |