Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C5×#4094 | C2 | semidirect |
| 3. #11716935 | C2 | semidirect |
| 4. C5×#3969 | C2 | semidirect |
| 5. #11716619 | C2 | semidirect |
| 6. #11716611 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 10. #87812 | C4 | semidirect |
| 11. #87811 | C4 | semidirect |
| 12. #87810 | C4 | semidirect |
| 13. #87809 | C4 | semidirect |
| 45. #4094 | D5 | semidirect |
| 49. #3969 | D5 | semidirect |
| 156. C52 | #444 | semidirect |
| 224. C5 | #65112 | semidirect |
| 225. C5 | #65434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717270 | 2 |
| C5×#4094 | 2 |
| #11716935 | 2 |
| C5×#3969 | 2 |
| #11716619 | 2 |
| #11716611 | 2 |
| #11716595 | 2 |
| #65434 | 5 |
| #65112 | 5 |