Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11717256 | C2 | semidirect |
| 2. C2×C5×#687 | C2 | semidirect |
| 4. #11716981 | C2 | semidirect |
| 5. C2×#87776 | C2 | semidirect |
| 6. C2×#87773 | C2 | semidirect |
| 7. #11716594 | C2 | semidirect |
| 48. C2×#687 | D5 | semidirect |
| 146. C52 | #495 | semidirect |
| 215. C5 | #65444 | semidirect |
| 216. C5 | #65457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717256 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×#686 | 2 |
| #11716981 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| #11716594 | 2 |
| #65457 | 5 |
| #65444 | 5 |