Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
298 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×C5×#681 | C2 | semidirect |
| 3. C2×D5×#168 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716597 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 42. C2×#681 | D5 | semidirect |
| 60. C2×C5×D5 | M16 | semidirect |
| 140. #168 | C22⋊D5 | semidirect |
| 148. C52 | #435 | semidirect |
| 166. C2×D5 | #681 | semidirect |
| 226. C5 | #65300 | semidirect |
| 227. C5 | #65416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C22⋊D5 | 2 |
| C2×C5×#681 | 2 |
| C2×D5×#168 | 2 |
| C22⋊#6029 | 2 |
| #11716612 | 2 |
| #11716597 | 2 |
| #11716595 | 2 |
| #65416 | 5 |
| #65300 | 5 |