Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
298 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 76 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×C5×#676 | C2 | semidirect |
| 3. C2×#87767 | C2 | semidirect |
| 4. #11716687 | C2 | semidirect |
| 5. C5×#3946 | C2 | semidirect |
| 6. #11716597 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 41. C2×#676 | D5 | semidirect |
| 52. #3946 | D5 | semidirect |
| 57. C2×C5⋊D5 | M16 | semidirect |
| 140. #168 | C22⋊D5 | semidirect |
| 148. C52 | #435 | semidirect |
| 226. C5 | #65125 | semidirect |
| 227. C5 | #65416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#676 | 2 |
| C4×#6038 | 2 |
| C2×#87767 | 2 |
| #11716687 | 2 |
| C5×#3946 | 2 |
| #11716597 | 2 |
| #11716595 | 2 |
| #65416 | 5 |
| #65125 | 5 |