Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 4. #11716689 | C2 | semidirect |
| 5. C5×#3954 | C2 | semidirect |
| 6. #11716619 | C2 | semidirect |
| 7. #11716618 | C2 | semidirect |
| 49. #3954 | D5 | direct (N × H) |
| 92. C5×D5 | #108 | semidirect |
| 130. C52 | C2×#108 | semidirect |
| 172. D5 | #3954 | direct (N × H) |
| 187. C5 | D5×#108 | semidirect |
| 188. C5 | C2×#3954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×M16 | 2 |
| D5×#681 | 2 |
| C2×D5×#168 | 2 |
| #11716689 | 2 |
| C5×#3954 | 2 |
| #11716619 | 2 |
| #11716618 | 2 |
| C2×#3954 | 5 |
| D5×#108 | 5 |