Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
214 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#3996 | C2 | semidirect |
| 5. C5×#3995 | C2 | semidirect |
| 18. #65729 | C5 | direct (N × H) |
| 38. #3996 | C2×C5 | semidirect |
| 39. #3995 | C2×C5 | semidirect |
| 111. C52 | #430 | semidirect |
| 166. C5 | C5×#430 | semidirect |
| 167. C5 | #65729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5⋊M16 | 2 |
| C2×C5×#700 | 2 |
| C5×D5×M16 | 2 |
| C5×#3996 | 2 |
| C5×#3995 | 2 |
| #65729 | 5 |
| C5×#430 | 5 |