Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
272 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3954 | C2 | semidirect |
| 16. #65413 | C5 | direct (N × H) |
| 35. #3954 | C2×C5 | semidirect |
| 105. C52 | #430 | semidirect |
| 163. C5 | #65413 | direct (N × H) |
| 164. C5 | C5×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C2×C5×#681 | 2 |
| C5×#3954 | 2 |
| C5×#430 | 5 |
| #65413 | 5 |