Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
209 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. #13014079 | C5 | direct (N × H) |
| 17. C5×#3928 | C8 | semidirect |
| 63. #3928 | C5×C8 | semidirect |
| 131. C52 | #7333 | semidirect |
| 168. C5 | C5×#7333 | semidirect |
| 169. C5 | #13014079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#10598537 | 2 |
| C5×#10597933 | 2 |
| #13014079 | 5 |
| C5×#7333 | 5 |