Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 14. #65271 | C5 | direct (N × H) |
| 108. C52 | #400 | semidirect |
| 172. C5 | #65271 | direct (N × H) |
| 173. C5 | C5×#400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×C4⋊C4 | 2 |
| C2×C5×#683 | 2 |
| C5×#3963 | 2 |
| C5×#400 | 5 |
| #65271 | 5 |