Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
236 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 12. #65358 | C5 | direct (N × H) |
| 70. C52 | #491 | semidirect |
| 104. C5 | #65358 | direct (N × H) |
| 105. C5 | C5×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C5×#4015 | 2 |
| C5×#3942 | 2 |
| C5×#3935 | 2 |
| C5×#491 | 5 |
| #65358 | 5 |