Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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. #65353 | C5 | direct (N × H) |
| 78. C52 | #499 | semidirect |
| 116. C5 | #65353 | direct (N × H) |
| 117. C5 | C5×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C5×#4016 | 2 |
| C5×#3940 | 2 |
| C5×#3939 | 2 |
| C4×C5×#168 | 2 |
| C5×#499 | 5 |
| #65353 | 5 |