Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 286 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 |
|---|---|---|
| 19. #87776 | C4 | semidirect |
| 132. C52 | #441 | semidirect |
| 193. C5 | #65005 | semidirect |
| 194. C5 | #65319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87776 | 2 |
| C5×#3935 | 2 |
| #11716614 | 2 |
| #11716608 | 2 |
| #11716607 | 2 |
| #65319 | 5 |
| #65005 | 5 |