Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
143 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 2. C5×#4005 | C2 | semidirect |
| 8. #64856 | C5 | direct (N × H) |
| 19. #4005 | C2×C5 | semidirect |
| 60. C52 | #355 | semidirect |
| 97. C5 | C5×#355 | semidirect |
| 98. C5 | #64856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4021 | 2 |
| C5×#4005 | 2 |
| #64856 | 5 |
| C5×#355 | 5 |