Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. C2×Dic52 | C2 | semidirect |
| 4. C5×#3963 | C2 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 11. #87779 | C4 | semidirect |
| 26. C2×C5×Dic5 | C2×C4 | semidirect |
| 32. #3963 | D5 | semidirect |
| 40. C2×C5⋊D5 | C42 | semidirect |
| 42. #1039 | C22⋊C4 | semidirect |
| 88. C2×Dic5 | C4×D5 | semidirect |
| 95. C52 | C4×C22⋊C4 | semidirect |
| 153. C5 | #64955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C2×#87779 | 2 |
| C2×Dic52 | 2 |
| C5×#3963 | 2 |
| #64955 | 5 |