Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
263 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 60 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×C22⋊#170 | C2 | semidirect |
| 8. #64933 | C5 | direct (N × H) |
| 14. C23×C52 | C8 | semidirect |
| 23. C22⋊#170 | C2×C5 | semidirect |
| 69. C23×C5 | C5×C8 | semidirect |
| 70. C23×C5 | #170 | semidirect |
| 85. C52 | #323 | semidirect |
| 147. C23 | C5×#170 | semidirect |
| 155. C5 | C5×#323 | semidirect |
| 156. C5 | #64933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊Dic5 | 2 |
| C5×C22⋊#170 | 2 |
| #64933 | 5 |
| C5×#323 | 5 |