Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
299 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 4. #11716752 | C2 | semidirect |
| 5. Dic5×#170 | C2 | semidirect |
| 10. #87849 | C4 | semidirect |
| 12. C5×#700 | C4 | semidirect |
| 30. #6032 | C2×C4 | semidirect |
| 31. C5×#170 | C2×C4 | semidirect |
| 48. #1039 | M16 | semidirect |
| 50. C5×Dic5 | M16 | semidirect |
| 62. #700 | Dic5 | direct (N × H) |
| 107. #170 | C2×Dic5 | semidirect |
| 115. C52 | C4×M16 | semidirect |
| 139. Dic5 | #700 | direct (N × H) |
| 178. C5 | M16×Dic5 | semidirect |
| 179. C5 | C4×#700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C2×C5×#700 | 2 |
| C4×D5×Dic5 | 2 |
| #11716752 | 2 |
| Dic5×#170 | 2 |
| C4×#700 | 5 |
| M16×Dic5 | 5 |