Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11717246 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. #11716621 | C2 | semidirect |
| 11. C2×C5×D20 | C4 | semidirect |
| 12. C2×C4×C5×D5 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 47. #4072 | D5 | semidirect |
| 79. C2×D20 | Dic5 | semidirect |
| 80. C2×C4×D5 | Dic5 | semidirect |
| 81. C2×Dic10 | Dic5 | semidirect |
| 153. C52 | #410 | semidirect |
| 238. C5 | #65295 | semidirect |
| 239. C5 | #65529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| #11717246 | 2 |
| C5×#4072 | 2 |
| #11716621 | 2 |
| #65529 | 5 |
| #65295 | 5 |