Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
261 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×#87829 | C2 | semidirect |
| 2. C2×#87828 | C2 | semidirect |
| 4. #11716847 | C2 | semidirect |
| 5. C4×C5×#170 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. #11716753 | C2 | semidirect |
| 38. C5×#170 | D4 | semidirect |
| 48. C4×#170 | D5 | semidirect |
| 63. C5×Dic5 | M16 | semidirect |
| 129. #170 | D20 | semidirect |
| 141. C52 | #436 | semidirect |
| 171. Dic5 | #676 | semidirect |
| 218. C5 | #64977 | semidirect |
| 219. C5 | #65695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| C2×#87828 | 2 |
| #11716998 | 2 |
| #11716847 | 2 |
| C4×C5×#170 | 2 |
| #11716754 | 2 |
| #11716753 | 2 |
| #65695 | 5 |
| #64977 | 5 |