Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
284 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11717208 | C2 | semidirect |
| 4. C5×#3940 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716613 | C2 | semidirect |
| 30. C5×D20 | Q8 | semidirect |
| 48. #3940 | D5 | semidirect |
| 115. D20 | Dic10 | semidirect |
| 131. C52 | #476 | semidirect |
| 197. C5 | #65050 | semidirect |
| 198. C5 | #65159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717208 | 2 |
| #11717017 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| #11716614 | 2 |
| #11716613 | 2 |
| #11716604 | 2 |
| #65159 | 5 |
| #65050 | 5 |