Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
268 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 54 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. #11717229 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. #11716935 | C2 | semidirect |
| 5. C5×#3955 | C2 | semidirect |
| 6. C5×#3954 | C2 | semidirect |
| 7. #11716602 | C2 | semidirect |
| 54. #3955 | D5 | semidirect |
| 55. #3954 | D5 | semidirect |
| 152. C52 | #471 | semidirect |
| 218. C5 | #65037 | semidirect |
| 219. C5 | #65187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717229 | 2 |
| #11716948 | 2 |
| C2×#87773 | 2 |
| #11716935 | 2 |
| C5×#3955 | 2 |
| C5×#3954 | 2 |
| #11716602 | 2 |
| #65187 | 5 |
| #65037 | 5 |