Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
209 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11716847 | C2 | semidirect |
| 5. #11716845 | C2 | semidirect |
| 6. C4⋊#6032 | C2 | semidirect |
| 7. C4×#6032 | C2 | semidirect |
| 123. C52 | #433 | semidirect |
| 189. C5 | #65289 | semidirect |
| 190. C5 | #65697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4023 | 2 |
| C22⋊#6032 | 2 |
| #11716847 | 2 |
| #11716845 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #65697 | 5 |
| #65289 | 5 |