Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11717448 | C2 | semidirect |
| 3. #11717438 | C2 | semidirect |
| 4. #11716765 | C2 | semidirect |
| 7. C2×C5×D20 | C4 | semidirect |
| 11. #87877 | C4 | semidirect |
| 15. #87862 | C22 | semidirect |
| 17. C4⋊#1043 | C22 | semidirect |
| 62. C2×D20 | AGL(1,𝔽5) | semidirect |
| 112. C52 | #418 | semidirect |
| 179. C5 | #65767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87877 | 2 |
| #11717448 | 2 |
| #11717438 | 2 |
| #11716765 | 2 |
| #65767 | 5 |