Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
193 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 45 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. #11716849 | C2 | semidirect |
| 3. #11716846 | C2 | semidirect |
| 6. C2×C5×D20 | C4 | semidirect |
| 9. C52×C4⋊C4 | C4 | semidirect |
| 50. C2×D20 | Dic5 | semidirect |
| 54. C5×C4⋊C4 | Dic5 | semidirect |
| 55. C5×C4⋊C4 | AGL(1,𝔽5) | semidirect |
| 97. C52 | #327 | semidirect |
| 130. C4⋊C4 | #1042 | semidirect |
| 161. C5 | #64757 | semidirect |
| 162. C5 | #64868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4041 | 2 |
| #11716849 | 2 |
| #11716846 | 2 |
| #64868 | 5 |
| #64757 | 5 |