Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11717425 | C2 | semidirect |
| 3. #11716854 | C2 | semidirect |
| 4. C2×C52×D4 | C4 | semidirect |
| 6. C22×C5×Dic5 | C4 | semidirect |
| 10. C2×C5×Dic10 | C4 | semidirect |
| 50. C2×C5×D4 | Dic5 | semidirect |
| 51. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 55. C22×Dic5 | Dic5 | semidirect |
| 59. C2×Dic10 | Dic5 | semidirect |
| 103. C52 | #410 | semidirect |
| 132. C2×D4 | #1042 | semidirect |
| 163. C5 | #65529 | semidirect |
| 164. C5 | #65771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| #11717425 | 2 |
| #11716854 | 2 |
| #65771 | 5 |
| #65529 | 5 |