Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 74 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. C5×#4130 | C2 | semidirect |
| 4. #11716756 | C2 | semidirect |
| 5. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 7. C2×C5×Dic10 | C4 | semidirect |
| 9. C2×#6036 | C4 | semidirect |
| 44. #4130 | D5 | semidirect |
| 80. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 145. C52 | #410 | semidirect |
| 225. C5 | #65295 | semidirect |
| 226. C5 | #65785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| #11717425 | 2 |
| C5×#4130 | 2 |
| #11716756 | 2 |
| #65785 | 5 |
| #65295 | 5 |