Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#87802 | C2 | semidirect |
| 4. C2×#87776 | C2 | semidirect |
| 6. C5×#3948 | C2 | semidirect |
| 7. #11716608 | C2 | semidirect |
| 57. #3948 | D5 | semidirect |
| 62. C2×C5×D5 | Q16 | semidirect |
| 162. C52 | #451 | semidirect |
| 171. C2×D5 | Dic20 | semidirect |
| 236. C5 | #65028 | semidirect |
| 237. C5 | #65097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| C2×#87802 | 2 |
| #11716975 | 2 |
| C2×#87776 | 2 |
| C5×#3952 | 2 |
| C5×#3948 | 2 |
| #11716608 | 2 |
| #65097 | 5 |
| #65028 | 5 |