Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. C52×#107 | C2 | semidirect |
| 4. #11716685 | C2 | semidirect |
| 5. #11716675 | C2 | semidirect |
| 13. C8×C5⋊D5 | C4 | semidirect |
| 26. C5×#107 | D5 | semidirect |
| 63. #107 | C5⋊D5 | semidirect |
| 65. C52 | #427 | semidirect |
| 96. C5 | #65169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C5⋊D5 | 2 |
| #11717212 | 2 |
| C52×#107 | 2 |
| #11716685 | 2 |
| #11716675 | 2 |
| #65169 | 5 |