Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
424 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #11717227 | C2 | semidirect |
| 3. C52×#108 | C2 | semidirect |
| 4. #11716692 | C2 | semidirect |
| 5. C8×#1039 | C2 | semidirect |
| 11. #87802 | C4 | semidirect |
| 12. #87801 | C4 | semidirect |
| 13. #87800 | C4 | semidirect |
| 30. C5×#108 | D5 | semidirect |
| 66. #108 | C5⋊D5 | semidirect |
| 69. C52 | #443 | semidirect |
| 100. C5 | #65184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717227 | 2 |
| #11717224 | 2 |
| C52×#108 | 2 |
| #11716692 | 2 |
| C8×#1039 | 2 |
| #65184 | 5 |