Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
258 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 258 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. #13099489 | C2 | semidirect |
| 3. C5×#64683 | C2 | semidirect |
| 19. C5×Dic20 | C8 | semidirect |
| 20. C5×D40 | C8 | semidirect |
| 28. #64683 | D5 | semidirect |
| 88. Dic20 | #168 | semidirect |
| 89. D40 | #168 | semidirect |
| 139. C52 | #1336 | semidirect |
| 189. C5 | #10598060 | semidirect |
| 190. C5 | #10598258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#64989 | 2 |
| #13099489 | 2 |
| C5×#64683 | 2 |
| #10598258 | 5 |
| #10598060 | 5 |