Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
658 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 4. C5×#64674 | C2 | semidirect |
| 5. #13099248 | C2 | semidirect |
| 31. #87767 | C8 | semidirect |
| 39. #64674 | D5 | semidirect |
| 53. C5×#168 | C2×C8 | semidirect |
| 118. C5⋊D5 | #322 | semidirect |
| 148. #168 | C8×D5 | semidirect |
| 160. C52 | C2×#322 | semidirect |
| 218. C5 | D5×#322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C5⋊D5 | 2 |
| C4×#87767 | 2 |
| C5×#64674 | 2 |
| #13099248 | 2 |
| D5×#322 | 5 |