Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
512 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4×C5×Dic5 | C2 | semidirect |
| 3. C2×#87781 | C2 | semidirect |
| 6. C5×#3963 | C2 | semidirect |
| 7. #11716620 | C2 | semidirect |
| 15. #87808 | C4 | semidirect |
| 58. C2×C4×Dic5 | D5 | semidirect |
| 62. #3963 | D5 | semidirect |
| 193. C52 | #388 | semidirect |
| 313. C5 | #64958 | semidirect |
| 314. C5 | #65229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87808 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87781 | 2 |
| C2×#87779 | 2 |
| C5×#3963 | 2 |
| #11716620 | 2 |
| #65229 | 5 |
| #64958 | 5 |