Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 78 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. C4⋊C4×C5⋊D5 | C2 | semidirect |
| 3. C2×#87769 | C2 | semidirect |
| 4. C5×#3942 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 7. #11716604 | C2 | semidirect |
| 15. #87871 | C4 | semidirect |
| 35. C5×D20 | C2×C4 | semidirect |
| 37. C5×Dic10 | C2×C4 | semidirect |
| 55. #3942 | D5 | semidirect |
| 56. #3941 | D5 | semidirect |
| 136. D20 | C4×D5 | semidirect |
| 148. Dic10 | C4×D5 | semidirect |
| 160. C52 | #417 | semidirect |
| 243. C5 | #65060 | semidirect |
| 244. C5 | #65092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| C2×#87769 | 2 |
| C5×#3942 | 2 |
| C5×#3941 | 2 |
| #11716607 | 2 |
| #11716604 | 2 |
| #65092 | 5 |
| #65060 | 5 |