Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
544 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 144 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×#87780 | C2 | semidirect |
| 4. #11716698 | C2 | semidirect |
| 5. C5×#3963 | C2 | semidirect |
| 12. C2×C4×C5×D5 | C4 | semidirect |
| 44. #3963 | D5 | semidirect |
| 54. C2×C5×D5 | C4⋊C4 | semidirect |
| 58. C5×Dic5 | C22⋊C4 | semidirect |
| 74. C2×C4×D5 | Dic5 | semidirect |
| 131. C52 | #380 | semidirect |
| 156. C2×D5 | C4⋊Dic5 | semidirect |
| 166. Dic5 | C22⋊Dic5 | semidirect |
| 211. C5 | #64956 | semidirect |
| 212. C5 | #65501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11716698 | 2 |
| C5×#3963 | 2 |
| #65501 | 5 |
| #64956 | 5 |