Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
342 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11716702 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 7. #11716606 | C2 | semidirect |
| 10. C5×Q8×D5 | C4 | semidirect |
| 53. #3967 | D5 | semidirect |
| 77. Q8×D5 | Dic5 | semidirect |
| 150. C52 | #419 | semidirect |
| 221. C5 | #65091 | semidirect |
| 222. C5 | #65514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| #11716959 | 2 |
| C2×#87768 | 2 |
| #11716702 | 2 |
| C5×#3967 | 2 |
| #11716607 | 2 |
| #11716606 | 2 |
| #65514 | 5 |
| #65091 | 5 |