Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
310 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 1. C4×#6045 | C2 | semidirect |
| 4. C5×#3935 | C2 | semidirect |
| 5. #11716616 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 19. #87773 | C4 | semidirect |
| 29. #6045 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 50. #3935 | D5 | semidirect |
| 130. #168 | C4×D5 | semidirect |
| 138. C52 | #440 | semidirect |
| 206. C5 | #64999 | semidirect |
| 207. C5 | #65307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C4×C5×D20 | 2 |
| C2×#87773 | 2 |
| C5×#3935 | 2 |
| #11716616 | 2 |
| #11716608 | 2 |
| #11716604 | 2 |
| #65307 | 5 |
| #64999 | 5 |