Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
310 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11717207 | C2 | semidirect |
| 5. C5×#3939 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 7. #11716596 | C2 | semidirect |
| 19. #87773 | C4 | semidirect |
| 29. #6045 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 50. #3939 | D5 | semidirect |
| 130. #168 | C4×D5 | semidirect |
| 138. C52 | #440 | semidirect |
| 206. C5 | #65046 | semidirect |
| 207. C5 | #65178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717207 | 2 |
| #11717017 | 2 |
| C2×#87773 | 2 |
| C5×#3941 | 2 |
| C5×#3939 | 2 |
| #11716608 | 2 |
| #11716596 | 2 |
| #65178 | 5 |
| #65046 | 5 |