Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
268 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 74 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. C52×#137 | C2 | semidirect |
| 3. C5×#4094 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. C5×#3968 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. C5×#3954 | C2 | semidirect |
| 24. #65492 | C5 | direct (N × H) |
| 42. C5×#137 | D5 | semidirect |
| 43. C5×#137 | C2×C5 | semidirect |
| 48. #4094 | C2×C5 | semidirect |
| 49. C2×#688 | C2×C5 | semidirect |
| 53. #3968 | C2×C5 | semidirect |
| 54. #3955 | C2×C5 | semidirect |
| 55. #3954 | C2×C5 | semidirect |
| 145. #137 | C5×D5 | semidirect |
| 152. C52 | #471 | semidirect |
| 218. C5 | #65492 | direct (N × H) |
| 219. C5 | C5×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#137 | 2 |
| C5×#4095 | 2 |
| C5×#4094 | 2 |
| C2×C5×#688 | 2 |
| C5×#3968 | 2 |
| C5×#3955 | 2 |
| C5×#3954 | 2 |
| C5×#471 | 5 |
| #65492 | 5 |