Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
238 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C5×#689 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 6. C5×#3956 | C2 | semidirect |
| 7. C5×#3954 | C2 | semidirect |
| 24. #65044 | C5 | direct (N × H) |
| 45. C2×#689 | C2×C5 | semidirect |
| 52. C5×#101 | D5 | semidirect |
| 53. C5×#101 | C2×C5 | semidirect |
| 54. #3956 | C2×C5 | semidirect |
| 55. #3954 | C2×C5 | semidirect |
| 144. #101 | C5×D5 | semidirect |
| 145. C52 | #473 | semidirect |
| 204. C5 | #65044 | direct (N × H) |
| 205. C5 | C5×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#689 | 2 |
| C5×#4088 | 2 |
| C5×#4055 | 2 |
| C5×#4053 | 2 |
| C52×#101 | 2 |
| C5×#3956 | 2 |
| C5×#3954 | 2 |
| C5×#473 | 5 |
| #65044 | 5 |