Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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×#124 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C4×C5×D20 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3964 | C2 | semidirect |
| 7. C5×C4⋊#168 | C2 | semidirect |
| 22. #65346 | C5 | direct (N × H) |
| 42. C5×#124 | D5 | semidirect |
| 43. C5×#124 | C2×C5 | semidirect |
| 45. C2×#688 | C2×C5 | semidirect |
| 47. C4×D20 | C2×C5 | semidirect |
| 51. #3967 | C2×C5 | semidirect |
| 52. #3964 | C2×C5 | semidirect |
| 53. C4⋊#168 | C2×C5 | semidirect |
| 147. #124 | C5×D5 | semidirect |
| 152. C52 | #463 | semidirect |
| 232. C5 | #65346 | direct (N × H) |
| 233. C5 | C5×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#686 | 2 |
| C4×C5×D20 | 2 |
| C5×#3967 | 2 |
| C5×#3964 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#463 | 5 |
| #65346 | 5 |