Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 270 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. C52×#131 | C2 | semidirect |
| 2. C5×#4097 | C2 | semidirect |
| 4. C2×C5×#677 | C2 | semidirect |
| 5. C5×#3956 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. C5×#3951 | C2 | semidirect |
| 24. #65430 | C5 | direct (N × H) |
| 45. C5×#131 | D5 | semidirect |
| 46. C5×#131 | C2×C5 | semidirect |
| 47. #4097 | C2×C5 | semidirect |
| 49. C2×#677 | C2×C5 | semidirect |
| 53. #3956 | C2×C5 | semidirect |
| 54. #3955 | C2×C5 | semidirect |
| 55. #3951 | C2×C5 | semidirect |
| 147. #131 | C5×D5 | semidirect |
| 151. C52 | #471 | semidirect |
| 216. C5 | #65430 | direct (N × H) |
| 217. C5 | C5×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#131 | 2 |
| C5×#4097 | 2 |
| C5×#4095 | 2 |
| C2×C5×#677 | 2 |
| C5×#3956 | 2 |
| C5×#3955 | 2 |
| C5×#3951 | 2 |
| C5×#471 | 5 |
| #65430 | 5 |