Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 278 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×#4095 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C5×#3955 | C2 | semidirect |
| 5. C5×#3951 | C2 | semidirect |
| 18. #65431 | C5 | direct (N × H) |
| 34. C5×#131 | D5 | semidirect |
| 35. C5×#131 | C2×C5 | semidirect |
| 36. #4095 | C2×C5 | semidirect |
| 37. C2×D40 | C2×C5 | semidirect |
| 40. #3955 | C2×C5 | semidirect |
| 41. #3951 | C2×C5 | semidirect |
| 115. #131 | C5×D5 | semidirect |
| 118. C52 | #472 | semidirect |
| 173. C5 | #65431 | direct (N × H) |
| 174. C5 | C5×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#131 | 2 |
| C5×#4095 | 2 |
| C2×C5×D40 | 2 |
| C5×#3955 | 2 |
| C5×#3951 | 2 |
| C5×#472 | 5 |
| #65431 | 5 |