Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C5×#4095 | C2 | semidirect |
| 3. C5×#4094 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. C5×#3965 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. C5×#3954 | C2 | semidirect |
| 24. #65488 | C5 | direct (N × H) |
| 43. C5×AGL(1,ℤ/8) | D5 | semidirect |
| 44. C5×AGL(1,ℤ/8) | C2×C5 | semidirect |
| 47. #4095 | C2×C5 | semidirect |
| 48. #4094 | C2×C5 | semidirect |
| 49. C2×#686 | C2×C5 | semidirect |
| 53. #3965 | C2×C5 | semidirect |
| 54. #3955 | C2×C5 | semidirect |
| 55. #3954 | C2×C5 | semidirect |
| 148. AGL(1,ℤ/8) | C5×D5 | semidirect |
| 154. C52 | #472 | semidirect |
| 226. C5 | #65488 | direct (N × H) |
| 227. C5 | C5×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×AGL(1,ℤ/8) | 2 |
| C5×#4095 | 2 |
| C5×#4094 | 2 |
| C2×C5×#686 | 2 |
| C5×#3965 | 2 |
| C5×#3955 | 2 |
| C5×#3954 | 2 |
| C5×#472 | 5 |
| #65488 | 5 |