Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
239 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C5×#3994 | C2 | semidirect |
| 4. C5×#3993 | C2 | semidirect |
| 9. C2×C52×C8 | C4 | semidirect |
| 10. C2×C5×#168 | C4 | semidirect |
| 11. C5×C8×D5 | C4 | semidirect |
| 12. C5×C8×D5 | C4 | semidirect |
| 15. #65721 | C5 | direct (N × H) |
| 33. #3994 | C2×C5 | semidirect |
| 34. #3993 | C2×C5 | semidirect |
| 57. C2×C5×C8 | C4×C5 | semidirect |
| 58. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 62. C2×#168 | C4×C5 | semidirect |
| 63. C8×D5 | C4×C5 | semidirect |
| 64. C8×D5 | C4×C5 | semidirect |
| 103. C52 | #427 | semidirect |
| 131. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 158. C5 | C5×#427 | semidirect |
| 159. C5 | #65721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4130 | 2 |
| C2×C5×C8×D5 | 2 |
| C5×#3994 | 2 |
| C5×#3993 | 2 |
| #65721 | 5 |
| C5×#427 | 5 |