Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
335 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C5×#4130 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. C5×#4008 | C2 | semidirect |
| 5. C2×C52×D4 | C4 | semidirect |
| 10. C5×#711 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 17. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 18. C5×#700 | C22 | semidirect |
| 20. #65769 | C5 | direct (N × H) |
| 43. #4130 | C2×C5 | semidirect |
| 44. D5⋊M16 | C2×C5 | semidirect |
| 47. #4008 | C2×C5 | semidirect |
| 68. C2×C5×D4 | C4×C5 | semidirect |
| 69. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 76. #711 | C4×C5 | semidirect |
| 79. C2×Dic10 | C4×C5 | semidirect |
| 83. C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 84. #700 | C22×C5 | semidirect |
| 144. C52 | #421 | semidirect |
| 180. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 222. C5 | C5×#421 | semidirect |
| 223. C5 | #65769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4008 | 2 |
| #65769 | 5 |
| C5×#421 | 5 |