Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
367 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. C5×#4008 | C2 | direct (N × H) |
| 6. C2×C52×D4 | C4 | semidirect |
| 11. C5×#711 | C4 | semidirect |
| 14. C2×C5×Dic10 | C4 | semidirect |
| 17. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 19. C5×#700 | C22 | semidirect |
| 20. C2×#4008 | C5 | direct (N × H) |
| 27. C52×D4 | C2×C4 | semidirect |
| 40. C5×Dic10 | C2×C4 | semidirect |
| 44. C2×C4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 45. C2×#700 | C2×C5 | semidirect |
| 48. #4008 | C2×C5 | direct (N × H) |
| 70. C2×C5×D4 | C4×C5 | semidirect |
| 71. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 79. #711 | C4×C5 | semidirect |
| 82. C2×Dic10 | C4×C5 | semidirect |
| 85. C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 87. #700 | C22×C5 | semidirect |
| 95. C2×C52 | #104 | semidirect |
| 114. C5×D4 | C2×C4×C5 | semidirect |
| 115. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 140. Dic10 | C2×C4×C5 | semidirect |
| 147. C52 | C2×#104 | semidirect |
| 183. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 199. C2×C5 | C5×#104 | semidirect |
| 200. C2×C5 | #4008 | direct (N × H) |
| 212. D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 226. C5 | C2×C5×#104 | semidirect |
| 227. C5 | C2×#4008 | direct (N × H) |
| 243. C2 | C5×#4008 | 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 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×C5×#700 | 2 |
| C5×#4008 | 2 |
| C2×#4008 | 5 |
| C2×C5×#104 | 5 |