Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10623899 | C2 | semidirect |
| 3. C3×C8×D15 | C2 | semidirect |
| 4. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. #10623797 | C2 | semidirect |
| 6. #10623796 | C2 | semidirect |
| 7. C3⋊C8×D15 | C2 | semidirect |
| 17. C32×C5×C8 | C22 | semidirect |
| 18. C3⋊(C3⋊#168) | C22 | semidirect |
| 19. C3×C3⋊#168 | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 31. C8×D15 | D3 | semidirect |
| 32. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 48. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 70. C3×C5×C8 | C2×D3 | semidirect |
| 71. C3×C5×C8 | C2×D3 | semidirect |
| 75. C3⋊#168 | C2×D3 | semidirect |
| 77. C5×C3⋊C8 | C2×D3 | semidirect |
| 82. C3×D15 | M16 | semidirect |
| 98. C32×C8 | C2×D5 | semidirect |
| 101. C3×C3⋊C8 | C2×D5 | semidirect |
| 133. ΓL(1,𝔽25) | D15 | direct (N × H) |
| 136. C32×C5 | C2×M16 | semidirect |
| 145. C5×C8 | D32 | semidirect |
| 164. D15 | ΓL(1,𝔽25) | direct (N × H) |
| 185. C3×C8 | D3×D5 | semidirect |
| 186. C3×C8 | C2×D15 | semidirect |
| 191. C3⋊C8 | C2×D15 | semidirect |
| 212. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 213. C3×C5 | D3×M16 | semidirect |
| 237. C32 | D5×M16 | semidirect |
| 248. C8 | D3×D15 | semidirect |
| 259. C5 | D3×ΓL(1,𝔽25) | semidirect |
| 269. C3 | D5×ΓL(1,𝔽25) | semidirect |
| 270. C3 | M16×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×D15 | 2 |
| #10623899 | 2 |
| C3×C8×D15 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| #10623797 | 2 |
| #10623796 | 2 |
| C3⋊C8×D15 | 2 |
| M16×D15 | 3 |
| D5×ΓL(1,𝔽25) | 3 |
| D3×ΓL(1,𝔽25) | 5 |