Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 66 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. D3×D60 | C2 | semidirect |
| 2. #10624197 | C2 | semidirect |
| 3. #10623901 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 6. #10623804 | C2 | semidirect |
| 7. #10623799 | C2 | semidirect |
| 12. C4⋊(C3⋊D15) | C22 | semidirect |
| 14. C3×Dic30 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 32. #6706 | D3 | semidirect |
| 33. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 50. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 66. Dic30 | C2×D3 | semidirect |
| 75. C3×C5×C8 | C2×D3 | semidirect |
| 76. C3×C5×C8 | C2×D3 | semidirect |
| 77. C5×C3⋊C8 | C2×D3 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 102. C3×C3⋊C8 | C2×D5 | semidirect |
| 136. ΓL(1,𝔽25) | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 148. C5×C8 | D32 | semidirect |
| 193. C3×C8 | D3×D5 | semidirect |
| 194. C3×C8 | C2×D15 | semidirect |
| 195. C3⋊C8 | C2×D15 | semidirect |
| 217. C3×C5 | #908 | semidirect |
| 218. C3×C5 | #914 | semidirect |
| 243. C32 | #4054 | semidirect |
| 254. C8 | D3×D15 | semidirect |
| 268. C5 | #63794 | semidirect |
| 278. C3 | #91253 | semidirect |
| 279. C3 | #91797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×D60 | 2 |
| #10624197 | 2 |
| #10623901 | 2 |
| C3×#6706 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| #10623804 | 2 |
| #10623799 | 2 |
| #91797 | 3 |
| #91253 | 3 |
| #63794 | 5 |