Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D3×D15 |
| commutator, hypocenter | C32×C5 | C22×C8 |
| Frattini | C4 | C2×D3×D15 |
| Fitting | C32×C5×C8 | C22 |
| socle | C2×C32×C5 | C22×C4 |
| prime radical | C2×D3×D15 | C4 |
| cosocle | C32×C4×C5 | C23 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×C3⋊D15 | C2 | semidirect |
| 3. C3×C8×D15 | C2 | semidirect |
| 4. C3×C5×D3×C8 | C2 | semidirect |
| 5. #10623794 | C2 | semidirect |
| 6. D3×C3⋊#168 | 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 | direct (N × H) |
| 32. C5×D3×C8 | D3 | semidirect |
| 40. D3×D15 | C8 | direct (N × H) |
| 49. C3×D3×C8 | 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 |
| 81. C3⋊D15 | C2×C8 | semidirect |
| 82. C3×D15 | C2×C8 | semidirect |
| 83. C3×C5×D3 | C2×C8 | semidirect |
| 98. C32×C8 | C2×D5 | semidirect |
| 101. C3×C3⋊C8 | C2×D5 | semidirect |
| 135. D3×C8 | D15 | direct (N × H) |
| 136. C32×C5 | C22×C8 | semidirect |
| 145. C5×C8 | D32 | semidirect |
| 164. D15 | D3×C8 | direct (N × H) |
| 166. C5×D3 | D3×C8 | semidirect |
| 185. C3×C8 | D3×D5 | semidirect |
| 186. C3×C8 | C2×D15 | semidirect |
| 191. C3⋊C8 | C2×D15 | semidirect |
| 203. C3×D3 | C8×D5 | semidirect |
| 212. C3×C5 | C2×D3×C8 | semidirect |
| 213. C3×C5 | C2×D3×C8 | semidirect |
| 237. C32 | C2×C8×D5 | semidirect |
| 248. C8 | D3×D15 | direct (N × H) |
| 258. D3 | C8×D15 | direct (N × H) |
| 259. C5 | D32×C8 | semidirect |
| 269. C3 | D3×C8×D5 | semidirect |
| 270. C3 | C2×C8×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 |
| C8×C3⋊D15 | 2 |
| C3×C8×D15 | 2 |
| C3×C5×D3×C8 | 2 |
| #10623794 | 2 |
| D3×C3⋊#168 | 2 |
| C3⋊C8×D15 | 2 |
| C2×C8×D15 | 3 |
| D3×C8×D5 | 3 |
| D32×C8 | 5 |