Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator | C2×C32×C5 | C22×C4 |
| Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C2×#67152 | C2 |
| hypocenter | C32×C5 | C4×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#67149 | C2 | semidirect |
| 3. C2×C3×D3×Dic5 | C2 | semidirect |
| 4. #10623828 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 6. #10623772 | C2 | semidirect |
| 7. C3×#6669 | C2 | semidirect |
| 17. #67152 | C4 | semidirect |
| 26. C2×D3×Dic5 | D3 | semidirect |
| 30. #6669 | D3 | semidirect |
| 39. C2×C3⋊D15 | C2×C4 | semidirect |
| 42. C2×C3×C5×D3 | C2×C4 | semidirect |
| 44. C3×Dic15 | C2×C4 | semidirect |
| 45. C3×Dic15 | D4 | semidirect |
| 54. (C2×D3)⋊Dic3 | D5 | semidirect |
| 120. C2×C5×D3 | C4×D3 | semidirect |
| 122. Dic15 | C4×D3 | semidirect |
| 123. Dic15 | #67 | semidirect |
| 148. C32×C5 | C4×D4 | semidirect |
| 165. C2×C3×D3 | C4×D5 | semidirect |
| 234. C3×C5 | #893 | semidirect |
| 235. C3×C5 | C4×#67 | semidirect |
| 253. C2×D3 | #1200 | semidirect |
| 271. C32 | #4027 | semidirect |
| 296. C5 | #63904 | semidirect |
| 310. C3 | #91406 | semidirect |
| 311. C3 | #91552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67152 | 2 |
| C2×#67149 | 2 |
| C2×C3×D3×Dic5 | 2 |
| #10623828 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| #10623772 | 2 |
| C3×#6669 | 2 |
| #91552 | 3 |
| #91406 | 3 |
| #63904 | 5 |