Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
694 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C5×Q8 | C22 |
| hypercenter | Q8 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×Q8×C3⋊D3 | C2 | semidirect |
| 2. C3×#6821 | C2 | semidirect |
| 3. #10624227 | C2 | semidirect |
| 4. C4×(C3⋊D3)⋊D5 | C2 | semidirect |
| 5. #10624221 | C2 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 10. C5×#634 | C22 | semidirect |
| 11. C3×D60 | C22 | semidirect |
| 12. C3×C4×D15 | C22 | semidirect |
| 13. #67157 | C22 | semidirect |
| 15. #67154 | C22 | semidirect |
| 17. #6821 | D3 | semidirect |
| 32. Q8×C3⋊D3 | D5 | semidirect |
| 39. C3×C5×Q8 | C2×D3 | semidirect |
| 40. D60 | C2×D3 | semidirect |
| 41. C4×D15 | C2×D3 | semidirect |
| 54. C5×C3⋊D3 | #41 | semidirect |
| 62. C32×Q8 | C2×D5 | semidirect |
| 64. #634 | C2×D5 | semidirect |
| 89. C32×C5 | C2×#41 | semidirect |
| 92. C5×Q8 | D32 | semidirect |
| 114. C3×Q8 | D3×D5 | semidirect |
| 134. C3⋊D3 | #713 | semidirect |
| 142. C3×C5 | D3×#41 | semidirect |
| 157. C32 | C2×#713 | semidirect |
| 160. Q8 | (C3⋊D3)⋊D5 | semidirect |
| 173. C5 | #64319 | semidirect |
| 181. C3 | D3×#713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C3×#6821 | 2 |
| #10624227 | 2 |
| C4×(C3⋊D3)⋊D5 | 2 |
| #10624221 | 2 |
| D3×#713 | 3 |
| #64319 | 5 |