Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
624 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 143 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 | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | 2−1+4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3828 | C2 | semidirect |
| 2. C3×#6817 | C2 | semidirect |
| 3. C2×C3×Dic30 | C2 | semidirect |
| 4. #10624230 | C2 | semidirect |
| 5. #10624224 | C2 | semidirect |
| 6. #10624222 | C2 | semidirect |
| 7. #10624220 | C2 | semidirect |
| 8. #10624219 | C2 | semidirect |
| 28. #6817 | D3 | semidirect |
| 29. C2×Dic30 | D3 | semidirect |
| 54. #3828 | D5 | semidirect |
| 167. C32×C5 | 2−1+4 | semidirect |
| 262. C3×C5 | #1007 | semidirect |
| 263. C3×C5 | #1010 | semidirect |
| 289. C32 | #4150 | semidirect |
| 317. C5 | #64297 | semidirect |
| 327. C3 | #92001 | semidirect |
| 328. C3 | #92004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C3×#6817 | 2 |
| C2×C3×Dic30 | 2 |
| #10624230 | 2 |
| #10624224 | 2 |
| #10624222 | 2 |
| #10624220 | 2 |
| #10624219 | 2 |
| #92004 | 3 |
| #92001 | 3 |
| #64297 | 5 |