Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D15 |
| hypocenter | C32×C5 | #121 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D60 | C2 | semidirect |
| 2. C2×C3×C4×C5×D3 | C2 | semidirect |
| 3. C2×#67150 | C2 | semidirect |
| 4. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 5. #10623811 | C2 | semidirect |
| 19. C2×D60 | D3 | semidirect |
| 20. C2×C4×C5×D3 | D3 | semidirect |
| 34. C2×C3×C5×D3 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 40. C2×C3×C4×D3 | D5 | semidirect |
| 93. C2×C5×D3 | D12 | semidirect |
| 99. C3×C4×C5 | #67 | semidirect |
| 100. C3×C4×C5 | #67 | semidirect |
| 110. C2×C4×D3 | D15 | semidirect |
| 116. C32×C5 | #121 | semidirect |
| 131. C2×C3×D3 | D20 | semidirect |
| 132. C32×C4 | C22⋊D5 | semidirect |
| 175. C4×C5 | #625 | semidirect |
| 188. C3×C5 | #930 | semidirect |
| 189. C3×C5 | #938 | semidirect |
| 204. C2×D3 | D60 | semidirect |
| 207. C3×C4 | #1201 | semidirect |
| 208. C3×C4 | #1220 | semidirect |
| 218. C32 | #4076 | semidirect |
| 240. C5 | #63908 | semidirect |
| 250. C4 | #67150 | semidirect |
| 252. C3 | #91456 | semidirect |
| 253. C3 | #91819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×C3×C4×C5×D3 | 2 |
| C2×#67150 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| #10623811 | 2 |
| #91819 | 3 |
| #91456 | 3 |
| #63908 | 5 |