Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 80 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×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C2×#67152 | C2 | semidirect |
| 3. C2×#67152 | C2 | semidirect |
| 4. C2×#67149 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 7. #10623813 | C2 | semidirect |
| 33. #6712 | D3 | semidirect |
| 34. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 43. C2×C3⋊D15 | D4 | semidirect |
| 49. C3×Dic15 | D4 | semidirect |
| 56. C3×(C2×D3)⋊C4 | D5 | semidirect |
| 143. Dic15 | D12 | semidirect |
| 160. (C2×D3)⋊C4 | D15 | semidirect |
| 162. C32×C5 | #121 | semidirect |
| 260. C3×C5 | #884 | semidirect |
| 261. C3×C5 | #895 | semidirect |
| 304. C32 | #4030 | semidirect |
| 333. C5 | #63910 | semidirect |
| 349. C3 | #91420 | semidirect |
| 350. C3 | #91773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C2×#67152 | 2 |
| C2×#67149 | 2 |
| C3×#6712 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| #10623813 | 2 |
| #91773 | 3 |
| #91420 | 3 |
| #63910 | 5 |