Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3×C4×D15 | C2 | semidirect |
| 3. C2×#67151 | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. #10623813 | C2 | semidirect |
| 21. C2×C4×D15 | D3 | semidirect |
| 26. C5×C4⋊Dic3 | D3 | semidirect |
| 34. C2×C3×D15 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 42. C3×C4⋊Dic3 | D5 | semidirect |
| 97. C2×D15 | D12 | semidirect |
| 103. C3×C4×C5 | D12 | semidirect |
| 104. C3×C4×C5 | #67 | semidirect |
| 118. C4⋊Dic3 | D15 | semidirect |
| 119. C32×C5 | #121 | semidirect |
| 135. C32×C4 | D20 | semidirect |
| 180. C4×C5 | #626 | semidirect |
| 193. C3×C5 | #895 | semidirect |
| 194. C3×C5 | #930 | semidirect |
| 216. C3×C4 | #1202 | semidirect |
| 217. C3×C4 | D60 | semidirect |
| 225. C32 | #4041 | semidirect |
| 248. C5 | #63909 | semidirect |
| 258. C4 | #67151 | semidirect |
| 260. C3 | #91450 | semidirect |
| 261. C3 | #91784 | 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×C3×C4×D15 | 2 |
| C2×#67151 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623813 | 2 |
| #91784 | 3 |
| #91450 | 3 |
| #63909 | 5 |