Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 430 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×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C2×C3×C4×C5×D3 | C2 | semidirect |
| 3. C2×#67152 | C2 | semidirect |
| 4. C3×C4⋊Dic15 | C2 | semidirect |
| 5. #10623813 | C2 | semidirect |
| 22. C2×C4×C5×D3 | D3 | semidirect |
| 25. C4⋊Dic15 | D3 | semidirect |
| 34. C2×C3×C5×D3 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 40. C2×C3×C4×D3 | D5 | semidirect |
| 100. C2×C5×D3 | D12 | semidirect |
| 103. C3×C4×C5 | D12 | semidirect |
| 104. C3×C4×C5 | #67 | semidirect |
| 114. C2×C4×D3 | D15 | semidirect |
| 119. C32×C5 | #121 | semidirect |
| 134. C2×C3×D3 | D20 | semidirect |
| 135. C32×C4 | C22⋊D5 | semidirect |
| 180. C4×C5 | #626 | semidirect |
| 193. C3×C5 | #895 | semidirect |
| 194. C3×C5 | #930 | semidirect |
| 212. C2×D3 | D60 | semidirect |
| 216. C3×C4 | #1203 | semidirect |
| 217. C3×C4 | #1220 | semidirect |
| 225. C32 | #4076 | semidirect |
| 248. C5 | #63909 | semidirect |
| 258. C4 | #67152 | semidirect |
| 260. C3 | #91460 | semidirect |
| 261. C3 | #91819 | 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×C5×D3 | 2 |
| C2×#67152 | 2 |
| C3×C4⋊Dic15 | 2 |
| #10623813 | 2 |
| #91819 | 3 |
| #91460 | 3 |
| #63909 | 5 |