Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 91 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×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C23×C32×C5 | C22 |
| hypercenter | C23 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | #121 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×#1220 | C2 | semidirect |
| 3. C2×#67157 | C2 | semidirect |
| 4. #10623832 | C2 | semidirect |
| 5. #10623829 | C2 | semidirect |
| 16. C2×#1220 | D3 | semidirect |
| 26. C22×C32×C5 | D4 | semidirect |
| 32. C5×C3⋊Dic3 | D4 | semidirect |
| 35. C22×C3⋊Dic3 | D5 | semidirect |
| 80. C22×C3×C5 | #67 | semidirect |
| 102. C32×C5 | #121 | semidirect |
| 113. C22×C32 | D20 | semidirect |
| 119. C3⋊Dic3 | C22⋊D5 | semidirect |
| 149. C22×C5 | #625 | semidirect |
| 168. C3×C5 | #939 | semidirect |
| 178. C22×C3 | #1202 | semidirect |
| 194. C32 | #4076 | semidirect |
| 213. C5 | #63980 | semidirect |
| 219. C22 | #67157 | semidirect |
| 225. C3 | #91569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×C3×#1220 | 2 |
| C2×#67157 | 2 |
| #10623832 | 2 |
| #10623829 | 2 |
| #91569 | 3 |
| #63980 | 5 |