Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C2×D32×D5 |
| Fitting, socle | C22×C32×C5 | C23 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67157 | C2 | semidirect |
| 2. C2×Dic3×D15 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 4. C2×D5×C3⋊Dic3 | C2 | semidirect |
| 5. C2×C3×#1202 | C2 | semidirect |
| 6. #10624047 | C2 | direct (N × H) |
| 13. #67157 | C22 | semidirect |
| 14. Dic3×D15 | C22 | semidirect |
| 15. C5×#627 | C22 | semidirect |
| 16. D5×C3⋊Dic3 | C22 | semidirect |
| 17. C3×#1202 | C22 | semidirect |
| 23. C2×#1202 | D3 | semidirect |
| 39. C2×#627 | D5 | semidirect |
| 57. #1202 | C2×D3 | semidirect |
| 62. C2×C32×C5 | #41 | semidirect |
| 79. #627 | C2×D5 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 129. C2×C3×C5 | #237 | semidirect |
| 162. C2×C32 | #713 | semidirect |
| 172. C3×C5 | C2×#237 | semidirect |
| 189. C2×C5 | #3805 | semidirect |
| 193. C32 | C2×#713 | semidirect |
| 209. C2×C3 | #6766 | semidirect |
| 212. C5 | C2×#3805 | semidirect |
| 222. C3 | C2×#6766 | semidirect |
| 225. C2 | #10624047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67157 | 2 |
| C2×Dic3×D15 | 2 |
| C2×C5×#627 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C2×C3×#1202 | 2 |
| #10624047 | 2 |
| C2×#6766 | 3 |
| C2×#3805 | 5 |