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×#67158 | C2 | semidirect |
| 2. C2×D3×Dic15 | C2 | semidirect |
| 3. C2×C5×#625 | C2 | semidirect |
| 4. C2×D5×C3⋊Dic3 | C2 | semidirect |
| 5. C2×C3×#1201 | C2 | semidirect |
| 6. #10624046 | C2 | direct (N × H) |
| 13. #67158 | C22 | semidirect |
| 14. D3×Dic15 | C22 | semidirect |
| 15. C5×#625 | C22 | semidirect |
| 16. D5×C3⋊Dic3 | C22 | semidirect |
| 17. C3×#1201 | C22 | semidirect |
| 23. C2×#1201 | D3 | semidirect |
| 40. C2×#625 | D5 | semidirect |
| 57. #1201 | C2×D3 | semidirect |
| 62. C2×C32×C5 | #41 | semidirect |
| 80. #625 | C2×D5 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 130. C2×C3×C5 | #237 | semidirect |
| 162. C2×C32 | #711 | semidirect |
| 172. C3×C5 | C2×#237 | semidirect |
| 190. C2×C5 | #3805 | semidirect |
| 193. C32 | C2×#711 | semidirect |
| 209. C2×C3 | #6780 | semidirect |
| 212. C5 | C2×#3805 | semidirect |
| 222. C3 | C2×#6780 | semidirect |
| 225. C2 | #10624046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67158 | 2 |
| C2×D3×Dic15 | 2 |
| C2×C5×#625 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C2×C3×#1201 | 2 |
| #10624046 | 2 |
| C2×#6780 | 3 |
| C2×#3805 | 5 |