Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator | C2×C32×C5 | C22×C4 |
| Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C2×#67138 | C2 |
| hypocenter | C32×C5 | C4×D4 |
| 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×#67155 | C2 | semidirect |
| 3. C2×C3×D5×Dic3 | C2 | semidirect |
| 4. #10623815 | C2 | semidirect |
| 5. Dic3×Dic15 | C2 | semidirect |
| 6. C5×#3722 | C2 | semidirect |
| 7. C3×#6665 | C2 | semidirect |
| 18. #67138 | C4 | semidirect |
| 27. C2×D5×Dic3 | D3 | semidirect |
| 34. #6665 | D3 | semidirect |
| 39. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 42. C2×C32×D5 | C2×C4 | semidirect |
| 43. C3⋊Dic15 | C2×C4 | semidirect |
| 45. C3×Dic15 | D4 | semidirect |
| 54. #3722 | D5 | semidirect |
| 123. C2×C3×D5 | C4×D3 | semidirect |
| 124. C2×C3×D5 | C4×D3 | semidirect |
| 131. Dic15 | #67 | semidirect |
| 151. C32×C5 | C4×D4 | semidirect |
| 168. C2×C3⋊D3 | C4×D5 | semidirect |
| 220. C2×D5 | #624 | semidirect |
| 239. C3×C5 | #67⋊C4 | semidirect |
| 240. C3×C5 | C4×#67 | semidirect |
| 278. C32 | #4027 | semidirect |
| 304. C5 | #63952 | semidirect |
| 318. C3 | #91440 | semidirect |
| 319. C3 | #91442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67155 | 2 |
| C2×#67138 | 2 |
| C2×C3×D5×Dic3 | 2 |
| #10623815 | 2 |
| Dic3×Dic15 | 2 |
| C5×#3722 | 2 |
| C3×#6665 | 2 |
| #91442 | 3 |
| #91440 | 3 |
| #63952 | 5 |