Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
696 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C5×Q8 | C22 |
| hypercenter | Q8 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3832 | C2 | semidirect |
| 2. C3×#6821 | C2 | semidirect |
| 3. C3×Q8×D15 | C2 | semidirect |
| 4. #10624226 | C2 | semidirect |
| 5. C4×(C3⋊D3)⋊D5 | C2 | semidirect |
| 6. #10624224 | C2 | semidirect |
| 7. #10624220 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C4×C5×C3⋊D3 | C22 | semidirect |
| 14. C3×D60 | C22 | semidirect |
| 16. C3×C4×D15 | C22 | semidirect |
| 17. C3×Dic30 | C22 | semidirect |
| 18. #67156 | C22 | semidirect |
| 19. #67155 | C22 | semidirect |
| 21. #67154 | C22 | semidirect |
| 23. #6821 | D3 | semidirect |
| 24. Q8×D15 | D3 | semidirect |
| 47. #3832 | D5 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 58. C3×C5×Q8 | C2×D3 | semidirect |
| 59. D60 | C2×D3 | semidirect |
| 61. C4×D15 | C2×D3 | semidirect |
| 62. Dic30 | C2×D3 | semidirect |
| 86. C3×D15 | #41 | semidirect |
| 95. C32×Q8 | C2×D5 | semidirect |
| 96. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 97. C4×C3⋊D3 | C2×D5 | semidirect |
| 140. C32×C5 | C2×#41 | semidirect |
| 142. C5×Q8 | D32 | semidirect |
| 166. D15 | #239 | semidirect |
| 176. C3×Q8 | D3×D5 | semidirect |
| 177. C3×Q8 | D3×D5 | semidirect |
| 219. C3×C5 | C2×#239 | semidirect |
| 220. C3×C5 | D3×#41 | semidirect |
| 244. C32 | D5×#41 | semidirect |
| 247. Q8 | (C3⋊D3)⋊D5 | semidirect |
| 267. C5 | D3×#239 | semidirect |
| 277. C3 | D5×#239 | semidirect |
| 278. C3 | #92034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| C3×#6821 | 2 |
| C3×Q8×D15 | 2 |
| #10624226 | 2 |
| C4×(C3⋊D3)⋊D5 | 2 |
| #10624224 | 2 |
| #10624220 | 2 |
| #92034 | 3 |
| D5×#239 | 3 |
| D3×#239 | 5 |