Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
996 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 200 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×D5×C3⋊D3 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | D5×C3⋊D3 |
| hypocenter | C32×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C5×#3828 | C2 | semidirect |
| 3. C32×#709 | C2 | semidirect |
| 4. #10624173 | C2 | semidirect |
| 5. C3⋊D3×D20 | C2 | semidirect |
| 6. D5×C4⋊(C3⋊D3) | C2 | semidirect |
| 7. #10624156 | C2 | semidirect |
| 8. #10624152 | C2 | semidirect |
| 10. C22×C3⋊D15 | C22 | semidirect |
| 11. C2×D5×C3⋊D3 | C22 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 13. C4⋊(C3⋊D15) | C22 | semidirect |
| 14. C4⋊(C3⋊D15) | C22 | semidirect |
| 15. C5×#638 | C22 | semidirect |
| 16. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 17. C4×C5×C3⋊D3 | C22 | semidirect |
| 18. C5×#634 | C22 | semidirect |
| 19. C32×C22⋊D5 | C22 | semidirect |
| 20. C32×D20 | C22 | semidirect |
| 21. C32×C4×D5 | C22 | semidirect |
| 22. C32×Dic10 | C22 | semidirect |
| 23. #67140 | C22 | semidirect |
| 24. #67139 | C22 | semidirect |
| 25. #67137 | C22 | semidirect |
| 29. C3×#709 | D3 | semidirect |
| 51. #3828 | D5 | semidirect |
| 56. C2×C3×C4×C5 | C2×D3 | semidirect |
| 63. C3×C22⋊D5 | C2×D3 | semidirect |
| 64. C3×D20 | C2×D3 | semidirect |
| 65. C3×C4×D5 | C2×D3 | semidirect |
| 66. C3×Dic10 | C2×D3 | semidirect |
| 81. #709 | C3⋊D3 | semidirect |
| 90. C2×C32×C4 | C2×D5 | semidirect |
| 92. #638 | C2×D5 | semidirect |
| 96. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 98. C4×C3⋊D3 | C2×D5 | semidirect |
| 99. #634 | C2×D5 | semidirect |
| 118. C32×C5 | H(5,𝔽2) | semidirect |
| 125. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 127. C22⋊D5 | C2×C3⋊D3 | semidirect |
| 131. D20 | C2×C3⋊D3 | semidirect |
| 133. C4×D5 | C2×C3⋊D3 | semidirect |
| 134. Dic10 | C2×C3⋊D3 | semidirect |
| 157. C2×C3×C4 | D3×D5 | semidirect |
| 190. C3×C5 | #1009 | semidirect |
| 206. C32 | #4149 | semidirect |
| 222. C2×C4 | D5×C3⋊D3 | semidirect |
| 228. C5 | #64366 | semidirect |
| 239. C3 | #92019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C5×#3828 | 2 |
| C32×#709 | 2 |
| #10624173 | 2 |
| C3⋊D3×D20 | 2 |
| D5×C4⋊(C3⋊D3) | 2 |
| #10624156 | 2 |
| #10624152 | 2 |
| #92019 | 3 |
| #64366 | 5 |