Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×D4 | C22 |
| hypercenter | D4 | D3×D5 |
| hypocenter | C3×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×D15 | C2 | semidirect |
| 2. C5×#237 | C2 | semidirect |
| 3. C3×D4×D5 | C2 | semidirect |
| 4. #6790 | C2 | semidirect |
| 5. D5×#67 | C2 | semidirect |
| 6. C2×#1202 | C2 | semidirect |
| 7. #6779 | C2 | semidirect |
| 8. D3×D20 | C2 | semidirect |
| 9. #6773 | C2 | semidirect |
| 10. #6771 | C2 | semidirect |
| 11. #6766 | C2 | semidirect |
| 13. C22×D15 | C22 | semidirect |
| 14. C22×C3×D5 | C22 | semidirect |
| 15. C2×D3×D5 | C22 | semidirect |
| 16. C3×C5×D4 | C22 | semidirect |
| 17. #1220 | C22 | semidirect |
| 18. D60 | C22 | semidirect |
| 19. C4×D15 | C22 | semidirect |
| 20. C5×#67 | C22 | semidirect |
| 21. C2×C5×Dic3 | C22 | semidirect |
| 22. C4×C5×D3 | C22 | semidirect |
| 23. C5×Dic6 | C22 | semidirect |
| 24. C3×C22⋊D5 | C22 | semidirect |
| 25. C3×D20 | C22 | semidirect |
| 26. C3×C4×D5 | C22 | semidirect |
| 27. #1204 | C22 | semidirect |
| 28. #1203 | C22 | semidirect |
| 29. #1202 | C22 | semidirect |
| 30. #1202 | C22 | semidirect |
| 31. #1202 | C22 | semidirect |
| 32. #1202 | C22 | semidirect |
| 33. #1201 | C22 | semidirect |
| 34. #1200 | C22 | semidirect |
| 35. D5×Dic3 | C22 | semidirect |
| 43. D4×D5 | D3 | semidirect |
| 67. #237 | D5 | semidirect |
| 75. C22×D5 | C2×D3 | semidirect |
| 78. C5×D4 | C2×D3 | semidirect |
| 84. C22⋊D5 | C2×D3 | semidirect |
| 90. D20 | C2×D3 | semidirect |
| 94. C4×D5 | C2×D3 | semidirect |
| 109. C3×D4 | C2×D5 | semidirect |
| 117. #67 | C2×D5 | semidirect |
| 119. C2×Dic3 | C2×D5 | semidirect |
| 124. C4×D3 | C2×D5 | semidirect |
| 126. Dic6 | C2×D5 | semidirect |
| 152. C3×C5 | H(5,𝔽2) | semidirect |
| 190. D4 | D3×D5 | semidirect |
| 204. C5 | #1004 | semidirect |
| 219. C3 | #4149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D15 | 2 |
| C5×#237 | 2 |
| C3×D4×D5 | 2 |
| #6790 | 2 |
| D5×#67 | 2 |
| C2×#1202 | 2 |
| #6779 | 2 |
| D3×D20 | 2 |
| #6773 | 2 |
| #6771 | 2 |
| #6766 | 2 |
| #4149 | 3 |
| #1004 | 5 |