Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
480 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C3×C5×#125 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C3×#125 | D5 |
| hypocenter | C5 | C3×#540 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#125 | C2 | semidirect |
| 2. C3×#4041 | C2 | semidirect |
| 3. C3×#4041 | C2 | semidirect |
| 4. C3×#4040 | C2 | semidirect |
| 5. C3×#4039 | C2 | semidirect |
| 6. C3×#4020 | C2 | semidirect |
| 7. C3×#4018 | C2 | semidirect |
| 8. #66032 | C3 | direct (N × H) |
| 23. C5×#125 | C2×C3 | semidirect |
| 24. #4041 | C2×C3 | semidirect |
| 25. #4041 | C2×C3 | semidirect |
| 26. #4040 | C2×C3 | semidirect |
| 27. #4039 | C2×C3 | semidirect |
| 28. #4020 | C2×C3 | semidirect |
| 29. #4018 | C2×C3 | semidirect |
| 43. C3×#125 | D5 | semidirect |
| 100. #125 | C3×D5 | semidirect |
| 146. C3×C5 | #540 | semidirect |
| 178. C5 | C3×#540 | semidirect |
| 190. C3 | #66032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C3×#4041 | 2 |
| C3×#4040 | 2 |
| C3×#4039 | 2 |
| C3×#4020 | 2 |
| C3×#4018 | 2 |
| #66032 | 3 |
| C3×#540 | 5 |