Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
668 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #535 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6817 | C2 | semidirect |
| 2. C22×C3×D20 | C2 | semidirect |
| 3. C5×#926 | C2 | semidirect |
| 4. #91564 | C2 | semidirect |
| 5. #91465 | C2 | semidirect |
| 6. #91458 | C2 | semidirect |
| 7. #91364 | C2 | semidirect |
| 13. C2×D60 | C22 | semidirect |
| 14. C2×C4×D15 | C22 | semidirect |
| 15. C2×Dic30 | C22 | semidirect |
| 19. C2×#1202 | C22 | semidirect |
| 21. C5×C4⋊Dic3 | C22 | semidirect |
| 22. C4×C5×Dic3 | C22 | semidirect |
| 23. #6665 | C22 | semidirect |
| 26. C22×D20 | D3 | semidirect |
| 37. C2×C3×C4×C5 | D4 | semidirect |
| 55. #926 | D5 | semidirect |
| 97. C4⋊Dic3 | C2×D5 | semidirect |
| 98. C4×Dic3 | C2×D5 | semidirect |
| 105. C2×C4×C5 | #67 | semidirect |
| 135. C2×C3×C4 | D20 | semidirect |
| 172. C3×C5 | #535 | semidirect |
| 204. C2×C4 | #1202 | semidirect |
| 212. C5 | #5805 | semidirect |
| 225. C3 | #65859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C22×C3×D20 | 2 |
| C5×#926 | 2 |
| #91564 | 2 |
| #91465 | 2 |
| #91458 | 2 |
| #91364 | 2 |
| #65859 | 3 |
| #5805 | 5 |