Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C2×C3×C5×Q8 | C22 |
| hypercenter | C2×Q8 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6821 | C2 | semidirect |
| 2. C2×#6766 | C2 | semidirect |
| 3. C5×#944 | C2 | semidirect |
| 4. C3×#4093 | C2 | semidirect |
| 5. #91459 | C2 | semidirect |
| 6. #91458 | C2 | semidirect |
| 7. C4×#1200 | C2 | semidirect |
| 8. #91396 | C2 | semidirect |
| 9. #91375 | C2 | semidirect |
| 35. #4093 | D3 | semidirect |
| 50. C4×D15 | D4 | semidirect |
| 63. #944 | D5 | semidirect |
| 101. C5×Dic3 | #41 | semidirect |
| 207. C3×C5 | #532 | semidirect |
| 220. Dic3 | #713 | semidirect |
| 251. C5 | #5668 | semidirect |
| 265. C3 | #66059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C2×#6766 | 2 |
| C5×#944 | 2 |
| C3×#4093 | 2 |
| #91459 | 2 |
| #91458 | 2 |
| C4×#1200 | 2 |
| #91396 | 2 |
| #91375 | 2 |
| #66059 | 3 |
| #5668 | 5 |