Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C22×D3×D5 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6817 | C2 | semidirect |
| 2. C2×C3×#709 | C2 | semidirect |
| 3. C2×C4×C5×Dic3 | C2 | semidirect |
| 4. #91569 | C2 | semidirect |
| 5. #91458 | C2 | semidirect |
| 6. C4×#1202 | C2 | semidirect |
| 7. #91389 | C2 | semidirect |
| 8. #91374 | C2 | semidirect |
| 9. #91364 | C2 | semidirect |
| 32. C2×#709 | D3 | semidirect |
| 43. C2×C3×C4×C5 | D4 | semidirect |
| 68. C2×C4×Dic3 | D5 | semidirect |
| 101. C5×Dic3 | #41 | semidirect |
| 127. C2×C4×C5 | #67 | semidirect |
| 163. C2×C3×C4 | D20 | semidirect |
| 207. C3×C5 | #532 | semidirect |
| 220. Dic3 | #709 | semidirect |
| 243. C2×C4 | #1202 | semidirect |
| 251. C5 | #5832 | semidirect |
| 265. C3 | #65811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×C3×#709 | 2 |
| C2×C4×C5×Dic3 | 2 |
| #91569 | 2 |
| #91458 | 2 |
| C4×#1202 | 2 |
| #91389 | 2 |
| #91374 | 2 |
| #91364 | 2 |
| #65811 | 3 |
| #5832 | 5 |