Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 164 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 | #550 |
| 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×C3×#713 | C2 | semidirect |
| 3. C5×Q8×Dic3 | C2 | semidirect |
| 4. #91465 | C2 | semidirect |
| 5. #91458 | C2 | semidirect |
| 6. #91450 | C2 | semidirect |
| 7. C4×#1202 | C2 | semidirect |
| 25. C2×#713 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 47. Q8×Dic3 | D5 | semidirect |
| 78. C5×Dic3 | #41 | semidirect |
| 95. C5×Q8 | #67 | semidirect |
| 121. C3×Q8 | D20 | semidirect |
| 159. C3×C5 | #550 | semidirect |
| 171. Dic3 | #713 | semidirect |
| 179. Q8 | #1202 | semidirect |
| 196. C5 | #5834 | semidirect |
| 209. C3 | #65911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C2×C3×#713 | 2 |
| C5×Q8×Dic3 | 2 |
| #91465 | 2 |
| #91458 | 2 |
| #91450 | 2 |
| C4×#1202 | 2 |
| #65911 | 3 |
| #5834 | 5 |