Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
580 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 179 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 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C22×C3×C5×Q8 | C2 |
| hypercenter | C22×Q8 | D15 |
| hypocenter | C3×C5 | #548 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C5×Q8 | C2 | semidirect |
| 2. C2×#6821 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. #91835 | C2 | semidirect |
| 5. Q8×Dic15 | C2 | semidirect |
| 6. #91819 | C2 | semidirect |
| 7. C4×#1220 | C2 | semidirect |
| 24. C22×C5×Q8 | D3 | semidirect |
| 34. C3×C5×Q8 | D4 | semidirect |
| 44. C22×C3×Q8 | D5 | semidirect |
| 68. C22×C3×C5 | #41 | semidirect |
| 95. C5×Q8 | #67 | semidirect |
| 106. C22×Q8 | D15 | semidirect |
| 120. C3×Q8 | C22⋊D5 | semidirect |
| 132. C22×C5 | #239 | semidirect |
| 156. C3×C5 | #548 | semidirect |
| 159. C22×C3 | #713 | semidirect |
| 177. Q8 | #1220 | semidirect |
| 192. C5 | #5817 | semidirect |
| 198. C22 | #6821 | semidirect |
| 205. C3 | #66151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C2×#6821 | 2 |
| #91836 | 2 |
| #91835 | 2 |
| Q8×Dic15 | 2 |
| #91819 | 2 |
| C4×#1220 | 2 |
| #66151 | 3 |
| #5817 | 5 |