Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
644 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D3×D5 |
| commutator, socle, cosocle | C23×C3×C5 | C23 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #392 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#1203 | C2 | semidirect |
| 2. C22×#1202 | C2 | semidirect |
| 3. C22×#1201 | C2 | semidirect |
| 4. C2×#6714 | C2 | semidirect |
| 5. C2×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×C3×#685 | C2 | semidirect |
| 7. #90994 | C2 | semidirect |
| 34. C2×#685 | D3 | semidirect |
| 43. C22×D15 | D4 | semidirect |
| 50. C22×C5×D3 | D4 | semidirect |
| 57. C22×C3×D5 | D4 | semidirect |
| 63. C2×Dic15 | D4 | semidirect |
| 66. C2×C5×Dic3 | D4 | semidirect |
| 69. C2×C3×Dic5 | D4 | semidirect |
| 78. C2×(C2×D3)⋊C4 | D5 | semidirect |
| 172. C22×D5 | D12 | semidirect |
| 186. C2×Dic5 | #67 | semidirect |
| 226. C22×D3 | D20 | semidirect |
| 240. C2×Dic3 | C22⋊D5 | semidirect |
| 293. C3×C5 | #392 | semidirect |
| 383. C5 | #4960 | semidirect |
| 416. C3 | #65249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1203 | 2 |
| C22×#1202 | 2 |
| C22×#1201 | 2 |
| C2×#6714 | 2 |
| C2×C5×(C2×D3)⋊C4 | 2 |
| C2×C3×#685 | 2 |
| #90994 | 2 |
| #65249 | 3 |
| #4960 | 5 |