Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1888 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 232 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 | C22×D3×D5 |
| commutator, socle, cosocle | C23×C3×C5 | C24 |
| Fitting | C22×C3×C5×Q8 | C22 |
| hypercenter | C22×Q8 | D3×D5 |
| hypocenter | C3×C5 | #2388 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6821 | C2 | semidirect |
| 2. C2×#91396 | C2 | semidirect |
| 3. C5×#5230 | C2 | semidirect |
| 4. C3×#65520 | C2 | semidirect |
| 5. #11748931 | C2 | semidirect |
| 6. #11748790 | C2 | semidirect |
| 7. #11748670 | C2 | semidirect |
| 27. #65520 | D3 | semidirect |
| 40. C2×C4×D15 | D4 | semidirect |
| 56. #5230 | D5 | semidirect |
| 83. C22×C3×D5 | #41 | semidirect |
| 93. C2×C5×Dic3 | #41 | semidirect |
| 187. C22×D5 | #239 | semidirect |
| 241. C2×Dic3 | #713 | semidirect |
| 282. C3×C5 | #2388 | semidirect |
| 332. C5 | #76777 | semidirect |
| 349. C3 | #10608900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6821 | 2 |
| C2×#91396 | 2 |
| C5×#5230 | 2 |
| C3×#65520 | 2 |
| #11748931 | 2 |
| #11748790 | 2 |
| #11748670 | 2 |
| #10608900 | 3 |
| #76777 | 5 |