Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1888 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 241 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 | C23×D15 |
| commutator, socle, cosocle | C23×C3×C5 | C24 |
| Fitting | C3×C5×#393 | C2 |
| hypercenter | #393 | D15 |
| hypocenter | C3×C5 | #2388 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6821 | C2 | semidirect |
| 2. C2×#91770 | C2 | semidirect |
| 3. C3×C5×#393 | C2 | semidirect |
| 4. #11751331 | C2 | semidirect |
| 5. #11751061 | C2 | semidirect |
| 6. #11750773 | C2 | semidirect |
| 7. #11750767 | C2 | semidirect |
| 26. C5×#393 | D3 | semidirect |
| 47. C2×C4×D15 | D4 | semidirect |
| 55. C3×#393 | D5 | semidirect |
| 77. C23×C3×C5 | #41 | semidirect |
| 95. C2×Dic15 | #41 | semidirect |
| 138. #393 | D15 | semidirect |
| 181. C23×C5 | #239 | semidirect |
| 223. C23×C3 | #713 | semidirect |
| 282. C3×C5 | #2388 | semidirect |
| 311. C23 | #6821 | semidirect |
| 332. C5 | #76777 | semidirect |
| 349. C3 | #10608508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6821 | 2 |
| C2×#91770 | 2 |
| C3×C5×#393 | 2 |
| #11751331 | 2 |
| #11751061 | 2 |
| #11750773 | 2 |
| #11750767 | 2 |
| #10608508 | 3 |
| #76777 | 5 |