Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C22×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C23×C5 |
| Frattini | C2 | C22×C5×S4 |
| Fitting | C5×H(5,𝔽2) | D3 |
| hypercenter | C5×Q8 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#994 | C2 | semidirect |
| 2. C5×#985 | C2 | semidirect |
| 3. C5×#984 | C2 | semidirect |
| 7. C5×GL(2,𝔽3) | C22 | semidirect |
| 8. C5×#226 | C22 | semidirect |
| 9. #5924 | C5 | direct (N × H) |
| 11. C5×H(5,𝔽2) | D3 | semidirect |
| 21. #994 | C2×C5 | semidirect |
| 22. #985 | C2×C5 | semidirect |
| 23. #984 | C2×C5 | semidirect |
| 44. GL(2,𝔽3) | C22×C5 | semidirect |
| 45. #226 | C22×C5 | semidirect |
| 61. H(5,𝔽2) | C5×D3 | semidirect |
| 116. C5 | #5924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#994 | 2 |
| C5×#985 | 2 |
| C5×#984 | 2 |
| C5×#577 | 3 |
| C5×D3×Q8 | 4 |
| #5924 | 5 |