Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C32×C5 | C22×C4 |
| prime radical, cosocle | C2×C32×D5 | C23 |
| hypocenter | C32×C5 | C4×Q8 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #67158 | C4 | semidirect |
| 11. #67153 | C4 | semidirect |
| 12. C5×#627 | C4 | semidirect |
| 25. C3⋊ΓL(1,𝔽16) | Q8 | semidirect |
| 68. #627 | AGL(1,𝔽5) | semidirect |
| 93. C32×C5 | C4×Q8 | semidirect |
| 148. C3×C5 | #887 | semidirect |
| 168. C32 | Q8×AGL(1,𝔽5) | semidirect |
| 183. C5 | #63838 | semidirect |
| 193. C3 | ΓL(1,𝔽16)⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#627 | 2 |
| #10623979 | 2 |
| Dic3×ΓL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×C3⋊Dic3 | 2 |
| C3×Dic3⋊AGL(1,𝔽5) | 2 |
| ΓL(1,𝔽16)⋊Q8 | 3 |
| #63838 | 5 |