Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
952 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 146 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 | #1781 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C22×Q8 | C23×C5 |
| prime radical | C5×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C23×C5 ◁ C23×C5×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2133 | C2 | semidirect |
| 3. C5×#1784 | C2 | semidirect |
| 18. #12710 | C5 | direct (N × H) |
| 54. #2133 | C2×C5 | semidirect |
| 55. #1784 | C2×C5 | semidirect |
| 275. C5 | #12710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3486 | 2 |
| C5×#2133 | 2 |
| C5×#1784 | 2 |
| #12710 | 5 |