Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
704 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×Q8 | C23×C5 |
| prime radical | C2×C5×2−1+4 | C22 |
| LCS | G ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2734 | C2 | semidirect |
| 3. C2×C5×#356 | C2 | semidirect |
| 5. C5×#1394 | C2 | semidirect |
| 22. #13359 | C5 | direct (N × H) |
| 63. #2734 | C2×C5 | semidirect |
| 64. C2×#356 | C2×C5 | semidirect |
| 66. #1394 | C2×C5 | semidirect |
| 341. C5 | #13359 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#456 | 2 |
| C5×#2734 | 2 |
| C2×C5×#356 | 2 |
| C5×#1793 | 2 |
| C5×#1394 | 2 |
| #13359 | 5 |