Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 138 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 | #1790 |
| commutator | C2×D4 | C22×C4×C5 |
| Frattini, cosocle | C2×#41 | C23×C5 |
| prime radical | C5×#3549 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2132 | C2 | semidirect |
| 3. C5×#2122 | C2 | semidirect |
| 4. C5×#1914 | C2 | semidirect |
| 5. C5×#1884 | C2 | semidirect |
| 6. C5×#568 | C22 | semidirect |
| 8. C5×H(3,𝔽4) | C4 | semidirect |
| 12. C5×D42 | C4 | semidirect |
| 19. C5×#413 | C22 | semidirect |
| 21. C5×#410 | C22 | semidirect |
| 27. #12769 | C5 | direct (N × H) |
| 78. #2132 | C2×C5 | semidirect |
| 79. #2122 | C2×C5 | semidirect |
| 80. #1914 | C2×C5 | semidirect |
| 81. #1884 | C2×C5 | semidirect |
| 142. #568 | C22×C5 | semidirect |
| 144. H(3,𝔽4) | C4×C5 | semidirect |
| 148. D42 | C4×C5 | semidirect |
| 155. #413 | C22×C5 | semidirect |
| 157. #410 | C22×C5 | semidirect |
| 385. C5 | #12769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3549 | 2 |
| C5×#2132 | 2 |
| C5×#2122 | 2 |
| C5×#1914 | 2 |
| C5×#1884 | 2 |
| #12769 | 5 |