Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 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 | C23×C5 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C5×#2733 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2024 | C2 | semidirect |
| 3. C5×#2023 | C2 | semidirect |
| 4. C5×#2013 | C2 | semidirect |
| 5. C5×#1272 | C2 | semidirect |
| 6. C5×#1270 | C2 | semidirect |
| 7. C5×#1270 | C2 | semidirect |
| 27. #7781 | C5 | direct (N × H) |
| 65. #2024 | C2×C5 | semidirect |
| 66. #2023 | C2×C5 | semidirect |
| 67. #2013 | C2×C5 | semidirect |
| 68. #1272 | C2×C5 | semidirect |
| 69. #1270 | C2×C5 | semidirect |
| 70. #1270 | C2×C5 | semidirect |
| 82. C2×C5×Q8 | SD16 | semidirect |
| 291. C2×Q8 | C5×SD16 | semidirect |
| 411. C5 | #7781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2733 | 2 |
| C5×#2024 | 2 |
| C5×#2023 | 2 |
| C5×#2013 | 2 |
| C5×#1272 | 2 |
| C5×#1270 | 2 |
| #7781 | 5 |