Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1254 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 382 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 | #99 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C2×Q8 | C24×C5 |
| prime radical | C24×C5 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C24×C5 ◁ C23×C5×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C5×#356 | C2 | direct (N × H) |
| 14. C5×#356 | C22 | direct (N × H) |
| 15. C22×#356 | C5 | direct (N × H) |
| 44. C2×#356 | C2×C5 | direct (N × H) |
| 92. #356 | C22×C5 | direct (N × H) |
| 149. C22×C5 | #356 | direct (N × H) |
| 198. C2×C5 | C2×#356 | direct (N × H) |
| 228. C5 | C22×#356 | direct (N × H) |
| 231. C22 | C5×#356 | direct (N × H) |
| 243. C2 | C2×C5×#356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊Q8 | 2 |
| C22×C5×#101 | 2 |
| C2×C5×#356 | 2 |
| C22×#356 | 5 |