Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
3176 conjugacy classes of subgroups; only the 867 normal subgroups are shown.
This group has 3176 conjugacy classes of subgroups — too many to draw. Only its 867 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×C5⋊D5 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C24×C5⋊D5 |
| Fitting | C22×C52×Q8 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C22×Q8 | C5⋊D5 |
| hypocenter | C52 | C2×2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×Q8 | C2 | semidirect |
| 2. #11717520 | C2 | direct (N × H) |
| 3. C2×#87904 | C2 | semidirect |
| 4. C2×Q8×C5⋊D5 | C2 | semidirect |
| 5. C2×#87900 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 10. #87904 | C22 | semidirect |
| 11. Q8×C5⋊D5 | C22 | semidirect |
| 12. #87900 | C22 | semidirect |
| 27. C22×C5×Q8 | D5 | semidirect |
| 40. C2×C5×Q8 | C2×D5 | semidirect |
| 51. C2×C52 | 2−1+4 | semidirect |
| 68. C22×Q8 | C5⋊D5 | semidirect |
| 69. C52 | C2×2−1+4 | semidirect |
| 82. C2×Q8 | C2×C5⋊D5 | semidirect |
| 88. C2×C5 | #4147 | semidirect |
| 101. C5 | C2×#4147 | semidirect |
| 111. C2 | #11717520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| #11717520 | 2 |
| C2×#87904 | 2 |
| C2×Q8×C5⋊D5 | 2 |
| C2×#87900 | 2 |
| C2×#4147 | 5 |