Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1752 conjugacy classes of subgroups; only the 536 normal subgroups are shown.
This group has 1752 conjugacy classes of subgroups — too many to draw. Only its 536 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C2×C52×Q8 | C22 |
| socle | C22×C52 | C24 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | C2×2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×C5×Q8×D5 | C2 | semidirect |
| 3. #11717481 | C2 | direct (N × H) |
| 4. C2×#87874 | C2 | semidirect |
| 5. C2×#87873 | C2 | semidirect |
| 6. C2×#87872 | C2 | semidirect |
| 8. #87904 | C22 | semidirect |
| 11. C5×Q8×D5 | C22 | semidirect |
| 18. #87874 | C22 | semidirect |
| 19. #87873 | C22 | semidirect |
| 20. #87872 | C22 | semidirect |
| 42. C2×Q8×D5 | D5 | semidirect |
| 64. Q8×D5 | C2×D5 | semidirect |
| 77. C2×C52 | 2−1+4 | semidirect |
| 112. C52 | C2×2−1+4 | semidirect |
| 146. C2×C5 | #4147 | semidirect |
| 166. C5 | C2×#4147 | semidirect |
| 177. C2 | #11717481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×C5×Q8×D5 | 2 |
| #11717481 | 2 |
| C2×#87874 | 2 |
| C2×#87873 | 2 |
| C2×#87872 | 2 |
| C2×#4147 | 5 |