Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1160 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×C4⋊Q8 | C2 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | C4⋊Q8 | C5⋊D5 |
| hypocenter | C52 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C52×C4⋊Q8 | C2 | semidirect |
| 3. #11717264 | C2 | semidirect |
| 5. #11717208 | C2 | semidirect |
| 7. #11717189 | C2 | semidirect |
| 32. C4×C5⋊D5 | Q8 | semidirect |
| 36. C5×C4⋊Q8 | D5 | semidirect |
| 47. C4×C52 | C2×Q8 | semidirect |
| 50. #1039 | C2×Q8 | semidirect |
| 67. C5⋊D5 | C4⋊Q8 | direct (N × H) |
| 85. C4⋊Q8 | C5⋊D5 | direct (N × H) |
| 88. C52 | C2×C4⋊Q8 | semidirect |
| 94. C4×C5 | Q8×D5 | semidirect |
| 127. C5 | D5×C4⋊Q8 | semidirect |
| 136. C4 | Q8×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C52×C4⋊Q8 | 2 |
| #11717264 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| #11717208 | 2 |
| C42×C5⋊D5 | 2 |
| #11717189 | 2 |
| D5×C4⋊Q8 | 5 |