Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 180 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| prime radical | C22×C5×D5 | C23 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11717264 | C2 | semidirect |
| 4. C5×#4090 | C2 | semidirect |
| 7. #11716985 | C2 | semidirect |
| 8. #11716983 | C2 | semidirect |
| 9. #11716957 | C2 | semidirect |
| 49. D5×Dic5 | Q8 | semidirect |
| 62. #4090 | D5 | direct (N × H) |
| 75. #1039 | C2×Q8 | semidirect |
| 79. C5×Dic5 | C2×Q8 | semidirect |
| 125. C5×D5 | C4⋊Q8 | semidirect |
| 179. C52 | C2×C4⋊Q8 | semidirect |
| 205. Dic5 | Q8×D5 | semidirect |
| 233. D5 | #4090 | direct (N × H) |
| 254. C5 | D5×C4⋊Q8 | semidirect |
| 255. C5 | C2×#4090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×D5×Dic10 | 2 |
| #11717264 | 2 |
| C5×#4090 | 2 |
| D5×#683 | 2 |
| C4×D5×Dic5 | 2 |
| #11716985 | 2 |
| #11716983 | 2 |
| #11716957 | 2 |
| C2×#4090 | 5 |
| D5×C4⋊Q8 | 5 |