Finite Group Databasebeta

← C23×C4×C5×C107 #72195022

Subgroups — C23×C4×C5×C107 #72195022

Order 17120.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C5×C107C211yesmaximal, characteristic
2C22×C4×C5×C107C2114yesmaximal, direct product factor
3C23×C5×C107C418yesdirect product factor
4C23×C5×C107C2217yes—
5C2×C4×C5×C107C22128yesdirect product factor
6C23×C4×C107C511yesmaximal, characteristic, direct product factor, Hall
7C22×C5×C107C2×C4128yesdirect product factor
8C22×C5×C107C2317yes—
9C4×C5×C107C2318yesdirect product factor
10C24×C107C2×C511yescharacteristic
11C22×C4×C107C2×C5114yesdirect product factor
12C2×C5×C107C22×C4114yesdirect product factor
13C2×C5×C107C2411yescharacteristic
14C23×C107C4×C518yesdirect product factor
15C23×C107C22×C517yes—
16C2×C4×C107C22×C5128yesdirect product factor
17C5×C107C23×C411yescharacteristic, direct product factor, Hall
18C22×C107C2×C4×C5128yesdirect product factor
19C22×C107C23×C517yes—
20C4×C107C23×C518yesdirect product factor
21C2×C107C22×C4×C5114yesdirect product factor
22C2×C107C24×C511yescharacteristic
23C23×C4×C5C10711yesmaximal, characteristic, direct product factor, Hall
24C107C23×C4×C511yescharacteristic, direct product factor, Sylow
25C24×C5C2×C10711yescharacteristic
26C22×C4×C5C2×C107114yesdirect product factor
27C23×C5C4×C10718yesdirect product factor
28C23×C5C22×C10717yes—
29C2×C4×C5C22×C107128yesdirect product factor
30C23×C4C5×C10711yescharacteristic, direct product factor, Sylow
31C22×C5C2×C4×C107128yesdirect product factor
32C22×C5C23×C10717yes—
33C4×C5C23×C10718yesdirect product factor
34C24C2×C5×C10711yescharacteristic
35C22×C4C2×C5×C107114yesdirect product factor
36C2×C5C22×C4×C107114yesdirect product factor
37C2×C5C24×C10711yescharacteristic
38C23C4×C5×C10718yesdirect product factor
39C23C22×C5×C10717yes—
40C2×C4C22×C5×C107128yesdirect product factor
41C5C23×C4×C10711yescharacteristic, direct product factor, Sylow
42C22C2×C4×C5×C107128yesdirect product factor
43C22C23×C5×C10717yes—
44C4C23×C5×C10718yesdirect product factor
45C2C22×C4×C5×C107114yesdirect product factor
46C2C24×C5×C10711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C5×C107
socle, prime radicalC24×C5×C107C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C4×C5×C107C2direct (N × H)
3. C23×C5×C107C4direct (N × H)
5. C2×C4×C5×C107C22direct (N × H)
6. C23×C4×C107C5direct (N × H)
7. C22×C5×C107C2×C4direct (N × H)
9. C4×C5×C107C23direct (N × H)
11. C22×C4×C107C2×C5direct (N × H)
12. C2×C5×C107C22×C4direct (N × H)
14. C23×C107C4×C5direct (N × H)
16. C2×C4×C107C22×C5direct (N × H)
17. C5×C107C23×C4direct (N × H)
18. C22×C107C2×C4×C5direct (N × H)
20. C4×C107C23×C5direct (N × H)
21. C2×C107C22×C4×C5direct (N × H)
23. C23×C4×C5C107direct (N × H)
24. C107C23×C4×C5direct (N × H)
26. C22×C4×C5C2×C107direct (N × H)
27. C23×C5C4×C107direct (N × H)
29. C2×C4×C5C22×C107direct (N × H)
30. C23×C4C5×C107direct (N × H)
31. C22×C5C2×C4×C107direct (N × H)
33. C4×C5C23×C107direct (N × H)
35. C22×C4C2×C5×C107direct (N × H)
36. C2×C5C22×C4×C107direct (N × H)
38. C23C4×C5×C107direct (N × H)
40. C2×C4C22×C5×C107direct (N × H)
41. C5C23×C4×C107direct (N × H)
42. C22C2×C4×C5×C107direct (N × H)
44. C4C23×C5×C107direct (N × H)
45. C2C22×C4×C5×C107direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×C5×C1072
C22×C4×C5×C1072
C23×C4×C1075
C23×C4×C5107