Finite Group Databasebeta

← C33×C4×C5×C47 #72202607

Subgroups — C33×C4×C5×C47 #72202607

Order 25380.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C33×C5×C47C211yesmaximal, characteristic
2C33×C5×C47C411yescharacteristic, direct product factor, Hall
3C33×C4×C47C511yesmaximal, characteristic, direct product factor, Hall
4C2×C33×C47C2×C511yescharacteristic
5C32×C4×C5×C47C3113yesmaximal, direct product factor
6C2×C32×C5×C47C2×C3113yes—
7C3×C4×C5×C47C32113yesdirect product factor
8C32×C5×C47C3×C4113yesdirect product factor
9C32×C4×C47C3×C5113yesdirect product factor
10C2×C3×C5×C47C2×C32113yes—
11C33×C47C4×C511yescharacteristic, direct product factor, Hall
12C4×C5×C47C3311yescharacteristic, direct product factor, Hall
13C2×C32×C47C2×C3×C5113yes—
14C3×C5×C47C32×C4113yesdirect product factor
15C3×C4×C47C32×C5113yesdirect product factor
16C33×C4×C5C4711yesmaximal, characteristic, direct product factor, Hall
17C2×C5×C47C2×C3311yescharacteristic
18C32×C47C3×C4×C5113yesdirect product factor
19C2×C3×C47C2×C32×C5113yes—
20C2×C33×C5C2×C4711yescharacteristic
21C5×C47C33×C411yescharacteristic, direct product factor, Hall
22C4×C47C33×C511yescharacteristic, direct product factor, Hall
23C32×C4×C5C3×C47113yesdirect product factor
24C3×C47C32×C4×C5113yesdirect product factor
25C33×C5C4×C4711yescharacteristic, direct product factor, Hall
26C33×C4C5×C4711yescharacteristic, direct product factor, Hall
27C2×C47C2×C33×C511yescharacteristic
28C2×C32×C5C2×C3×C47113yes—
29C3×C4×C5C32×C47113yesdirect product factor
30C2×C33C2×C5×C4711yescharacteristic
31C47C33×C4×C511yescharacteristic, direct product factor, Sylow
32C32×C5C3×C4×C47113yesdirect product factor
33C32×C4C3×C5×C47113yesdirect product factor
34C2×C3×C5C2×C32×C47113yes—
35C33C4×C5×C4711yescharacteristic, direct product factor, Sylow
36C4×C5C33×C4711yescharacteristic, direct product factor, Hall
37C2×C32C2×C3×C5×C47113yes—
38C3×C5C32×C4×C47113yesdirect product factor
39C3×C4C32×C5×C47113yesdirect product factor
40C2×C5C2×C33×C4711yescharacteristic
41C32C3×C4×C5×C47113yesdirect product factor
42C2×C3C2×C32×C5×C47113yes—
43C5C33×C4×C4711yescharacteristic, direct product factor, Sylow
44C4C33×C5×C4711yescharacteristic, direct product factor, Sylow
45C3C32×C4×C5×C47113yesdirect product factor
46C2C2×C33×C5×C4711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C33×C5×C47
socle, prime radicalC2×C33×C5×C47C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C33×C5×C47C4direct (N × H)
3. C33×C4×C47C5direct (N × H)
5. C32×C4×C5×C47C3direct (N × H)
7. C3×C4×C5×C47C32direct (N × H)
8. C32×C5×C47C3×C4direct (N × H)
9. C32×C4×C47C3×C5direct (N × H)
11. C33×C47C4×C5direct (N × H)
12. C4×C5×C47C33direct (N × H)
14. C3×C5×C47C32×C4direct (N × H)
15. C3×C4×C47C32×C5direct (N × H)
16. C33×C4×C5C47direct (N × H)
18. C32×C47C3×C4×C5direct (N × H)
21. C5×C47C33×C4direct (N × H)
22. C4×C47C33×C5direct (N × H)
23. C32×C4×C5C3×C47direct (N × H)
24. C3×C47C32×C4×C5direct (N × H)
25. C33×C5C4×C47direct (N × H)
26. C33×C4C5×C47direct (N × H)
29. C3×C4×C5C32×C47direct (N × H)
31. C47C33×C4×C5direct (N × H)
32. C32×C5C3×C4×C47direct (N × H)
33. C32×C4C3×C5×C47direct (N × H)
35. C33C4×C5×C47direct (N × H)
36. C4×C5C33×C47direct (N × H)
38. C3×C5C32×C4×C47direct (N × H)
39. C3×C4C32×C5×C47direct (N × H)
41. C32C3×C4×C5×C47direct (N × H)
43. C5C33×C4×C47direct (N × H)
44. C4C33×C5×C47direct (N × H)
45. C3C32×C4×C5×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×C5×C472
C33×C4×C475
C32×C4×C5×C473
C33×C4×C547