Finite Group Databasebeta

← C22×C32×C5×C25 #72183992

Subgroups — C22×C32×C5×C25 #72183992

Order 4500.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C25C213yesmaximal, direct product factor
2C22×C3×C5×C25C314yesmaximal, direct product factor
3C32×C5×C25C2211yescharacteristic, direct product factor, Hall
4C22×C32×C52C511yesmaximal, characteristic
5C22×C32×C25C515yesmaximal, direct product factor
6C2×C3×C5×C25C2×C3112yesdirect product factor
7C22×C5×C25C3211yescharacteristic, direct product factor, Hall
8C2×C32×C52C2×C513yes—
9C2×C32×C25C2×C5115yesdirect product factor
10C3×C5×C25C22×C314yesdirect product factor
11C22×C3×C52C3×C514yes—
12C22×C3×C25C3×C5120yesdirect product factor
13C2×C5×C25C2×C3213yesdirect product factor
14C32×C52C22×C511yescharacteristic
15C32×C25C22×C515yesdirect product factor
16C22×C32×C5C2515yesdirect product factor
17C22×C32×C5C5211yescharacteristic
18C2×C3×C52C2×C3×C5112yes—
19C2×C3×C25C2×C3×C5160yesdirect product factor
20C5×C25C22×C3211yescharacteristic, direct product factor, Sylow
21C22×C52C32×C511yescharacteristic
22C22×C25C32×C515yesdirect product factor
23C2×C32×C5C2×C25115yesdirect product factor
24C2×C32×C5C2×C5213yes—
25C3×C52C22×C3×C514yes—
26C3×C25C22×C3×C5120yesdirect product factor
27C22×C3×C5C3×C25120yesdirect product factor
28C22×C3×C5C3×C5214yes—
29C2×C52C2×C32×C513yes—
30C2×C25C2×C32×C5115yesdirect product factor
31C32×C5C22×C2515yesdirect product factor
32C32×C5C22×C5211yescharacteristic
33C22×C32C5×C2511yescharacteristic, direct product factor, Hall
34C2×C3×C5C2×C3×C25160yesdirect product factor
35C2×C3×C5C2×C3×C52112yes—
36C52C22×C32×C511yescharacteristic
37C25C22×C32×C515yesdirect product factor
38C22×C5C32×C2515yesdirect product factor
39C22×C5C32×C5211yescharacteristic
40C2×C32C2×C5×C2513yesdirect product factor
41C3×C5C22×C3×C25120yesdirect product factor
42C3×C5C22×C3×C5214yes—
43C22×C3C3×C5×C2514yesdirect product factor
44C2×C5C2×C32×C25115yesdirect product factor
45C2×C5C2×C32×C5213yes—
46C32C22×C5×C2511yescharacteristic, direct product factor, Sylow
47C2×C3C2×C3×C5×C25112yesdirect product factor
48C5C22×C32×C2515yesdirect product factor
49C5C22×C32×C5211yescharacteristic
50C22C32×C5×C2511yescharacteristic, direct product factor, Sylow
51C3C22×C3×C5×C2514yesdirect product factor
52C2C2×C32×C5×C2513yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C22×C32×C52
socle, prime radicalC22×C32×C52C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×C25C2direct (N × H)
2. C22×C3×C5×C25C3direct (N × H)
3. C32×C5×C25C22direct (N × H)
5. C22×C32×C25C5direct (N × H)
6. C2×C3×C5×C25C2×C3direct (N × H)
7. C22×C5×C25C32direct (N × H)
9. C2×C32×C25C2×C5direct (N × H)
10. C3×C5×C25C22×C3direct (N × H)
12. C22×C3×C25C3×C5direct (N × H)
13. C2×C5×C25C2×C32direct (N × H)
15. C32×C25C22×C5direct (N × H)
16. C22×C32×C5C25direct (N × H)
19. C2×C3×C25C2×C3×C5direct (N × H)
20. C5×C25C22×C32direct (N × H)
22. C22×C25C32×C5direct (N × H)
23. C2×C32×C5C2×C25direct (N × H)
26. C3×C25C22×C3×C5direct (N × H)
27. C22×C3×C5C3×C25direct (N × H)
30. C2×C25C2×C32×C5direct (N × H)
31. C32×C5C22×C25direct (N × H)
33. C22×C32C5×C25direct (N × H)
34. C2×C3×C5C2×C3×C25direct (N × H)
37. C25C22×C32×C5direct (N × H)
38. C22×C5C32×C25direct (N × H)
40. C2×C32C2×C5×C25direct (N × H)
41. C3×C5C22×C3×C25direct (N × H)
43. C22×C3C3×C5×C25direct (N × H)
44. C2×C5C2×C32×C25direct (N × H)
46. C32C22×C5×C25direct (N × H)
47. C2×C3C2×C3×C5×C25direct (N × H)
48. C5C22×C32×C25direct (N × H)
50. C22C32×C5×C25direct (N × H)
51. C3C22×C3×C5×C25direct (N × H)
52. C2C2×C32×C5×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×C252
C22×C3×C5×C253
C22×C32×C525
C22×C32×C255