Finite Group Databasebeta

← C22×C32×C4×C52 #72183271

Subgroups — C22×C32×C4×C52 #72183271

Order 3600.

1296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C52C211yesmaximal, characteristic
2C2×C32×C4×C52C216yesmaximal, direct product factor
3C22×C3×C4×C52C314yesmaximal, direct product factor
4C22×C32×C52C414yesdirect product factor
5C22×C32×C52C2213yes—
6C32×C4×C52C2214yesdirect product factor
7C22×C32×C4×C5C516yesmaximal, direct product factor
8C23×C3×C52C2×C314yes—
9C2×C3×C4×C52C2×C3124yesdirect product factor
10C2×C32×C52C2×C416yesdirect product factor
11C2×C32×C52C2311yescharacteristic
12C22×C4×C52C3211yescharacteristic, direct product factor, Hall
13C23×C32×C5C2×C516yes—
14C2×C32×C4×C5C2×C5136yesdirect product factor
15C22×C3×C52C3×C4116yesdirect product factor
16C22×C3×C52C22×C3112yes—
17C3×C4×C52C22×C3116yesdirect product factor
18C22×C3×C4×C5C3×C5124yesdirect product factor
19C32×C52C22×C411yescharacteristic, direct product factor, Hall
20C23×C52C2×C3211yescharacteristic
21C2×C4×C52C2×C3216yesdirect product factor
22C22×C32×C5C4×C5124yesdirect product factor
23C22×C32×C5C22×C5118yes—
24C32×C4×C5C22×C5124yesdirect product factor
25C2×C3×C52C2×C3×C4124yesdirect product factor
26C2×C3×C52C23×C314yes—
27C22×C32×C4C5211yescharacteristic, direct product factor, Hall
28C23×C3×C5C2×C3×C5124yes—
29C2×C3×C4×C5C2×C3×C51144yesdirect product factor
30C22×C52C32×C414yesdirect product factor
31C22×C52C22×C3213yes—
32C4×C52C22×C3214yesdirect product factor
33C2×C32×C5C2×C4×C5136yesdirect product factor
34C2×C32×C5C23×C516yes—
35C22×C4×C5C32×C516yesdirect product factor
36C3×C52C22×C3×C414yesdirect product factor
37C23×C32C2×C5211yescharacteristic
38C2×C32×C4C2×C5216yesdirect product factor
39C22×C3×C5C3×C4×C5196yesdirect product factor
40C22×C3×C5C22×C3×C5172yes—
41C3×C4×C5C22×C3×C5196yesdirect product factor
42C2×C52C2×C32×C416yesdirect product factor
43C2×C52C23×C3211yescharacteristic
44C22×C3×C4C3×C5214yesdirect product factor
45C32×C5C22×C4×C516yesdirect product factor
46C23×C5C2×C32×C516yes—
47C2×C4×C5C2×C32×C5136yesdirect product factor
48C22×C32C4×C5214yesdirect product factor
49C22×C32C22×C5213yes—
50C32×C4C22×C5214yesdirect product factor
51C2×C3×C5C2×C3×C4×C51144yesdirect product factor
52C2×C3×C5C23×C3×C5124yes—
53C52C22×C32×C411yescharacteristic, direct product factor, Sylow
54C23×C3C2×C3×C5214yes—
55C2×C3×C4C2×C3×C52124yesdirect product factor
56C22×C5C32×C4×C5124yesdirect product factor
57C22×C5C22×C32×C5118yes—
58C4×C5C22×C32×C5124yesdirect product factor
59C2×C32C2×C4×C5216yesdirect product factor
60C2×C32C23×C5211yescharacteristic
61C22×C4C32×C5211yescharacteristic, direct product factor, Sylow
62C3×C5C22×C3×C4×C5124yesdirect product factor
63C22×C3C3×C4×C52116yesdirect product factor
64C22×C3C22×C3×C52112yes—
65C3×C4C22×C3×C52116yesdirect product factor
66C2×C5C2×C32×C4×C5136yesdirect product factor
67C2×C5C23×C32×C516yes—
68C32C22×C4×C5211yescharacteristic, direct product factor, Sylow
69C23C2×C32×C5211yescharacteristic
70C2×C4C2×C32×C5216yesdirect product factor
71C2×C3C2×C3×C4×C52124yesdirect product factor
72C2×C3C23×C3×C5214yes—
73C5C22×C32×C4×C516yesdirect product factor
74C22C32×C4×C5214yesdirect product factor
75C22C22×C32×C5213yes—
76C4C22×C32×C5214yesdirect product factor
77C3C22×C3×C4×C5214yesdirect product factor
78C2C2×C32×C4×C5216yesdirect product factor
79C2C23×C32×C5211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C52
socle, prime radicalC23×C32×C52C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×C52C2direct (N × H)
3. C22×C3×C4×C52C3direct (N × H)
4. C22×C32×C52C4direct (N × H)
6. C32×C4×C52C22direct (N × H)
7. C22×C32×C4×C5C5direct (N × H)
9. C2×C3×C4×C52C2×C3direct (N × H)
10. C2×C32×C52C2×C4direct (N × H)
12. C22×C4×C52C32direct (N × H)
14. C2×C32×C4×C5C2×C5direct (N × H)
15. C22×C3×C52C3×C4direct (N × H)
17. C3×C4×C52C22×C3direct (N × H)
18. C22×C3×C4×C5C3×C5direct (N × H)
19. C32×C52C22×C4direct (N × H)
21. C2×C4×C52C2×C32direct (N × H)
22. C22×C32×C5C4×C5direct (N × H)
24. C32×C4×C5C22×C5direct (N × H)
25. C2×C3×C52C2×C3×C4direct (N × H)
27. C22×C32×C4C52direct (N × H)
29. C2×C3×C4×C5C2×C3×C5direct (N × H)
30. C22×C52C32×C4direct (N × H)
32. C4×C52C22×C32direct (N × H)
33. C2×C32×C5C2×C4×C5direct (N × H)
35. C22×C4×C5C32×C5direct (N × H)
36. C3×C52C22×C3×C4direct (N × H)
38. C2×C32×C4C2×C52direct (N × H)
39. C22×C3×C5C3×C4×C5direct (N × H)
41. C3×C4×C5C22×C3×C5direct (N × H)
42. C2×C52C2×C32×C4direct (N × H)
44. C22×C3×C4C3×C52direct (N × H)
45. C32×C5C22×C4×C5direct (N × H)
47. C2×C4×C5C2×C32×C5direct (N × H)
48. C22×C32C4×C52direct (N × H)
50. C32×C4C22×C52direct (N × H)
51. C2×C3×C5C2×C3×C4×C5direct (N × H)
53. C52C22×C32×C4direct (N × H)
55. C2×C3×C4C2×C3×C52direct (N × H)
56. C22×C5C32×C4×C5direct (N × H)
58. C4×C5C22×C32×C5direct (N × H)
59. C2×C32C2×C4×C52direct (N × H)
61. C22×C4C32×C52direct (N × H)
62. C3×C5C22×C3×C4×C5direct (N × H)
63. C22×C3C3×C4×C52direct (N × H)
65. C3×C4C22×C3×C52direct (N × H)
66. C2×C5C2×C32×C4×C5direct (N × H)
68. C32C22×C4×C52direct (N × H)
70. C2×C4C2×C32×C52direct (N × H)
71. C2×C3C2×C3×C4×C52direct (N × H)
73. C5C22×C32×C4×C5direct (N × H)
74. C22C32×C4×C52direct (N × H)
76. C4C22×C32×C52direct (N × H)
77. C3C22×C3×C4×C52direct (N × H)
78. C2C2×C32×C4×C52direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C522
C2×C32×C4×C522
C22×C3×C4×C523
C22×C32×C4×C55