Finite Group Databasebeta

← C23×C4×C52×C31 #72202097

Subgroups — C23×C4×C52×C31 #72202097

Order 24800.

1888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C52×C31C211yesmaximal, characteristic
2C22×C4×C52×C31C2114yesmaximal, direct product factor
3C23×C52×C31C418yesdirect product factor
4C23×C52×C31C2217yes—
5C2×C4×C52×C31C22128yesdirect product factor
6C23×C4×C5×C31C516yesmaximal, direct product factor
7C24×C5×C31C2×C516yes—
8C22×C4×C5×C31C2×C5184yesdirect product factor
9C22×C52×C31C2×C4128yesdirect product factor
10C22×C52×C31C2317yes—
11C4×C52×C31C2318yesdirect product factor
12C2×C52×C31C22×C4114yesdirect product factor
13C2×C52×C31C2411yescharacteristic
14C23×C5×C31C4×C5148yesdirect product factor
15C23×C5×C31C22×C5142yes—
16C2×C4×C5×C31C22×C51168yesdirect product factor
17C23×C4×C31C5211yescharacteristic, direct product factor, Hall
18C23×C4×C52C3111yesmaximal, characteristic, direct product factor, Hall
19C52×C31C23×C411yescharacteristic, direct product factor, Hall
20C22×C5×C31C2×C4×C51168yesdirect product factor
21C22×C5×C31C23×C5142yes—
22C4×C5×C31C23×C5148yesdirect product factor
23C24×C31C2×C5211yescharacteristic
24C22×C4×C31C2×C52114yesdirect product factor
25C24×C52C2×C3111yescharacteristic
26C22×C4×C52C2×C31114yesdirect product factor
27C2×C5×C31C22×C4×C5184yesdirect product factor
28C2×C5×C31C24×C516yes—
29C23×C31C4×C5218yesdirect product factor
30C23×C31C22×C5217yes—
31C2×C4×C31C22×C52128yesdirect product factor
32C23×C52C4×C3118yesdirect product factor
33C23×C52C22×C3117yes—
34C2×C4×C52C22×C31128yesdirect product factor
35C23×C4×C5C5×C3116yesdirect product factor
36C5×C31C23×C4×C516yesdirect product factor
37C22×C31C2×C4×C52128yesdirect product factor
38C22×C31C23×C5217yes—
39C4×C31C23×C5218yesdirect product factor
40C22×C52C2×C4×C31128yesdirect product factor
41C22×C52C23×C3117yes—
42C4×C52C23×C3118yesdirect product factor
43C24×C5C2×C5×C3116yes—
44C22×C4×C5C2×C5×C31184yesdirect product factor
45C2×C31C22×C4×C52114yesdirect product factor
46C2×C31C24×C5211yescharacteristic
47C2×C52C22×C4×C31114yesdirect product factor
48C2×C52C24×C3111yescharacteristic
49C23×C5C4×C5×C31148yesdirect product factor
50C23×C5C22×C5×C31142yes—
51C2×C4×C5C22×C5×C311168yesdirect product factor
52C23×C4C52×C3111yescharacteristic, direct product factor, Sylow
53C31C23×C4×C5211yescharacteristic, direct product factor, Sylow
54C52C23×C4×C3111yescharacteristic, direct product factor, Sylow
55C22×C5C2×C4×C5×C311168yesdirect product factor
56C22×C5C23×C5×C31142yes—
57C4×C5C23×C5×C31148yesdirect product factor
58C24C2×C52×C3111yescharacteristic
59C22×C4C2×C52×C31114yesdirect product factor
60C2×C5C22×C4×C5×C31184yesdirect product factor
61C2×C5C24×C5×C3116yes—
62C23C4×C52×C3118yesdirect product factor
63C23C22×C52×C3117yes—
64C2×C4C22×C52×C31128yesdirect product factor
65C5C23×C4×C5×C3116yesdirect product factor
66C22C2×C4×C52×C31128yesdirect product factor
67C22C23×C52×C3117yes—
68C4C23×C52×C3118yesdirect product factor
69C2C22×C4×C52×C31114yesdirect product factor
70C2C24×C52×C3111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C52×C31
socle, prime radicalC24×C52×C31C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C52×C31C2direct (N × H)
3. C23×C52×C31C4direct (N × H)
5. C2×C4×C52×C31C22direct (N × H)
6. C23×C4×C5×C31C5direct (N × H)
8. C22×C4×C5×C31C2×C5direct (N × H)
9. C22×C52×C31C2×C4direct (N × H)
11. C4×C52×C31C23direct (N × H)
12. C2×C52×C31C22×C4direct (N × H)
14. C23×C5×C31C4×C5direct (N × H)
16. C2×C4×C5×C31C22×C5direct (N × H)
17. C23×C4×C31C52direct (N × H)
18. C23×C4×C52C31direct (N × H)
19. C52×C31C23×C4direct (N × H)
20. C22×C5×C31C2×C4×C5direct (N × H)
22. C4×C5×C31C23×C5direct (N × H)
24. C22×C4×C31C2×C52direct (N × H)
26. C22×C4×C52C2×C31direct (N × H)
27. C2×C5×C31C22×C4×C5direct (N × H)
29. C23×C31C4×C52direct (N × H)
31. C2×C4×C31C22×C52direct (N × H)
32. C23×C52C4×C31direct (N × H)
34. C2×C4×C52C22×C31direct (N × H)
35. C23×C4×C5C5×C31direct (N × H)
36. C5×C31C23×C4×C5direct (N × H)
37. C22×C31C2×C4×C52direct (N × H)
39. C4×C31C23×C52direct (N × H)
40. C22×C52C2×C4×C31direct (N × H)
42. C4×C52C23×C31direct (N × H)
44. C22×C4×C5C2×C5×C31direct (N × H)
45. C2×C31C22×C4×C52direct (N × H)
47. C2×C52C22×C4×C31direct (N × H)
49. C23×C5C4×C5×C31direct (N × H)
51. C2×C4×C5C22×C5×C31direct (N × H)
52. C23×C4C52×C31direct (N × H)
53. C31C23×C4×C52direct (N × H)
54. C52C23×C4×C31direct (N × H)
55. C22×C5C2×C4×C5×C31direct (N × H)
57. C4×C5C23×C5×C31direct (N × H)
59. C22×C4C2×C52×C31direct (N × H)
60. C2×C5C22×C4×C5×C31direct (N × H)
62. C23C4×C52×C31direct (N × H)
64. C2×C4C22×C52×C31direct (N × H)
65. C5C23×C4×C5×C31direct (N × H)
66. C22C2×C4×C52×C31direct (N × H)
68. C4C23×C52×C31direct (N × H)
69. C2C22×C4×C52×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C52×C312
C22×C4×C52×C312
C23×C4×C5×C315
C23×C4×C5231