Finite Group Databasebeta

← C22×C3×C4×C5×C101 #72201530

Subgroups — C22×C3×C4×C5×C101 #72201530

Order 24240.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C101C211yesmaximal, characteristic
2C2×C3×C4×C5×C101C216yesmaximal, direct product factor
3C22×C4×C5×C101C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C4×C101C511yesmaximal, characteristic, direct product factor, Hall
5C23×C5×C101C2×C311yescharacteristic
6C2×C4×C5×C101C2×C316yesdirect product factor
7C23×C3×C101C2×C511yescharacteristic
8C2×C3×C4×C101C2×C516yesdirect product factor
9C22×C3×C5×C101C414yesdirect product factor
10C22×C3×C5×C101C2213yes—
11C3×C4×C5×C101C2214yesdirect product factor
12C2×C3×C5×C101C2×C416yesdirect product factor
13C2×C3×C5×C101C2311yescharacteristic
14C22×C5×C101C3×C414yesdirect product factor
15C22×C5×C101C22×C313yes—
16C4×C5×C101C22×C314yesdirect product factor
17C22×C4×C101C3×C511yescharacteristic, direct product factor, Hall
18C3×C5×C101C22×C411yescharacteristic, direct product factor, Hall
19C22×C3×C101C4×C514yesdirect product factor
20C22×C3×C101C22×C513yes—
21C3×C4×C101C22×C514yesdirect product factor
22C2×C5×C101C2×C3×C416yesdirect product factor
23C2×C5×C101C23×C311yescharacteristic
24C23×C101C2×C3×C511yescharacteristic
25C2×C4×C101C2×C3×C516yesdirect product factor
26C2×C3×C101C2×C4×C516yesdirect product factor
27C2×C3×C101C23×C511yescharacteristic
28C5×C101C22×C3×C411yescharacteristic, direct product factor, Hall
29C22×C101C3×C4×C514yesdirect product factor
30C22×C101C22×C3×C513yes—
31C4×C101C22×C3×C514yesdirect product factor
32C3×C101C22×C4×C511yescharacteristic, direct product factor, Hall
33C22×C3×C4×C5C10111yesmaximal, characteristic, direct product factor, Hall
34C2×C101C2×C3×C4×C516yesdirect product factor
35C2×C101C23×C3×C511yescharacteristic
36C23×C3×C5C2×C10111yescharacteristic
37C2×C3×C4×C5C2×C10116yesdirect product factor
38C101C22×C3×C4×C511yescharacteristic, direct product factor, Sylow
39C22×C4×C5C3×C10111yescharacteristic, direct product factor, Hall
40C22×C3×C5C4×C10114yesdirect product factor
41C22×C3×C5C22×C10113yes—
42C3×C4×C5C22×C10114yesdirect product factor
43C22×C3×C4C5×C10111yescharacteristic, direct product factor, Hall
44C23×C5C2×C3×C10111yescharacteristic
45C2×C4×C5C2×C3×C10116yesdirect product factor
46C2×C3×C5C2×C4×C10116yesdirect product factor
47C2×C3×C5C23×C10111yescharacteristic
48C23×C3C2×C5×C10111yescharacteristic
49C2×C3×C4C2×C5×C10116yesdirect product factor
50C22×C5C3×C4×C10114yesdirect product factor
51C22×C5C22×C3×C10113yes—
52C4×C5C22×C3×C10114yesdirect product factor
53C22×C4C3×C5×C10111yescharacteristic, direct product factor, Sylow
54C3×C5C22×C4×C10111yescharacteristic, direct product factor, Hall
55C22×C3C4×C5×C10114yesdirect product factor
56C22×C3C22×C5×C10113yes—
57C3×C4C22×C5×C10114yesdirect product factor
58C2×C5C2×C3×C4×C10116yesdirect product factor
59C2×C5C23×C3×C10111yescharacteristic
60C23C2×C3×C5×C10111yescharacteristic
61C2×C4C2×C3×C5×C10116yesdirect product factor
62C2×C3C2×C4×C5×C10116yesdirect product factor
63C2×C3C23×C5×C10111yescharacteristic
64C5C22×C3×C4×C10111yescharacteristic, direct product factor, Sylow
65C22C3×C4×C5×C10114yesdirect product factor
66C22C22×C3×C5×C10113yes—
67C4C22×C3×C5×C10114yesdirect product factor
68C3C22×C4×C5×C10111yescharacteristic, direct product factor, Sylow
69C2C2×C3×C4×C5×C10116yesdirect product factor
70C2C23×C3×C5×C10111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C5×C101
socle, prime radicalC23×C3×C5×C101C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×C101C2direct (N × H)
3. C22×C4×C5×C101C3direct (N × H)
4. C22×C3×C4×C101C5direct (N × H)
6. C2×C4×C5×C101C2×C3direct (N × H)
8. C2×C3×C4×C101C2×C5direct (N × H)
9. C22×C3×C5×C101C4direct (N × H)
11. C3×C4×C5×C101C22direct (N × H)
12. C2×C3×C5×C101C2×C4direct (N × H)
14. C22×C5×C101C3×C4direct (N × H)
16. C4×C5×C101C22×C3direct (N × H)
17. C22×C4×C101C3×C5direct (N × H)
18. C3×C5×C101C22×C4direct (N × H)
19. C22×C3×C101C4×C5direct (N × H)
21. C3×C4×C101C22×C5direct (N × H)
22. C2×C5×C101C2×C3×C4direct (N × H)
25. C2×C4×C101C2×C3×C5direct (N × H)
26. C2×C3×C101C2×C4×C5direct (N × H)
28. C5×C101C22×C3×C4direct (N × H)
29. C22×C101C3×C4×C5direct (N × H)
31. C4×C101C22×C3×C5direct (N × H)
32. C3×C101C22×C4×C5direct (N × H)
33. C22×C3×C4×C5C101direct (N × H)
34. C2×C101C2×C3×C4×C5direct (N × H)
37. C2×C3×C4×C5C2×C101direct (N × H)
38. C101C22×C3×C4×C5direct (N × H)
39. C22×C4×C5C3×C101direct (N × H)
40. C22×C3×C5C4×C101direct (N × H)
42. C3×C4×C5C22×C101direct (N × H)
43. C22×C3×C4C5×C101direct (N × H)
45. C2×C4×C5C2×C3×C101direct (N × H)
46. C2×C3×C5C2×C4×C101direct (N × H)
49. C2×C3×C4C2×C5×C101direct (N × H)
50. C22×C5C3×C4×C101direct (N × H)
52. C4×C5C22×C3×C101direct (N × H)
53. C22×C4C3×C5×C101direct (N × H)
54. C3×C5C22×C4×C101direct (N × H)
55. C22×C3C4×C5×C101direct (N × H)
57. C3×C4C22×C5×C101direct (N × H)
58. C2×C5C2×C3×C4×C101direct (N × H)
61. C2×C4C2×C3×C5×C101direct (N × H)
62. C2×C3C2×C4×C5×C101direct (N × H)
64. C5C22×C3×C4×C101direct (N × H)
65. C22C3×C4×C5×C101direct (N × H)
67. C4C22×C3×C5×C101direct (N × H)
68. C3C22×C4×C5×C101direct (N × H)
69. C2C2×C3×C4×C5×C101direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×C1012
C2×C3×C4×C5×C1012
C22×C4×C5×C1013
C22×C3×C4×C1015
C22×C3×C4×C5101