Finite Group Databasebeta

← C2×C3×C5×D3×C132 #44478342

Subgroups — C2×C3×C5×D3×C132 #44478342

Order 30420.

704 conjugacy classes of subgroups; only the 448 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 448 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D3×C132C212yesmaximal, direct product factor
2C2×C32×C5×C132C211yesmaximal, characteristic, complemented
3C2×C5×D3×C132C311yesmaximal, characteristic, direct product factor
4C22×C3×C5×C132—31nomaximal
5C32×C5×C132C2211yescharacteristic, complemented, Hall
6C2×C3×D3×C132C511yesmaximal, characteristic, direct product factor, Hall
7C5×D3×C132C2×C312yesdirect product factor
8C2×C3×C5×C132—21no—
9C2×C3×C5×C132—32no—
10C2×C3×C5×C132D311yescharacteristic, direct product factor
11C2×C3×C5×C132C2×C311yescharacteristic, complemented
12C22×C5×C132—31noHall
13C3×D3×C132C2×C512yesdirect product factor
14C2×C32×C132C2×C511yescharacteristic, complemented
15C3×C5×C132—21no—
16C3×C5×C132C2×D311yescharacteristic, direct product factor
17C3×C5×C132C22×C311yescharacteristic, complemented
18C2×C3×C5×D3×C13C13114yesmaximal, direct product factor
19C2×D3×C132C3×C511yescharacteristic, direct product factor
20C22×C3×C132—31no—
21C2×C5×C132—32no—
22C2×C5×C132C3×D311yescharacteristic, direct product factor
23C32×C132C22×C511yescharacteristic, complemented, Hall
24C2×C32×C5×C13C2×C13114yescomplemented
25C3×C5×D3×C13C2×C13128yesdirect product factor
26C2×C3×C132—21no—
27C2×C3×C132—32no—
28C2×C3×C132C5×D311yescharacteristic, direct product factor
29C2×C3×C132C2×C3×C511yescharacteristic, complemented
30D3×C132C2×C3×C512yesdirect product factor
31C5×C132C2×C3×D311yescharacteristic, direct product factor, Hall
32C22×C3×C5×C13—314no—
33C2×C5×D3×C13C3×C13114yesdirect product factor
34C22×C132—31noHall
35C32×C5×C13C22×C13114yescomplemented
36C3×C132—21no—
37C3×C132C2×C5×D311yescharacteristic, direct product factor
38C3×C132C22×C3×C511yescharacteristic, complemented
39C2×C3×D3×C13C5×C13114yesdirect product factor
40C2×C3×C5×C13—214no—
41C2×C3×C5×C13—328no—
42C2×C3×C5×C13D3×C13114yesdirect product factor
43C2×C3×C5×C13C2×C3×C13114yescomplemented
44C5×D3×C13C2×C3×C13128yesdirect product factor
45C2×C132—32no—
46C2×C132C3×C5×D311yescharacteristic, direct product factor
47C22×C5×C13—314no—
48C2×C32×C13C2×C5×C13114yescomplemented
49C3×D3×C13C2×C5×C13128yesdirect product factor
50C3×C5×C13—214no—
51C3×C5×C13C2×D3×C13114yesdirect product factor
52C3×C5×C13C22×C3×C13114yescomplemented
53C2×C3×C5×D3C13211yescharacteristic, direct product factor, Hall
54C132C2×C3×C5×D311yescharacteristic, direct product factor, Sylow
55C22×C3×C13—314no—
56C2×D3×C13C3×C5×C13114yesdirect product factor
57C2×C5×C13—328no—
58C2×C5×C13C3×D3×C13114yesdirect product factor
59C32×C13C22×C5×C13114yescomplemented
60C2×C32×C5C2×C13211yescharacteristic, complemented
61C3×C5×D3C2×C13212yesdirect product factor
62C2×C3×C13—214no—
63C2×C3×C13—328no—
64C2×C3×C13C5×D3×C13114yesdirect product factor
65C2×C3×C13C2×C3×C5×C13114yescomplemented
66D3×C13C2×C3×C5×C13128yesdirect product factor
67C5×C13C2×C3×D3×C13114yesdirect product factor
68C22×C3×C5—31no—
69C2×C5×D3C3×C13211yescharacteristic, direct product factor
70C22×C13—314no—
71C32×C5C22×C13211yescharacteristic, complemented, Hall
72C3×C13—214no—
73C3×C13C2×C5×D3×C13114yesdirect product factor
74C3×C13C22×C3×C5×C13114yescomplemented
75C2×C3×D3C5×C13211yescharacteristic, direct product factor, Hall
76C2×C3×C5—21no—
77C2×C3×C5—32no—
78C2×C3×C5D3×C13211yescharacteristic, direct product factor
79C2×C3×C5C2×C3×C13211yescharacteristic, complemented
80C5×D3C2×C3×C13212yesdirect product factor
81C2×C13—328no—
82C2×C13C3×C5×D3×C13114yesdirect product factor
83C22×C5—31noHall
84C2×C32C2×C5×C13211yescharacteristic, complemented
85C3×D3C2×C5×C13212yesdirect product factor
86C3×C5—21no—
87C3×C5C22×C3×C13211yescharacteristic, complemented
88C3×C5C2×D3×C13211yescharacteristic, direct product factor
89C13C2×C3×C5×D3×C13114yesdirect product factor
90C22×C3—31no—
91C2×D3C3×C5×C13211yescharacteristic, direct product factor
92C2×C5—32no—
93C2×C5C3×D3×C13211yescharacteristic, direct product factor
94C32C22×C5×C13211yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—32no—
97C2×C3C2×C3×C5×C13211yescharacteristic, complemented
98C2×C3C5×D3×C13211yescharacteristic, direct product factor
99D3C2×C3×C5×C13212yesdirect product factor
100C5C2×C3×D3×C13211yescharacteristic, direct product factor, Sylow
101C22—31noSylow
102C3—21no—
103C3C22×C3×C5×C13211yescharacteristic, complemented
104C3C2×C5×D3×C13211yescharacteristic, direct product factor
105C2—32no—
106C2C3×C5×D3×C13211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C132D3
commutator, cosocle, hypocenterC3C22×C3×C5×C132
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C132

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C132C2direct (N × H)
2. C2×C32×C5×C132C2semidirect
3. C2×C5×D3×C132C3direct (N × H)
5. C32×C5×C132C22semidirect
6. C2×C3×D3×C132C5direct (N × H)
7. C5×D3×C132C2×C3direct (N × H)
10. C2×C3×C5×C132D3direct (N × H)
11. C2×C3×C5×C132C2×C3semidirect
13. C3×D3×C132C2×C5direct (N × H)
14. C2×C32×C132C2×C5semidirect
16. C3×C5×C132C2×D3direct (N × H)
17. C3×C5×C132C22×C3semidirect
18. C2×C3×C5×D3×C13C13direct (N × H)
19. C2×D3×C132C3×C5direct (N × H)
22. C2×C5×C132C3×D3direct (N × H)
23. C32×C132C22×C5semidirect
24. C2×C32×C5×C13C2×C13semidirect
25. C3×C5×D3×C13C2×C13direct (N × H)
28. C2×C3×C132C5×D3direct (N × H)
29. C2×C3×C132C2×C3×C5semidirect
30. D3×C132C2×C3×C5direct (N × H)
31. C5×C132C2×C3×D3direct (N × H)
33. C2×C5×D3×C13C3×C13direct (N × H)
35. C32×C5×C13C22×C13semidirect
37. C3×C132C2×C5×D3direct (N × H)
38. C3×C132C22×C3×C5semidirect
39. C2×C3×D3×C13C5×C13direct (N × H)
42. C2×C3×C5×C13D3×C13direct (N × H)
43. C2×C3×C5×C13C2×C3×C13semidirect
44. C5×D3×C13C2×C3×C13direct (N × H)
46. C2×C132C3×C5×D3direct (N × H)
48. C2×C32×C13C2×C5×C13semidirect
49. C3×D3×C13C2×C5×C13direct (N × H)
51. C3×C5×C13C2×D3×C13direct (N × H)
52. C3×C5×C13C22×C3×C13semidirect
53. C2×C3×C5×D3C132direct (N × H)
54. C132C2×C3×C5×D3direct (N × H)
56. C2×D3×C13C3×C5×C13direct (N × H)
58. C2×C5×C13C3×D3×C13direct (N × H)
59. C32×C13C22×C5×C13semidirect
60. C2×C32×C5C2×C132semidirect
61. C3×C5×D3C2×C132direct (N × H)
64. C2×C3×C13C5×D3×C13direct (N × H)
65. C2×C3×C13C2×C3×C5×C13semidirect
66. D3×C13C2×C3×C5×C13direct (N × H)
67. C5×C13C2×C3×D3×C13direct (N × H)
69. C2×C5×D3C3×C132direct (N × H)
71. C32×C5C22×C132semidirect
73. C3×C13C2×C5×D3×C13direct (N × H)
74. C3×C13C22×C3×C5×C13semidirect
75. C2×C3×D3C5×C132direct (N × H)
78. C2×C3×C5D3×C132direct (N × H)
79. C2×C3×C5C2×C3×C132semidirect
80. C5×D3C2×C3×C132direct (N × H)
82. C2×C13C3×C5×D3×C13direct (N × H)
84. C2×C32C2×C5×C132semidirect
85. C3×D3C2×C5×C132direct (N × H)
87. C3×C5C22×C3×C132semidirect
88. C3×C5C2×D3×C132direct (N × H)
89. C13C2×C3×C5×D3×C13direct (N × H)
91. C2×D3C3×C5×C132direct (N × H)
93. C2×C5C3×D3×C132direct (N × H)
94. C32C22×C5×C132semidirect
97. C2×C3C2×C3×C5×C132semidirect
98. C2×C3C5×D3×C132direct (N × H)
99. D3C2×C3×C5×C132direct (N × H)
100. C5C2×C3×D3×C132direct (N × H)
103. C3C22×C3×C5×C132semidirect
104. C3C2×C5×D3×C132direct (N × H)
106. C2C3×C5×D3×C132direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D3×C1322
C2×C32×C5×C1322
C2×C5×D3×C1323
C22×C3×C5×C1323
C2×C3×D3×C1325
C2×C3×C5×D3×C1313