Finite Group Databasebeta

← C2×C32×C5×C13×D13 #44478337

Subgroups — C2×C32×C5×C13×D13 #44478337

Order 30420.

384 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C32×C5×C13×D13C212yesmaximal, direct product factor
2C2×C32×C5×C132C211yesmaximal, characteristic, complemented
3C2×C3×C5×C13×D13C314yesmaximal, direct product factor
4C32×C5×C132C2211yescharacteristic, complemented, Hall
5C2×C32×C13×D13C511yesmaximal, characteristic, direct product factor, Hall
6C3×C5×C13×D13C2×C318yesdirect product factor
7C2×C3×C5×C132C2×C314yescomplemented
8C2×C5×C13×D13C3211yescharacteristic, direct product factor, Hall
9C32×C13×D13C2×C512yesdirect product factor
10C2×C32×C132C2×C511yescharacteristic, complemented
11C3×C5×C132C22×C314yescomplemented
12C2×C32×C5×D13C1311yesmaximal, characteristic, direct product factor
13C22×C32×C5×C13—131nomaximal
14C2×C3×C13×D13C3×C514yesdirect product factor
15C2×C5×C132C2×C3211yescharacteristic, complemented
16C5×C13×D13C2×C3212yesdirect product factor
17C32×C132C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C13—26no—
19C2×C32×C5×C13—132no—
20C2×C32×C5×C13D1311yescharacteristic, direct product factor
21C2×C32×C5×C13C2×C1311yescharacteristic, complemented
22C32×C5×D13C2×C1312yesdirect product factor
23C2×C3×C132C2×C3×C514yescomplemented
24C3×C13×D13C2×C3×C518yesdirect product factor
25C5×C132C22×C3211yescharacteristic, complemented, Hall
26C22×C3×C5×C13—134no—
27C2×C3×C5×D13C3×C1314yesdirect product factor
28C2×C13×D13C32×C511yescharacteristic, direct product factor, Hall
29C32×C5×C13—26no—
30C32×C5×C13C2×D1311yescharacteristic, direct product factor
31C32×C5×C13C22×C1311yescharacteristic, complemented
32C3×C132C22×C3×C514yescomplemented
33C22×C32×C13—131no—
34C2×C32×D13C5×C1311yescharacteristic, direct product factor
35C2×C3×C5×C13—224no—
36C2×C3×C5×C13—138no—
37C2×C3×C5×C13C3×D1314yesdirect product factor
38C2×C3×C5×C13C2×C3×C1314yescomplemented
39C3×C5×D13C2×C3×C1318yesdirect product factor
40C2×C132C2×C32×C511yescharacteristic, complemented
41C13×D13C2×C32×C512yesdirect product factor
42C22×C5×C13—131no—
43C2×C5×D13C32×C1311yescharacteristic, direct product factor
44C2×C32×C13—26no—
45C2×C32×C13—132no—
46C2×C32×C13C5×D1311yescharacteristic, direct product factor
47C2×C32×C13C2×C5×C1311yescharacteristic, complemented
48C32×D13C2×C5×C1312yesdirect product factor
49C3×C5×C13—224no—
50C3×C5×C13C2×C3×D1314yesdirect product factor
51C3×C5×C13C22×C3×C1314yescomplemented
52C22×C32×C5—131noHall
53C132C22×C32×C511yescharacteristic, complemented, Sylow
54C22×C3×C13—134no—
55C2×C3×D13C3×C5×C1314yesdirect product factor
56C2×C5×C13—26no—
57C2×C5×C13—132no—
58C2×C5×C13C32×D1311yescharacteristic, direct product factor
59C2×C5×C13C2×C32×C1311yescharacteristic, complemented
60C5×D13C2×C32×C1312yesdirect product factor
61C32×C13—26no—
62C32×C13C2×C5×D1311yescharacteristic, direct product factor
63C32×C13C22×C5×C1311yescharacteristic, complemented
64C2×C32×C5—132no—
65C2×C32×C5C13×D1311yescharacteristic, direct product factor
66C2×C3×C13—224no—
67C2×C3×C13—138no—
68C2×C3×C13C3×C5×D1314yesdirect product factor
69C2×C3×C13C2×C3×C5×C1314yescomplemented
70C3×D13C2×C3×C5×C1318yesdirect product factor
71C5×C13—26no—
72C5×C13C2×C32×D1311yescharacteristic, direct product factor
73C5×C13C22×C32×C1311yescharacteristic, complemented
74C22×C3×C5—134no—
75C22×C13—131no—
76C2×D13C32×C5×C1311yescharacteristic, direct product factor
77C32×C5C2×C13×D1311yescharacteristic, direct product factor, Hall
78C3×C13—224no—
79C3×C13C2×C3×C5×D1314yesdirect product factor
80C3×C13C22×C3×C5×C1314yescomplemented
81C22×C32—131noHall
82C2×C3×C5—138no—
83C2×C3×C5C3×C13×D1314yesdirect product factor
84C2×C13—26no—
85C2×C13—132no—
86C2×C13C32×C5×D1311yescharacteristic, direct product factor
87C2×C13C2×C32×C5×C1311yescharacteristic, complemented
88D13C2×C32×C5×C1312yesdirect product factor
89C22×C5—131noHall
90C2×C32—132no—
91C2×C32C5×C13×D1311yescharacteristic, direct product factor
92C3×C5C2×C3×C13×D1314yesdirect product factor
93C13—26no—
94C13C22×C32×C5×C1311yescharacteristic, complemented
95C13C2×C32×C5×D1311yescharacteristic, direct product factor
96C22×C3—134no—
97C2×C5—132no—
98C2×C5C32×C13×D1311yescharacteristic, direct product factor
99C32C2×C5×C13×D1311yescharacteristic, direct product factor, Sylow
100C2×C3—138no—
101C2×C3C3×C5×C13×D1314yesdirect product factor
102C5C2×C32×C13×D1311yescharacteristic, direct product factor, Sylow
103C22—131noSylow
104C3C2×C3×C5×C13×D1314yesdirect product factor
105C2—132no—
106C2C32×C5×C13×D1311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5×C13D13
commutator, cosocle, hypocenterC13C22×C32×C5×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C13
UCSC1 ◁ C2×C32×C5×C13

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D13C2direct (N × H)
2. C2×C32×C5×C132C2semidirect
3. C2×C3×C5×C13×D13C3direct (N × H)
4. C32×C5×C132C22semidirect
5. C2×C32×C13×D13C5direct (N × H)
6. C3×C5×C13×D13C2×C3direct (N × H)
7. C2×C3×C5×C132C2×C3semidirect
8. C2×C5×C13×D13C32direct (N × H)
9. C32×C13×D13C2×C5direct (N × H)
10. C2×C32×C132C2×C5semidirect
11. C3×C5×C132C22×C3semidirect
12. C2×C32×C5×D13C13direct (N × H)
14. C2×C3×C13×D13C3×C5direct (N × H)
15. C2×C5×C132C2×C32semidirect
16. C5×C13×D13C2×C32direct (N × H)
17. C32×C132C22×C5semidirect
20. C2×C32×C5×C13D13direct (N × H)
21. C2×C32×C5×C13C2×C13semidirect
22. C32×C5×D13C2×C13direct (N × H)
23. C2×C3×C132C2×C3×C5semidirect
24. C3×C13×D13C2×C3×C5direct (N × H)
25. C5×C132C22×C32semidirect
27. C2×C3×C5×D13C3×C13direct (N × H)
28. C2×C13×D13C32×C5direct (N × H)
30. C32×C5×C13C2×D13direct (N × H)
31. C32×C5×C13C22×C13semidirect
32. C3×C132C22×C3×C5semidirect
34. C2×C32×D13C5×C13direct (N × H)
37. C2×C3×C5×C13C3×D13direct (N × H)
38. C2×C3×C5×C13C2×C3×C13semidirect
39. C3×C5×D13C2×C3×C13direct (N × H)
40. C2×C132C2×C32×C5semidirect
41. C13×D13C2×C32×C5direct (N × H)
43. C2×C5×D13C32×C13direct (N × H)
46. C2×C32×C13C5×D13direct (N × H)
47. C2×C32×C13C2×C5×C13semidirect
48. C32×D13C2×C5×C13direct (N × H)
50. C3×C5×C13C2×C3×D13direct (N × H)
51. C3×C5×C13C22×C3×C13semidirect
53. C132C22×C32×C5semidirect
55. C2×C3×D13C3×C5×C13direct (N × H)
58. C2×C5×C13C32×D13direct (N × H)
59. C2×C5×C13C2×C32×C13semidirect
60. C5×D13C2×C32×C13direct (N × H)
62. C32×C13C2×C5×D13direct (N × H)
63. C32×C13C22×C5×C13semidirect
65. C2×C32×C5C13×D13direct (N × H)
68. C2×C3×C13C3×C5×D13direct (N × H)
69. C2×C3×C13C2×C3×C5×C13semidirect
70. C3×D13C2×C3×C5×C13direct (N × H)
72. C5×C13C2×C32×D13direct (N × H)
73. C5×C13C22×C32×C13semidirect
76. C2×D13C32×C5×C13direct (N × H)
77. C32×C5C2×C13×D13direct (N × H)
79. C3×C13C2×C3×C5×D13direct (N × H)
80. C3×C13C22×C3×C5×C13semidirect
83. C2×C3×C5C3×C13×D13direct (N × H)
86. C2×C13C32×C5×D13direct (N × H)
87. C2×C13C2×C32×C5×C13semidirect
88. D13C2×C32×C5×C13direct (N × H)
91. C2×C32C5×C13×D13direct (N × H)
92. C3×C5C2×C3×C13×D13direct (N × H)
94. C13C22×C32×C5×C13semidirect
95. C13C2×C32×C5×D13direct (N × H)
98. C2×C5C32×C13×D13direct (N × H)
99. C32C2×C5×C13×D13direct (N × H)
101. C2×C3C3×C5×C13×D13direct (N × H)
102. C5C2×C32×C13×D13direct (N × H)
104. C3C2×C3×C5×C13×D13direct (N × H)
106. C2C32×C5×C13×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13×D132
C2×C32×C5×C1322
C2×C3×C5×C13×D133
C2×C32×C13×D135
C2×C32×C5×D1313
C22×C32×C5×C1313