Finite Group Databasebeta

← C2×C32×C13×D65 #44478340

Subgroups — C2×C32×C13×D65 #44478340

Order 30420.

384 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 132 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×C13×D65C212yesmaximal, direct product factor
2C2×C32×C5×C132C211yesmaximal, characteristic, complemented
3C2×C3×C13×D65C314yesmaximal, direct product factor
4C32×C5×C132C2211yescharacteristic, complemented, Hall
5C2×C32×C13×D13—51nomaximal, Hall
6C3×C13×D65C2×C318yesdirect product factor
7C2×C3×C5×C132C2×C314yescomplemented
8C2×C13×D65C3211yescharacteristic, direct product factor, Hall
9C32×C13×D13—52no—
10C2×C32×C132D511yescharacteristic, complemented
11C3×C5×C132C22×C314yescomplemented
12C2×C32×D5×C13—131nomaximal
13C2×C32×D65C1311yesmaximal, characteristic, direct product factor
14C2×C3×C13×D13—54no—
15C2×C5×C132C2×C3211yescharacteristic, complemented
16C13×D65C2×C3212yesdirect product factor
17C32×C132C2×D511yescharacteristic, complemented, Hall
18C2×C32×C5×C13—26no—
19C2×C32×C5×C13D1311yescharacteristic, complemented
20C2×C32×C5×C13C2×C1311yescharacteristic, complemented
21C32×D65C2×C1312yesdirect product factor
22C32×D5×C13—132no—
23C2×C3×C132C3×D514yescomplemented
24C3×C13×D13—58no—
25C5×C132C22×C3211yescharacteristic, complemented, Hall
26C2×C3×D65C3×C1314yesdirect product factor
27C2×C3×D5×C13—134no—
28C2×C13×D13—51noHall
29C32×C5×C13—26no—
30C32×C5×C13C2×D1311yescharacteristic, complemented
31C32×C5×C13C22×C1311yescharacteristic, complemented
32C3×C132C2×C3×D514yescomplemented
33C22×C32×C13—651no—
34C2×C32×D13—51no—
35C2×C3×C5×C13—224no—
36C2×C3×C5×C13C3×D1314yescomplemented
37C2×C3×C5×C13C2×C3×C1314yescomplemented
38C3×D65C2×C3×C1318yesdirect product factor
39C3×D5×C13—138no—
40C2×C132C32×D511yescharacteristic, complemented
41C13×D13—52no—
42C2×D65C32×C1311yescharacteristic, direct product factor
43C2×D5×C13—131no—
44C2×C32×C13—26no—
45C2×C32×C13—652no—
46C2×C32×C13D5×C1311yescharacteristic, complemented
47C2×C32×C13D6511yescharacteristic, direct product factor
48C32×D13—52no—
49C3×C5×C13—224no—
50C3×C5×C13C2×C3×D1314yescomplemented
51C3×C5×C13C22×C3×C1314yescomplemented
52C2×C32×D5—131noHall
53C132C2×C32×D511yescharacteristic, complemented, Sylow
54C22×C3×C13—654no—
55C2×C3×D13—54no—
56C2×C5×C13—26no—
57C2×C5×C13C32×D1311yescharacteristic, complemented
58C2×C5×C13C2×C32×C1311yescharacteristic, complemented
59D65C2×C32×C1312yesdirect product factor
60D5×C13—132no—
61C32×C13—26no—
62C32×C13C2×D5×C1311yescharacteristic, complemented
63C32×C13C2×D6511yescharacteristic, direct product factor
64C2×C32×C5C13×D1311yescharacteristic, complemented
65C32×D5—132no—
66C2×C3×C13—224no—
67C2×C3×C13—658no—
68C2×C3×C13C3×D5×C1314yescomplemented
69C2×C3×C13C3×D6514yesdirect product factor
70C3×D13—58no—
71C5×C13—26no—
72C5×C13C2×C32×D1311yescharacteristic, complemented
73C5×C13C22×C32×C1311yescharacteristic, complemented
74C2×C3×D5—134no—
75C22×C13—651no—
76C2×D13—51no—
77C32×C5C2×C13×D1311yescharacteristic, complemented, Hall
78C3×C13—224no—
79C3×C13C2×C3×D5×C1314yescomplemented
80C3×C13C2×C3×D6514yesdirect product factor
81C22×C32—651noHall
82C2×C3×C5C3×C13×D1314yescomplemented
83C3×D5—138no—
84C2×C13—26no—
85C2×C13—652no—
86C2×C13C32×D5×C1311yescharacteristic, complemented
87C2×C13C32×D6511yescharacteristic, direct product factor
88D13—52no—
89C2×D5—131noHall
90C2×C32—652no—
91C2×C32C13×D6511yescharacteristic, direct product factor
92C3×C5C2×C3×C13×D1314yescomplemented
93C13—26no—
94C13C2×C32×D6511yescharacteristic, direct product factor
95C13C2×C32×D5×C1311yescharacteristic, complemented
96C22×C3—654no—
97C2×C5C32×C13×D1311yescharacteristic, complemented
98D5—132no—
99C32C2×C13×D6511yescharacteristic, direct product factor, Sylow
100C2×C3—658no—
101C2×C3C3×C13×D6514yesdirect product factor
102C5C2×C32×C13×D1311yescharacteristic, complemented, Sylow
103C22—651noSylow
104C3C2×C3×C13×D6514yesdirect product factor
105C2—652no—
106C2C32×C13×D6511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C13D65
commutator, cosocle, hypocenterC5×C13C22×C32×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C32×C13

Complements

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

NH ≅ G/Ntype
1. C32×C13×D65C2direct (N × H)
2. C2×C32×C5×C132C2semidirect
3. C2×C3×C13×D65C3direct (N × H)
4. C32×C5×C132C22semidirect
6. C3×C13×D65C2×C3direct (N × H)
7. C2×C3×C5×C132C2×C3semidirect
8. C2×C13×D65C32direct (N × H)
10. C2×C32×C132D5semidirect
11. C3×C5×C132C22×C3semidirect
13. C2×C32×D65C13direct (N × H)
15. C2×C5×C132C2×C32semidirect
16. C13×D65C2×C32direct (N × H)
17. C32×C132C2×D5semidirect
19. C2×C32×C5×C13D13semidirect
20. C2×C32×C5×C13C2×C13semidirect
21. C32×D65C2×C13direct (N × H)
23. C2×C3×C132C3×D5semidirect
25. C5×C132C22×C32semidirect
26. C2×C3×D65C3×C13direct (N × H)
30. C32×C5×C13C2×D13semidirect
31. C32×C5×C13C22×C13semidirect
32. C3×C132C2×C3×D5semidirect
36. C2×C3×C5×C13C3×D13semidirect
37. C2×C3×C5×C13C2×C3×C13semidirect
38. C3×D65C2×C3×C13direct (N × H)
40. C2×C132C32×D5semidirect
42. C2×D65C32×C13direct (N × H)
46. C2×C32×C13D5×C13semidirect
47. C2×C32×C13D65direct (N × H)
50. C3×C5×C13C2×C3×D13semidirect
51. C3×C5×C13C22×C3×C13semidirect
53. C132C2×C32×D5semidirect
57. C2×C5×C13C32×D13semidirect
58. C2×C5×C13C2×C32×C13semidirect
59. D65C2×C32×C13direct (N × H)
62. C32×C13C2×D5×C13semidirect
63. C32×C13C2×D65direct (N × H)
64. C2×C32×C5C13×D13semidirect
68. C2×C3×C13C3×D5×C13semidirect
69. C2×C3×C13C3×D65direct (N × H)
72. C5×C13C2×C32×D13semidirect
73. C5×C13C22×C32×C13semidirect
77. C32×C5C2×C13×D13semidirect
79. C3×C13C2×C3×D5×C13semidirect
80. C3×C13C2×C3×D65direct (N × H)
82. C2×C3×C5C3×C13×D13semidirect
86. C2×C13C32×D5×C13semidirect
87. C2×C13C32×D65direct (N × H)
91. C2×C32C13×D65direct (N × H)
92. C3×C5C2×C3×C13×D13semidirect
94. C13C2×C32×D65direct (N × H)
95. C13C2×C32×D5×C13semidirect
97. C2×C5C32×C13×D13semidirect
99. C32C2×C13×D65direct (N × H)
101. C2×C3C3×C13×D65direct (N × H)
102. C5C2×C32×C13×D13semidirect
104. C3C2×C3×C13×D65direct (N × H)
106. C2C32×C13×D65direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C13×D652
C2×C32×C5×C1322
C2×C3×C13×D653
C2×C32×C13×D135
C2×C32×D5×C1313
C2×C32×D6513