Finite Group Databasebeta

← C2×C3×C5×D13×C13⋊C3 #44478149

Subgroups — C2×C3×C5×D13×C13⋊C3 #44478149

Order 30420.

256 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×C3×C5×C13×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C5×D13×C13⋊C3C212yesmaximal, direct product factor
3C2×C3×C5×C13×D13C311yesmaximal, characteristic, complemented
4C2×C5×D13×C13⋊C3C313yesmaximal, direct product factor
5C3×C5×C13×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C3×D13×C13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C13×D13C2×C312yescomplemented
8C2×C5×C13×C13⋊C3C2×C313yescomplemented
9C5×D13×C13⋊C3C2×C316yesdirect product factor
10C2×C3×C5×C132C2×C311yescharacteristic, complemented
11C2×C5×C13×D13C3211yescharacteristic, complemented, Hall
12C2×C3×C13×C13⋊C3C2×C511yescharacteristic, complemented
13C3×D13×C13⋊C3C2×C512yesdirect product factor
14C5×C13×C13⋊C3C22×C313yescomplemented
15C3×C5×C132C22×C311yescharacteristic, complemented
16C2×C32×C5×D13—131nomaximal
17C22×C3×C5×C13⋊C3—131nomaximal
18C2×C3×C13×D13C3×C511yescharacteristic, complemented
19C2×D13×C13⋊C3C3×C513yesdirect product factor
20C2×C5×C132C2×C3211yescharacteristic, complemented
21C5×C13×D13C2×C3212yescomplemented
22C3×C13×C13⋊C3C22×C511yescharacteristic, complemented, Hall
23C2×C32×C5×C13—131no—
24C32×C5×D13—132no—
25C2×C3×C5×C13⋊C3—132no—
26C2×C3×C5×C13⋊C3D1311yescharacteristic, direct product factor
27C2×C3×C132C2×C3×C511yescharacteristic, complemented
28C3×C13×D13C2×C3×C512yescomplemented
29C2×C13×C13⋊C3C2×C3×C513yescomplemented
30D13×C13⋊C3C2×C3×C516yesdirect product factor
31C5×C132C22×C3211yescharacteristic, complemented, Hall
32C22×C3×C5×C13—131no—
33C2×C3×C5×D13—133no—
34C2×C3×C5×D13C13⋊C311yescharacteristic, direct product factor
35C22×C5×C13⋊C3—133no—
36C2×C13×D13C32×C511yescharacteristic, complemented, Hall
37C32×C5×C13—131no—
38C3×C5×C13⋊C3C2×D1311yescharacteristic, direct product factor
39C3×C132C22×C3×C511yescharacteristic, complemented
40C13×C13⋊C3C22×C3×C513yescomplemented
41C2×C32×D13—131no—
42C22×C3×C13⋊C3—131no—
43C2×C3×C5×C13—62no—
44C2×C3×C5×C13—132no—
45C2×C3×C5×C13—133no—
46C2×C3×C5×C13C2×C13⋊C311yescharacteristic, complemented
47C2×C3×C5×C13C3×D1311yescharacteristic, complemented
48C3×C5×D13—136no—
49C3×C5×D13C2×C13⋊C312yesdirect product factor
50C2×C5×C13⋊C3—136no—
51C2×C5×C13⋊C3C3×D1313yesdirect product factor
52C2×C132C2×C32×C511yescharacteristic, complemented
53C13×D13C2×C32×C512yescomplemented
54C22×C5×C13—131no—
55C2×C5×D13C3×C13⋊C311yescharacteristic, direct product factor
56C2×C32×C13—131no—
57C32×D13—132no—
58C2×C3×C13⋊C3—132no—
59C2×C3×C13⋊C3C5×D1311yescharacteristic, direct product factor
60C3×C5×C13—62no—
61C3×C5×C13—133no—
62C3×C5×C13C22×C13⋊C311yescharacteristic, complemented
63C3×C5×C13C2×C3×D1311yescharacteristic, complemented
64C5×C13⋊C3C2×C3×D1313yesdirect product factor
65C22×C32×C5—1691noHall
66C132C22×C32×C511yescharacteristic, complemented, Sylow
67C22×C3×C13—131no—
68C2×C3×D13—133no—
69C2×C3×D13C5×C13⋊C311yescharacteristic, direct product factor
70C22×C13⋊C3—133no—
71C2×C5×C13—62no—
72C2×C5×C13—132no—
73C2×C5×C13C2×C3×C13⋊C311yescharacteristic, complemented
74C2×C5×C13C32×D1311yescharacteristic, complemented
75C5×D13C2×C3×C13⋊C312yesdirect product factor
76C32×C13—131no—
77C3×C13⋊C3C2×C5×D1311yescharacteristic, direct product factor
78C2×C32×C5—131no—
79C2×C32×C5—1692no—
80C2×C3×C13—62no—
81C2×C3×C13—132no—
82C2×C3×C13—133no—
83C2×C3×C13C2×C5×C13⋊C311yescharacteristic, complemented
84C2×C3×C13C3×C5×D1311yescharacteristic, complemented
85C3×D13—136no—
86C3×D13C2×C5×C13⋊C312yesdirect product factor
87C2×C13⋊C3—136no—
88C2×C13⋊C3C3×C5×D1313yesdirect product factor
89C5×C13—62no—
90C5×C13C22×C3×C13⋊C311yescharacteristic, complemented
91C5×C13C2×C32×D1311yescharacteristic, complemented
92C22×C3×C5—131no—
93C22×C3×C5—1693no—
94C22×C13—131no—
95C2×D13C3×C5×C13⋊C311yescharacteristic, direct product factor
96C32×C5—131noHall
97C3×C13—62no—
98C3×C13—133no—
99C3×C13C22×C5×C13⋊C311yescharacteristic, complemented
100C3×C13C2×C3×C5×D1311yescharacteristic, complemented
101C13⋊C3C2×C3×C5×D1313yesdirect product factor
102C22×C32—1691noHall
103C2×C3×C5—132no—
104C2×C3×C5—133no—
105C2×C3×C5—1696no—
106C2×C3×C5D13×C13⋊C311yescharacteristic, direct product factor
107C2×C13—62no—
108C2×C13—132no—
109C2×C13C2×C3×C5×C13⋊C311yescharacteristic, complemented
110C2×C13C32×C5×D1311yescharacteristic, complemented
111D13C2×C3×C5×C13⋊C312yesdirect product factor
112C22×C5—131noHall
113C2×C32—131no—
114C2×C32—1692no—
115C3×C5—133no—
116C3×C5C2×D13×C13⋊C311yescharacteristic, direct product factor
117C13—62no—
118C13C22×C3×C5×C13⋊C311yescharacteristic, complemented
119C13C2×C32×C5×D1311yescharacteristic, complemented
120C22×C3—131no—
121C22×C3—1693no—
122C2×C5—132no—
123C2×C5C3×D13×C13⋊C311yescharacteristic, direct product factor
124C32—131noSylow
125C2×C3—132no—
126C2×C3—133no—
127C2×C3—1696no—
128C2×C3C5×D13×C13⋊C311yescharacteristic, direct product factor
129C5C2×C3×D13×C13⋊C311yescharacteristic, direct product factor, Sylow
130C22—131noSylow
131C3—133no—
132C3C2×C5×D13×C13⋊C311yescharacteristic, direct product factor
133C2—132no—
134C2C3×C5×D13×C13⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D13×C13⋊C3
commutator, cosocle, hypocenterC132C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C132C2×C3
LCSG ▷ C132
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C13×C13⋊C3C2semidirect
2. C3×C5×D13×C13⋊C3C2direct (N × H)
3. C2×C3×C5×C13×D13C3semidirect
4. C2×C5×D13×C13⋊C3C3direct (N × H)
5. C3×C5×C13×C13⋊C3C22semidirect
6. C2×C3×D13×C13⋊C3C5direct (N × H)
7. C3×C5×C13×D13C2×C3semidirect
8. C2×C5×C13×C13⋊C3C2×C3semidirect
9. C5×D13×C13⋊C3C2×C3direct (N × H)
10. C2×C3×C5×C132C2×C3semidirect
11. C2×C5×C13×D13C32semidirect
12. C2×C3×C13×C13⋊C3C2×C5semidirect
13. C3×D13×C13⋊C3C2×C5direct (N × H)
14. C5×C13×C13⋊C3C22×C3semidirect
15. C3×C5×C132C22×C3semidirect
18. C2×C3×C13×D13C3×C5semidirect
19. C2×D13×C13⋊C3C3×C5direct (N × H)
20. C2×C5×C132C2×C32semidirect
21. C5×C13×D13C2×C32semidirect
22. C3×C13×C13⋊C3C22×C5semidirect
26. C2×C3×C5×C13⋊C3D13direct (N × H)
27. C2×C3×C132C2×C3×C5semidirect
28. C3×C13×D13C2×C3×C5semidirect
29. C2×C13×C13⋊C3C2×C3×C5semidirect
30. D13×C13⋊C3C2×C3×C5direct (N × H)
31. C5×C132C22×C32semidirect
34. C2×C3×C5×D13C13⋊C3direct (N × H)
36. C2×C13×D13C32×C5semidirect
38. C3×C5×C13⋊C3C2×D13direct (N × H)
39. C3×C132C22×C3×C5semidirect
40. C13×C13⋊C3C22×C3×C5semidirect
46. C2×C3×C5×C13C2×C13⋊C3semidirect
47. C2×C3×C5×C13C3×D13semidirect
49. C3×C5×D13C2×C13⋊C3direct (N × H)
51. C2×C5×C13⋊C3C3×D13direct (N × H)
52. C2×C132C2×C32×C5semidirect
53. C13×D13C2×C32×C5semidirect
55. C2×C5×D13C3×C13⋊C3direct (N × H)
59. C2×C3×C13⋊C3C5×D13direct (N × H)
62. C3×C5×C13C22×C13⋊C3semidirect
63. C3×C5×C13C2×C3×D13semidirect
64. C5×C13⋊C3C2×C3×D13direct (N × H)
66. C132C22×C32×C5semidirect
69. C2×C3×D13C5×C13⋊C3direct (N × H)
73. C2×C5×C13C2×C3×C13⋊C3semidirect
74. C2×C5×C13C32×D13semidirect
75. C5×D13C2×C3×C13⋊C3direct (N × H)
77. C3×C13⋊C3C2×C5×D13direct (N × H)
83. C2×C3×C13C2×C5×C13⋊C3semidirect
84. C2×C3×C13C3×C5×D13semidirect
86. C3×D13C2×C5×C13⋊C3direct (N × H)
88. C2×C13⋊C3C3×C5×D13direct (N × H)
90. C5×C13C22×C3×C13⋊C3semidirect
91. C5×C13C2×C32×D13semidirect
95. C2×D13C3×C5×C13⋊C3direct (N × H)
99. C3×C13C22×C5×C13⋊C3semidirect
100. C3×C13C2×C3×C5×D13semidirect
101. C13⋊C3C2×C3×C5×D13direct (N × H)
106. C2×C3×C5D13×C13⋊C3direct (N × H)
109. C2×C13C2×C3×C5×C13⋊C3semidirect
110. C2×C13C32×C5×D13semidirect
111. D13C2×C3×C5×C13⋊C3direct (N × H)
116. C3×C5C2×D13×C13⋊C3direct (N × H)
118. C13C22×C3×C5×C13⋊C3semidirect
119. C13C2×C32×C5×D13semidirect
123. C2×C5C3×D13×C13⋊C3direct (N × H)
128. C2×C3C5×D13×C13⋊C3direct (N × H)
129. C5C2×C3×D13×C13⋊C3direct (N × H)
132. C3C2×C5×D13×C13⋊C3direct (N × H)
134. C2C3×C5×D13×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C13×C13⋊C32
C3×C5×D13×C13⋊C32
C2×C3×C5×C13×D133
C2×C5×D13×C13⋊C33
C2×C3×D13×C13⋊C35
C2×C32×C5×D1313
C22×C3×C5×C13⋊C313