Finite Group Databasebeta

← C22×C3×C5×C13×C13⋊C3 #44478334

Subgroups — C22×C3×C5×C13×C13⋊C3 #44478334

Order 30420.

320 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 160 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⋊C3C213yesmaximal, direct product factor
2C22×C5×C13×C13⋊C3C313yesmaximal, direct product factor
3C22×C3×C5×C132C311yesmaximal, characteristic, complemented
4C3×C5×C13×C13⋊C3C2211yescharacteristic, direct product factor, Hall
5C22×C3×C13×C13⋊C3C511yesmaximal, characteristic, direct product factor, Hall
6C2×C5×C13×C13⋊C3C2×C319yesdirect product factor
7C2×C3×C5×C132C2×C313yescomplemented
8C22×C5×C132C3211yescharacteristic, complemented, Hall
9C2×C3×C13×C13⋊C3C2×C513yesdirect product factor
10C5×C13×C13⋊C3C22×C313yesdirect product factor
11C3×C5×C132C22×C311yescharacteristic, complemented
12C22×C3×C5×C13⋊C3C1311yesmaximal, characteristic, direct product factor
13C22×C32×C5×C13—131nomaximal
14C22×C13×C13⋊C3C3×C513yesdirect product factor
15C22×C3×C132C3×C511yescharacteristic, complemented
16C2×C5×C132C2×C3213yescomplemented
17C3×C13×C13⋊C3C22×C511yescharacteristic, direct product factor, Hall
18C2×C32×C5×C13—133no—
19C2×C3×C5×C13⋊C3C2×C1313yesdirect product factor
20C2×C3×C132C2×C3×C513yescomplemented
21C2×C13×C13⋊C3C2×C3×C519yesdirect product factor
22C5×C132C22×C3211yescharacteristic, complemented, Hall
23C22×C3×C5×C13—34no—
24C22×C3×C5×C13—133no—
25C22×C3×C5×C13C13⋊C311yescharacteristic, direct product factor
26C22×C3×C5×C13C3×C1311yescharacteristic, complemented
27C22×C5×C13⋊C3C3×C1313yesdirect product factor
28C22×C132C32×C511yescharacteristic, complemented, Hall
29C32×C5×C13—131no—
30C3×C5×C13⋊C3C22×C1311yescharacteristic, direct product factor
31C3×C132C22×C3×C511yescharacteristic, complemented
32C13×C13⋊C3C22×C3×C513yesdirect product factor
33C22×C32×C13—131no—
34C22×C3×C13⋊C3C5×C1311yescharacteristic, direct product factor
35C2×C3×C5×C13—312no—
36C2×C3×C5×C13—139no—
37C2×C3×C5×C13C2×C13⋊C313yesdirect product factor
38C2×C3×C5×C13C2×C3×C1313yescomplemented
39C2×C5×C13⋊C3C2×C3×C1319yesdirect product factor
40C2×C132C2×C32×C513yescomplemented
41C22×C5×C13—34no—
42C22×C5×C13C3×C13⋊C311yescharacteristic, direct product factor
43C22×C5×C13C32×C1311yescharacteristic, complemented
44C2×C32×C13—133no—
45C2×C3×C13⋊C3C2×C5×C1313yesdirect product factor
46C3×C5×C13—34no—
47C3×C5×C13—133no—
48C3×C5×C13C22×C13⋊C311yescharacteristic, direct product factor
49C3×C5×C13C22×C3×C1311yescharacteristic, complemented
50C5×C13⋊C3C22×C3×C1313yesdirect product factor
51C22×C32×C5—131noHall
52C132C22×C32×C511yescharacteristic, complemented, Sylow
53C22×C3×C13—34no—
54C22×C3×C13—133no—
55C22×C3×C13C5×C13⋊C311yescharacteristic, direct product factor
56C22×C3×C13C3×C5×C1311yescharacteristic, complemented
57C22×C13⋊C3C3×C5×C1313yesdirect product factor
58C2×C5×C13—312no—
59C2×C5×C13C2×C3×C13⋊C313yesdirect product factor
60C2×C5×C13C2×C32×C1313yescomplemented
61C32×C13—131no—
62C3×C13⋊C3C22×C5×C1311yescharacteristic, direct product factor
63C2×C32×C5—133no—
64C2×C3×C13—312no—
65C2×C3×C13—139no—
66C2×C3×C13C2×C5×C13⋊C313yesdirect product factor
67C2×C3×C13C2×C3×C5×C1313yescomplemented
68C2×C13⋊C3C2×C3×C5×C1319yesdirect product factor
69C5×C13—34no—
70C5×C13C22×C3×C13⋊C311yescharacteristic, direct product factor
71C5×C13C22×C32×C1311yescharacteristic, complemented
72C22×C3×C5—133no—
73C22×C3×C5C13×C13⋊C311yescharacteristic, direct product factor
74C22×C13—34no—
75C22×C13C3×C5×C13⋊C311yescharacteristic, direct product factor
76C22×C13C32×C5×C1311yescharacteristic, complemented
77C32×C5—131noHall
78C3×C13—34no—
79C3×C13—133no—
80C3×C13C22×C5×C13⋊C311yescharacteristic, direct product factor
81C3×C13C22×C3×C5×C1311yescharacteristic, complemented
82C13⋊C3C22×C3×C5×C1313yesdirect product factor
83C22×C32—131noHall
84C2×C3×C5—139no—
85C2×C3×C5C2×C13×C13⋊C313yesdirect product factor
86C2×C13—312no—
87C2×C13C2×C3×C5×C13⋊C313yesdirect product factor
88C2×C13C2×C32×C5×C1313yescomplemented
89C22×C5C3×C13×C13⋊C311yescharacteristic, direct product factor, Hall
90C2×C32—133no—
91C3×C5—133no—
92C3×C5C22×C13×C13⋊C311yescharacteristic, direct product factor
93C13—34no—
94C13C22×C32×C5×C1311yescharacteristic, complemented
95C13C22×C3×C5×C13⋊C311yescharacteristic, direct product factor
96C22×C3—133no—
97C22×C3C5×C13×C13⋊C311yescharacteristic, direct product factor
98C2×C5C2×C3×C13×C13⋊C313yesdirect product factor
99C32—131noSylow
100C2×C3—139no—
101C2×C3C2×C5×C13×C13⋊C313yesdirect product factor
102C5C22×C3×C13×C13⋊C311yescharacteristic, direct product factor, Sylow
103C22C3×C5×C13×C13⋊C311yescharacteristic, direct product factor, Sylow
104C3—133no—
105C3C22×C5×C13×C13⋊C311yescharacteristic, direct product factor
106C2C2×C3×C5×C13×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C5×C13C13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C5×C13
FrattiniC1G
Fitting, socleC22×C3×C5×C132C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C5×C13

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C13×C13⋊C3C2direct (N × H)
2. C22×C5×C13×C13⋊C3C3direct (N × H)
3. C22×C3×C5×C132C3semidirect
4. C3×C5×C13×C13⋊C3C22direct (N × H)
5. C22×C3×C13×C13⋊C3C5direct (N × H)
6. C2×C5×C13×C13⋊C3C2×C3direct (N × H)
7. C2×C3×C5×C132C2×C3semidirect
8. C22×C5×C132C32semidirect
9. C2×C3×C13×C13⋊C3C2×C5direct (N × H)
10. C5×C13×C13⋊C3C22×C3direct (N × H)
11. C3×C5×C132C22×C3semidirect
12. C22×C3×C5×C13⋊C3C13direct (N × H)
14. C22×C13×C13⋊C3C3×C5direct (N × H)
15. C22×C3×C132C3×C5semidirect
16. C2×C5×C132C2×C32semidirect
17. C3×C13×C13⋊C3C22×C5direct (N × H)
19. C2×C3×C5×C13⋊C3C2×C13direct (N × H)
20. C2×C3×C132C2×C3×C5semidirect
21. C2×C13×C13⋊C3C2×C3×C5direct (N × H)
22. C5×C132C22×C32semidirect
25. C22×C3×C5×C13C13⋊C3direct (N × H)
26. C22×C3×C5×C13C3×C13semidirect
27. C22×C5×C13⋊C3C3×C13direct (N × H)
28. C22×C132C32×C5semidirect
30. C3×C5×C13⋊C3C22×C13direct (N × H)
31. C3×C132C22×C3×C5semidirect
32. C13×C13⋊C3C22×C3×C5direct (N × H)
34. C22×C3×C13⋊C3C5×C13direct (N × H)
37. C2×C3×C5×C13C2×C13⋊C3direct (N × H)
38. C2×C3×C5×C13C2×C3×C13semidirect
39. C2×C5×C13⋊C3C2×C3×C13direct (N × H)
40. C2×C132C2×C32×C5semidirect
42. C22×C5×C13C3×C13⋊C3direct (N × H)
43. C22×C5×C13C32×C13semidirect
45. C2×C3×C13⋊C3C2×C5×C13direct (N × H)
48. C3×C5×C13C22×C13⋊C3direct (N × H)
49. C3×C5×C13C22×C3×C13semidirect
50. C5×C13⋊C3C22×C3×C13direct (N × H)
52. C132C22×C32×C5semidirect
55. C22×C3×C13C5×C13⋊C3direct (N × H)
56. C22×C3×C13C3×C5×C13semidirect
57. C22×C13⋊C3C3×C5×C13direct (N × H)
59. C2×C5×C13C2×C3×C13⋊C3direct (N × H)
60. C2×C5×C13C2×C32×C13semidirect
62. C3×C13⋊C3C22×C5×C13direct (N × H)
66. C2×C3×C13C2×C5×C13⋊C3direct (N × H)
67. C2×C3×C13C2×C3×C5×C13semidirect
68. C2×C13⋊C3C2×C3×C5×C13direct (N × H)
70. C5×C13C22×C3×C13⋊C3direct (N × H)
71. C5×C13C22×C32×C13semidirect
73. C22×C3×C5C13×C13⋊C3direct (N × H)
75. C22×C13C3×C5×C13⋊C3direct (N × H)
76. C22×C13C32×C5×C13semidirect
80. C3×C13C22×C5×C13⋊C3direct (N × H)
81. C3×C13C22×C3×C5×C13semidirect
82. C13⋊C3C22×C3×C5×C13direct (N × H)
85. C2×C3×C5C2×C13×C13⋊C3direct (N × H)
87. C2×C13C2×C3×C5×C13⋊C3direct (N × H)
88. C2×C13C2×C32×C5×C13semidirect
89. C22×C5C3×C13×C13⋊C3direct (N × H)
92. C3×C5C22×C13×C13⋊C3direct (N × H)
94. C13C22×C32×C5×C13semidirect
95. C13C22×C3×C5×C13⋊C3direct (N × H)
97. C22×C3C5×C13×C13⋊C3direct (N × H)
98. C2×C5C2×C3×C13×C13⋊C3direct (N × H)
101. C2×C3C2×C5×C13×C13⋊C3direct (N × H)
102. C5C22×C3×C13×C13⋊C3direct (N × H)
103. C22C3×C5×C13×C13⋊C3direct (N × H)
105. C3C22×C5×C13×C13⋊C3direct (N × H)
106. C2C2×C3×C5×C13×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
C22×C5×C13×C13⋊C33
C22×C3×C5×C1323
C22×C3×C13×C13⋊C35
C22×C3×C5×C13⋊C313
C22×C32×C5×C1313