Finite Group Databasebeta

← C2×C13×C3⋊D195 #44478352

Subgroups — C2×C13×C3⋊D195 #44478352

Order 30420.

384 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C13×C3⋊D195C212yesmaximal, direct product factor
2C2×C32×C5×C132C211yesmaximal, characteristic, complemented
3C2×C13×D195—34nomaximal
4C32×C5×C132C2211yescharacteristic, complemented, Hall
5C2×C13×C3⋊D39—51nomaximal, Hall
6C13×D195—38no—
7C2×C3×C5×C132D314yescomplemented
8C2×C13×D65—91noHall
9C13×C3⋊D39—52no—
10C2×C32×C132D511yescharacteristic, complemented
11C3×C5×C132C2×D314yescomplemented
12C2×C13×C3⋊D15—131nomaximal
13C2×C3⋊D195C1311yesmaximal, characteristic, direct product factor
14C2×C13×D39—154no—
15C2×C5×C132C3⋊D311yescharacteristic, complemented
16C13×D65—92no—
17C32×C132C2×D511yescharacteristic, complemented, Hall
18C2×C32×C5×C13—26no—
19C2×C32×C5×C13D1311yescharacteristic, complemented
20C2×C32×C5×C13C2×C1311yescharacteristic, complemented
21C3⋊D195C2×C1312yesdirect product factor
22C13×C3⋊D15—132no—
23C2×C3×C132D1514yescomplemented
24C13×D39—158no—
25C5×C132C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×D195—34no—
27C2×C13×D15—394no—
28C2×C13×D13—451noHall
29C32×C5×C13—26no—
30C32×C5×C13C2×D1311yescharacteristic, complemented
31C32×C5×C13C22×C1311yescharacteristic, complemented
32C3×C132C2×D1514yescomplemented
33C2×C3⋊D39—51no—
34C2×C13×C3⋊D3—651no—
35C2×C3×C5×C13—224no—
36C2×C3×C5×C13D3×C1314yescomplemented
37C2×C3×C5×C13D3914yescomplemented
38D195—38no—
39C13×D15—398no—
40C2×C132C3⋊D1511yescharacteristic, complemented
41C13×D13—452no—
42C2×D65—91no—
43C2×D5×C13—1171no—
44C2×C32×C13—26no—
45C2×C32×C13D5×C1311yescharacteristic, complemented
46C2×C32×C13D6511yescharacteristic, complemented
47C3⋊D39—52no—
48C13×C3⋊D3—652no—
49C3×C5×C13—224no—
50C3×C5×C13C2×D3×C1314yescomplemented
51C3×C5×C13C2×D3914yescomplemented
52C2×C3⋊D15—131noHall
53C132C2×C3⋊D1511yescharacteristic, complemented, Sylow
54C2×D39—154no—
55C2×D3×C13—1954no—
56C2×C5×C13—26no—
57C2×C5×C13C13×C3⋊D311yescharacteristic, complemented
58C2×C5×C13C3⋊D3911yescharacteristic, complemented
59D65—92no—
60D5×C13—1172no—
61C32×C13—26no—
62C32×C13C2×D5×C1311yescharacteristic, complemented
63C32×C13C2×D6511yescharacteristic, complemented
64C2×C32×C5C13×D1311yescharacteristic, complemented
65C3⋊D15—132no—
66C2×C3×C13—224no—
67C2×C3×C13C13×D1514yescomplemented
68C2×C3×C13D19514yescomplemented
69D39—158no—
70D3×C13—1958no—
71C5×C13—26no—
72C5×C13C2×C13×C3⋊D311yescharacteristic, complemented
73C5×C13C2×C3⋊D3911yescharacteristic, complemented
74C2×D15—394no—
75C22×C13—5851no—
76C2×D13—451no—
77C32×C5C2×C13×D1311yescharacteristic, complemented, Hall
78C3×C13—224no—
79C3×C13C2×C13×D1514yescomplemented
80C3×C13C2×D19514yescomplemented
81C2×C3⋊D3—651noHall
82C2×C3×C5C13×D3914yescomplemented
83D15—398no—
84C2×C13—26no—
85C2×C13—5852no—
86C2×C13C13×C3⋊D1511yescharacteristic, complemented
87C2×C13C3⋊D19511yescharacteristic, direct product factor
88D13—452no—
89C2×D5—1171noHall
90C2×C32C13×D6511yescharacteristic, complemented
91C3⋊D3—652no—
92C3×C5C2×C13×D3914yescomplemented
93C13—26no—
94C13C2×C3⋊D19511yescharacteristic, direct product factor
95C13C2×C13×C3⋊D1511yescharacteristic, complemented
96C2×D3—1954no—
97C2×C5C13×C3⋊D3911yescharacteristic, complemented
98D5—1172no—
99C32C2×C13×D6511yescharacteristic, complemented, Sylow
100C2×C3C13×D19514yescomplemented
101D3—1958no—
102C5C2×C13×C3⋊D3911yescharacteristic, complemented, Sylow
103C22—5851noSylow
104C3C2×C13×D19514yescomplemented
105C2—5852no—
106C2C13×C3⋊D19511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C13C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C22×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C2×C13

Complements

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

NH ≅ G/Ntype
1. C13×C3⋊D195C2direct (N × H)
2. C2×C32×C5×C132C2semidirect
4. C32×C5×C132C22semidirect
7. C2×C3×C5×C132D3semidirect
10. C2×C32×C132D5semidirect
11. C3×C5×C132C2×D3semidirect
13. C2×C3⋊D195C13direct (N × H)
15. C2×C5×C132C3⋊D3semidirect
17. C32×C132C2×D5semidirect
19. C2×C32×C5×C13D13semidirect
20. C2×C32×C5×C13C2×C13semidirect
21. C3⋊D195C2×C13direct (N × H)
23. C2×C3×C132D15semidirect
25. C5×C132C2×C3⋊D3semidirect
30. C32×C5×C13C2×D13semidirect
31. C32×C5×C13C22×C13semidirect
32. C3×C132C2×D15semidirect
36. C2×C3×C5×C13D3×C13semidirect
37. C2×C3×C5×C13D39semidirect
40. C2×C132C3⋊D15semidirect
45. C2×C32×C13D5×C13semidirect
46. C2×C32×C13D65semidirect
50. C3×C5×C13C2×D3×C13semidirect
51. C3×C5×C13C2×D39semidirect
53. C132C2×C3⋊D15semidirect
57. C2×C5×C13C13×C3⋊D3semidirect
58. C2×C5×C13C3⋊D39semidirect
62. C32×C13C2×D5×C13semidirect
63. C32×C13C2×D65semidirect
64. C2×C32×C5C13×D13semidirect
67. C2×C3×C13C13×D15semidirect
68. C2×C3×C13D195semidirect
72. C5×C13C2×C13×C3⋊D3semidirect
73. C5×C13C2×C3⋊D39semidirect
77. C32×C5C2×C13×D13semidirect
79. C3×C13C2×C13×D15semidirect
80. C3×C13C2×D195semidirect
82. C2×C3×C5C13×D39semidirect
86. C2×C13C13×C3⋊D15semidirect
87. C2×C13C3⋊D195direct (N × H)
90. C2×C32C13×D65semidirect
92. C3×C5C2×C13×D39semidirect
94. C13C2×C3⋊D195direct (N × H)
95. C13C2×C13×C3⋊D15semidirect
97. C2×C5C13×C3⋊D39semidirect
99. C32C2×C13×D65semidirect
100. C2×C3C13×D195semidirect
102. C5C2×C13×C3⋊D39semidirect
104. C3C2×C13×D195semidirect
106. C2C13×C3⋊D195direct (N × H)

Maximal subgroups

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

subgroupindex
C13×C3⋊D1952
C2×C32×C5×C1322
C2×C13×D1953
C2×C13×C3⋊D395
C2×C13×C3⋊D1513
C2×C3⋊D19513