Finite Group Databasebeta

← C3×C5×D3×C13⋊D13 #44478239

Subgroups — C3×C5×D3×C13⋊D13 #44478239

Order 30420.

704 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 208 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⋊D13C211yesmaximal, characteristic, complemented
2C3×C5×D3×C132C211yesmaximal, characteristic, complemented
3C3×C5×C3⋊(C13⋊D13)C211yesmaximal, characteristic, complemented
4C2×C3×C5×C13⋊D13—31nomaximal
5C5×D3×C13⋊D13C311yesmaximal, characteristic, direct product factor
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7C3×D3×C13⋊D13C511yesmaximal, characteristic, direct product factor, Hall
8C5×C3⋊(C13⋊D13)C2×C311yescharacteristic, complemented
9C5×D3×C132C2×C311yescharacteristic, complemented
10C3×C5×C13⋊D13—21no—
11C3×C5×C13⋊D13—31no—
12C3×C5×C13⋊D13D311yescharacteristic, direct product factor
13C3×C5×C13⋊D13C2×C311yescharacteristic, complemented
14C2×C3×C5×C132—31no—
15C2×C5×C13⋊D13—31noHall
16C3×C3⋊(C13⋊D13)C2×C511yescharacteristic, complemented
17C3×D3×C132C2×C511yescharacteristic, complemented
18C32×C13⋊D13C2×C511yescharacteristic, complemented
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C3×C5×D3×D13—1314nomaximal
23C2×C3×C13⋊D13—31no—
24D3×C13⋊D13C3×C511yescharacteristic, direct product factor
25C2×C5×C132—31no—
26C5×C13⋊D13—31no—
27C5×C13⋊D13C3×D311yescharacteristic, direct product factor
28C32×C132C22×C511yescharacteristic, complemented, Hall
29C3×C5×D39—1314no—
30C3×C5×D3×C13D13114yescomplemented
31C32×C5×D13—1314no—
32C2×C3×C132—31no—
33C3⋊(C13⋊D13)C2×C3×C511yescharacteristic, complemented
34D3×C132C2×C3×C511yescharacteristic, complemented
35C3×C13⋊D13—21no—
36C3×C13⋊D13—31no—
37C3×C13⋊D13C5×D311yescharacteristic, direct product factor
38C3×C13⋊D13C2×C3×C511yescharacteristic, complemented
39C5×C132C2×C3×D311yescharacteristic, complemented, Hall
40C2×C3×C5×D13—3914no—
41C5×D3×D13—1314no—
42C2×C13⋊D13—31noHall
43C32×C5×C13C2×D13114yescomplemented
44C3×C132—21no—
45C3×C132C2×C5×D311yescharacteristic, complemented
46C3×C132C22×C3×C511yescharacteristic, complemented
47C3×D3×D13—1314no—
48C2×C3×C5×C13—314no—
49C5×D39—1314no—
50C5×D3×C13C3×D13114yescomplemented
51C3×C5×D13—1314no—
52C3×C5×D13—1314no—
53C3×C5×D13—2614no—
54C3×C5×D13—3914no—
55C2×C132—31no—
56C13⋊D13—31no—
57C13⋊D13C3×C5×D311yescharacteristic, direct product factor
58C2×C5×D13—3914no—
59C3×D39—1314no—
60C3×D3×C13C5×D13114yescomplemented
61C32×D13—1314no—
62C3×C5×C13—214no—
63C3×C5×C13D3×D13114yescomplemented
64C3×C5×C13C2×C3×D13114yescomplemented
65C2×C3×C5×D3—1691noHall
66C132C2×C3×C5×D311yescharacteristic, complemented, Sylow
67C2×C3×D13—3914no—
68D3×D13—1314no—
69C2×C5×C13—314no—
70C5×D13—1314no—
71C5×D13—3914no—
72C32×C13C2×C5×D13114yescomplemented
73C2×C32×C5—1691no—
74C3×C5×D3—1691no—
75C3×C5×D3C13⋊D1311yescharacteristic, direct product factor
76C2×C3×C13—314no—
77D39—1314no—
78C3×D13—1314no—
79C3×D13—1314no—
80C3×D13—2614no—
81C3×D13—3914no—
82D3×C13C3×C5×D13114yescomplemented
83C5×C13C3×D3×D13114yescomplemented
84C22×C3×C5—5071no—
85C2×C5×D3—1691no—
86C2×D13—3914no—
87C32×C5C2×C13⋊D1311yescharacteristic, complemented, Hall
88C3×C13—214no—
89C3×C13C5×D3×D13114yescomplemented
90C3×C13C2×C3×C5×D13114yescomplemented
91C2×C3×D3—1691noHall
92C2×C3×C5—31no—
93C2×C3×C5—3381no—
94C2×C3×C5—1691no—
95C2×C3×C5—1691no—
96C2×C3×C5—5071no—
97C5×D3—1691no—
98C5×D3C3×C13⋊D1311yescharacteristic, direct product factor
99C2×C13—314no—
100D13—1314no—
101D13—3914no—
102C22×C5—5071noHall
103C2×C32—1691no—
104C3×D3—1691no—
105C3×D3C5×C13⋊D1311yescharacteristic, direct product factor
106C3×C5—21no—
107C3×C5D3×C13⋊D1311yescharacteristic, direct product factor
108C3×C5C2×C3×C13⋊D1311yescharacteristic, complemented
109C13C3×C5×D3×D13114yescomplemented
110C22×C3—5071no—
111C2×D3—1691no—
112C2×C5—31no—
113C2×C5—1691no—
114C2×C5—5071no—
115C32C2×C5×C13⋊D1311yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—3381no—
118C2×C3—1691no—
119C2×C3—1691no—
120C2×C3—5071no—
121D3—1691no—
122D3C3×C5×C13⋊D1311yescharacteristic, direct product factor
123C5C3×D3×C13⋊D1311yescharacteristic, direct product factor, Sylow
124C22—5071noSylow
125C3—21no—
126C3C5×D3×C13⋊D1311yescharacteristic, direct product factor
127C3C2×C3×C5×C13⋊D1311yescharacteristic, complemented
128C2—31no—
129C2—1691no—
130C2—5071no—
subgroupG/H
center, hypercenterC3×C5D3×C13⋊D13
commutator, cosocle, hypocenterC3×C132C22×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C132C22
LCSG ▷ C3×C132
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13⋊D13C2semidirect
2. C3×C5×D3×C132C2semidirect
3. C3×C5×C3⋊(C13⋊D13)C2semidirect
5. C5×D3×C13⋊D13C3direct (N × H)
6. C32×C5×C132C22semidirect
7. C3×D3×C13⋊D13C5direct (N × H)
8. C5×C3⋊(C13⋊D13)C2×C3semidirect
9. C5×D3×C132C2×C3semidirect
12. C3×C5×C13⋊D13D3direct (N × H)
13. C3×C5×C13⋊D13C2×C3semidirect
16. C3×C3⋊(C13⋊D13)C2×C5semidirect
17. C3×D3×C132C2×C5semidirect
18. C32×C13⋊D13C2×C5semidirect
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
24. D3×C13⋊D13C3×C5direct (N × H)
27. C5×C13⋊D13C3×D3direct (N × H)
28. C32×C132C22×C5semidirect
30. C3×C5×D3×C13D13semidirect
33. C3⋊(C13⋊D13)C2×C3×C5semidirect
34. D3×C132C2×C3×C5semidirect
37. C3×C13⋊D13C5×D3direct (N × H)
38. C3×C13⋊D13C2×C3×C5semidirect
39. C5×C132C2×C3×D3semidirect
43. C32×C5×C13C2×D13semidirect
45. C3×C132C2×C5×D3semidirect
46. C3×C132C22×C3×C5semidirect
50. C5×D3×C13C3×D13semidirect
57. C13⋊D13C3×C5×D3direct (N × H)
60. C3×D3×C13C5×D13semidirect
63. C3×C5×C13D3×D13semidirect
64. C3×C5×C13C2×C3×D13semidirect
66. C132C2×C3×C5×D3semidirect
72. C32×C13C2×C5×D13semidirect
75. C3×C5×D3C13⋊D13direct (N × H)
82. D3×C13C3×C5×D13semidirect
83. C5×C13C3×D3×D13semidirect
87. C32×C5C2×C13⋊D13semidirect
89. C3×C13C5×D3×D13semidirect
90. C3×C13C2×C3×C5×D13semidirect
98. C5×D3C3×C13⋊D13direct (N × H)
105. C3×D3C5×C13⋊D13direct (N × H)
107. C3×C5D3×C13⋊D13direct (N × H)
108. C3×C5C2×C3×C13⋊D13semidirect
109. C13C3×C5×D3×D13semidirect
115. C32C2×C5×C13⋊D13semidirect
122. D3C3×C5×C13⋊D13direct (N × H)
123. C5C3×D3×C13⋊D13direct (N × H)
126. C3C5×D3×C13⋊D13direct (N × H)
127. C3C2×C3×C5×C13⋊D13semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C13⋊D132
C3×C5×D3×C1322
C3×C5×C3⋊(C13⋊D13)2
C2×C3×C5×C13⋊D133
C5×D3×C13⋊D133
C3×D3×C13⋊D135
C3×C5×D3×D1313