Finite Group Databasebeta

← C5×D32×C11×C13 #38788222

Subgroups — C5×D32×C11×C13 #38788222

Order 25740.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C3×C5×D3×C11×C13C212yesmaximal, complemented
2C5×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C5×D3×C11×C13—32nomaximal
4C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
5D32×C11×C13C511yesmaximal, characteristic, direct product factor, Hall
6C5×D3×C11×C13—32no—
7C5×D3×C11×C13—61no—
8C5×D3×C11×C13D312yesdirect product factor
9C2×C3×C5×C11×C13—32no—
10C22×C5×C11×C13—91noHall
11C11×C13×C3⋊D3C2×C511yescharacteristic, complemented
12C3×D3×C11×C13C2×C512yescomplemented
13C5×D32×C13C1111yesmaximal, characteristic, direct product factor, Hall
14C3×C5×C11×C13—21no—
15C3×C5×C11×C13C2×D312yescomplemented
16C5×D32×C11C1311yesmaximal, characteristic, direct product factor, Hall
17C2×D3×C11×C13—32no—
18C2×C5×C11×C13—32no—
19C2×C5×C11×C13—91no—
20C32×C11×C13C22×C511yescharacteristic, complemented, Hall
21C5×C13×C3⋊D3C2×C1111yescharacteristic, complemented
22C3×C5×D3×C13C2×C1112yescomplemented
23C5×C11×C3⋊D3C2×C1311yescharacteristic, complemented
24C3×C5×D3×C11C2×C1312yescomplemented
25C2×C3×C11×C13—32no—
26D3×C11×C13—32no—
27D3×C11×C13—61no—
28D3×C11×C13C5×D312yesdirect product factor
29C2×C5×D3×C13—32no—
30C5×C11×C13D3211yescharacteristic, direct product factor, Hall
31C2×C5×D3×C11—32no—
32C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
33C22×C11×C13—91noHall
34C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
35D32×C13C5×C1111yescharacteristic, direct product factor, Hall
36C3×C11×C13—21no—
37C3×C11×C13C2×C5×D312yescomplemented
38D32×C11C5×C1311yescharacteristic, direct product factor, Hall
39C2×C3×C5×C13—32no—
40C5×D3×C13—32no—
41C5×D3×C13—61no—
42C5×D3×C13D3×C1112yesdirect product factor
43C2×C3×C5×C11—32no—
44C5×D3×C11—32no—
45C5×D3×C11—61no—
46C5×D3×C11D3×C1312yesdirect product factor
47C2×C11×C13—32no—
48C2×C11×C13—91no—
49C22×C5×C13—91noHall
50C13×C3⋊D3C2×C5×C1111yescharacteristic, complemented
51C3×D3×C13C2×C5×C1112yescomplemented
52C22×C5×C11—91noHall
53C11×C3⋊D3C2×C5×C1311yescharacteristic, complemented
54C3×D3×C11C2×C5×C1312yescomplemented
55C3×C5×C13—21no—
56C3×C5×C13C2×D3×C1112yescomplemented
57C5×D32C11×C1311yescharacteristic, direct product factor, Hall
58C3×C5×C11—21no—
59C3×C5×C11C2×D3×C1312yescomplemented
60C2×D3×C13—32no—
61C11×C13C5×D3211yescharacteristic, direct product factor, Hall
62C2×D3×C11—32no—
63C2×C5×C13—32no—
64C2×C5×C13—91no—
65C32×C13C22×C5×C1111yescharacteristic, complemented, Hall
66C2×C5×C11—32no—
67C2×C5×C11—91no—
68C32×C11C22×C5×C1311yescharacteristic, complemented, Hall
69C5×C3⋊D3C2×C11×C1311yescharacteristic, complemented
70C3×C5×D3C2×C11×C1312yescomplemented
71C2×C3×C13—32no—
72D3×C13—32no—
73D3×C13—61no—
74D3×C13C5×D3×C1112yesdirect product factor
75C2×C3×C11—32no—
76D3×C11—32no—
77D3×C11—61no—
78D3×C11C5×D3×C1312yesdirect product factor
79C5×C13D32×C1111yescharacteristic, direct product factor, Hall
80C2×C5×D3—32no—
81C5×C11D32×C1311yescharacteristic, direct product factor, Hall
82C22×C13—91noHall
83C32×C5C22×C11×C1311yescharacteristic, complemented, Hall
84C22×C11—91noHall
85C3×C13—21no—
86C3×C13C2×C5×D3×C1112yescomplemented
87D32C5×C11×C1311yescharacteristic, direct product factor, Hall
88C3×C11—21no—
89C3×C11C2×C5×D3×C1312yescomplemented
90C2×C3×C5—32no—
91C5×D3—32no—
92C5×D3—61no—
93C5×D3D3×C11×C1312yesdirect product factor
94C2×C13—32no—
95C2×C13—91no—
96C2×C11—32no—
97C2×C11—91no—
98C22×C5—91noHall
99C3⋊D3C2×C5×C11×C1311yescharacteristic, complemented
100C3×D3C2×C5×C11×C1312yescomplemented
101C3×C5—21no—
102C3×C5C2×D3×C11×C1312yescomplemented
103C13C5×D32×C1111yescharacteristic, direct product factor, Sylow
104C2×D3—32no—
105C11C5×D32×C1311yescharacteristic, direct product factor, Sylow
106C2×C5—32no—
107C2×C5—91no—
108C32C22×C5×C11×C1311yescharacteristic, complemented, Sylow
109C2×C3—32no—
110D3—32no—
111D3—61no—
112D3C5×D3×C11×C1312yesdirect product factor
113C5D32×C11×C1311yescharacteristic, direct product factor, Sylow
114C22—91noSylow
115C3—21no—
116C3C2×C5×D3×C11×C1312yescomplemented
117C2—32no—
118C2—91no—
subgroupG/H
center, hypercenterC5×C11×C13D32
commutator, cosocle, hypocenterC32C22×C5×C11×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32
UCSC1 ◁ C5×C11×C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C11×C13C2semidirect
2. C5×C11×C13×C3⋊D3C2semidirect
4. C32×C5×C11×C13C22semidirect
5. D32×C11×C13C5direct (N × H)
8. C5×D3×C11×C13D3direct (N × H)
11. C11×C13×C3⋊D3C2×C5semidirect
12. C3×D3×C11×C13C2×C5semidirect
13. C5×D32×C13C11direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
16. C5×D32×C11C13direct (N × H)
20. C32×C11×C13C22×C5semidirect
21. C5×C13×C3⋊D3C2×C11semidirect
22. C3×C5×D3×C13C2×C11semidirect
23. C5×C11×C3⋊D3C2×C13semidirect
24. C3×C5×D3×C11C2×C13semidirect
28. D3×C11×C13C5×D3direct (N × H)
30. C5×C11×C13D32direct (N × H)
32. C32×C5×C13C22×C11semidirect
34. C32×C5×C11C22×C13semidirect
35. D32×C13C5×C11direct (N × H)
37. C3×C11×C13C2×C5×D3semidirect
38. D32×C11C5×C13direct (N × H)
42. C5×D3×C13D3×C11direct (N × H)
46. C5×D3×C11D3×C13direct (N × H)
50. C13×C3⋊D3C2×C5×C11semidirect
51. C3×D3×C13C2×C5×C11semidirect
53. C11×C3⋊D3C2×C5×C13semidirect
54. C3×D3×C11C2×C5×C13semidirect
56. C3×C5×C13C2×D3×C11semidirect
57. C5×D32C11×C13direct (N × H)
59. C3×C5×C11C2×D3×C13semidirect
61. C11×C13C5×D32direct (N × H)
65. C32×C13C22×C5×C11semidirect
68. C32×C11C22×C5×C13semidirect
69. C5×C3⋊D3C2×C11×C13semidirect
70. C3×C5×D3C2×C11×C13semidirect
74. D3×C13C5×D3×C11direct (N × H)
78. D3×C11C5×D3×C13direct (N × H)
79. C5×C13D32×C11direct (N × H)
81. C5×C11D32×C13direct (N × H)
83. C32×C5C22×C11×C13semidirect
86. C3×C13C2×C5×D3×C11semidirect
87. D32C5×C11×C13direct (N × H)
89. C3×C11C2×C5×D3×C13semidirect
93. C5×D3D3×C11×C13direct (N × H)
99. C3⋊D3C2×C5×C11×C13semidirect
100. C3×D3C2×C5×C11×C13semidirect
102. C3×C5C2×D3×C11×C13semidirect
103. C13C5×D32×C11direct (N × H)
105. C11C5×D32×C13direct (N × H)
108. C32C22×C5×C11×C13semidirect
112. D3C5×D3×C11×C13direct (N × H)
113. C5D32×C11×C13direct (N × H)
116. C3C2×C5×D3×C11×C13semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C11×C132
C5×C11×C13×C3⋊D32
C2×C5×D3×C11×C133
D32×C11×C135
C5×D32×C1311
C5×D32×C1113