Finite Group Databasebeta

← C5×(C3⋊D3)⋊D143 #38788231

Subgroups — C5×(C3⋊D3)⋊D143 #38788231

Order 25740.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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×D429C212yesmaximal, complemented
2C5×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×D3×D143—32nomaximal
4C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D143C511yesmaximal, characteristic, direct product factor, Hall
6C5×D429D312yescomplemented
7C5×D3×C11×C13—32no—
8C5×D3×C11×C13—61no—
9C3×C5×D143—32no—
10C2×C5×D143—91noHall
11C11×C13×C3⋊D3C2×C511yescharacteristic, complemented
12C3×D429C2×C512yescomplemented
13C5×(C3⋊D3)⋊D13—111nomaximal, Hall
14C3×C5×C11×C13—21no—
15C3×C5×C11×C13C2×D312yescomplemented
16C5×(C3⋊D3)⋊D11—131nomaximal, Hall
17D3×D143—32no—
18C2×C5×C11×C13—91no—
19C5×D143—32no—
20C32×C11×C13C22×C511yescharacteristic, complemented, Hall
21C5×C13×C3⋊D3D1111yescharacteristic, complemented
22C3×C5×D39—112no—
23C5×C11×C3⋊D3D1311yescharacteristic, complemented
24C3×C5×D33—132no—
25D429C5×D312yescomplemented
26D3×C11×C13—32no—
27D3×C11×C13—61no—
28C3×D143—32no—
29C5×D3×D13—332no—
30C5×C11×C13D3211yescharacteristic, complemented, Hall
31C5×D3×D11—392no—
32C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
33C2×D143—91noHall
34C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
35(C3⋊D3)⋊D13—111noHall
36C3×C11×C13—21no—
37C3×C11×C13C2×C5×D312yescomplemented
38(C3⋊D3)⋊D11—131noHall
39C5×D39—112no—
40C5×D3×C13—32no—
41C5×D3×C13—61no—
42C3×C5×D13—332no—
43C5×D33—132no—
44C5×D3×C11—32no—
45C5×D3×C11—61no—
46C3×C5×D11—392no—
47C2×C11×C13—91no—
48D143—32no—
49C2×C5×D13—991noHall
50C13×C3⋊D3C5×D1111yescharacteristic, complemented
51C3×D39—112no—
52C2×C5×D11—1171noHall
53C11×C3⋊D3C5×D1311yescharacteristic, complemented
54C3×D33—132no—
55C3×C5×C13—21no—
56C3×C5×C13D3×D1112yescomplemented
57C5×D32—1431noHall
58C3×C5×C11—21no—
59C3×C5×C11D3×D1312yescomplemented
60D3×D13—332no—
61C11×C13C5×D3211yescharacteristic, complemented, Hall
62D3×D11—392no—
63C2×C5×C13—91no—
64C5×D13—332no—
65C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
66C2×C5×C11—91no—
67C5×D11—392no—
68C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
69C5×C3⋊D3D14311yescharacteristic, complemented
70C3×C5×D3—1432no—
71D39—112no—
72C3×D13—332no—
73D3×C13—32no—
74D3×C13—61no—
75D33—132no—
76C3×D11—392no—
77D3×C11—32no—
78D3×C11—61no—
79C5×C13(C3⋊D3)⋊D1111yescharacteristic, complemented, Hall
80C2×C5×D3—4292no—
81C5×C11(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
82C2×D13—991noHall
83C32×C5C2×D14311yescharacteristic, complemented, Hall
84C2×D11—1171noHall
85C3×C13—21no—
86C3×C13C5×D3×D1112yescomplemented
87D32—1431noHall
88C3×C11—21no—
89C3×C11C5×D3×D1312yescomplemented
90C2×C3×C5—4292no—
91C5×D3—32no—
92C5×D3—61no—
93C5×D3—1432no—
94C2×C13—91no—
95D13—332no—
96C2×C11—91no—
97D11—392no—
98C22×C5—12871noHall
99C3⋊D3C5×D14311yescharacteristic, complemented
100C3×D3—1432no—
101C3×C5—21no—
102C3×C5D3×D14312yescomplemented
103C13C5×(C3⋊D3)⋊D1111yescharacteristic, complemented, Sylow
104C2×D3—4292no—
105C11C5×(C3⋊D3)⋊D1311yescharacteristic, complemented, Sylow
106C2×C5—91no—
107C2×C5—4292no—
108C32C2×C5×D14311yescharacteristic, complemented, Sylow
109C2×C3—4292no—
110D3—32no—
111D3—61no—
112D3—1432no—
113C5(C3⋊D3)⋊D14311yescharacteristic, direct product factor, Sylow
114C22—12871noSylow
115C3—21no—
116C3C5×D3×D14312yescomplemented
117C2—91no—
118C2—4292no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D143
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D429C2semidirect
2. C5×C11×C13×C3⋊D3C2semidirect
4. C32×C5×C11×C13C22semidirect
5. (C3⋊D3)⋊D143C5direct (N × H)
6. C5×D429D3semidirect
11. C11×C13×C3⋊D3C2×C5semidirect
12. C3×D429C2×C5semidirect
15. C3×C5×C11×C13C2×D3semidirect
20. C32×C11×C13C22×C5semidirect
21. C5×C13×C3⋊D3D11semidirect
23. C5×C11×C3⋊D3D13semidirect
25. D429C5×D3semidirect
30. C5×C11×C13D32semidirect
32. C32×C5×C13C2×D11semidirect
34. C32×C5×C11C2×D13semidirect
37. C3×C11×C13C2×C5×D3semidirect
50. C13×C3⋊D3C5×D11semidirect
53. C11×C3⋊D3C5×D13semidirect
56. C3×C5×C13D3×D11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13C5×D32semidirect
65. C32×C13C2×C5×D11semidirect
68. C32×C11C2×C5×D13semidirect
69. C5×C3⋊D3D143semidirect
79. C5×C13(C3⋊D3)⋊D11semidirect
81. C5×C11(C3⋊D3)⋊D13semidirect
83. C32×C5C2×D143semidirect
86. C3×C13C5×D3×D11semidirect
89. C3×C11C5×D3×D13semidirect
99. C3⋊D3C5×D143semidirect
102. C3×C5D3×D143semidirect
103. C13C5×(C3⋊D3)⋊D11semidirect
105. C11C5×(C3⋊D3)⋊D13semidirect
108. C32C2×C5×D143semidirect
113. C5(C3⋊D3)⋊D143direct (N × H)
116. C3C5×D3×D143semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4292
C5×C11×C13×C3⋊D32
C5×D3×D1433
(C3⋊D3)⋊D1435
C5×(C3⋊D3)⋊D1311
C5×(C3⋊D3)⋊D1113