Finite Group Databasebeta

← D5×C3⋊D429 #38788287

Subgroups — D5×C3⋊D429 #38788287

Order 25740.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×D5×C11×C13C211yesmaximal, characteristic, complemented
2C5×C3⋊D429C211yesmaximal, characteristic, complemented
3C3⋊D2145C211yesmaximal, characteristic, complemented
4D5×D429—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C3⋊D429—51nomaximal, Hall
7D2145—34no—
8C5×D429—34no—
9C3×D5×C11×C13D314yescomplemented
10D5×D143—91noHall
11C3⋊D429—51no—
12C3⋊D429D511yescharacteristic, direct product factor
13C2×C32×C11×C13—51no—
14D5×C3⋊D39—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D5×C3⋊D33—131nomaximal, Hall
17C2×D429—154no—
18D715—91no—
19D5×C11×C13C3⋊D311yescharacteristic, complemented
20C5×D143—91no—
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C3⋊D195—111no—
23C5×C3⋊D39—111no—
24C32×D5×C13D1111yescharacteristic, complemented
25C3⋊D165—131no—
26C5×C3⋊D33—131no—
27C32×D5×C11D1311yescharacteristic, complemented
28C2×C3×C11×C13—54no—
29D429—34no—
30D429—154no—
31D5×D39—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D5×D33—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35C2×D143—451noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C2×C3⋊D39—551noHall
38C3×C11×C13D3×D514yescomplemented
39C2×C3⋊D33—651noHall
40D195—334no—
41C5×D39—334no—
42C3×D5×C13D3314yescomplemented
43D165—394no—
44C5×D33—394no—
45C3×D5×C11D3914yescomplemented
46C2×C11×C13—51no—
47D143—91no—
48D143—451no—
49D5×D13—991noHall
50C2×C32×C13—51no—
51C3⋊D39—111no—
52C3⋊D39—551no—
53D5×D11—1171noHall
54C2×C32×C11—51no—
55C3⋊D33—131no—
56C3⋊D33—651no—
57C3×C5×C13C2×D3314yescomplemented
58D5×C3⋊D3—1431noHall
59C3×C5×C11C2×D3914yescomplemented
60C2×D39—1654no—
61C11×C13D5×C3⋊D311yescharacteristic, complemented, Hall
62C2×D33—1954no—
63D65—991no—
64C5×D13—991no—
65D5×C13C3⋊D3311yescharacteristic, complemented
66C32×C13D5×D1111yescharacteristic, complemented, Hall
67D55—1171no—
68C5×D11—1171no—
69D5×C11C3⋊D3911yescharacteristic, complemented
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C3⋊D15—1431no—
72C5×C3⋊D3—1431no—
73C32×D5D14311yescharacteristic, complemented
74C2×C3×C13—54no—
75D39—334no—
76D39—1654no—
77C2×C3×C11—54no—
78D33—394no—
79D33—1954no—
80C5×C13C2×C3⋊D3311yescharacteristic, complemented, Hall
81D3×D5—4294no—
82C5×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
83C2×D13—4951noHall
84C32×C5C2×D14311yescharacteristic, complemented, Hall
85C2×D11—5851noHall
86C3×C13D5×D3314yescomplemented
87C2×C3⋊D3—7151noHall
88C3×C11D5×D3914yescomplemented
89D15—4294no—
90C3×D5D42914yescomplemented
91C5×D3—4294no—
92C2×C13—51no—
93D13—991no—
94D13—4951no—
95C2×C11—51no—
96D11—5851no—
97D11—1171no—
98C2×D5—12871noHall
99C2×C32—51no—
100C3⋊D3—1431no—
101C3⋊D3—7151no—
102C3×C5C2×D42914yescomplemented
103C13D5×C3⋊D3311yescharacteristic, complemented, Sylow
104C2×D3—21454no—
105C11D5×C3⋊D3911yescharacteristic, complemented, Sylow
106C2×C5—12871no—
107D5—12871no—
108D5C3⋊D42911yescharacteristic, direct product factor
109C32D5×D14311yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—21454no—
112D3—4294no—
113C5C2×C3⋊D42911yescharacteristic, complemented, Sylow
114C22—64351noSylow
115C3D5×D42914yescomplemented
116C2—51no—
117C2—12871no—
118C2—64351no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C13C22
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C13C2semidirect
2. C5×C3⋊D429C2semidirect
3. C3⋊D2145C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×D5×C11×C13D3semidirect
12. C3⋊D429D5direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
19. D5×C11×C13C3⋊D3semidirect
21. C32×C11×C13C2×D5semidirect
24. C32×D5×C13D11semidirect
27. C32×D5×C11D13semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13D3×D5semidirect
42. C3×D5×C13D33semidirect
45. C3×D5×C11D39semidirect
57. C3×C5×C13C2×D33semidirect
59. C3×C5×C11C2×D39semidirect
61. C11×C13D5×C3⋊D3semidirect
65. D5×C13C3⋊D33semidirect
66. C32×C13D5×D11semidirect
69. D5×C11C3⋊D39semidirect
70. C32×C11D5×D13semidirect
73. C32×D5D143semidirect
80. C5×C13C2×C3⋊D33semidirect
82. C5×C11C2×C3⋊D39semidirect
84. C32×C5C2×D143semidirect
86. C3×C13D5×D33semidirect
88. C3×C11D5×D39semidirect
90. C3×D5D429semidirect
102. C3×C5C2×D429semidirect
103. C13D5×C3⋊D33semidirect
105. C11D5×C3⋊D39semidirect
108. D5C3⋊D429direct (N × H)
109. C32D5×D143semidirect
113. C5C2×C3⋊D429semidirect
115. C3D5×D429semidirect

Maximal subgroups

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

subgroupindex
C32×D5×C11×C132
C5×C3⋊D4292
C3⋊D21452
D5×D4293
C2×C3⋊D4295
D5×C3⋊D3911
D5×C3⋊D3313