Finite Group Databasebeta

← C5×C3⋊D3×D145 #39908190

Subgroups — C5×C3⋊D3×D145 #39908190

Order 26100.

288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 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×D145C211yesmaximal, characteristic, complemented
2C52×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×C3⋊D435C211yesmaximal, characteristic, complemented
4C5×D3×D145—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6C3⋊D3×D145C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D29—51nomaximal
8C5×D435—34no—
9C52×D3×C29—34no—
10C3×C5×D145D314yescomplemented
11C2×C5×D145—91noHall
12C3⋊D435C2×C511yescharacteristic, complemented
13C5×C3⋊D87—51no—
14C5×C3⋊D3×C29—22no—
15C5×C3⋊D3×C29D511yescharacteristic, complemented
16C5×C3⋊D3×C29C2×C511yescharacteristic, complemented
17C32×D145C2×C511yescharacteristic, complemented
18C32×C5×D29—51no—
19C3×C52×C29C2×D314yescomplemented
20D3×D145—34no—
21C5×D3×D29—154no—
22C2×C52×C29—91no—
23C5×D145—91no—
24C5×D145C3⋊D311yescharacteristic, direct product factor
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C22×C511yescharacteristic, complemented
28C3⋊D3×D29—51noHall
29C5×D5×C3⋊D3—291nomaximal, Hall
30D435—34no—
31C5×D87—154no—
32C5×D3×C29—34no—
33C5×D3×C29—34no—
34C5×D3×C29—68no—
35C3×D145C5×D314yescomplemented
36C3×C5×D29—54no—
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D145—91no—
39C2×C5×D29—451no—
40C3⋊D87—51no—
41C3⋊D3×C29C5×D511yescharacteristic, complemented
42C32×D29—51no—
43C5×C3⋊D15—291no—
44C52×C3⋊D3D2911yescharacteristic, complemented
45C32×C5×D5—291no—
46C3×C5×C29—28no—
47C3×C5×C29D3×D514yescomplemented
48C3×C5×C29C2×C5×D314yescomplemented
49D3×D29—154no—
50C5×D3×D5—874no—
51C2×C5×C29—91no—
52C2×C5×C29—91no—
53C2×C5×C29—182no—
54D145—91no—
55D145C5×C3⋊D311yescharacteristic, direct product factor
56C5×D29—51no—
57C5×D29—451no—
58C32×C29C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60C2×C5×C3⋊D3—1451no—
61D5×C3⋊D3—291no—
62D87—154no—
63C3×D29—54no—
64D3×C29—34no—
65C5×D15—874no—
66C52×D3—34no—
67C3×C5×D5—294no—
68C5×C29—22no—
69C5×C29D5×C3⋊D311yescharacteristic, complemented
70C5×C29C2×C5×C3⋊D311yescharacteristic, complemented
71C2×D29—451noHall
72C2×C5×D5—2611noHall
73C2×C32×C5—1451no—
74C3⋊D15—291no—
75C5×C3⋊D3—22no—
76C5×C3⋊D3—1451no—
77C5×C3⋊D3C5×D2911yescharacteristic, complemented
78C5×C3⋊D3D14511yescharacteristic, direct product factor
79C32×D5—291no—
80C3×C29C5×D3×D514yescomplemented
81C3×C52D3×D2914yescomplemented
82C2×C5×D3—4354no—
83D3×D5—874no—
84C2×C29—91no—
85D29—51no—
86D29—451no—
87C2×C52—91no—
88C5×D5—2611no—
89C5×D5—291no—
90C32×C5—22no—
91C32×C5C2×C5×D2911yescharacteristic, complemented
92C32×C5C2×D14511yescharacteristic, complemented
93C2×C3⋊D3—1451noHall
94C2×C3×C5—1454no—
95D15—874no—
96C3×D5—294no—
97C5×D3—34no—
98C5×D3—34no—
99C5×D3—68no—
100C5×D3—4354no—
101C29C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
102C52C3⋊D3×D2911yescharacteristic, complemented, Sylow
103C22×C5—13051no—
104C2×D5—2611no—
105C2×C32—1451no—
106C3⋊D3—1451no—
107C3⋊D3C5×D14511yescharacteristic, direct product factor
108C3×C5—28no—
109C3×C5C5×D3×D2914yescomplemented
110C3×C5D3×D14514yescomplemented
111C2×D3—4354no—
112C2×C5—91no—
113C2×C5—91no—
114C2×C5—182no—
115C2×C5—13051no—
116C2×C5—1451no—
117D5—2611no—
118D5—291no—
119C32C2×C5×D14511yescharacteristic, complemented, Sylow
120C2×C3—1454no—
121D3—34no—
122D3—4354no—
123C5—22no—
124C5C5×C3⋊D3×D2911yescharacteristic, complemented
125C5C3⋊D3×D14511yescharacteristic, direct product factor
126C22—13051noSylow
127C3C5×D3×D14514yescomplemented
128C2—91no—
129C2—13051no—
130C2—1451no—
subgroupG/H
center, hypercenterC5C3⋊D3×D145
commutator, cosocle, hypocenterC32×C5×C29C22×C5
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D145C2semidirect
2. C52×C3⋊D3×C29C2semidirect
3. C5×C3⋊D435C2semidirect
5. C32×C52×C29C22semidirect
6. C3⋊D3×D145C5direct (N × H)
10. C3×C5×D145D3semidirect
12. C3⋊D435C2×C5semidirect
15. C5×C3⋊D3×C29D5semidirect
16. C5×C3⋊D3×C29C2×C5semidirect
17. C32×D145C2×C5semidirect
19. C3×C52×C29C2×D3semidirect
24. C5×D145C3⋊D3direct (N × H)
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C22×C5semidirect
35. C3×D145C5×D3semidirect
37. C52×C29C2×C3⋊D3semidirect
41. C3⋊D3×C29C5×D5semidirect
44. C52×C3⋊D3D29semidirect
47. C3×C5×C29D3×D5semidirect
48. C3×C5×C29C2×C5×D3semidirect
55. D145C5×C3⋊D3direct (N × H)
58. C32×C29C2×C5×D5semidirect
59. C32×C52C2×D29semidirect
69. C5×C29D5×C3⋊D3semidirect
70. C5×C29C2×C5×C3⋊D3semidirect
77. C5×C3⋊D3C5×D29semidirect
78. C5×C3⋊D3D145direct (N × H)
80. C3×C29C5×D3×D5semidirect
81. C3×C52D3×D29semidirect
91. C32×C5C2×C5×D29semidirect
92. C32×C5C2×D145semidirect
101. C29C5×D5×C3⋊D3semidirect
102. C52C3⋊D3×D29semidirect
107. C3⋊D3C5×D145direct (N × H)
109. C3×C5C5×D3×D29semidirect
110. C3×C5D3×D145semidirect
119. C32C2×C5×D145semidirect
124. C5C5×C3⋊D3×D29semidirect
125. C5C3⋊D3×D145direct (N × H)
127. C3C5×D3×D145semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1452
C52×C3⋊D3×C292
C5×C3⋊D4352
C5×D3×D1453
C3⋊D3×D1455
C5×C3⋊D3×D295
C5×D5×C3⋊D329