Finite Group Databasebeta

← C5×D85⋊(C3⋊D3) #29505995

Subgroups — C5×D85⋊(C3⋊D3) #29505995

Order 15300.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C5×C17×C3⋊D15C211yesmaximal, characteristic, complemented
2C52×C3⋊D51C211yesmaximal, characteristic, complemented
3C32×C5×D85C211yesmaximal, characteristic, complemented
4C5×D15⋊D17—34nomaximal
5C32×C52×C17C2211yescharacteristic, complemented, Hall
6D85⋊(C3⋊D3)C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D17—51nomaximal
8C5×C17×D15—34no—
9C52×D51—34no—
10C3×C5×D85D314yescomplemented
11C5×D5×D17—91noHall
12C17×C3⋊D15C2×C511yescharacteristic, complemented
13C5×C3⋊D51—22no—
14C5×C3⋊D51D511yescharacteristic, complemented
15C5×C3⋊D51C2×C511yescharacteristic, complemented
16C5×C17×C3⋊D3—51no—
17C32×D85C2×C511yescharacteristic, complemented
18C32×C5×D17—51no—
19C3×C52×C17C2×D314yescomplemented
20D15⋊D17—34no—
21C5×D3×D17—154no—
22C5×D5×C3⋊D3—171nomaximal, Hall
23C5×D85C3⋊D311yescharacteristic, complemented
24C5×D5×C17—91no—
25C52×D17—91no—
26C32×C5×C17—22no—
27C32×C5×C17C2×D511yescharacteristic, complemented
28C32×C5×C17C22×C511yescharacteristic, complemented
29C3⋊D3×D17—51noHall
30C17×D15—34no—
31C5×D51—34no—
32C5×D51—34no—
33C5×D51—68no—
34C5×D3×C17—154no—
35C3×D85C5×D314yescomplemented
36C3×C5×D17—54no—
37C5×C3⋊D15D1711yescharacteristic, complemented
38C52×C3⋊D3—171no—
39C32×C5×D5—171no—
40C52×C17C2×C3⋊D311yescharacteristic, complemented, Hall
41C2×C5×D17—451no—
42D5×D17—91no—
43C3⋊D51C5×D511yescharacteristic, complemented
44C17×C3⋊D3—51no—
45C32×D17—51no—
46C5×D3×D5—514no—
47C3×C5×C17—28no—
48C3×C5×C17D3×D514yescomplemented
49C3×C5×C17C2×C5×D314yescomplemented
50C32×C52C2×D1711yescharacteristic, complemented, Hall
51D3×D17—154no—
52C2×C5×C3⋊D3—851no—
53D5×C3⋊D3—171no—
54C2×C5×C17—451no—
55D85C5×C3⋊D311yescharacteristic, complemented
56C5×D17—51no—
57C5×D17—91no—
58C5×D17—91no—
59C5×D17—182no—
60D5×C17—91no—
61C32×C17C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—34no—
63C52×D3—514no—
64C3×C5×D5—174no—
65D51—34no—
66C3×D17—54no—
67D3×C17—154no—
68C2×C5×D5—1531noHall
69C2×C32×C5—851no—
70C3⋊D15C5×D1711yescharacteristic, complemented
71C5×C3⋊D3—51no—
72C5×C3⋊D3—171no—
73C5×C3⋊D3—171no—
74C5×C3⋊D3—342no—
75C32×D5—171no—
76C5×C17—22no—
77C5×C17D5×C3⋊D311yescharacteristic, complemented
78C5×C17C2×C5×C3⋊D311yescharacteristic, complemented
79C3×C52D3×D1714yescomplemented
80C2×D17—451noHall
81C2×C5×D3—2554no—
82D3×D5—514no—
83C3×C17C5×D3×D514yescomplemented
84C2×C52—1531no—
85C5×D5—91no—
86C5×D5—171no—
87C32×C5—22no—
88C32×C5D5×D1711yescharacteristic, complemented
89C32×C5C2×C5×D1711yescharacteristic, complemented
90C2×C3⋊D3—851noHall
91C2×C17—451no—
92D17—51no—
93D17—91no—
94C2×C3×C5—854no—
95D15—34no—
96C3×D5—174no—
97C5×D3—154no—
98C5×D3—514no—
99C5×D3—514no—
100C5×D3—1028no—
101C52C3⋊D3×D1711yescharacteristic, complemented, Sylow
102C22×C5—7651no—
103C2×D5—1531no—
104C2×C32—851no—
105C3⋊D3—51no—
106C3⋊D3—171no—
107C17C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
108C3×C5—28no—
109C3×C5C5×D3×D1714yescomplemented
110C3×C5D15⋊D1714yescomplemented
111C2×D3—2554no—
112C2×C5—451no—
113C2×C5—3062no—
114C2×C5—851no—
115C2×C5—1531no—
116C2×C5—1531no—
117D5—91no—
118D5—171no—
119C32C5×D5×D1711yescharacteristic, complemented, Sylow
120C2×C3—854no—
121D3—154no—
122D3—514no—
123C5—22no—
124C5C5×C3⋊D3×D1711yescharacteristic, complemented
125C5D85⋊(C3⋊D3)11yescharacteristic, direct product factor
126C22—7651noSylow
127C3C5×D15⋊D1714yescomplemented
128C2—451no—
129C2—851no—
130C2—1531no—
subgroupG/H
center, hypercenterC5D85⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C17C22×C5
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C5×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C17×C3⋊D15C2semidirect
2. C52×C3⋊D51C2semidirect
3. C32×C5×D85C2semidirect
5. C32×C52×C17C22semidirect
6. D85⋊(C3⋊D3)C5direct (N × H)
10. C3×C5×D85D3semidirect
12. C17×C3⋊D15C2×C5semidirect
14. C5×C3⋊D51D5semidirect
15. C5×C3⋊D51C2×C5semidirect
17. C32×D85C2×C5semidirect
19. C3×C52×C17C2×D3semidirect
23. C5×D85C3⋊D3semidirect
27. C32×C5×C17C2×D5semidirect
28. C32×C5×C17C22×C5semidirect
35. C3×D85C5×D3semidirect
37. C5×C3⋊D15D17semidirect
40. C52×C17C2×C3⋊D3semidirect
43. C3⋊D51C5×D5semidirect
48. C3×C5×C17D3×D5semidirect
49. C3×C5×C17C2×C5×D3semidirect
50. C32×C52C2×D17semidirect
55. D85C5×C3⋊D3semidirect
61. C32×C17C2×C5×D5semidirect
70. C3⋊D15C5×D17semidirect
77. C5×C17D5×C3⋊D3semidirect
78. C5×C17C2×C5×C3⋊D3semidirect
79. C3×C52D3×D17semidirect
83. C3×C17C5×D3×D5semidirect
88. C32×C5D5×D17semidirect
89. C32×C5C2×C5×D17semidirect
101. C52C3⋊D3×D17semidirect
107. C17C5×D5×C3⋊D3semidirect
109. C3×C5C5×D3×D17semidirect
110. C3×C5D15⋊D17semidirect
119. C32C5×D5×D17semidirect
124. C5C5×C3⋊D3×D17semidirect
125. C5D85⋊(C3⋊D3)direct (N × H)
127. C3C5×D15⋊D17semidirect

Maximal subgroups

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

subgroupindex
C5×C17×C3⋊D152
C52×C3⋊D512
C32×C5×D852
C5×D15⋊D173
D85⋊(C3⋊D3)5
C5×C3⋊D3×D175
C5×D5×C3⋊D317