Finite Group Databasebeta

← C5×D5×C17×D9 #29505797

Subgroups — C5×D5×C17×D9 #29505797

Order 15300.

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 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×D45C211yesmaximal, characteristic, complemented
2C52×C17×D9C211yesmaximal, characteristic, complemented
3C5×C9×D5×C17C211yesmaximal, characteristic, complemented
4C5×D3×D5×C17—31nomaximal
5C52×C9×C17C2211yescharacteristic, complemented, Hall
6C2×C5×C17×D9—51nomaximal
7D5×C17×D9C511yesmaximal, characteristic, direct product factor
8C5×C17×D15—31no—
9C52×D3×C17—31no—
10C3×C5×D5×C17D311yescharacteristic
11C2×C5×D5×C17—91noHall
12C2×C5×C9×C17—51no—
13C17×D45C2×C511yescharacteristic, complemented
14C5×C17×D9—22no—
15C5×C17×D9—51no—
16C5×C17×D9D511yescharacteristic, direct product factor
17C5×C17×D9C2×C511yescharacteristic, complemented
18C9×D5×C17C2×C511yescharacteristic, complemented
19C3×C52×C17C2×D311yescharacteristic
20C2×C5×D3×C17—151no—
21D3×D5×C17—31no—
22C5×D5×D9C1711yesmaximal, characteristic, direct product factor, Hall
23C2×C52×C17—91no—
24C5×D5×C17—91no—
25C5×D5×C17D911yescharacteristic, direct product factor
26C5×C9×C17—22no—
27C5×C9×C17C2×D511yescharacteristic, complemented
28C5×C9×C17C22×C511yescharacteristic, complemented
29C2×C17×D9—51noHall
30C2×C3×C5×C17—51no—
31C17×D15—31no—
32C5×D3×C17—31no—
33C5×D3×C17—31no—
34C5×D3×C17—62no—
35C5×D3×C17—151no—
36C3×D5×C17C5×D311yescharacteristic
37C5×D45C2×C1711yescharacteristic, complemented
38C52×D9C2×C1711yescharacteristic, complemented
39C5×C9×D5C2×C1711yescharacteristic, complemented
40C52×C17C2×D911yescharacteristic, complemented, Hall
41C22×C5×C17—451no—
42C2×D5×C17—91no—
43C2×C9×C17—51no—
44C17×D9—51no—
45C17×D9C5×D511yescharacteristic, direct product factor
46C5×D3×D5—31no—
47C3×C5×C17—22no—
48C3×C5×C17D3×D511yescharacteristic
49C3×C5×C17C2×C5×D311yescharacteristic
50C52×C9C22×C1711yescharacteristic, complemented, Hall
51C2×D3×C17—151no—
52C2×C5×D9—51no—
53D5×D9C5×C1711yescharacteristic, direct product factor
54C2×C5×C17—51no—
55C2×C5×C17—91no—
56C2×C5×C17—91no—
57C2×C5×C17—182no—
58C2×C5×C17—451no—
59D5×C17—91no—
60D5×C17C5×D911yescharacteristic, direct product factor
61C9×C17C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—31no—
63C52×D3—31no—
64C3×C5×D5D3×C1711yescharacteristic
65C2×C3×C17—51no—
66D3×C17—31no—
67D3×C17—151no—
68C2×C5×D5—91noHall
69C2×C5×C9—51no—
70D45C2×C5×C1711yescharacteristic, complemented
71C9×D5C2×C5×C1711yescharacteristic, complemented
72C5×D9—22no—
73C5×D9—51no—
74C5×D9D5×C1711yescharacteristic, direct product factor
75C5×D9C2×C5×C1711yescharacteristic, complemented
76C5×C17—22no—
77C5×C17D5×D911yescharacteristic, direct product factor
78C5×C17C2×C5×D911yescharacteristic, complemented
79C3×C52C2×D3×C1711yescharacteristic
80C22×C17—451noHall
81C2×C5×D3—151no—
82D3×D5—31no—
83C3×C17C5×D3×D511yescharacteristic
84C2×C52—91no—
85C5×D5—91no—
86C5×D5C17×D911yescharacteristic, direct product factor
87C5×C9—22no—
88C5×C9C2×D5×C1711yescharacteristic, complemented
89C5×C9C22×C5×C1711yescharacteristic, complemented
90C2×D9—51noHall
91C2×C17—51no—
92C2×C17—91no—
93C2×C17—451no—
94C2×C3×C5—51no—
95D15—31no—
96C3×D5C5×D3×C1711yescharacteristic
97C5×D3—31no—
98C5×D3—31no—
99C5×D3—62no—
100C5×D3—151no—
101C52C2×C17×D911yescharacteristic, complemented, Sylow
102C22×C5—451no—
103C2×D5—91no—
104C2×C9—51no—
105D9—51no—
106D9C5×D5×C1711yescharacteristic, direct product factor
107C17C5×D5×D911yescharacteristic, direct product factor, Sylow
108C3×C5—22no—
109C3×C5D3×D5×C1711yescharacteristic
110C3×C5C2×C5×D3×C1711yescharacteristic
111C2×D3—151no—
112C2×C5—51no—
113C2×C5—91no—
114C2×C5—91no—
115C2×C5—182no—
116C2×C5—451no—
117D5—91no—
118D5C5×C17×D911yescharacteristic, direct product factor
119C9C2×C5×D5×C1711yescharacteristic, complemented, Sylow
120C2×C3—51no—
121D3—31no—
122D3—151no—
123C5—22no—
124C5D5×C17×D911yescharacteristic, direct product factor
125C5C2×C5×C17×D911yescharacteristic, complemented
126C22—451noSylow
127C3C5×D3×D5×C1711yescharacteristic
128C2—51no—
129C2—91no—
130C2—451no—
subgroupG/H
center, hypercenterC5×C17D5×D9
commutator, cosocle, hypocenterC5×C9C22×C5×C17
FrattiniC3C5×D3×D5×C17
FittingC52×C9×C17C22
socleC3×C52×C17C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C5×C17

Complements

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

NH ≅ G/Ntype
1. C5×C17×D45C2semidirect
2. C52×C17×D9C2semidirect
3. C5×C9×D5×C17C2semidirect
5. C52×C9×C17C22semidirect
7. D5×C17×D9C5direct (N × H)
13. C17×D45C2×C5semidirect
16. C5×C17×D9D5direct (N × H)
17. C5×C17×D9C2×C5semidirect
18. C9×D5×C17C2×C5semidirect
22. C5×D5×D9C17direct (N × H)
25. C5×D5×C17D9direct (N × H)
27. C5×C9×C17C2×D5semidirect
28. C5×C9×C17C22×C5semidirect
37. C5×D45C2×C17semidirect
38. C52×D9C2×C17semidirect
39. C5×C9×D5C2×C17semidirect
40. C52×C17C2×D9semidirect
45. C17×D9C5×D5direct (N × H)
50. C52×C9C22×C17semidirect
53. D5×D9C5×C17direct (N × H)
60. D5×C17C5×D9direct (N × H)
61. C9×C17C2×C5×D5semidirect
70. D45C2×C5×C17semidirect
71. C9×D5C2×C5×C17semidirect
74. C5×D9D5×C17direct (N × H)
75. C5×D9C2×C5×C17semidirect
77. C5×C17D5×D9direct (N × H)
78. C5×C17C2×C5×D9semidirect
86. C5×D5C17×D9direct (N × H)
88. C5×C9C2×D5×C17semidirect
89. C5×C9C22×C5×C17semidirect
101. C52C2×C17×D9semidirect
106. D9C5×D5×C17direct (N × H)
107. C17C5×D5×D9direct (N × H)
118. D5C5×C17×D9direct (N × H)
119. C9C2×C5×D5×C17semidirect
124. C5D5×C17×D9direct (N × H)
125. C5C2×C5×C17×D9semidirect

Maximal subgroups

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

subgroupindex
C5×C17×D452
C52×C17×D92
C5×C9×D5×C172
C5×D3×D5×C173
C2×C5×C17×D95
D5×C17×D95
C5×D5×D917