Finite Group Databasebeta

← C5×D9×D85 #29505799

Subgroups — C5×D9×D85 #29505799

Order 15300.

144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 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×D765C211yesmaximal, characteristic, complemented
2C52×C17×D9C211yesmaximal, characteristic, complemented
3C5×C9×D85C211yesmaximal, characteristic, complemented
4C5×D3×D85—31nomaximal
5C52×C9×C17C2211yescharacteristic, complemented, Hall
6D9×D85C511yesmaximal, characteristic, direct product factor
7C5×D9×D17—51nomaximal
8C5×D255—31no—
9C52×D3×C17—31no—
10C3×C5×D85D311yescharacteristic
11C2×C5×D85—91noHall
12D765C2×C511yescharacteristic, complemented
13C5×D153—51no—
14C5×C17×D9—22no—
15C5×C17×D9D511yescharacteristic, complemented
16C5×C17×D9C2×C511yescharacteristic, complemented
17C9×D85C2×C511yescharacteristic, complemented
18C5×C9×D17—51no—
19C3×C52×C17C2×D311yescharacteristic
20D3×D85—31no—
21C5×D3×D17—151no—
22C5×D5×D9—171nomaximal, Hall
23C2×C52×C17—91no—
24C5×D85—91no—
25C5×D85D911yescharacteristic, direct product factor
26C5×C9×C17—22no—
27C5×C9×C17C2×D511yescharacteristic, complemented
28C5×C9×C17C22×C511yescharacteristic, complemented
29D9×D17—51noHall
30D255—31no—
31C5×D51—151no—
32C5×D3×C17—31no—
33C5×D3×C17—31no—
34C5×D3×C17—62no—
35C3×D85C5×D311yescharacteristic
36C3×C5×D17—51no—
37C5×D45—171no—
38C52×D9D1711yescharacteristic, complemented
39C5×C9×D5—171no—
40C52×C17C2×D911yescharacteristic, complemented, Hall
41C2×D85—91no—
42C2×C5×D17—451no—
43D153—51no—
44C9×D17—51no—
45C17×D9C5×D511yescharacteristic, complemented
46C5×D3×D5—511no—
47C3×C5×C17—22no—
48C3×C5×C17D3×D511yescharacteristic
49C3×C5×C17C2×C5×D311yescharacteristic
50C52×C9C2×D1711yescharacteristic, complemented, Hall
51D3×D17—151no—
52C2×C5×D9—851no—
53D5×D9—171no—
54C2×C5×C17—91no—
55C2×C5×C17—91no—
56C2×C5×C17—182no—
57D85—91no—
58D85C5×D911yescharacteristic, direct product factor
59C5×D17—51no—
60C5×D17—451no—
61C9×C17C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—511no—
63C52×D3—31no—
64C3×C5×D5—171no—
65D51—151no—
66C3×D17—51no—
67D3×C17—31no—
68C2×C5×D5—1531noHall
69C2×C5×C9—851no—
70D45—171no—
71C9×D5—171no—
72C5×D9—22no—
73C5×D9—851no—
74C5×D9C5×D1711yescharacteristic, complemented
75C5×D9D8511yescharacteristic, direct product factor
76C5×C17—22no—
77C5×C17D5×D911yescharacteristic, complemented
78C5×C17C2×C5×D911yescharacteristic, complemented
79C3×C52D3×D1711yescharacteristic
80C2×D17—451noHall
81C2×C5×D3—2551no—
82D3×D5—511no—
83C3×C17C5×D3×D511yescharacteristic
84C2×C52—91no—
85C5×D5—171no—
86C5×D5—1531no—
87C5×C9—22no—
88C5×C9C2×C5×D1711yescharacteristic, complemented
89C5×C9C2×D8511yescharacteristic, complemented
90C2×D9—851noHall
91C2×C17—91no—
92D17—51no—
93D17—451no—
94C2×C3×C5—851no—
95D15—511no—
96C3×D5—171no—
97C5×D3—31no—
98C5×D3—31no—
99C5×D3—62no—
100C5×D3—2551no—
101C52D9×D1711yescharacteristic, complemented, Sylow
102C22×C5—7651no—
103C2×D5—1531no—
104C2×C9—851no—
105D9—851no—
106D9C5×D8511yescharacteristic, direct product factor
107C17C5×D5×D911yescharacteristic, complemented, Sylow
108C3×C5—22no—
109C3×C5C5×D3×D1711yescharacteristic
110C3×C5D3×D8511yescharacteristic
111C2×D3—2551no—
112C2×C5—91no—
113C2×C5—91no—
114C2×C5—182no—
115C2×C5—851no—
116C2×C5—7651no—
117D5—171no—
118D5—1531no—
119C9C2×C5×D8511yescharacteristic, complemented, Sylow
120C2×C3—851no—
121D3—31no—
122D3—2551no—
123C5—22no—
124C5C5×D9×D1711yescharacteristic, complemented
125C5D9×D8511yescharacteristic, direct product factor
126C22—7651noSylow
127C3C5×D3×D8511yescharacteristic
128C2—91no—
129C2—851no—
130C2—7651no—
subgroupG/H
center, hypercenterC5D9×D85
commutator, cosocle, hypocenterC5×C9×C17C22×C5
FrattiniC3C5×D3×D85
FittingC52×C9×C17C22
socleC3×C52×C17C2×D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D765C2semidirect
2. C52×C17×D9C2semidirect
3. C5×C9×D85C2semidirect
5. C52×C9×C17C22semidirect
6. D9×D85C5direct (N × H)
12. D765C2×C5semidirect
15. C5×C17×D9D5semidirect
16. C5×C17×D9C2×C5semidirect
17. C9×D85C2×C5semidirect
25. C5×D85D9direct (N × H)
27. C5×C9×C17C2×D5semidirect
28. C5×C9×C17C22×C5semidirect
38. C52×D9D17semidirect
40. C52×C17C2×D9semidirect
45. C17×D9C5×D5semidirect
50. C52×C9C2×D17semidirect
58. D85C5×D9direct (N × H)
61. C9×C17C2×C5×D5semidirect
74. C5×D9C5×D17semidirect
75. C5×D9D85direct (N × H)
77. C5×C17D5×D9semidirect
78. C5×C17C2×C5×D9semidirect
88. C5×C9C2×C5×D17semidirect
89. C5×C9C2×D85semidirect
101. C52D9×D17semidirect
106. D9C5×D85direct (N × H)
107. C17C5×D5×D9semidirect
119. C9C2×C5×D85semidirect
124. C5C5×D9×D17semidirect
125. C5D9×D85direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D7652
C52×C17×D92
C5×C9×D852
C5×D3×D853
D9×D855
C5×D9×D175
C5×D5×D917