Finite Group Databasebeta

← C5×D17×D45 #29505796

Subgroups — C5×D17×D45 #29505796

Order 15300.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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
2C5×C17×D45C211yesmaximal, characteristic, complemented
3C52×C9×D17C211yesmaximal, characteristic, complemented
4C5×D15×D17—31nomaximal
5C52×C9×C17C2211yescharacteristic, complemented, Hall
6D17×D45C511yesmaximal, characteristic, direct product factor
7C5×D9×D17—51nomaximal
8C5×D255—31no—
9C5×C17×D15—31no—
10C3×C52×D17D311yescharacteristic
11C5×D5×D17—91noHall
12D765C2×C511yescharacteristic, complemented
13C17×D45C2×C511yescharacteristic, complemented
14C5×D153—51no—
15C5×C17×D9—51no—
16C5×C9×D17—22no—
17C5×C9×D17D511yescharacteristic, complemented
18C5×C9×D17C2×C511yescharacteristic, complemented
19C3×C52×C17C2×D311yescharacteristic
20D15×D17—31no—
21C5×D3×D17—151no—
22C2×C5×D45—171nomaximal, Hall
23C5×D85—91no—
24C5×D5×C17—91no—
25C52×D17D911yescharacteristic, complemented
26C5×C9×C17—22no—
27C5×C9×C17C2×D511yescharacteristic, complemented
28C5×C9×C17C22×C511yescharacteristic, complemented
29D9×D17—51noHall
30D255—31no—
31C17×D15—31no—
32C5×D51—151no—
33C5×D3×C17—151no—
34C3×C5×D17—22no—
35C3×C5×D17C5×D311yescharacteristic
36C3×C5×D17D1511yescharacteristic
37C2×C52×C9—171no—
38C5×D45—171no—
39C5×D45D1711yescharacteristic, direct product factor
40C52×C17C2×D911yescharacteristic, complemented, Hall
41C2×C5×D17—451no—
42D5×D17—91no—
43D153—51no—
44C9×D17C5×D511yescharacteristic, complemented
45C17×D9—51no—
46C2×C5×D15—511no—
47C3×C5×C17—22no—
48C3×C5×C17C2×C5×D311yescharacteristic
49C3×C5×C17C2×D1511yescharacteristic
50C52×C9C2×D1711yescharacteristic, complemented, Hall
51D3×D17—151no—
52C2×D45—171no—
53C2×C5×D9—851no—
54C2×C5×C17—451no—
55D85—91no—
56C5×D17—22no—
57C5×D17—451no—
58C5×D17C5×D911yescharacteristic, complemented
59C5×D17D4511yescharacteristic, direct product factor
60D5×C17—91no—
61C9×C17C2×C5×D511yescharacteristic, complemented, Hall
62C2×C3×C52—171no—
63C5×D15—31no—
64C5×D15—511no—
65D51—151no—
66C3×D17C5×D1511yescharacteristic
67D3×C17—151no—
68C2×C5×D5—1531noHall
69C2×C5×C9—171no—
70C2×C5×C9—171no—
71C2×C5×C9—342no—
72D45—171no—
73D45C5×D1711yescharacteristic, direct product factor
74C5×D9—51no—
75C5×D9—851no—
76C5×C17—22no—
77C5×C17C2×C5×D911yescharacteristic, complemented
78C5×C17C2×D4511yescharacteristic, complemented
79C3×C52D3×D1711yescharacteristic
80C2×D17—451noHall
81C2×D15—511no—
82C2×C5×D3—2551no—
83C3×C17C2×C5×D1511yescharacteristic
84C2×C52—171no—
85C5×D5—91no—
86C5×D5—1531no—
87C5×C9—22no—
88C5×C9D5×D1711yescharacteristic, complemented
89C5×C9C2×C5×D1711yescharacteristic, complemented
90C2×D9—851noHall
91C2×C17—451no—
92D17—451no—
93D17C5×D4511yescharacteristic, direct product factor
94C2×C3×C5—171no—
95C2×C3×C5—171no—
96C2×C3×C5—342no—
97D15—31no—
98D15—511no—
99C5×D3—151no—
100C5×D3—2551no—
101C52D9×D1711yescharacteristic, complemented, Sylow
102C22×C5—7651no—
103C2×D5—1531no—
104C2×C9—171no—
105D9—51no—
106D9—851no—
107C17C2×C5×D4511yescharacteristic, complemented, Sylow
108C3×C5—22no—
109C3×C5C5×D3×D1711yescharacteristic
110C3×C5D15×D1711yescharacteristic
111C2×D3—2551no—
112C2×C5—171no—
113C2×C5—171no—
114C2×C5—342no—
115C2×C5—451no—
116C2×C5—7651no—
117D5—91no—
118D5—1531no—
119C9C5×D5×D1711yescharacteristic, complemented, Sylow
120C2×C3—171no—
121D3—151no—
122D3—2551no—
123C5—22no—
124C5C5×D9×D1711yescharacteristic, complemented
125C5D17×D4511yescharacteristic, direct product factor
126C22—7651noSylow
127C3C5×D15×D1711yescharacteristic
128C2—171no—
129C2—451no—
130C2—7651no—
subgroupG/H
center, hypercenterC5D17×D45
commutator, cosocle, hypocenterC5×C9×C17C22×C5
FrattiniC3C5×D15×D17
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. C5×C17×D45C2semidirect
3. C52×C9×D17C2semidirect
5. C52×C9×C17C22semidirect
6. D17×D45C5direct (N × H)
12. D765C2×C5semidirect
13. C17×D45C2×C5semidirect
17. C5×C9×D17D5semidirect
18. C5×C9×D17C2×C5semidirect
25. C52×D17D9semidirect
27. C5×C9×C17C2×D5semidirect
28. C5×C9×C17C22×C5semidirect
39. C5×D45D17direct (N × H)
40. C52×C17C2×D9semidirect
44. C9×D17C5×D5semidirect
50. C52×C9C2×D17semidirect
58. C5×D17C5×D9semidirect
59. C5×D17D45direct (N × H)
61. C9×C17C2×C5×D5semidirect
73. D45C5×D17direct (N × H)
77. C5×C17C2×C5×D9semidirect
78. C5×C17C2×D45semidirect
88. C5×C9D5×D17semidirect
89. C5×C9C2×C5×D17semidirect
93. D17C5×D45direct (N × H)
101. C52D9×D17semidirect
107. C17C2×C5×D45semidirect
119. C9C5×D5×D17semidirect
124. C5C5×D9×D17semidirect
125. C5D17×D45direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D7652
C5×C17×D452
C52×C9×D172
C5×D15×D173
D17×D455
C5×D9×D175
C2×C5×D4517