Finite Group Databasebeta

← C2×C5×C17×D45 #29505835

Subgroups — C2×C5×C17×D45 #29505835

Order 15300.

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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×D45C212yesmaximal, direct product factor
2C2×C52×C9×C17C211yesmaximal, characteristic, complemented
3C2×C5×C17×D15—31nomaximal
4C52×C9×C17C2211yescharacteristic, complemented, Hall
5C2×C17×D45C511yesmaximal, characteristic, direct product factor
6C2×C5×C17×D9—51nomaximal
7C5×C17×D15—32no—
8C2×C3×C52×C17D311yescharacteristic
9C2×C5×D5×C17—91noHall
10C2×C5×C9×C17—22no—
11C2×C5×C9×C17D511yescharacteristic, complemented
12C2×C5×C9×C17C2×C511yescharacteristic, complemented
13C17×D45C2×C512yesdirect product factor
14C5×C17×D9—52no—
15C3×C52×C17C2×D311yescharacteristic
16C2×C17×D15—31no—
17C2×C5×D3×C17—151no—
18C2×C5×D45C1711yesmaximal, characteristic, direct product factor, Hall
19C2×C52×C17D911yescharacteristic, complemented
20C5×D5×C17—92no—
21C5×C9×C17—22no—
22C5×C9×C17C2×D511yescharacteristic, complemented
23C5×C9×C17C22×C511yescharacteristic, complemented
24C2×C17×D9—51noHall
25C2×C3×C5×C17—22no—
26C2×C3×C5×C17C5×D311yescharacteristic
27C2×C3×C5×C17D1511yescharacteristic
28C17×D15—32no—
29C5×D3×C17—152no—
30C2×C52×C9C2×C1711yescharacteristic, complemented
31C5×D45C2×C1712yesdirect product factor
32C52×C17C2×D911yescharacteristic, complemented, Hall
33C22×C5×C17—451no—
34C2×D5×C17—91no—
35C2×C9×C17C5×D511yescharacteristic, complemented
36C17×D9—52no—
37C2×C5×D15—31no—
38C3×C5×C17—22no—
39C3×C5×C17C2×C5×D311yescharacteristic
40C3×C5×C17C2×D1511yescharacteristic
41C52×C9C22×C1711yescharacteristic, complemented, Hall
42C2×D3×C17—151no—
43C2×D45C5×C1711yescharacteristic, direct product factor
44C2×C5×D9—51no—
45C2×C5×C17—22no—
46C2×C5×C17—452no—
47C2×C5×C17C5×D911yescharacteristic, complemented
48C2×C5×C17D4511yescharacteristic, direct product factor
49D5×C17—92no—
50C9×C17C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52D3×C1711yescharacteristic
52C5×D15—32no—
53C2×C3×C17C5×D1511yescharacteristic
54D3×C17—152no—
55C2×C5×D5—91noHall
56C2×C5×C9—22no—
57C2×C5×C9D5×C1711yescharacteristic, complemented
58C2×C5×C9C2×C5×C1711yescharacteristic, complemented
59D45C2×C5×C1712yesdirect product factor
60C5×D9—52no—
61C5×C17—22no—
62C5×C17C2×C5×D911yescharacteristic, complemented
63C5×C17C2×D4511yescharacteristic, direct product factor
64C3×C52C2×D3×C1711yescharacteristic
65C22×C17—451noHall
66C2×D15—31no—
67C2×C5×D3—151no—
68C3×C17C2×C5×D1511yescharacteristic
69C2×C52C17×D911yescharacteristic, complemented
70C5×D5—92no—
71C5×C9—22no—
72C5×C9C2×D5×C1711yescharacteristic, complemented
73C5×C9C22×C5×C1711yescharacteristic, complemented
74C2×D9—51noHall
75C2×C17—452no—
76C2×C17C5×D4511yescharacteristic, direct product factor
77C2×C3×C5—22no—
78C2×C3×C5C5×D3×C1711yescharacteristic
79C2×C3×C5C17×D1511yescharacteristic
80D15—32no—
81C5×D3—152no—
82C52C2×C17×D911yescharacteristic, complemented, Sylow
83C22×C5—451no—
84C2×D5—91no—
85C2×C9C5×D5×C1711yescharacteristic, complemented
86D9—52no—
87C17C2×C5×D4511yescharacteristic, direct product factor, Sylow
88C3×C5—22no—
89C3×C5C2×C5×D3×C1711yescharacteristic
90C3×C5C2×C17×D1511yescharacteristic
91C2×D3—151no—
92C2×C5—22no—
93C2×C5—452no—
94C2×C5C5×C17×D911yescharacteristic, complemented
95C2×C5C17×D4511yescharacteristic, direct product factor
96D5—92no—
97C9C2×C5×D5×C1711yescharacteristic, complemented, Sylow
98C2×C3C5×C17×D1511yescharacteristic
99D3—152no—
100C5—22no—
101C5C2×C5×C17×D911yescharacteristic, complemented
102C5C2×C17×D4511yescharacteristic, direct product factor
103C22—451noSylow
104C3C2×C5×C17×D1511yescharacteristic
105C2—452no—
106C2C5×C17×D4511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C17D45
commutator, cosocle, hypocenterC5×C9C22×C5×C17
FrattiniC3C2×C5×C17×D15
FittingC2×C52×C9×C17C2
socleC2×C3×C52×C17D3
LCSG ▷ C5×C9
UCSC1 ◁ C2×C5×C17

Complements

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

NH ≅ G/Ntype
1. C5×C17×D45C2direct (N × H)
2. C2×C52×C9×C17C2semidirect
4. C52×C9×C17C22semidirect
5. C2×C17×D45C5direct (N × H)
11. C2×C5×C9×C17D5semidirect
12. C2×C5×C9×C17C2×C5semidirect
13. C17×D45C2×C5direct (N × H)
18. C2×C5×D45C17direct (N × H)
19. C2×C52×C17D9semidirect
22. C5×C9×C17C2×D5semidirect
23. C5×C9×C17C22×C5semidirect
30. C2×C52×C9C2×C17semidirect
31. C5×D45C2×C17direct (N × H)
32. C52×C17C2×D9semidirect
35. C2×C9×C17C5×D5semidirect
41. C52×C9C22×C17semidirect
43. C2×D45C5×C17direct (N × H)
47. C2×C5×C17C5×D9semidirect
48. C2×C5×C17D45direct (N × H)
50. C9×C17C2×C5×D5semidirect
57. C2×C5×C9D5×C17semidirect
58. C2×C5×C9C2×C5×C17semidirect
59. D45C2×C5×C17direct (N × H)
62. C5×C17C2×C5×D9semidirect
63. C5×C17C2×D45direct (N × H)
69. C2×C52C17×D9semidirect
72. C5×C9C2×D5×C17semidirect
73. C5×C9C22×C5×C17semidirect
76. C2×C17C5×D45direct (N × H)
82. C52C2×C17×D9semidirect
85. C2×C9C5×D5×C17semidirect
87. C17C2×C5×D45direct (N × H)
94. C2×C5C5×C17×D9semidirect
95. C2×C5C17×D45direct (N × H)
97. C9C2×C5×D5×C17semidirect
101. C5C2×C5×C17×D9semidirect
102. C5C2×C17×D45direct (N × H)
106. C2C5×C17×D45direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C17×D452
C2×C52×C9×C172
C2×C5×C17×D153
C2×C17×D455
C2×C5×C17×D95
C2×C5×D4517