Finite Group Databasebeta

← C2×C5×C9×D85 #29505830

Subgroups — C2×C5×C9×D85 #29505830

Order 15300.

144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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×C9×D85C212yesmaximal, direct product factor
2C2×C52×C9×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×D85C311yesmaximal, characteristic
4C52×C9×C17C2211yescharacteristic, complemented, Hall
5C2×C9×D85C511yesmaximal, characteristic, direct product factor
6C2×C5×C9×D17—51nomaximal
7C3×C5×D85C2×C312yes—
8C2×C3×C52×C17C2×C311yescharacteristic
9C2×C5×D85C911yescharacteristic, direct product factor, Hall
10C2×C5×C9×C17—22no—
11C2×C5×C9×C17D511yescharacteristic, complemented
12C2×C5×C9×C17C2×C511yescharacteristic, complemented
13C9×D85C2×C512yesdirect product factor
14C5×C9×D17—52no—
15C3×C52×C17C22×C311yescharacteristic
16C2×C3×D85C3×C511yescharacteristic
17C2×C3×C5×D17—51no—
18C2×C5×C9×D5—171nomaximal, Hall
19C2×C52×C17C2×C911yescharacteristic, complemented
20C5×D85C2×C912yesdirect product factor
21C5×C9×C17—22no—
22C5×C9×C17C2×D511yescharacteristic, complemented
23C5×C9×C17C22×C511yescharacteristic, complemented
24C2×C9×D17—51noHall
25C2×C3×C5×C17—22no—
26C2×C3×C5×C17C3×D511yescharacteristic
27C2×C3×C5×C17C2×C3×C511yescharacteristic
28C3×D85C2×C3×C512yes—
29C3×C5×D17—52no—
30C2×C52×C9D1711yescharacteristic, complemented
31C5×C9×D5—172no—
32C52×C17C22×C911yescharacteristic, complemented, Hall
33C2×D85C5×C911yescharacteristic, direct product factor
34C2×C5×D17—51no—
35C2×C9×C17C5×D511yescharacteristic, complemented
36C9×D17—52no—
37C2×C3×C5×D5—171no—
38C3×C5×C17—22no—
39C3×C5×C17C2×C3×D511yescharacteristic
40C3×C5×C17C22×C3×C511yescharacteristic
41C52×C9C2×D1711yescharacteristic, complemented, Hall
42C2×C3×D17—51no—
43C22×C5×C9—851no—
44C2×C9×D5—171no—
45C2×C5×C17—22no—
46C2×C5×C17C9×D511yescharacteristic, complemented
47C2×C5×C17C2×C5×C911yescharacteristic, complemented
48D85C2×C5×C912yesdirect product factor
49C5×D17—52no—
50C9×C17C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52C3×D1711yescharacteristic
52C3×C5×D5—172no—
53C2×C3×C17C3×C5×D511yescharacteristic
54C3×D17—52no—
55C2×C5×D5—171noHall
56C2×C5×C9—22no—
57C2×C5×C9—852no—
58C2×C5×C9C5×D1711yescharacteristic, complemented
59C2×C5×C9D8511yescharacteristic, direct product factor
60C9×D5—172no—
61C5×C17—22no—
62C5×C17C2×C9×D511yescharacteristic, complemented
63C5×C17C22×C5×C911yescharacteristic, complemented
64C3×C52C2×C3×D1711yescharacteristic
65C2×D17—51noHall
66C22×C3×C5—851no—
67C2×C3×D5—171no—
68C3×C17C2×C3×C5×D511yescharacteristic
69C2×C52C9×D1711yescharacteristic, complemented
70C5×D5—172no—
71C5×C9—22no—
72C5×C9C2×C5×D1711yescharacteristic, complemented
73C5×C9C2×D8511yescharacteristic, direct product factor
74C22×C9—851noHall
75C2×C17C5×C9×D511yescharacteristic, complemented
76D17—52no—
77C2×C3×C5—22no—
78C2×C3×C5—852no—
79C2×C3×C5C3×C5×D1711yescharacteristic
80C2×C3×C5C3×D8511yescharacteristic
81C3×D5—172no—
82C52C2×C9×D1711yescharacteristic, complemented, Sylow
83C22×C5—851no—
84C2×D5—171no—
85C2×C9—852no—
86C2×C9C5×D8511yescharacteristic, direct product factor
87C17C2×C5×C9×D511yescharacteristic, complemented, Sylow
88C3×C5—22no—
89C3×C5C2×C3×C5×D1711yescharacteristic
90C3×C5C2×C3×D8511yescharacteristic
91C22×C3—851no—
92C2×C5—22no—
93C2×C5—852no—
94C2×C5C5×C9×D1711yescharacteristic, complemented
95C2×C5C9×D8511yescharacteristic, direct product factor
96D5—172no—
97C9C2×C5×D8511yescharacteristic, direct product factor, Sylow
98C2×C3—852no—
99C2×C3C3×C5×D8511yescharacteristic
100C5—22no—
101C5C2×C5×C9×D1711yescharacteristic, complemented
102C5C2×C9×D8511yescharacteristic, direct product factor
103C22—851noSylow
104C3C2×C3×C5×D8511yescharacteristic
105C2—852no—
106C2C5×C9×D8511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C9D85
commutator, hypocenterC5×C17C22×C5×C9
FrattiniC3C2×C3×C5×D85
FittingC2×C52×C9×C17C2
socleC2×C3×C52×C17C2×C3
prime radicalC2×C3×C5×D85C3
cosocleC3×C5×C17C22×C3×C5
LCSG ▷ C5×C17
UCSC1 ◁ C2×C5×C9

Complements

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

NH ≅ G/Ntype
1. C5×C9×D85C2direct (N × H)
2. C2×C52×C9×C17C2semidirect
4. C52×C9×C17C22semidirect
5. C2×C9×D85C5direct (N × H)
9. C2×C5×D85C9direct (N × H)
11. C2×C5×C9×C17D5semidirect
12. C2×C5×C9×C17C2×C5semidirect
13. C9×D85C2×C5direct (N × H)
19. C2×C52×C17C2×C9semidirect
20. C5×D85C2×C9direct (N × H)
22. C5×C9×C17C2×D5semidirect
23. C5×C9×C17C22×C5semidirect
30. C2×C52×C9D17semidirect
32. C52×C17C22×C9semidirect
33. C2×D85C5×C9direct (N × H)
35. C2×C9×C17C5×D5semidirect
41. C52×C9C2×D17semidirect
46. C2×C5×C17C9×D5semidirect
47. C2×C5×C17C2×C5×C9semidirect
48. D85C2×C5×C9direct (N × H)
50. C9×C17C2×C5×D5semidirect
58. C2×C5×C9C5×D17semidirect
59. C2×C5×C9D85direct (N × H)
62. C5×C17C2×C9×D5semidirect
63. C5×C17C22×C5×C9semidirect
69. C2×C52C9×D17semidirect
72. C5×C9C2×C5×D17semidirect
73. C5×C9C2×D85direct (N × H)
75. C2×C17C5×C9×D5semidirect
82. C52C2×C9×D17semidirect
86. C2×C9C5×D85direct (N × H)
87. C17C2×C5×C9×D5semidirect
94. C2×C5C5×C9×D17semidirect
95. C2×C5C9×D85direct (N × H)
97. C9C2×C5×D85direct (N × H)
101. C5C2×C5×C9×D17semidirect
102. C5C2×C9×D85direct (N × H)
106. C2C5×C9×D85direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C9×D852
C2×C52×C9×C172
C2×C3×C5×D853
C2×C9×D855
C2×C5×C9×D175
C2×C5×C9×D517