Finite Group Databasebeta

← C2×C5×C17×C3⋊D15 #29506074

Subgroups — C2×C5×C17×C3⋊D15 #29506074

Order 15300.

288 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 108 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×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C52×C17C211yesmaximal, characteristic, complemented
3C2×C5×C17×D15—34nomaximal
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5C2×C5×C17×C3⋊D3—51nomaximal
6C2×C17×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×C17×D15—38no—
8C2×C3×C52×C17D314yescomplemented
9C2×C5×D5×C17—91noHall
10C2×C32×C5×C17—22no—
11C2×C32×C5×C17D511yescharacteristic, complemented
12C2×C32×C5×C17C2×C511yescharacteristic, complemented
13C17×C3⋊D15C2×C512yesdirect product factor
14C5×C17×C3⋊D3—52no—
15C3×C52×C17C2×D314yescomplemented
16C2×C17×D15—34no—
17C2×C5×D3×C17—154no—
18C2×C5×C3⋊D15C1711yesmaximal, characteristic, direct product factor, Hall
19C2×C52×C17C3⋊D311yescharacteristic, complemented
20C5×D5×C17—92no—
21C32×C5×C17—22no—
22C32×C5×C17C2×D511yescharacteristic, complemented
23C32×C5×C17C22×C511yescharacteristic, complemented
24C2×C17×C3⋊D3—51noHall
25C2×C3×C5×C17—28no—
26C2×C3×C5×C17C5×D314yescomplemented
27C2×C3×C5×C17D1514yescomplemented
28C17×D15—38no—
29C5×D3×C17—158no—
30C2×C32×C52C2×C1711yescharacteristic, complemented
31C5×C3⋊D15C2×C1712yesdirect product factor
32C52×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33C22×C5×C17—451no—
34C2×D5×C17—91no—
35C2×C32×C17C5×D511yescharacteristic, complemented
36C17×C3⋊D3—52no—
37C2×C5×D15—34no—
38C3×C5×C17—28no—
39C3×C5×C17C2×C5×D314yescomplemented
40C3×C5×C17C2×D1514yescomplemented
41C32×C52C22×C1711yescharacteristic, complemented, Hall
42C2×D3×C17—154no—
43C2×C3⋊D15C5×C1711yescharacteristic, direct product factor
44C2×C5×C3⋊D3—51no—
45C2×C5×C17—22no—
46C2×C5×C17—452no—
47C2×C5×C17C5×C3⋊D311yescharacteristic, complemented
48C2×C5×C17C3⋊D1511yescharacteristic, direct product factor
49D5×C17—92no—
50C32×C17C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52D3×C1714yescomplemented
52C5×D15—38no—
53C2×C3×C17C5×D1514yescomplemented
54D3×C17—158no—
55C2×C5×D5—91noHall
56C2×C32×C5—22no—
57C2×C32×C5D5×C1711yescharacteristic, complemented
58C2×C32×C5C2×C5×C1711yescharacteristic, complemented
59C3⋊D15C2×C5×C1712yesdirect product factor
60C5×C3⋊D3—52no—
61C5×C17—22no—
62C5×C17C2×C5×C3⋊D311yescharacteristic, complemented
63C5×C17C2×C3⋊D1511yescharacteristic, direct product factor
64C3×C52C2×D3×C1714yescomplemented
65C22×C17—451noHall
66C2×D15—34no—
67C2×C5×D3—154no—
68C3×C17C2×C5×D1514yescomplemented
69C2×C52C17×C3⋊D311yescharacteristic, complemented
70C5×D5—92no—
71C32×C5—22no—
72C32×C5C2×D5×C1711yescharacteristic, complemented
73C32×C5C22×C5×C1711yescharacteristic, complemented
74C2×C3⋊D3—51noHall
75C2×C17—452no—
76C2×C17C5×C3⋊D1511yescharacteristic, direct product factor
77C2×C3×C5—28no—
78C2×C3×C5C5×D3×C1714yescomplemented
79C2×C3×C5C17×D1514yescomplemented
80D15—38no—
81C5×D3—158no—
82C52C2×C17×C3⋊D311yescharacteristic, complemented, Sylow
83C22×C5—451no—
84C2×D5—91no—
85C2×C32C5×D5×C1711yescharacteristic, complemented
86C3⋊D3—52no—
87C17C2×C5×C3⋊D1511yescharacteristic, direct product factor, Sylow
88C3×C5—28no—
89C3×C5C2×C5×D3×C1714yescomplemented
90C3×C5C2×C17×D1514yescomplemented
91C2×D3—154no—
92C2×C5—22no—
93C2×C5—452no—
94C2×C5C5×C17×C3⋊D311yescharacteristic, complemented
95C2×C5C17×C3⋊D1511yescharacteristic, direct product factor
96D5—92no—
97C32C2×C5×D5×C1711yescharacteristic, complemented, Sylow
98C2×C3C5×C17×D1514yescomplemented
99D3—158no—
100C5—22no—
101C5C2×C17×C3⋊D1511yescharacteristic, direct product factor
102C5C2×C5×C17×C3⋊D311yescharacteristic, complemented
103C22—451noSylow
104C3C2×C5×C17×D1514yescomplemented
105C2—452no—
106C2C5×C17×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C17C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C52×C17C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C17

Complements

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

NH ≅ G/Ntype
1. C5×C17×C3⋊D15C2direct (N × H)
2. C2×C32×C52×C17C2semidirect
4. C32×C52×C17C22semidirect
6. C2×C17×C3⋊D15C5direct (N × H)
8. C2×C3×C52×C17D3semidirect
11. C2×C32×C5×C17D5semidirect
12. C2×C32×C5×C17C2×C5semidirect
13. C17×C3⋊D15C2×C5direct (N × H)
15. C3×C52×C17C2×D3semidirect
18. C2×C5×C3⋊D15C17direct (N × H)
19. C2×C52×C17C3⋊D3semidirect
22. C32×C5×C17C2×D5semidirect
23. C32×C5×C17C22×C5semidirect
26. C2×C3×C5×C17C5×D3semidirect
27. C2×C3×C5×C17D15semidirect
30. C2×C32×C52C2×C17semidirect
31. C5×C3⋊D15C2×C17direct (N × H)
32. C52×C17C2×C3⋊D3semidirect
35. C2×C32×C17C5×D5semidirect
39. C3×C5×C17C2×C5×D3semidirect
40. C3×C5×C17C2×D15semidirect
41. C32×C52C22×C17semidirect
43. C2×C3⋊D15C5×C17direct (N × H)
47. C2×C5×C17C5×C3⋊D3semidirect
48. C2×C5×C17C3⋊D15direct (N × H)
50. C32×C17C2×C5×D5semidirect
51. C2×C3×C52D3×C17semidirect
53. C2×C3×C17C5×D15semidirect
57. C2×C32×C5D5×C17semidirect
58. C2×C32×C5C2×C5×C17semidirect
59. C3⋊D15C2×C5×C17direct (N × H)
62. C5×C17C2×C5×C3⋊D3semidirect
63. C5×C17C2×C3⋊D15direct (N × H)
64. C3×C52C2×D3×C17semidirect
68. C3×C17C2×C5×D15semidirect
69. C2×C52C17×C3⋊D3semidirect
72. C32×C5C2×D5×C17semidirect
73. C32×C5C22×C5×C17semidirect
76. C2×C17C5×C3⋊D15direct (N × H)
78. C2×C3×C5C5×D3×C17semidirect
79. C2×C3×C5C17×D15semidirect
82. C52C2×C17×C3⋊D3semidirect
85. C2×C32C5×D5×C17semidirect
87. C17C2×C5×C3⋊D15direct (N × H)
89. C3×C5C2×C5×D3×C17semidirect
90. C3×C5C2×C17×D15semidirect
94. C2×C5C5×C17×C3⋊D3semidirect
95. C2×C5C17×C3⋊D15direct (N × H)
97. C32C2×C5×D5×C17semidirect
98. C2×C3C5×C17×D15semidirect
101. C5C2×C17×C3⋊D15direct (N × H)
102. C5C2×C5×C17×C3⋊D3semidirect
104. C3C2×C5×C17×D15semidirect
106. C2C5×C17×C3⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C17×C3⋊D152
C2×C32×C52×C172
C2×C5×C17×D153
C2×C5×C17×C3⋊D35
C2×C17×C3⋊D155
C2×C5×C3⋊D1517