Finite Group Databasebeta

← C2×C5×C3⋊D555 #45686523

Subgroups — C2×C5×C3⋊D555 #45686523

Order 33300.

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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×C3⋊D555C212yesmaximal, direct product factor
2C2×C32×C52×C37C211yesmaximal, characteristic, complemented
3C2×C5×D555—34nomaximal
4C32×C52×C37C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D111—51nomaximal
6C2×C3⋊D555C511yesmaximal, characteristic, direct product factor
7C5×D555—38no—
8C2×C3×C52×C37D314yescomplemented
9C2×C5×D185—91noHall
10C3⋊D555C2×C512yesdirect product factor
11C5×C3⋊D111—52no—
12C2×C32×C5×C37—22no—
13C2×C32×C5×C37D511yescharacteristic, complemented
14C2×C32×C5×C37C2×C511yescharacteristic, complemented
15C3×C52×C37C2×D314yescomplemented
16C2×D555—34no—
17C2×C5×D111—154no—
18C2×C52×C37C3⋊D311yescharacteristic, complemented
19C5×D185—92no—
20C32×C5×C37—22no—
21C32×C5×C37C2×D511yescharacteristic, complemented
22C32×C5×C37C22×C511yescharacteristic, complemented
23C2×C3⋊D111—51noHall
24C2×C3×C5×C37—28no—
25C2×C3×C5×C37C5×D314yescomplemented
26C2×C3×C5×C37D1514yescomplemented
27D555—38no—
28C5×D111—158no—
29C52×C37C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×C5×C3⋊D15—371nomaximal, Hall
31C2×D185—91no—
32C2×C5×D37—451no—
33C2×C32×C37C5×D511yescharacteristic, complemented
34C3⋊D111—52no—
35C3×C5×C37—28no—
36C3×C5×C37C2×C5×D314yescomplemented
37C3×C5×C37C2×D1514yescomplemented
38C2×C32×C52D3711yescharacteristic, complemented
39C5×C3⋊D15—372no—
40C2×D111—154no—
41C2×C5×C37—22no—
42C2×C5×C37C5×C3⋊D311yescharacteristic, complemented
43C2×C5×C37C3⋊D1511yescharacteristic, complemented
44D185—92no—
45C5×D37—452no—
46C32×C37C2×C5×D511yescharacteristic, complemented, Hall
47C2×C5×D15—1114no—
48C32×C52C2×D3711yescharacteristic, complemented, Hall
49C2×C3×C37C5×D1514yescomplemented
50D111—158no—
51C5×C37—22no—
52C5×C37C2×C5×C3⋊D311yescharacteristic, complemented
53C5×C37C2×C3⋊D1511yescharacteristic, complemented
54C2×C3⋊D15—371no—
55C2×C5×C3⋊D3—1851no—
56C2×C3×C52D11114yescomplemented
57C5×D15—1118no—
58C2×D37—451noHall
59C3×C37C2×C5×D1514yescomplemented
60C2×C5×D5—3331noHall
61C2×C32×C5—22no—
62C2×C32×C5C5×D3711yescharacteristic, complemented
63C2×C32×C5D18511yescharacteristic, complemented
64C3⋊D15—372no—
65C5×C3⋊D3—1852no—
66C3×C52C2×D11114yescomplemented
67C2×C37C5×C3⋊D1511yescharacteristic, complemented
68D37—452no—
69C2×D15—1114no—
70C2×C5×D3—5554no—
71C2×C52C3⋊D11111yescharacteristic, complemented
72C5×D5—3332no—
73C32×C5—22no—
74C32×C5C2×C5×D3711yescharacteristic, complemented
75C32×C5C2×D18511yescharacteristic, complemented
76C37C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
77C2×C3⋊D3—1851noHall
78C2×C3×C5—28no—
79C2×C3×C5C5×D11114yescomplemented
80C2×C3×C5D55514yescomplemented
81D15—1118no—
82C5×D3—5558no—
83C52C2×C3⋊D11111yescharacteristic, complemented, Sylow
84C22×C5—16651no—
85C2×D5—3331no—
86C2×C32C5×D18511yescharacteristic, complemented
87C3⋊D3—1852no—
88C3×C5—28no—
89C3×C5C2×C5×D11114yescomplemented
90C3×C5C2×D55514yescomplemented
91C2×D3—5554no—
92C2×C5—22no—
93C2×C5—16652no—
94C2×C5C5×C3⋊D11111yescharacteristic, complemented
95C2×C5C3⋊D55511yescharacteristic, direct product factor
96D5—3332no—
97C32C2×C5×D18511yescharacteristic, complemented, Sylow
98C2×C3C5×D55514yescomplemented
99D3—5558no—
100C5—22no—
101C5C2×C3⋊D55511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D11111yescharacteristic, complemented
103C22—16651noSylow
104C3C2×C5×D55514yescomplemented
105C2—16652no—
106C2C5×C3⋊D55511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊D555
commutator, cosocle, hypocenterC32×C5×C37C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C37C2
LCSG ▷ C32×C5×C37
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D555C2direct (N × H)
2. C2×C32×C52×C37C2semidirect
4. C32×C52×C37C22semidirect
6. C2×C3⋊D555C5direct (N × H)
8. C2×C3×C52×C37D3semidirect
10. C3⋊D555C2×C5direct (N × H)
13. C2×C32×C5×C37D5semidirect
14. C2×C32×C5×C37C2×C5semidirect
15. C3×C52×C37C2×D3semidirect
18. C2×C52×C37C3⋊D3semidirect
21. C32×C5×C37C2×D5semidirect
22. C32×C5×C37C22×C5semidirect
25. C2×C3×C5×C37C5×D3semidirect
26. C2×C3×C5×C37D15semidirect
29. C52×C37C2×C3⋊D3semidirect
33. C2×C32×C37C5×D5semidirect
36. C3×C5×C37C2×C5×D3semidirect
37. C3×C5×C37C2×D15semidirect
38. C2×C32×C52D37semidirect
42. C2×C5×C37C5×C3⋊D3semidirect
43. C2×C5×C37C3⋊D15semidirect
46. C32×C37C2×C5×D5semidirect
48. C32×C52C2×D37semidirect
49. C2×C3×C37C5×D15semidirect
52. C5×C37C2×C5×C3⋊D3semidirect
53. C5×C37C2×C3⋊D15semidirect
56. C2×C3×C52D111semidirect
59. C3×C37C2×C5×D15semidirect
62. C2×C32×C5C5×D37semidirect
63. C2×C32×C5D185semidirect
66. C3×C52C2×D111semidirect
67. C2×C37C5×C3⋊D15semidirect
71. C2×C52C3⋊D111semidirect
74. C32×C5C2×C5×D37semidirect
75. C32×C5C2×D185semidirect
76. C37C2×C5×C3⋊D15semidirect
79. C2×C3×C5C5×D111semidirect
80. C2×C3×C5D555semidirect
83. C52C2×C3⋊D111semidirect
86. C2×C32C5×D185semidirect
89. C3×C5C2×C5×D111semidirect
90. C3×C5C2×D555semidirect
94. C2×C5C5×C3⋊D111semidirect
95. C2×C5C3⋊D555direct (N × H)
97. C32C2×C5×D185semidirect
98. C2×C3C5×D555semidirect
101. C5C2×C3⋊D555direct (N × H)
102. C5C2×C5×C3⋊D111semidirect
104. C3C2×C5×D555semidirect
106. C2C5×C3⋊D555direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C3⋊D5552
C2×C32×C52×C372
C2×C5×D5553
C2×C5×C3⋊D1115
C2×C3⋊D5555
C2×C5×C3⋊D1537