Finite Group Databasebeta

← C2×C5×C37×C3⋊D15 #45686522

Subgroups — C2×C5×C37×C3⋊D15 #45686522

Order 33300.

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×C37×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C52×C37C211yesmaximal, characteristic, complemented
3C2×C5×D15×C37—34nomaximal
4C32×C52×C37C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D3×C37—51nomaximal
6C2×C37×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×D15×C37—38no—
8C2×C3×C52×C37D314yescomplemented
9C2×C5×D5×C37—91noHall
10C37×C3⋊D15C2×C512yesdirect product factor
11C5×C3⋊D3×C37—52no—
12C2×C32×C5×C37—22no—
13C2×C32×C5×C37D511yescharacteristic, complemented
14C2×C32×C5×C37C2×C511yescharacteristic, complemented
15C3×C52×C37C2×D314yescomplemented
16C2×D15×C37—34no—
17C2×C5×D3×C37—154no—
18C2×C52×C37C3⋊D311yescharacteristic, complemented
19C5×D5×C37—92no—
20C32×C5×C37—22no—
21C32×C5×C37C2×D511yescharacteristic, complemented
22C32×C5×C37C22×C511yescharacteristic, complemented
23C2×C3⋊D3×C37—51noHall
24C2×C3×C5×C37—28no—
25C2×C3×C5×C37C5×D314yescomplemented
26C2×C3×C5×C37D1514yescomplemented
27D15×C37—38no—
28C5×D3×C37—158no—
29C52×C37C2×C3⋊D311yescharacteristic, complemented, Hall
30C2×C5×C3⋊D15C3711yesmaximal, characteristic, direct product factor, Hall
31C22×C5×C37—451no—
32C2×D5×C37—91no—
33C2×C32×C37C5×D511yescharacteristic, complemented
34C3⋊D3×C37—52no—
35C3×C5×C37—28no—
36C3×C5×C37C2×C5×D314yescomplemented
37C3×C5×C37C2×D1514yescomplemented
38C2×C32×C52C2×C3711yescharacteristic, complemented
39C5×C3⋊D15C2×C3712yesdirect product factor
40C2×D3×C37—154no—
41C2×C5×C37—22no—
42C2×C5×C37—452no—
43C2×C5×C37C5×C3⋊D311yescharacteristic, complemented
44C2×C5×C37C3⋊D1511yescharacteristic, direct product factor
45D5×C37—92no—
46C32×C37C2×C5×D511yescharacteristic, complemented, Hall
47C2×C5×D15—34no—
48C32×C52C22×C3711yescharacteristic, complemented, Hall
49C2×C3×C37C5×D1514yescomplemented
50D3×C37—158no—
51C5×C37—22no—
52C5×C37C2×C5×C3⋊D311yescharacteristic, complemented
53C5×C37C2×C3⋊D1511yescharacteristic, direct product factor
54C2×C3⋊D15C5×C3711yescharacteristic, direct product factor
55C2×C5×C3⋊D3—51no—
56C2×C3×C52D3×C3714yescomplemented
57C5×D15—38no—
58C22×C37—451noHall
59C3×C37C2×C5×D1514yescomplemented
60C2×C5×D5—91noHall
61C2×C32×C5—22no—
62C2×C32×C5D5×C3711yescharacteristic, complemented
63C2×C32×C5C2×C5×C3711yescharacteristic, complemented
64C3⋊D15C2×C5×C3712yesdirect product factor
65C5×C3⋊D3—52no—
66C3×C52C2×D3×C3714yescomplemented
67C2×C37—452no—
68C2×C37C5×C3⋊D1511yescharacteristic, direct product factor
69C2×D15—34no—
70C2×C5×D3—154no—
71C2×C52C3⋊D3×C3711yescharacteristic, complemented
72C5×D5—92no—
73C32×C5—22no—
74C32×C5C2×D5×C3711yescharacteristic, complemented
75C32×C5C22×C5×C3711yescharacteristic, complemented
76C37C2×C5×C3⋊D1511yescharacteristic, direct product factor, Sylow
77C2×C3⋊D3—51noHall
78C2×C3×C5—28no—
79C2×C3×C5C5×D3×C3714yescomplemented
80C2×C3×C5D15×C3714yescomplemented
81D15—38no—
82C5×D3—158no—
83C52C2×C3⋊D3×C3711yescharacteristic, complemented, Sylow
84C22×C5—451no—
85C2×D5—91no—
86C2×C32C5×D5×C3711yescharacteristic, complemented
87C3⋊D3—52no—
88C3×C5—28no—
89C3×C5C2×C5×D3×C3714yescomplemented
90C3×C5C2×D15×C3714yescomplemented
91C2×D3—154no—
92C2×C5—22no—
93C2×C5—452no—
94C2×C5C5×C3⋊D3×C3711yescharacteristic, complemented
95C2×C5C37×C3⋊D1511yescharacteristic, direct product factor
96D5—92no—
97C32C2×C5×D5×C3711yescharacteristic, complemented, Sylow
98C2×C3C5×D15×C3714yescomplemented
99D3—158no—
100C5—22no—
101C5C2×C37×C3⋊D1511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D3×C3711yescharacteristic, complemented
103C22—451noSylow
104C3C2×C5×D15×C3714yescomplemented
105C2—452no—
106C2C5×C37×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C37C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C5×C37
FrattiniC1G
Fitting, socleC2×C32×C52×C37C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C37

Complements

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

NH ≅ G/Ntype
1. C5×C37×C3⋊D15C2direct (N × H)
2. C2×C32×C52×C37C2semidirect
4. C32×C52×C37C22semidirect
6. C2×C37×C3⋊D15C5direct (N × H)
8. C2×C3×C52×C37D3semidirect
10. C37×C3⋊D15C2×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
30. C2×C5×C3⋊D15C37direct (N × H)
33. C2×C32×C37C5×D5semidirect
36. C3×C5×C37C2×C5×D3semidirect
37. C3×C5×C37C2×D15semidirect
38. C2×C32×C52C2×C37semidirect
39. C5×C3⋊D15C2×C37direct (N × H)
43. C2×C5×C37C5×C3⋊D3semidirect
44. C2×C5×C37C3⋊D15direct (N × H)
46. C32×C37C2×C5×D5semidirect
48. C32×C52C22×C37semidirect
49. C2×C3×C37C5×D15semidirect
52. C5×C37C2×C5×C3⋊D3semidirect
53. C5×C37C2×C3⋊D15direct (N × H)
54. C2×C3⋊D15C5×C37direct (N × H)
56. C2×C3×C52D3×C37semidirect
59. C3×C37C2×C5×D15semidirect
62. C2×C32×C5D5×C37semidirect
63. C2×C32×C5C2×C5×C37semidirect
64. C3⋊D15C2×C5×C37direct (N × H)
66. C3×C52C2×D3×C37semidirect
68. C2×C37C5×C3⋊D15direct (N × H)
71. C2×C52C3⋊D3×C37semidirect
74. C32×C5C2×D5×C37semidirect
75. C32×C5C22×C5×C37semidirect
76. C37C2×C5×C3⋊D15direct (N × H)
79. C2×C3×C5C5×D3×C37semidirect
80. C2×C3×C5D15×C37semidirect
83. C52C2×C3⋊D3×C37semidirect
86. C2×C32C5×D5×C37semidirect
89. C3×C5C2×C5×D3×C37semidirect
90. C3×C5C2×D15×C37semidirect
94. C2×C5C5×C3⋊D3×C37semidirect
95. C2×C5C37×C3⋊D15direct (N × H)
97. C32C2×C5×D5×C37semidirect
98. C2×C3C5×D15×C37semidirect
101. C5C2×C37×C3⋊D15direct (N × H)
102. C5C2×C5×C3⋊D3×C37semidirect
104. C3C2×C5×D15×C37semidirect
106. C2C5×C37×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×C37×C3⋊D152
C2×C32×C52×C372
C2×C5×D15×C373
C2×C5×C3⋊D3×C375
C2×C37×C3⋊D155
C2×C5×C3⋊D1537