Finite Group Databasebeta

← C5×D37×C3⋊D15 #45686469

Subgroups — C5×D37×C3⋊D15 #45686469

Order 33300.

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C52×D37C211yesmaximal, characteristic, complemented
2C5×C37×C3⋊D15C211yesmaximal, characteristic, complemented
3C5×C3⋊D555C211yesmaximal, characteristic, complemented
4C5×D15×D37—34nomaximal
5C32×C52×C37C2211yescharacteristic, complemented, Hall
6D37×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×C3⋊D3×D37—51nomaximal
8C5×D555—34no—
9C5×D15×C37—34no—
10C3×C52×D37D314yescomplemented
11C5×D5×D37—91noHall
12C3⋊D555C2×C511yescharacteristic, complemented
13C37×C3⋊D15C2×C511yescharacteristic, complemented
14C5×C3⋊D111—51no—
15C5×C3⋊D3×C37—51no—
16C32×C5×D37—22no—
17C32×C5×D37D511yescharacteristic, complemented
18C32×C5×D37C2×C511yescharacteristic, complemented
19C3×C52×C37C2×D314yescomplemented
20D15×D37—34no—
21C5×D3×D37—154no—
22C5×D185—91no—
23C5×D5×C37—91no—
24C52×D37C3⋊D311yescharacteristic, complemented
25C32×C5×C37—22no—
26C32×C5×C37C2×D511yescharacteristic, complemented
27C32×C5×C37C22×C511yescharacteristic, complemented
28C3⋊D3×D37—51noHall
29D555—34no—
30D15×C37—34no—
31C5×D111—154no—
32C5×D3×C37—154no—
33C3×C5×D37—28no—
34C3×C5×D37C5×D314yescomplemented
35C3×C5×D37D1514yescomplemented
36C52×C37C2×C3⋊D311yescharacteristic, complemented, Hall
37C2×C5×C3⋊D15—371nomaximal, Hall
38C2×C5×D37—451no—
39D5×D37—91no—
40C3⋊D111—51no—
41C3⋊D3×C37—51no—
42C32×D37C5×D511yescharacteristic, complemented
43C3×C5×C37—28no—
44C3×C5×C37C2×C5×D314yescomplemented
45C3×C5×C37C2×D1514yescomplemented
46C2×C32×C52—371no—
47C5×C3⋊D15—371no—
48C5×C3⋊D15D3711yescharacteristic, direct product factor
49D3×D37—154no—
50C2×C5×C37—451no—
51D185—91no—
52C5×D37—22no—
53C5×D37—451no—
54C5×D37C5×C3⋊D311yescharacteristic, complemented
55C5×D37C3⋊D1511yescharacteristic, direct product factor
56D5×C37—91no—
57C32×C37C2×C5×D511yescharacteristic, complemented, Hall
58C2×C5×D15—1114no—
59C32×C52C2×D3711yescharacteristic, complemented, Hall
60D111—154no—
61C3×D37C5×D1514yescomplemented
62D3×C37—154no—
63C5×C37—22no—
64C5×C37C2×C5×C3⋊D311yescharacteristic, complemented
65C5×C37C2×C3⋊D1511yescharacteristic, complemented
66C2×C3⋊D15—371no—
67C2×C5×C3⋊D3—1851no—
68C2×C3×C52—374no—
69C5×D15—34no—
70C5×D15—1114no—
71C2×D37—451noHall
72C3×C37C2×C5×D1514yescomplemented
73C2×C5×D5—3331noHall
74C2×C32×C5—371no—
75C2×C32×C5—371no—
76C2×C32×C5—742no—
77C3⋊D15—371no—
78C3⋊D15C5×D3711yescharacteristic, direct product factor
79C5×C3⋊D3—51no—
80C5×C3⋊D3—1851no—
81C3×C52D3×D3714yescomplemented
82C2×C37—451no—
83D37—451no—
84D37C5×C3⋊D1511yescharacteristic, direct product factor
85C2×D15—1114no—
86C2×C5×D3—5554no—
87C2×C52—371no—
88C5×D5—91no—
89C5×D5—3331no—
90C32×C5—22no—
91C32×C5D5×D3711yescharacteristic, complemented
92C32×C5C2×C5×D3711yescharacteristic, complemented
93C37C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
94C2×C3⋊D3—1851noHall
95C2×C3×C5—374no—
96C2×C3×C5—374no—
97C2×C3×C5—748no—
98D15—34no—
99D15—1114no—
100C5×D3—154no—
101C5×D3—5554no—
102C52C3⋊D3×D3711yescharacteristic, complemented, Sylow
103C22×C5—16651no—
104C2×D5—3331no—
105C2×C32—371no—
106C3⋊D3—51no—
107C3⋊D3—1851no—
108C3×C5—28no—
109C3×C5C5×D3×D3714yescomplemented
110C3×C5D15×D3714yescomplemented
111C2×D3—5554no—
112C2×C5—371no—
113C2×C5—371no—
114C2×C5—451no—
115C2×C5—742no—
116C2×C5—16651no—
117D5—91no—
118D5—3331no—
119C32C5×D5×D3711yescharacteristic, complemented, Sylow
120C2×C3—374no—
121D3—154no—
122D3—5554no—
123C5—22no—
124C5C5×C3⋊D3×D3711yescharacteristic, complemented
125C5D37×C3⋊D1511yescharacteristic, direct product factor
126C22—16651noSylow
127C3C5×D15×D3714yescomplemented
128C2—371no—
129C2—451no—
130C2—16651no—
subgroupG/H
center, hypercenterC5D37×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C37C22×C5
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C32×C5×C37
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C52×D37C2semidirect
2. C5×C37×C3⋊D15C2semidirect
3. C5×C3⋊D555C2semidirect
5. C32×C52×C37C22semidirect
6. D37×C3⋊D15C5direct (N × H)
10. C3×C52×D37D3semidirect
12. C3⋊D555C2×C5semidirect
13. C37×C3⋊D15C2×C5semidirect
17. C32×C5×D37D5semidirect
18. C32×C5×D37C2×C5semidirect
19. C3×C52×C37C2×D3semidirect
24. C52×D37C3⋊D3semidirect
26. C32×C5×C37C2×D5semidirect
27. C32×C5×C37C22×C5semidirect
34. C3×C5×D37C5×D3semidirect
35. C3×C5×D37D15semidirect
36. C52×C37C2×C3⋊D3semidirect
42. C32×D37C5×D5semidirect
44. C3×C5×C37C2×C5×D3semidirect
45. C3×C5×C37C2×D15semidirect
48. C5×C3⋊D15D37direct (N × H)
54. C5×D37C5×C3⋊D3semidirect
55. C5×D37C3⋊D15direct (N × H)
57. C32×C37C2×C5×D5semidirect
59. C32×C52C2×D37semidirect
61. C3×D37C5×D15semidirect
64. C5×C37C2×C5×C3⋊D3semidirect
65. C5×C37C2×C3⋊D15semidirect
72. C3×C37C2×C5×D15semidirect
78. C3⋊D15C5×D37direct (N × H)
81. C3×C52D3×D37semidirect
84. D37C5×C3⋊D15direct (N × H)
91. C32×C5D5×D37semidirect
92. C32×C5C2×C5×D37semidirect
93. C37C2×C5×C3⋊D15semidirect
102. C52C3⋊D3×D37semidirect
109. C3×C5C5×D3×D37semidirect
110. C3×C5D15×D37semidirect
119. C32C5×D5×D37semidirect
124. C5C5×C3⋊D3×D37semidirect
125. C5D37×C3⋊D15direct (N × H)
127. C3C5×D15×D37semidirect

Maximal subgroups

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

subgroupindex
C32×C52×D372
C5×C37×C3⋊D152
C5×C3⋊D5552
C5×D15×D373
D37×C3⋊D155
C5×C3⋊D3×D375
C2×C5×C3⋊D1537