Finite Group Databasebeta

← C32×C5×D5×D37 #45686385

Subgroups — C32×C5×D5×D37 #45686385

Order 33300.

288 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 120 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
2C32×C5×D5×C37C211yesmaximal, characteristic, complemented
3C32×C5×D185C211yesmaximal, characteristic, complemented
4C3×C5×D5×D37C314yesmaximal, direct product factor
5C32×C52×C37C2211yescharacteristic, complemented, Hall
6C2×C32×C5×D37—51nomaximal
7C32×D5×D37C511yesmaximal, characteristic, direct product factor
8C3×C5×D185C2×C314yescomplemented
9C3×C5×D5×C37C2×C314yescomplemented
10C3×C52×D37C2×C314yescomplemented
11C5×D5×D37C3211yescharacteristic, direct product factor, Hall
12C32×D185C2×C511yescharacteristic, complemented
13C32×D5×C37C2×C511yescharacteristic, complemented
14C32×C5×D37—22no—
15C32×C5×D37—51no—
16C32×C5×D37D511yescharacteristic, direct product factor
17C32×C5×D37C2×C511yescharacteristic, complemented
18C2×C32×C5×C37—51no—
19C3×C52×C37C22×C314yescomplemented
20C2×C3×C5×D37—54no—
21C3×D5×D37C3×C514yesdirect product factor
22C5×D185C2×C3211yescharacteristic, complemented
23C5×D5×C37C2×C3211yescharacteristic, complemented
24C52×D37C2×C3211yescharacteristic, complemented
25C32×C5×C37—22no—
26C32×C5×C37C2×D511yescharacteristic, complemented
27C32×C5×C37C22×C511yescharacteristic, complemented
28C2×C32×D37—51noHall
29C2×C3×C5×C37—54no—
30C3×D185C2×C3×C514yescomplemented
31C3×D5×C37C2×C3×C514yescomplemented
32C3×C5×D37—28no—
33C3×C5×D37—54no—
34C3×C5×D37C3×D514yesdirect product factor
35C3×C5×D37C2×C3×C514yescomplemented
36C52×C37C22×C3211yescharacteristic, complemented, Hall
37C2×C32×C5×D5—371nomaximal, Hall
38C2×C5×D37—51no—
39D5×D37C32×C511yescharacteristic, direct product factor
40C2×C32×C37—51no—
41C32×D37—51no—
42C32×D37C5×D511yescharacteristic, direct product factor
43C3×C5×C37—28no—
44C3×C5×C37C2×C3×D514yescomplemented
45C3×C5×C37C22×C3×C514yescomplemented
46C2×C32×C52—371no—
47C32×C5×D5—371no—
48C32×C5×D5D3711yescharacteristic, direct product factor
49C2×C3×D37—54no—
50C2×C5×C37—51no—
51D185C2×C32×C511yescharacteristic, complemented
52C5×D37—22no—
53C5×D37—51no—
54C5×D37C32×D511yescharacteristic, direct product factor
55C5×D37C2×C32×C511yescharacteristic, complemented
56D5×C37C2×C32×C511yescharacteristic, complemented
57C32×C37C2×C5×D511yescharacteristic, complemented, Hall
58C2×C3×C5×D5—374no—
59C32×C52C2×D3711yescharacteristic, complemented, Hall
60C2×C3×C37—54no—
61C3×D37—54no—
62C3×D37C3×C5×D514yesdirect product factor
63C5×C37—22no—
64C5×C37C2×C32×D511yescharacteristic, complemented
65C5×C37C22×C32×C511yescharacteristic, complemented
66C22×C32×C5—1851no—
67C2×C32×D5—371no—
68C2×C3×C52—374no—
69C3×C5×D5—374no—
70C3×C5×D5C3×D3714yesdirect product factor
71C2×D37—51noHall
72C3×C37C2×C3×C5×D514yescomplemented
73C2×C5×D5—371noHall
74C2×C32×C5—51no—
75C2×C32×C5—371no—
76C2×C32×C5—371no—
77C2×C32×C5—742no—
78C2×C32×C5—1851no—
79C32×D5—371no—
80C32×D5C5×D3711yescharacteristic, direct product factor
81C3×C52C2×C3×D3714yescomplemented
82C2×C37—51no—
83D37—51no—
84D37C32×C5×D511yescharacteristic, direct product factor
85C22×C3×C5—1854no—
86C2×C3×D5—374no—
87C2×C52—371no—
88C5×D5—371no—
89C5×D5C32×D3711yescharacteristic, direct product factor
90C32×C5—22no—
91C32×C5D5×D3711yescharacteristic, direct product factor
92C32×C5C2×C5×D3711yescharacteristic, complemented
93C37C2×C32×C5×D511yescharacteristic, complemented, Sylow
94C22×C32—1851noHall
95C2×C3×C5—54no—
96C2×C3×C5—374no—
97C2×C3×C5—374no—
98C2×C3×C5—748no—
99C2×C3×C5—1854no—
100C3×D5—374no—
101C3×D5C3×C5×D3714yesdirect product factor
102C52C2×C32×D3711yescharacteristic, complemented, Sylow
103C22×C5—1851no—
104C2×D5—371no—
105C2×C32—51no—
106C2×C32—371no—
107C2×C32—1851no—
108C3×C5—28no—
109C3×C5C3×D5×D3714yesdirect product factor
110C3×C5C2×C3×C5×D3714yescomplemented
111C22×C3—1854no—
112C2×C5—51no—
113C2×C5—371no—
114C2×C5—371no—
115C2×C5—742no—
116C2×C5—1851no—
117D5—371no—
118D5C32×C5×D3711yescharacteristic, direct product factor
119C32C5×D5×D3711yescharacteristic, direct product factor, Sylow
120C2×C3—54no—
121C2×C3—374no—
122C2×C3—1854no—
123C5—22no—
124C5C32×D5×D3711yescharacteristic, direct product factor
125C5C2×C32×C5×D3711yescharacteristic, complemented
126C22—1851noSylow
127C3C3×C5×D5×D3714yesdirect product factor
128C2—51no—
129C2—371no—
130C2—1851no—
subgroupG/H
center, hypercenterC32×C5D5×D37
commutator, cosocle, hypocenterC5×C37C22×C32×C5
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C5×C37
UCSC1 ◁ C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C52×D37C2semidirect
2. C32×C5×D5×C37C2semidirect
3. C32×C5×D185C2semidirect
4. C3×C5×D5×D37C3direct (N × H)
5. C32×C52×C37C22semidirect
7. C32×D5×D37C5direct (N × H)
8. C3×C5×D185C2×C3semidirect
9. C3×C5×D5×C37C2×C3semidirect
10. C3×C52×D37C2×C3semidirect
11. C5×D5×D37C32direct (N × H)
12. C32×D185C2×C5semidirect
13. C32×D5×C37C2×C5semidirect
16. C32×C5×D37D5direct (N × H)
17. C32×C5×D37C2×C5semidirect
19. C3×C52×C37C22×C3semidirect
21. C3×D5×D37C3×C5direct (N × H)
22. C5×D185C2×C32semidirect
23. C5×D5×C37C2×C32semidirect
24. C52×D37C2×C32semidirect
26. C32×C5×C37C2×D5semidirect
27. C32×C5×C37C22×C5semidirect
30. C3×D185C2×C3×C5semidirect
31. C3×D5×C37C2×C3×C5semidirect
34. C3×C5×D37C3×D5direct (N × H)
35. C3×C5×D37C2×C3×C5semidirect
36. C52×C37C22×C32semidirect
39. D5×D37C32×C5direct (N × H)
42. C32×D37C5×D5direct (N × H)
44. C3×C5×C37C2×C3×D5semidirect
45. C3×C5×C37C22×C3×C5semidirect
48. C32×C5×D5D37direct (N × H)
51. D185C2×C32×C5semidirect
54. C5×D37C32×D5direct (N × H)
55. C5×D37C2×C32×C5semidirect
56. D5×C37C2×C32×C5semidirect
57. C32×C37C2×C5×D5semidirect
59. C32×C52C2×D37semidirect
62. C3×D37C3×C5×D5direct (N × H)
64. C5×C37C2×C32×D5semidirect
65. C5×C37C22×C32×C5semidirect
70. C3×C5×D5C3×D37direct (N × H)
72. C3×C37C2×C3×C5×D5semidirect
80. C32×D5C5×D37direct (N × H)
81. C3×C52C2×C3×D37semidirect
84. D37C32×C5×D5direct (N × H)
89. C5×D5C32×D37direct (N × H)
91. C32×C5D5×D37direct (N × H)
92. C32×C5C2×C5×D37semidirect
93. C37C2×C32×C5×D5semidirect
101. C3×D5C3×C5×D37direct (N × H)
102. C52C2×C32×D37semidirect
109. C3×C5C3×D5×D37direct (N × H)
110. C3×C5C2×C3×C5×D37semidirect
118. D5C32×C5×D37direct (N × H)
119. C32C5×D5×D37direct (N × H)
124. C5C32×D5×D37direct (N × H)
125. C5C2×C32×C5×D37semidirect
127. C3C3×C5×D5×D37direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×D372
C32×C5×D5×C372
C32×C5×D1852
C3×C5×D5×D373
C2×C32×C5×D375
C32×D5×D375
C2×C32×C5×D537