Finite Group Databasebeta

← D5×C37×D45 #45686048

Subgroups — D5×C37×D45 #45686048

Order 33300.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C37×C5⋊D45C211yesmaximal, characteristic, complemented
2C5×C37×D45C211yesmaximal, characteristic, complemented
3C5×C9×D5×C37C211yesmaximal, characteristic, complemented
4D5×D15×C37—31nomaximal
5C52×C9×C37C2211yescharacteristic, complemented, Hall
6C2×C37×D45—51nomaximal
7D5×D9×C37—51nomaximal
8C37×C3⋊(C5⋊D5)—31no—
9C5×D15×C37—31no—
10C3×C5×D5×C37D311yescharacteristic
11D52×C37—91noHall
12C37×D45—51no—
13C37×D45—51no—
14C37×D45—102no—
15C37×D45D511yescharacteristic, direct product factor
16C5×D9×C37—51no—
17C9×D5×C37D511yescharacteristic, complemented
18C2×C5×C9×C37—51no—
19C3×C52×C37C2×D311yescharacteristic
20C2×D15×C37—151no—
21D3×D5×C37—151no—
22C37×C5⋊D5—91no—
23C5×D5×C37—91no—
24C5×D5×C37D911yescharacteristic, complemented
25C5×C9×C37—22no—
26C5×C9×C37C2×D511yescharacteristic, complemented
27C5×C9×C37C2×D511yescharacteristic, complemented
28C2×D9×C37—251noHall
29C2×C3×C5×C37—51no—
30D15×C37—31no—
31D15×C37—151no—
32D15×C37—151no—
33D15×C37—302no—
34C5×D3×C37—151no—
35C3×D5×C37D1511yescharacteristic
36C52×C37C2×D911yescharacteristic, complemented, Hall
37D5×D45C3711yesmaximal, characteristic, direct product factor, Hall
38C2×D5×C37—451no—
39C2×D5×C37—451no—
40C2×C9×C37—51no—
41D9×C37—51no—
42D9×C37—251no—
43C3×C5×C37—22no—
44C3×C5×C37D3×D511yescharacteristic
45C3×C5×C37C2×D1511yescharacteristic
46C5⋊D45C2×C3711yescharacteristic, complemented
47C5×D45C2×C3711yescharacteristic, complemented
48C5×C9×D5C2×C3711yescharacteristic, complemented
49C2×D3×C37—751no—
50C2×C5×C37—51no—
51C2×C5×C37—451no—
52D5×C37—91no—
53D5×C37—451no—
54D5×C37—451no—
55D5×C37—902no—
56D5×C37D4511yescharacteristic, direct product factor
57C9×C37D5211yescharacteristic, complemented, Hall
58D5×D15—31no—
59C52×C9C22×C3711yescharacteristic, complemented, Hall
60C2×C3×C37—51no—
61D3×C37—151no—
62D3×C37—751no—
63C5×C37—22no—
64C5×C37D5×D911yescharacteristic, complemented
65C5×C37C2×D4511yescharacteristic, complemented
66C2×D45—51no—
67D5×D9—51no—
68C3⋊(C5⋊D5)—31no—
69C5×D15—31no—
70C3×C5×D5D3×C3711yescharacteristic
71C22×C37—2251noHall
72C3×C37D5×D1511yescharacteristic
73D52—91noHall
74C2×C5×C9—51no—
75D45—51no—
76D45—51no—
77D45—102no—
78D45D5×C3711yescharacteristic, direct product factor
79C9×D5D5×C3711yescharacteristic, complemented
80C5×D9—51no—
81C3×C52C2×D3×C3711yescharacteristic
82C2×C37—51no—
83C2×C37—451no—
84C2×C37—2251no—
85C2×D15—151no—
86D3×D5—151no—
87C5⋊D5—91no—
88C5×D5—91no—
89C5×D5D9×C3711yescharacteristic, complemented
90C5×C9—22no—
91C5×C9C2×D5×C3711yescharacteristic, complemented
92C5×C9C2×D5×C3711yescharacteristic, complemented
93C37D5×D4511yescharacteristic, direct product factor, Sylow
94C2×D9—251noHall
95C2×C3×C5—51no—
96D15—31no—
97D15—151no—
98D15—151no—
99D15—302no—
100C3×D5D15×C3711yescharacteristic
101C5×D3—151no—
102C52C2×D9×C3711yescharacteristic, complemented, Sylow
103C2×D5—451no—
104C2×D5—451no—
105C2×C9—51no—
106D9—51no—
107D9—251no—
108C3×C5—22no—
109C3×C5D3×D5×C3711yescharacteristic
110C3×C5C2×D15×C3711yescharacteristic
111C2×D3—751no—
112C2×C5—51no—
113C2×C5—451no—
114D5—91no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5C37×D4511yescharacteristic, direct product factor
119C9D52×C3711yescharacteristic, complemented, Sylow
120C2×C3—51no—
121D3—151no—
122D3—751no—
123C5—22no—
124C5D5×D9×C3711yescharacteristic, complemented
125C5C2×C37×D4511yescharacteristic, complemented
126C22—2251noSylow
127C3D5×D15×C3711yescharacteristic
128C2—51no—
129C2—451no—
130C2—2251no—
subgroupG/H
center, hypercenterC37D5×D45
commutator, cosocle, hypocenterC52×C9C22×C37
FrattiniC3D5×D15×C37
FittingC52×C9×C37C22
socleC3×C52×C37C2×D3
LCSG ▷ C52×C9
UCSC1 ◁ C37

Complements

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

NH ≅ G/Ntype
1. C37×C5⋊D45C2semidirect
2. C5×C37×D45C2semidirect
3. C5×C9×D5×C37C2semidirect
5. C52×C9×C37C22semidirect
15. C37×D45D5direct (N × H)
17. C9×D5×C37D5semidirect
24. C5×D5×C37D9semidirect
26. C5×C9×C37C2×D5semidirect
27. C5×C9×C37C2×D5semidirect
36. C52×C37C2×D9semidirect
37. D5×D45C37direct (N × H)
46. C5⋊D45C2×C37semidirect
47. C5×D45C2×C37semidirect
48. C5×C9×D5C2×C37semidirect
56. D5×C37D45direct (N × H)
57. C9×C37D52semidirect
59. C52×C9C22×C37semidirect
64. C5×C37D5×D9semidirect
65. C5×C37C2×D45semidirect
78. D45D5×C37direct (N × H)
79. C9×D5D5×C37semidirect
89. C5×D5D9×C37semidirect
91. C5×C9C2×D5×C37semidirect
92. C5×C9C2×D5×C37semidirect
93. C37D5×D45direct (N × H)
102. C52C2×D9×C37semidirect
118. D5C37×D45direct (N × H)
119. C9D52×C37semidirect
124. C5D5×D9×C37semidirect
125. C5C2×C37×D45semidirect

Maximal subgroups

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

subgroupindex
C37×C5⋊D452
C5×C37×D452
C5×C9×D5×C372
D5×D15×C373
C2×C37×D455
D5×D9×C375
D5×D4537