Finite Group Databasebeta

← D185⋊D45 #45686051

Subgroups — D185⋊D45 #45686051

Order 33300.

144 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 35 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×D1665C211yesmaximal, characteristic, complemented
3C5×C9×D185C211yesmaximal, characteristic, complemented
4D185⋊D15—31nomaximal
5C52×C9×C37C2211yescharacteristic, complemented, Hall
6D45⋊D37—51nomaximal
7D37×D45—51nomaximal
8C37×C3⋊(C5⋊D5)—31no—
9C5×D555—31no—
10C3×C5×D185D311yescharacteristic
11(C5⋊D5)⋊D37—91noHall
12D1665D511yescharacteristic, complemented
13C37×D45—51no—
14C37×D45—51no—
15C37×D45—102no—
16C5×D333—51no—
17C9×D185D511yescharacteristic, complemented
18C5×C9×D37—51no—
19C3×C52×C37C2×D311yescharacteristic
20D15⋊D37—151no—
21D15×D37—151no—
22C37×C5⋊D5—91no—
23C5×D185—91no—
24C5×D185D911yescharacteristic, complemented
25C5×C9×C37—22no—
26C5×C9×C37C2×D511yescharacteristic, complemented
27C5×C9×C37C2×D511yescharacteristic, complemented
28D9×D37—251noHall
29D555—31no—
30D15×C37—151no—
31D15×C37—151no—
32D15×C37—302no—
33C5×D111—151no—
34C3×D185D1511yescharacteristic
35C3×C5×D37—51no—
36C52×C37C2×D911yescharacteristic, complemented, Hall
37D5×D45—371nomaximal, Hall
38D5×D37—451no—
39D5×D37—451no—
40D333—51no—
41C9×D37—51no—
42D9×C37—251no—
43C3×C5×C37—22no—
44C3×C5×C37D3×D511yescharacteristic
45C3×C5×C37C2×D1511yescharacteristic
46C5⋊D45D3711yescharacteristic, complemented
47C5×D45—371no—
48C5×C9×D5—371no—
49D3×D37—751no—
50D185—91no—
51D185D4511yescharacteristic, complemented
52C5×D37—51no—
53C5×D37—451no—
54D5×C37—451no—
55D5×C37—451no—
56D5×C37—902no—
57C9×C37D5211yescharacteristic, complemented, Hall
58D5×D15—1111no—
59C52×C9C2×D3711yescharacteristic, complemented, Hall
60D111—151no—
61C3×D37—51no—
62D3×C37—751no—
63C5×C37—22no—
64C5×C37D5×D911yescharacteristic, complemented
65C5×C37C2×D4511yescharacteristic, complemented
66C2×D45—1851no—
67D5×D9—1851no—
68C3⋊(C5⋊D5)—31no—
69C5×D15—1111no—
70C3×C5×D5—371no—
71C2×D37—2251noHall
72C3×C37D5×D1511yescharacteristic
73D52—3331noHall
74C2×C5×C9—1851no—
75D45—51no—
76D45—51no—
77D45—102no—
78D45—371no—
79C9×D5—371no—
80C5×D9—1851no—
81C3×C52D3×D3711yescharacteristic
82C2×C37—2251no—
83D37—51no—
84D37—451no—
85C2×D15—5551no—
86D3×D5—5551no—
87C5⋊D5—91no—
88C5×D5—371no—
89C5×D5—3331no—
90C5×C9—22no—
91C5×C9D5×D3711yescharacteristic, complemented
92C5×C9D5×D3711yescharacteristic, complemented
93C37D5×D4511yescharacteristic, complemented, Sylow
94C2×D9—9251noHall
95C2×C3×C5—1851no—
96D15—151no—
97D15—151no—
98D15—302no—
99D15—1111no—
100C3×D5—371no—
101C5×D3—5551no—
102C52D9×D3711yescharacteristic, complemented, Sylow
103C2×D5—16651no—
104C2×D5—16651no—
105C2×C9—1851no—
106D9—251no—
107D9—1851no—
108C3×C5—22no—
109C3×C5D15×D3711yescharacteristic
110C3×C5D15⋊D3711yescharacteristic
111C2×D3—27751no—
112C2×C5—16651no—
113C2×C5—1851no—
114D5—371no—
115D5—451no—
116D5—451no—
117D5—3331no—
118D5—902no—
119C9(C5⋊D5)⋊D3711yescharacteristic, complemented, Sylow
120C2×C3—1851no—
121D3—5551no—
122D3—751no—
123C5—22no—
124C5D37×D4511yescharacteristic, complemented
125C5D45⋊D3711yescharacteristic, complemented
126C22—83251noSylow
127C3D185⋊D1511yescharacteristic
128C2—16651no—
129C2—1851no—
130C2—2251no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC52×C9×C37C22
FrattiniC3D185⋊D15
socleC3×C52×C37C2×D3
LCSG ▷ C52×C9×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C37×C5⋊D45C2semidirect
2. C5×D1665C2semidirect
3. C5×C9×D185C2semidirect
5. C52×C9×C37C22semidirect
12. D1665D5semidirect
17. C9×D185D5semidirect
24. C5×D185D9semidirect
26. C5×C9×C37C2×D5semidirect
27. C5×C9×C37C2×D5semidirect
36. C52×C37C2×D9semidirect
46. C5⋊D45D37semidirect
51. D185D45semidirect
57. C9×C37D52semidirect
59. C52×C9C2×D37semidirect
64. C5×C37D5×D9semidirect
65. C5×C37C2×D45semidirect
91. C5×C9D5×D37semidirect
92. C5×C9D5×D37semidirect
93. C37D5×D45semidirect
102. C52D9×D37semidirect
119. C9(C5⋊D5)⋊D37semidirect
124. C5D37×D45semidirect
125. C5D45⋊D37semidirect

Maximal subgroups

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

subgroupindex
C37×C5⋊D452
C5×D16652
C5×C9×D1852
D185⋊D153
D45⋊D375
D37×D455
D5×D4537