Finite Group Databasebeta

← D185⋊(C3⋊D15) #45686485

Subgroups — D185⋊(C3⋊D15) #45686485

Order 33300.

288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 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×C5×D185C211yesmaximal, characteristic, complemented
2C5×C3⋊D555C211yesmaximal, characteristic, complemented
3C37×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4D185⋊D15—34nomaximal
5C32×C52×C37C2211yescharacteristic, complemented, Hall
6D185⋊(C3⋊D3)—51nomaximal
7D37×C3⋊D15—51nomaximal
8C37×C3⋊(C5⋊D5)—34no—
9C5×D555—34no—
10C3×C5×D185D314yescomplemented
11(C5⋊D5)⋊D37—91noHall
12C3⋊D555D511yescharacteristic, complemented
13C37×C3⋊D15—51no—
14C37×C3⋊D15—51no—
15C37×C3⋊D15—102no—
16C5×C3⋊D111—51no—
17C32×D185D511yescharacteristic, complemented
18C32×C5×D37—51no—
19C3×C52×C37C2×D314yescomplemented
20D15⋊D37—154no—
21D15×D37—154no—
22C37×C5⋊D5—91no—
23C5×D185—91no—
24C5×D185C3⋊D311yescharacteristic, complemented
25C32×C5×C37—22no—
26C32×C5×C37C2×D511yescharacteristic, complemented
27C32×C5×C37C2×D511yescharacteristic, complemented
28C3⋊D3×D37—251noHall
29D555—34no—
30D15×C37—154no—
31D15×C37—154no—
32D15×C37—308no—
33C5×D111—154no—
34C3×D185D1514yescomplemented
35C3×C5×D37—54no—
36C52×C37C2×C3⋊D311yescharacteristic, complemented, Hall
37D5×C3⋊D15—371nomaximal, Hall
38D5×D37—451no—
39D5×D37—451no—
40C3⋊D111—51no—
41C3⋊D3×C37—251no—
42C32×D37—51no—
43C3×C5×C37—28no—
44C3×C5×C37D3×D514yescomplemented
45C3×C5×C37C2×D1514yescomplemented
46C3⋊(C3⋊(C5⋊D5))D3711yescharacteristic, complemented
47C5×C3⋊D15—371no—
48C32×C5×D5—371no—
49D3×D37—754no—
50D185—91no—
51D185C3⋊D1511yescharacteristic, complemented
52C5×D37—51no—
53C5×D37—451no—
54D5×C37—451no—
55D5×C37—451no—
56D5×C37—902no—
57C32×C37D5211yescharacteristic, complemented, Hall
58D5×D15—1114no—
59C32×C52C2×D3711yescharacteristic, complemented, Hall
60D111—154no—
61C3×D37—54no—
62D3×C37—754no—
63C5×C37—22no—
64C5×C37D5×C3⋊D311yescharacteristic, complemented
65C5×C37C2×C3⋊D1511yescharacteristic, complemented
66C2×C3⋊D15—1851no—
67D5×C3⋊D3—1851no—
68C3⋊(C5⋊D5)—34no—
69C5×D15—1114no—
70C3×C5×D5—374no—
71C2×D37—2251noHall
72C3×C37D5×D1514yescomplemented
73D52—3331noHall
74C2×C32×C5—1851no—
75C3⋊D15—51no—
76C3⋊D15—51no—
77C3⋊D15—102no—
78C3⋊D15—371no—
79C5×C3⋊D3—1851no—
80C32×D5—371no—
81C3×C52D3×D3714yescomplemented
82C2×C37—2251no—
83D37—51no—
84D37—451no—
85C2×D15—5554no—
86D3×D5—5554no—
87C5⋊D5—91no—
88C5×D5—371no—
89C5×D5—3331no—
90C32×C5—22no—
91C32×C5D5×D3711yescharacteristic, complemented
92C32×C5D5×D3711yescharacteristic, complemented
93C37D5×C3⋊D1511yescharacteristic, complemented, Sylow
94C2×C3⋊D3—9251noHall
95C2×C3×C5—1854no—
96D15—154no—
97D15—154no—
98D15—308no—
99D15—1114no—
100C3×D5—374no—
101C5×D3—5554no—
102C52C3⋊D3×D3711yescharacteristic, complemented, Sylow
103C2×D5—16651no—
104C2×D5—16651no—
105C2×C32—1851no—
106C3⋊D3—251no—
107C3⋊D3—1851no—
108C3×C5—28no—
109C3×C5D15×D3714yescomplemented
110C3×C5D15⋊D3714yescomplemented
111C2×D3—27754no—
112C2×C5—16651no—
113C2×C5—1851no—
114D5—371no—
115D5—451no—
116D5—451no—
117D5—3331no—
118D5—902no—
119C32(C5⋊D5)⋊D3711yescharacteristic, complemented, Sylow
120C2×C3—1854no—
121D3—5554no—
122D3—754no—
123C5—22no—
124C5D37×C3⋊D1511yescharacteristic, complemented
125C5D185⋊(C3⋊D3)11yescharacteristic, complemented
126C22—83251noSylow
127C3D185⋊D1514yescomplemented
128C2—16651no—
129C2—1851no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C37C22
LCSG ▷ C32×C52×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×D185C2semidirect
2. C5×C3⋊D555C2semidirect
3. C37×C3⋊(C3⋊(C5⋊D5))C2semidirect
5. C32×C52×C37C22semidirect
10. C3×C5×D185D3semidirect
12. C3⋊D555D5semidirect
17. C32×D185D5semidirect
19. C3×C52×C37C2×D3semidirect
24. C5×D185C3⋊D3semidirect
26. C32×C5×C37C2×D5semidirect
27. C32×C5×C37C2×D5semidirect
34. C3×D185D15semidirect
36. C52×C37C2×C3⋊D3semidirect
44. C3×C5×C37D3×D5semidirect
45. C3×C5×C37C2×D15semidirect
46. C3⋊(C3⋊(C5⋊D5))D37semidirect
51. D185C3⋊D15semidirect
57. C32×C37D52semidirect
59. C32×C52C2×D37semidirect
64. C5×C37D5×C3⋊D3semidirect
65. C5×C37C2×C3⋊D15semidirect
72. C3×C37D5×D15semidirect
81. C3×C52D3×D37semidirect
91. C32×C5D5×D37semidirect
92. C32×C5D5×D37semidirect
93. C37D5×C3⋊D15semidirect
102. C52C3⋊D3×D37semidirect
109. C3×C5D15×D37semidirect
110. C3×C5D15⋊D37semidirect
119. C32(C5⋊D5)⋊D37semidirect
124. C5D37×C3⋊D15semidirect
125. C5D185⋊(C3⋊D3)semidirect
127. C3D185⋊D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1852
C5×C3⋊D5552
C37×C3⋊(C3⋊(C5⋊D5))2
D185⋊D153
D185⋊(C3⋊D3)5
D37×C3⋊D155
D5×C3⋊D1537