Finite Group Databasebeta

← D152×C37 #45686452

Subgroups — D152×C37 #45686452

Order 33300.

224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C3×C5×D15×C37C212yesmaximal, complemented
2C37×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
3D5×D15×C37—32nomaximal
4C32×C52×C37C2211yescharacteristic, complemented, Hall
5D3×D15×C37—52nomaximal
6C37×C3⋊(C5⋊D5)—32no—
7C37×C3⋊(C5⋊D5)—61no—
8C5×D15×C37D312yescomplemented
9C3×C5×D5×C37—32no—
10D52×C37—91noHall
11C37×C3⋊D15—52no—
12C37×C3⋊D15—102no—
13C3×D15×C37D512yescomplemented
14C3×C5×D3×C37—52no—
15C3×C52×C37—21no—
16C3×C52×C37C2×D312yescomplemented
17C2×D15×C37—152no—
18D3×D5×C37—152no—
19C37×C5⋊D5—91no—
20C5×D5×C37—32no—
21C32×C5×C37—22no—
22C32×C5×C37C2×D512yescomplemented
23D32×C37—251noHall
24C2×C3×C5×C37—152no—
25D15×C37—152no—
26D15×C37—152no—
27D15×C37—304no—
28D15×C37—302no—
29D15×C37—304no—
30D15×C37D1512yesdirect product factor
31C5×D3×C37—52no—
32C3×D5×C37—32no—
33C52×C37D3211yescharacteristic, complemented, Hall
34D152C3711yesmaximal, characteristic, direct product factor, Hall
35C2×D5×C37—452no—
36C3⋊D3×C37—251no—
37C3×D3×C37—52no—
38C3×C5×C37—24no—
39C3×C5×C37—24no—
40C3×C5×C37—22no—
41C3×C5×C37D3×D512yescomplemented
42C3×C5×C37C2×D1512yescomplemented
43C3⋊(C3⋊(C5⋊D5))C2×C3711yescharacteristic, complemented
44C3×C5×D15C2×C3712yescomplemented
45C2×D3×C37—752no—
46C2×C5×C37—152no—
47D5×C37—32no—
48D5×C37—452no—
49D5×C37—902no—
50C32×C37D5211yescharacteristic, complemented, Hall
51D5×D15—32no—
52C32×C52C22×C3711yescharacteristic, complemented, Hall
53C2×C3×C37—152no—
54D3×C37—52no—
55D3×C37—752no—
56D3×C37—1501no—
57C5×C37—22no—
58C5×C37D3×D1512yescomplemented
59D3×D15—52no—
60C3⋊(C5⋊D5)—32no—
61C3⋊(C5⋊D5)—61no—
62C5×D15D3×C3712yescomplemented
63C3×C5×D5—32no—
64C22×C37—2251noHall
65C3×C37—21no—
66C3×C37D5×D1512yescomplemented
67D52—91noHall
68C3⋊D15—52no—
69C3⋊D15—102no—
70C3×D15D5×C3712yescomplemented
71C3×C5×D3—52no—
72C3×C52—21no—
73C3×C52C2×D3×C3712yescomplemented
74C2×C37—152no—
75C2×C37—2251no—
76C2×D15—152no—
77D3×D5—152no—
78C5⋊D5—91no—
79C5×D5—32no—
80C32×C5—22no—
81C32×C5C2×D5×C3712yescomplemented
82C37D15211yescharacteristic, direct product factor, Sylow
83D32—251noHall
84C2×C3×C5—152no—
85D15—152no—
86D15—152no—
87D15—304no—
88D15—302no—
89D15—304no—
90D15D15×C3712yesdirect product factor
91C3×D5—32no—
92C5×D3—52no—
93C52D32×C3711yescharacteristic, complemented, Sylow
94C2×D5—452no—
95C3⋊D3—251no—
96C3×D3—52no—
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D3×D5×C3712yescomplemented
101C3×C5C2×D15×C3712yescomplemented
102C2×D3—752no—
103C2×C5—152no—
104D5—32no—
105D5—452no—
106D5—902no—
107C32D52×C3711yescharacteristic, complemented, Sylow
108C2×C3—152no—
109D3—52no—
110D3—752no—
111D3—1501no—
112C5—22no—
113C5D3×D15×C3712yescomplemented
114C22—2251noSylow
115C3—21no—
116C3D5×D15×C3712yescomplemented
117C2—152no—
118C2—2251no—
subgroupG/H
center, hypercenterC37D152
commutator, cosocle, hypocenterC32×C52C22×C37
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C32×C52
UCSC1 ◁ C37

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C37C2semidirect
2. C37×C3⋊(C3⋊(C5⋊D5))C2semidirect
4. C32×C52×C37C22semidirect
8. C5×D15×C37D3semidirect
13. C3×D15×C37D5semidirect
16. C3×C52×C37C2×D3semidirect
22. C32×C5×C37C2×D5semidirect
30. D15×C37D15direct (N × H)
33. C52×C37D32semidirect
34. D152C37direct (N × H)
41. C3×C5×C37D3×D5semidirect
42. C3×C5×C37C2×D15semidirect
43. C3⋊(C3⋊(C5⋊D5))C2×C37semidirect
44. C3×C5×D15C2×C37semidirect
50. C32×C37D52semidirect
52. C32×C52C22×C37semidirect
58. C5×C37D3×D15semidirect
62. C5×D15D3×C37semidirect
66. C3×C37D5×D15semidirect
70. C3×D15D5×C37semidirect
73. C3×C52C2×D3×C37semidirect
81. C32×C5C2×D5×C37semidirect
82. C37D152direct (N × H)
90. D15D15×C37direct (N × H)
93. C52D32×C37semidirect
100. C3×C5D3×D5×C37semidirect
101. C3×C5C2×D15×C37semidirect
107. C32D52×C37semidirect
113. C5D3×D15×C37semidirect
116. C3D5×D15×C37semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C372
C37×C3⋊(C3⋊(C5⋊D5))2
D5×D15×C373
D3×D15×C375
D15237