Finite Group Databasebeta

← #45686454

Subgroups — #45686454

Order 33300.

224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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×D555C212yesmaximal, complemented
2C37×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
3D185⋊D15—32nomaximal
4C32×C52×C37C2211yescharacteristic, complemented, Hall
5D111⋊D15—52nomaximal
6C37×C3⋊(C5⋊D5)—32no—
7C37×C3⋊(C5⋊D5)—61no—
8C5×D555D312yescomplemented
9C3×C5×D185—32no—
10(C5⋊D5)⋊D37—91noHall
11C37×C3⋊D15—52no—
12C37×C3⋊D15—102no—
13C3×D555D512yescomplemented
14C3×C5×D111—52no—
15C3×C52×C37—21no—
16C3×C52×C37C2×D312yescomplemented
17D15⋊D37—152no—
18D15×D37—152no—
19C37×C5⋊D5—91no—
20C5×D185—32no—
21C32×C5×C37—22no—
22C32×C5×C37C2×D512yescomplemented
23(C3⋊D3)⋊D37—251noHall
24D555D1512yescomplemented
25D15×C37—152no—
26D15×C37—152no—
27D15×C37—304no—
28D15×C37—302no—
29D15×C37—304no—
30C5×D111—52no—
31C3×D185—32no—
32C3×C5×D37—152no—
33C52×C37D3211yescharacteristic, complemented, Hall
34D152—371nomaximal, Hall
35D5×D37—452no—
36C3⋊D3×C37—251no—
37C3×D111—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))D3711yescharacteristic, complemented
44C3×C5×D15—372no—
45D3×D37—752no—
46D185—32no—
47C5×D37—152no—
48D5×C37—452no—
49D5×C37—902no—
50C32×C37D5211yescharacteristic, complemented, Hall
51D5×D15—1112no—
52C32×C52C2×D3711yescharacteristic, complemented, Hall
53D111—52no—
54C3×D37—152no—
55D3×C37—752no—
56D3×C37—1501no—
57C5×C37—22no—
58C5×C37D3×D1512yescomplemented
59D3×D15—1852no—
60C3⋊(C5⋊D5)—32no—
61C3⋊(C5⋊D5)—61no—
62C5×D15—372no—
63C3×C5×D5—1112no—
64C2×D37—2251noHall
65C3×C37—21no—
66C3×C37D5×D1512yescomplemented
67D52—3331noHall
68C3⋊D15—52no—
69C3⋊D15—102no—
70C3×D15—372no—
71C3×C5×D3—1852no—
72C3×C52—21no—
73C3×C52D3×D3712yescomplemented
74C2×C37—2251no—
75D37—152no—
76C2×D15—5552no—
77D3×D5—5552no—
78C5⋊D5—91no—
79C5×D5—1112no—
80C32×C5—22no—
81C32×C5D5×D3712yescomplemented
82C37D15211yescharacteristic, complemented, Sylow
83D32—9251noHall
84C2×C3×C5—5552no—
85D15—152no—
86D15—152no—
87D15—304no—
88D15—302no—
89D15—304no—
90D15—372no—
91C3×D5—1112no—
92C5×D3—1852no—
93C52(C3⋊D3)⋊D3711yescharacteristic, complemented, Sylow
94C2×D5—16652no—
95C3⋊D3—251no—
96C3×D3—1852no—
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D15×D3712yescomplemented
101C3×C5D15⋊D3712yescomplemented
102C2×D3—27752no—
103C2×C5—5552no—
104D5—452no—
105D5—902no—
106D5—1112no—
107C32(C5⋊D5)⋊D3711yescharacteristic, complemented, Sylow
108C2×C3—5552no—
109D3—752no—
110D3—1501no—
111D3—1852no—
112C5—22no—
113C5D111⋊D1512yescomplemented
114C22—83251noSylow
115C3—21no—
116C3D185⋊D1512yescomplemented
117C2—5552no—
118C2—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. C3×C5×D555C2semidirect
2. C37×C3⋊(C3⋊(C5⋊D5))C2semidirect
4. C32×C52×C37C22semidirect
8. C5×D555D3semidirect
13. C3×D555D5semidirect
16. C3×C52×C37C2×D3semidirect
22. C32×C5×C37C2×D5semidirect
24. D555D15semidirect
33. C52×C37D32semidirect
41. C3×C5×C37D3×D5semidirect
42. C3×C5×C37C2×D15semidirect
43. C3⋊(C3⋊(C5⋊D5))D37semidirect
50. C32×C37D52semidirect
52. C32×C52C2×D37semidirect
58. C5×C37D3×D15semidirect
66. C3×C37D5×D15semidirect
73. C3×C52D3×D37semidirect
81. C32×C5D5×D37semidirect
82. C37D152semidirect
93. C52(C3⋊D3)⋊D37semidirect
100. C3×C5D15×D37semidirect
101. C3×C5D15⋊D37semidirect
107. C32(C5⋊D5)⋊D37semidirect
113. C5D111⋊D15semidirect
116. C3D185⋊D15semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D5552
C37×C3⋊(C3⋊(C5⋊D5))2
D185⋊D153
D111⋊D155
D15237