Finite Group Databasebeta

← ((C5⋊D5)⋊(C37⋊C3))⋊D3 #45686258

Subgroups — ((C5⋊D5)⋊(C37⋊C3))⋊D3 #45686258

Order 33300.

128 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 23 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⋊(D37⋊(C52⋊C3))C211yesmaximal, characteristic, complemented
2C3⋊#19149851C211yesmaximal, characteristic, complemented
3C3×(C5⋊D5)⋊(C37⋊C3)C211yesmaximal, characteristic, complemented
4C5⋊D5×D111C311yesmaximal, characteristic, complemented
5D37⋊((C5⋊D5)⋊C3)—31nomaximal
6C3×C52⋊(C37⋊C3)C2211yescharacteristic, complemented, Hall
7C3⋊(C5⋊D185)C2×C311yescharacteristic, complemented
8C52×D111C2×C311yescharacteristic, complemented
9C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
10D37⋊(C52⋊C3)—31no—
11(C5⋊D5)⋊(C37⋊C3)—21no—
12(C5⋊D5)⋊(C37⋊C3)D311yescharacteristic, complemented
13#19149851—31no—
14C5⋊D5×D37—31noHall
15C52⋊(C37⋊C3)—21no—
16C52⋊(C37⋊C3)C2×D311yescharacteristic, complemented
17C3×C52×C37C22×C311yescharacteristic, complemented
18D5×D111—152no—
19C5⋊D185—31no—
20C37×C5⋊D5C3×D311yescharacteristic, complemented
21C52×D37—31no—
22C2×C3⋊(D37⋊C3)—251nomaximal, Hall
23D555—152no—
24C5×D111—32no—
25C3×D5×C37—152no—
26C52×C37C2×C3×D311yescharacteristic, complemented, Hall
27D3×(C5⋊D5)⋊C3—371nomaximal, Hall
28D5×D37—452no—
29C2×C3×C37⋊C3—251no—
30C3⋊(D37⋊C3)—251no—
31C3⋊(D37⋊C3)—251no—
32C3×C5×C37—32no—
33C3⋊((C5⋊D5)⋊C3)—371no—
34D3×C52⋊C3—371no—
35C3×(C5⋊D5)⋊C3—371no—
36C2×D111—251no—
37C2×D37⋊C3—751no—
38D185—452no—
39C5×D37—92no—
40D5×C37—152no—
41C3×C37⋊C3—251noHall
42D3×C5⋊D5—371no—
43C2×(C5⋊D5)⋊C3—1111no—
44C3×C52⋊C3—371noHall
45C2×C3×C37—251no—
46D111—251no—
47D111(C5⋊D5)⋊C311yescharacteristic, complemented
48C2×C37⋊C3—251no—
49C2×C37⋊C3—501no—
50D37⋊C3—751no—
51D37⋊C3—751no—
52C5×C37—32no—
53C3⋊(C5⋊D5)—371no—
54C52×D3—371no—
55C3×C5⋊D5D37⋊C311yescharacteristic, complemented
56C2×C52⋊C3—1111no—
57(C5⋊D5)⋊C3—371no—
58(C5⋊D5)⋊C3—741no—
59(C5⋊D5)⋊C3—1111no—
60C2×D37—751noHall
61C3×C37C2×(C5⋊D5)⋊C311yescharacteristic, complemented
62C37⋊C3—251no—
63C37⋊C3—501no—
64C2×C5⋊D5—1111noHall
65C3×C52C2×D37⋊C311yescharacteristic, complemented
66C52⋊C3—371no—
67C52⋊C3—741no—
68C2×C37—251no—
69D37—31no—
70D37—751no—
71D3×D5—5552no—
72C2×C52—1111no—
73C5⋊D5—1111no—
74C5⋊D5C3⋊(D37⋊C3)11yescharacteristic, complemented
75C37D3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
76C2×C3×D3—9251noHall
77D15—5552no—
78C3×D5—152no—
79C5×D3—1112no—
80C52C2×C3⋊(D37⋊C3)11yescharacteristic, complemented, Sylow
81C2×D5—16652no—
82C2×C32—9251no—
83C3×D3—9251no—
84C3×D3—9251no—
85C3×C5—32no—
86C22×C3—27751no—
87C2×D3—9251no—
88C2×C5—3332no—
89D5—152no—
90D5—16652no—
91C32—9251noSylow
92C2×C3—251no—
93C2×C3—18501no—
94C2×C3—9251no—
95C2×C3—27751no—
96C2×C3—27751no—
97D3—371no—
98D3—9251no—
99C5—32no—
100C22—27751noSylow
101C3—18501no—
102C3—9251no—
103C3D37⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented
104C2—251no—
105C2—1111no—
106C2—27751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C37C22×C3
LCSG ▷ C3×C52×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(D37⋊(C52⋊C3))C2semidirect
2. C3⋊#19149851C2semidirect
3. C3×(C5⋊D5)⋊(C37⋊C3)C2semidirect
4. C5⋊D5×D111C3semidirect
6. C3×C52⋊(C37⋊C3)C22semidirect
7. C3⋊(C5⋊D185)C2×C3semidirect
8. C52×D111C2×C3semidirect
9. C3×C37×C5⋊D5C2×C3semidirect
12. (C5⋊D5)⋊(C37⋊C3)D3semidirect
16. C52⋊(C37⋊C3)C2×D3semidirect
17. C3×C52×C37C22×C3semidirect
20. C37×C5⋊D5C3×D3semidirect
26. C52×C37C2×C3×D3semidirect
47. D111(C5⋊D5)⋊C3semidirect
55. C3×C5⋊D5D37⋊C3semidirect
61. C3×C37C2×(C5⋊D5)⋊C3semidirect
65. C3×C52C2×D37⋊C3semidirect
74. C5⋊D5C3⋊(D37⋊C3)semidirect
75. C37D3×(C5⋊D5)⋊C3semidirect
80. C52C2×C3⋊(D37⋊C3)semidirect
103. C3D37⋊((C5⋊D5)⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C3⋊(D37⋊(C52⋊C3))2
C3⋊#191498512
C3×(C5⋊D5)⋊(C37⋊C3)2
C5⋊D5×D1113
D37⋊((C5⋊D5)⋊C3)3
C2×C3⋊(D37⋊C3)25
D3×(C5⋊D5)⋊C337