Finite Group Databasebeta

← #45686264

Subgroups — #45686264

Order 33300.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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
1C52⋊C3×D111C211yesmaximal, characteristic, complemented
2C37×C3⋊((C5⋊D5)⋊C3)C211yesmaximal, characteristic, complemented
3C3×#19149853C211yesmaximal, characteristic, complemented
4D111⋊(C5⋊D5)C311yesmaximal, characteristic, complemented
5D37×(C5⋊D5)⋊C3—31nomaximal
6C3×C37×C52⋊C3C2211yescharacteristic, complemented, Hall
7C37×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
8C52×D111C2×C311yescharacteristic, complemented
9C3×C5⋊D185C2×C311yescharacteristic, complemented
10D37×C52⋊C3—31no—
11#19149853—21no—
12#19149853D311yescharacteristic, complemented
13C37×(C5⋊D5)⋊C3—31no—
14C5⋊D5×D37—31noHall
15C37×C52⋊C3—21no—
16C37×C52⋊C3C2×D311yescharacteristic, complemented
17C3×C52×C37C22×C311yescharacteristic, complemented
18D15⋊D37—152no—
19C5⋊D185C3×D311yescharacteristic, complemented
20C37×C5⋊D5—31no—
21C52×D37—31no—
22C3×D3×D37—251nomaximal, Hall
23D15×C37—152no—
24C5×D111—32no—
25C3×D185—152no—
26C52×C37C2×C3×D311yescharacteristic, complemented, Hall
27D3×(C5⋊D5)⋊C3—371nomaximal, Hall
28D5×D37—452no—
29C3×D111—251no—
30C3×D3×C37—251no—
31C32×D37—251no—
32C3×C5×C37—32no—
33C3⋊((C5⋊D5)⋊C3)D3711yescharacteristic, complemented
34D3×C52⋊C3—371no—
35C3×(C5⋊D5)⋊C3—371no—
36C2×C3×D37—751no—
37D3×D37—251no—
38D185—152no—
39C5×D37—92no—
40D5×C37—452no—
41C32×C37—251noHall
42D3×C5⋊D5—371no—
43C2×(C5⋊D5)⋊C3—1111no—
44C3×C52⋊C3C2×D3711yescharacteristic, complemented, Hall
45C2×C3×C37—751no—
46D111(C5⋊D5)⋊C311yescharacteristic, complemented
47C3×D37—251no—
48C3×D37—251no—
49C3×D37—501no—
50C3×D37—751no—
51D3×C37—251no—
52C5×C37—32no—
53C3⋊(C5⋊D5)C3×D3711yescharacteristic, complemented
54C52×D3—371no—
55C3×C5⋊D5—371no—
56C2×C52⋊C3—1111no—
57(C5⋊D5)⋊C3—31no—
58(C5⋊D5)⋊C3—371no—
59(C5⋊D5)⋊C3—741no—
60C2×D37—751noHall
61C3×C37—251no—
62C3×C37—501no—
63C3×C37C2×(C5⋊D5)⋊C311yescharacteristic, complemented
64C2×C5⋊D5—1111noHall
65C3×C52C2×C3×D3711yescharacteristic, complemented
66C52⋊C3—21no—
67C52⋊C3D3×D3711yescharacteristic, complemented
68C2×C37—751no—
69D37—31no—
70D37—251no—
71D3×D5—5552no—
72C2×C52—1111no—
73C5⋊D5—31no—
74C5⋊D5—371no—
75C37D3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
76C2×C3×D3—9251noHall
77D15—152no—
78C3×D5—5552no—
79C5×D3—1112no—
80C52C3×D3×D3711yescharacteristic, complemented, Sylow
81C2×D5—16652no—
82C2×C32—9251no—
83C3×D3—251no—
84C3×D3—9251no—
85C3×C5—32no—
86C22×C3—27751no—
87C2×D3—9251no—
88C2×C5—3332no—
89D5—5552no—
90D5—452no—
91C32—251noSylow
92C2×C3—18501no—
93C2×C3—751no—
94C2×C3—9251no—
95C2×C3—9251no—
96C2×C3—27751no—
97D3—251no—
98D3—371no—
99C5—32no—
100C22—27751noSylow
101C3—251no—
102C3—501no—
103C3D37×(C5⋊D5)⋊C311yescharacteristic, complemented
104C2—751no—
105C2—1111no—
106C2—9251no—
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. C52⋊C3×D111C2semidirect
2. C37×C3⋊((C5⋊D5)⋊C3)C2semidirect
3. C3×#19149853C2semidirect
4. D111⋊(C5⋊D5)C3semidirect
6. C3×C37×C52⋊C3C22semidirect
7. C37×C3⋊(C5⋊D5)C2×C3semidirect
8. C52×D111C2×C3semidirect
9. C3×C5⋊D185C2×C3semidirect
12. #19149853D3semidirect
16. C37×C52⋊C3C2×D3semidirect
17. C3×C52×C37C22×C3semidirect
19. C5⋊D185C3×D3semidirect
26. C52×C37C2×C3×D3semidirect
33. C3⋊((C5⋊D5)⋊C3)D37semidirect
44. C3×C52⋊C3C2×D37semidirect
46. D111(C5⋊D5)⋊C3semidirect
53. C3⋊(C5⋊D5)C3×D37semidirect
63. C3×C37C2×(C5⋊D5)⋊C3semidirect
65. C3×C52C2×C3×D37semidirect
67. C52⋊C3D3×D37semidirect
75. C37D3×(C5⋊D5)⋊C3semidirect
80. C52C3×D3×D37semidirect
103. C3D37×(C5⋊D5)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C52⋊C3×D1112
C37×C3⋊((C5⋊D5)⋊C3)2
C3×#191498532
D111⋊(C5⋊D5)3
D37×(C5⋊D5)⋊C33
C3×D3×D3725
D3×(C5⋊D5)⋊C337