Finite Group Databasebeta

← D3×(C5⋊D5)⋊(C37⋊C3) #45686261

Subgroups — D3×(C5⋊D5)⋊(C37⋊C3) #45686261

Order 33300.

128 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 27 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
1D3×C52⋊(C37⋊C3)C211yesmaximal, characteristic, complemented
2C3⋊((C5⋊D5)⋊(C37⋊C3))C211yesmaximal, characteristic, complemented
3C3×(C5⋊D5)⋊(C37⋊C3)C211yesmaximal, characteristic, complemented
4D3×C37×C5⋊D5C311yesmaximal, characteristic, complemented
5C2×(C5⋊D5)⋊(C37⋊C3)—31nomaximal
6C3×C52⋊(C37⋊C3)C2211yescharacteristic, complemented, Hall
7C37×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
8C52×D3×C37C2×C311yescharacteristic, complemented
9C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
10C2×C52⋊(C37⋊C3)—31no—
11(C5⋊D5)⋊(C37⋊C3)—21no—
12(C5⋊D5)⋊(C37⋊C3)—31no—
13(C5⋊D5)⋊(C37⋊C3)D311yescharacteristic, direct product factor
14C2×C37×C5⋊D5—31noHall
15C52⋊(C37⋊C3)—21no—
16C52⋊(C37⋊C3)C2×D311yescharacteristic, complemented
17C3×C52×C37C22×C311yescharacteristic, complemented
18D3×D5×C37—152no—
19C2×C52×C37—31no—
20C37×C5⋊D5—31no—
21C37×C5⋊D5C3×D311yescharacteristic, complemented
22C2×D3×C37⋊C3—251nomaximal, Hall
23D15×C37—152no—
24C5×D3×C37—32no—
25C3×D5×C37—152no—
26C52×C37C2×C3×D311yescharacteristic, complemented, Hall
27D3×(C5⋊D5)⋊C3—371nomaximal, Hall
28C2×D5×C37—452no—
29C2×C3×C37⋊C3—251no—
30D3×C37⋊C3—251no—
31D3×C37⋊C3—251no—
32C3×C5×C37—32no—
33C3⋊((C5⋊D5)⋊C3)—371no—
34D3×C52⋊C3—371no—
35C3×(C5⋊D5)⋊C3—371no—
36C2×D3×C37—251no—
37C22×C37⋊C3—751no—
38C2×C5×C37—92no—
39D5×C37—152no—
40D5×C37—452no—
41C3×C37⋊C3—251noHall
42D3×C5⋊D5C37⋊C311yescharacteristic, complemented
43C2×(C5⋊D5)⋊C3—1111no—
44C3×C52⋊C3—371noHall
45C2×C3×C37—251no—
46D3×C37—251no—
47D3×C37(C5⋊D5)⋊C311yescharacteristic, complemented
48C2×C37⋊C3—251no—
49C2×C37⋊C3—501no—
50C2×C37⋊C3—751no—
51C2×C37⋊C3—751no—
52C5×C37—32no—
53C3⋊(C5⋊D5)C2×C37⋊C311yescharacteristic, complemented
54C52×D3C2×C37⋊C311yescharacteristic, complemented
55C3×C5⋊D5C2×C37⋊C311yescharacteristic, complemented
56C2×C52⋊C3—1111no—
57(C5⋊D5)⋊C3—371no—
58(C5⋊D5)⋊C3—741no—
59(C5⋊D5)⋊C3—1111no—
60C22×C37—751noHall
61C3×C37C2×(C5⋊D5)⋊C311yescharacteristic, complemented
62C37⋊C3—251no—
63C37⋊C3—501no—
64C2×C5⋊D5—31noHall
65C3×C52C22×C37⋊C311yescharacteristic, complemented
66C52⋊C3—371no—
67C52⋊C3—741no—
68C2×C37—31no—
69C2×C37—251no—
70C2×C37—751no—
71D3×D5—152no—
72C2×C52—31no—
73C5⋊D5—31no—
74C5⋊D5D3×C37⋊C311yescharacteristic, complemented
75C37D3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
76C2×C3×D3—9251noHall
77D15—152no—
78C3×D5—152no—
79C5×D3—32no—
80C52C2×D3×C37⋊C311yescharacteristic, complemented, Sylow
81C2×D5—452no—
82C2×C32—9251no—
83C3×D3—9251no—
84C3×D3—9251no—
85C3×C5—32no—
86C22×C3—27751no—
87C2×D3—251no—
88C2×C5—92no—
89D5—152no—
90D5—452no—
91C32—9251noSylow
92C2×C3—251no—
93C2×C3—18501no—
94C2×C3—9251no—
95C2×C3—27751no—
96C2×C3—27751no—
97D3—251no—
98D3(C5⋊D5)⋊(C37⋊C3)11yescharacteristic, direct product factor
99C5—32no—
100C22—751noSylow
101C3—18501no—
102C3—9251no—
103C3C2×(C5⋊D5)⋊(C37⋊C3)11yescharacteristic, complemented
104C2—31no—
105C2—251no—
106C2—751no—
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. D3×C52⋊(C37⋊C3)C2semidirect
2. C3⋊((C5⋊D5)⋊(C37⋊C3))C2semidirect
3. C3×(C5⋊D5)⋊(C37⋊C3)C2semidirect
4. D3×C37×C5⋊D5C3semidirect
6. C3×C52⋊(C37⋊C3)C22semidirect
7. C37×C3⋊(C5⋊D5)C2×C3semidirect
8. C52×D3×C37C2×C3semidirect
9. C3×C37×C5⋊D5C2×C3semidirect
13. (C5⋊D5)⋊(C37⋊C3)D3direct (N × H)
16. C52⋊(C37⋊C3)C2×D3semidirect
17. C3×C52×C37C22×C3semidirect
21. C37×C5⋊D5C3×D3semidirect
26. C52×C37C2×C3×D3semidirect
42. D3×C5⋊D5C37⋊C3semidirect
47. D3×C37(C5⋊D5)⋊C3semidirect
53. C3⋊(C5⋊D5)C2×C37⋊C3semidirect
54. C52×D3C2×C37⋊C3semidirect
55. C3×C5⋊D5C2×C37⋊C3semidirect
61. C3×C37C2×(C5⋊D5)⋊C3semidirect
65. C3×C52C22×C37⋊C3semidirect
74. C5⋊D5D3×C37⋊C3semidirect
75. C37D3×(C5⋊D5)⋊C3semidirect
80. C52C2×D3×C37⋊C3semidirect
98. D3(C5⋊D5)⋊(C37⋊C3)direct (N × H)
103. C3C2×(C5⋊D5)⋊(C37⋊C3)semidirect

Maximal subgroups

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

subgroupindex
D3×C52⋊(C37⋊C3)2
C3⋊((C5⋊D5)⋊(C37⋊C3))2
C3×(C5⋊D5)⋊(C37⋊C3)2
D3×C37×C5⋊D53
C2×(C5⋊D5)⋊(C37⋊C3)3
C2×D3×C37⋊C325
D3×(C5⋊D5)⋊C337