Finite Group Databasebeta

← C3×D3×C17×C5⋊D5 #29505973

Subgroups — C3×D3×C17×C5⋊D5 #29505973

Order 15300.

352 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 112 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×C17×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C52×D3×C17C211yesmaximal, characteristic, complemented
3C32×C17×C5⋊D5C211yesmaximal, characteristic, complemented
4C2×C3×C17×C5⋊D5—31nomaximal
5D3×C17×C5⋊D5C311yesmaximal, characteristic, direct product factor
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7C3×D3×D5×C17—56nomaximal
8C17×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D3×C17C2×C311yescharacteristic, complemented
10C3×C17×C5⋊D5—21no—
11C3×C17×C5⋊D5—31no—
12C3×C17×C5⋊D5D311yescharacteristic, direct product factor
13C3×C17×C5⋊D5C2×C311yescharacteristic, complemented
14C2×C3×C52×C17—31no—
15C2×C17×C5⋊D5—31noHall
16C3×C17×D15—56no—
17C3×C5×D3×C17D516yescomplemented
18C32×D5×C17—56no—
19C3×C52×C17—21no—
20C3×C52×C17C2×D311yescharacteristic, complemented
21C3×C52×C17C22×C311yescharacteristic, complemented
22C2×C3×D5×C17—156no—
23D3×D5×C17—56no—
24C3×D3×C5⋊D5C1711yesmaximal, characteristic, direct product factor, Hall
25C2×C52×C17—31no—
26C17×C5⋊D5—31no—
27C17×C5⋊D5C3×D311yescharacteristic, direct product factor
28C32×C5×C17C2×D516yescomplemented
29C2×C3×D3×C17—251noHall
30C2×C3×C5×C17—36no—
31C17×D15—56no—
32C5×D3×C17C3×D516yescomplemented
33C3×D5×C17—56no—
34C3×D5×C17—56no—
35C3×D5×C17—106no—
36C3×D5×C17—156no—
37C3×C3⋊(C5⋊D5)C2×C1711yescharacteristic, complemented
38C3×C52×D3C2×C1711yescharacteristic, complemented
39C32×C5⋊D5C2×C1711yescharacteristic, complemented
40C52×C17C2×C3×D311yescharacteristic, complemented, Hall
41C2×D5×C17—156no—
42C2×C32×C17—251no—
43C3×D3×C17—251no—
44C3×D3×C17C5⋊D511yescharacteristic, direct product factor
45C2×C3×C5⋊D5—31no—
46D3×C5⋊D5C3×C1711yescharacteristic, direct product factor
47C3×C5×C17—26no—
48C3×C5×C17D3×D516yescomplemented
49C3×C5×C17C2×C3×D516yescomplemented
50C32×C52C22×C1711yescharacteristic, complemented, Hall
51C22×C3×C17—751no—
52C2×D3×C17—251no—
53C3×D3×D5—56no—
54C2×C5×C17—36no—
55D5×C17—56no—
56D5×C17—156no—
57C32×C17C2×C5⋊D511yescharacteristic, complemented, Hall
58C2×C3×C52—31no—
59C3⋊(C5⋊D5)C2×C3×C1711yescharacteristic, complemented
60C52×D3C2×C3×C1711yescharacteristic, complemented
61C3×C5⋊D5—21no—
62C3×C5⋊D5—31no—
63C3×C5⋊D5D3×C1711yescharacteristic, direct product factor
64C3×C5⋊D5C2×C3×C1711yescharacteristic, complemented
65C2×C3×C17—31no—
66C2×C3×C17—251no—
67C2×C3×C17—251no—
68C2×C3×C17—501no—
69C2×C3×C17—751no—
70D3×C17—251no—
71D3×C17C3×C5⋊D511yescharacteristic, direct product factor
72C2×C5⋊D5—31noHall
73C3×D15—56no—
74C3×C5×D3D5×C1716yescomplemented
75C32×D5—56no—
76C5×C17C3×D3×D516yescomplemented
77C3×C52—21no—
78C3×C52C2×D3×C1711yescharacteristic, complemented
79C3×C52C22×C3×C1711yescharacteristic, complemented
80C22×C17—751noHall
81C2×C3×D5—156no—
82D3×D5—56no—
83C3×C17—21no—
84C3×C17D3×C5⋊D511yescharacteristic, direct product factor
85C3×C17C2×C3×C5⋊D511yescharacteristic, complemented
86C2×C52—31no—
87C5⋊D5—31no—
88C5⋊D5C3×D3×C1711yescharacteristic, direct product factor
89C32×C5C2×D5×C1716yescomplemented
90C2×C3×D3—251noHall
91C2×C17—31no—
92C2×C17—251no—
93C2×C17—751no—
94C2×C3×C5—36no—
95D15—56no—
96C3×D5—56no—
97C3×D5—56no—
98C3×D5—106no—
99C3×D5—156no—
100C5×D3C3×D5×C1716yescomplemented
101C52C2×C3×D3×C1711yescharacteristic, complemented, Sylow
102C2×D5—156no—
103C2×C32—251no—
104C3×D3—251no—
105C3×D3C17×C5⋊D511yescharacteristic, direct product factor
106C17C3×D3×C5⋊D511yescharacteristic, direct product factor, Sylow
107C3×C5—26no—
108C3×C5D3×D5×C1716yescomplemented
109C3×C5C2×C3×D5×C1716yescomplemented
110C22×C3—751no—
111C2×D3—251no—
112C2×C5—36no—
113D5—56no—
114D5—156no—
115C32C2×C17×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—251no—
118C2×C3—251no—
119C2×C3—501no—
120C2×C3—751no—
121D3—251no—
122D3C3×C17×C5⋊D511yescharacteristic, direct product factor
123C5C3×D3×D5×C1716yescomplemented
124C22—751noSylow
125C3—21no—
126C3D3×C17×C5⋊D511yescharacteristic, direct product factor
127C3C2×C3×C17×C5⋊D511yescharacteristic, complemented
128C2—31no—
129C2—251no—
130C2—751no—
subgroupG/H
center, hypercenterC3×C17D3×C5⋊D5
commutator, cosocle, hypocenterC3×C52C22×C3×C17
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C3×C52
UCSC1 ◁ C3×C17

Complements

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

NH ≅ G/Ntype
1. C3×C17×C3⋊(C5⋊D5)C2semidirect
2. C3×C52×D3×C17C2semidirect
3. C32×C17×C5⋊D5C2semidirect
5. D3×C17×C5⋊D5C3direct (N × H)
6. C32×C52×C17C22semidirect
8. C17×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D3×C17C2×C3semidirect
12. C3×C17×C5⋊D5D3direct (N × H)
13. C3×C17×C5⋊D5C2×C3semidirect
17. C3×C5×D3×C17D5semidirect
20. C3×C52×C17C2×D3semidirect
21. C3×C52×C17C22×C3semidirect
24. C3×D3×C5⋊D5C17direct (N × H)
27. C17×C5⋊D5C3×D3direct (N × H)
28. C32×C5×C17C2×D5semidirect
32. C5×D3×C17C3×D5semidirect
37. C3×C3⋊(C5⋊D5)C2×C17semidirect
38. C3×C52×D3C2×C17semidirect
39. C32×C5⋊D5C2×C17semidirect
40. C52×C17C2×C3×D3semidirect
44. C3×D3×C17C5⋊D5direct (N × H)
46. D3×C5⋊D5C3×C17direct (N × H)
48. C3×C5×C17D3×D5semidirect
49. C3×C5×C17C2×C3×D5semidirect
50. C32×C52C22×C17semidirect
57. C32×C17C2×C5⋊D5semidirect
59. C3⋊(C5⋊D5)C2×C3×C17semidirect
60. C52×D3C2×C3×C17semidirect
63. C3×C5⋊D5D3×C17direct (N × H)
64. C3×C5⋊D5C2×C3×C17semidirect
71. D3×C17C3×C5⋊D5direct (N × H)
74. C3×C5×D3D5×C17semidirect
76. C5×C17C3×D3×D5semidirect
78. C3×C52C2×D3×C17semidirect
79. C3×C52C22×C3×C17semidirect
84. C3×C17D3×C5⋊D5direct (N × H)
85. C3×C17C2×C3×C5⋊D5semidirect
88. C5⋊D5C3×D3×C17direct (N × H)
89. C32×C5C2×D5×C17semidirect
100. C5×D3C3×D5×C17semidirect
101. C52C2×C3×D3×C17semidirect
105. C3×D3C17×C5⋊D5direct (N × H)
106. C17C3×D3×C5⋊D5direct (N × H)
108. C3×C5D3×D5×C17semidirect
109. C3×C5C2×C3×D5×C17semidirect
115. C32C2×C17×C5⋊D5semidirect
122. D3C3×C17×C5⋊D5direct (N × H)
123. C5C3×D3×D5×C17semidirect
126. C3D3×C17×C5⋊D5direct (N × H)
127. C3C2×C3×C17×C5⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C17×C3⋊(C5⋊D5)2
C3×C52×D3×C172
C32×C17×C5⋊D52
C2×C3×C17×C5⋊D53
D3×C17×C5⋊D53
C3×D3×D5×C175
C3×D3×C5⋊D517