Finite Group Databasebeta

← C5×D5×C3⋊D123 #49147170

Subgroups — C5×D5×C3⋊D123 #49147170

Order 36900.

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C5×D5×C41C211yesmaximal, characteristic, complemented
2C52×C3⋊D123C211yesmaximal, characteristic, complemented
3C5×C3⋊D615C211yesmaximal, characteristic, complemented
4C5×D5×D123—34nomaximal
5C32×C52×C41C2211yescharacteristic, complemented, Hall
6C2×C5×C3⋊D123—51nomaximal
7D5×C3⋊D123C511yesmaximal, characteristic, direct product factor
8C5×D615—34no—
9C52×D123—34no—
10C3×C5×D5×C41D314yescomplemented
11C5×D5×D41—91noHall
12C3⋊D615C2×C511yescharacteristic, complemented
13C5×C3⋊D123—22no—
14C5×C3⋊D123—51no—
15C5×C3⋊D123D511yescharacteristic, direct product factor
16C5×C3⋊D123C2×C511yescharacteristic, complemented
17C32×D5×C41C2×C511yescharacteristic, complemented
18C2×C32×C5×C41—51no—
19C3×C52×C41C2×D314yescomplemented
20C2×C5×D123—154no—
21D5×D123—34no—
22C5×D205—91no—
23C5×D5×C41C3⋊D311yescharacteristic, complemented
24C52×D41—91no—
25C32×C5×C41—22no—
26C32×C5×C41C2×D511yescharacteristic, complemented
27C32×C5×C41C22×C511yescharacteristic, complemented
28C2×C3⋊D123—51noHall
29C2×C3×C5×C41—54no—
30D615—34no—
31C5×D123—34no—
32C5×D123—34no—
33C5×D123—68no—
34C5×D123—154no—
35C3×D5×C41C5×D314yescomplemented
36C52×C41C2×C3⋊D311yescharacteristic, complemented, Hall
37C5×D5×C3⋊D3—411nomaximal, Hall
38C2×C5×D41—451no—
39D5×D41—91no—
40C2×C32×C41—51no—
41C3⋊D123—51no—
42C3⋊D123C5×D511yescharacteristic, direct product factor
43C3×C5×C41—28no—
44C3×C5×C41D3×D514yescomplemented
45C3×C5×C41C2×C5×D314yescomplemented
46C2×D123—154no—
47C5×C3⋊D15—411no—
48C52×C3⋊D3—411no—
49C32×C5×D5D4111yescharacteristic, complemented
50C2×C5×C41—51no—
51D205—91no—
52C5×D41—91no—
53C5×D41—91no—
54C5×D41—182no—
55C5×D41—451no—
56D5×C41C5×C3⋊D311yescharacteristic, complemented
57C32×C41C2×C5×D511yescharacteristic, complemented, Hall
58C5×D3×D5—1234no—
59C2×C3×C41—54no—
60D123—34no—
61D123—154no—
62C32×C52C2×D4111yescharacteristic, complemented, Hall
63C5×C41—22no—
64C5×C41D5×C3⋊D311yescharacteristic, complemented
65C5×C41C2×C5×C3⋊D311yescharacteristic, complemented
66C2×C5×C3⋊D3—2051no—
67D5×C3⋊D3—411no—
68C2×D41—451noHall
69C5×D15—1234no—
70C52×D3—1234no—
71C3×C5×D5D12314yescomplemented
72C3×C41C5×D3×D514yescomplemented
73C2×C5×D5—3691noHall
74C2×C32×C5—51no—
75C3⋊D15—411no—
76C5×C3⋊D3—411no—
77C5×C3⋊D3—411no—
78C5×C3⋊D3—822no—
79C5×C3⋊D3—2051no—
80C32×D5C5×D4111yescharacteristic, complemented
81C2×C41—51no—
82D41—91no—
83D41—451no—
84C3×C52C2×D12314yescomplemented
85C2×C5×D3—6154no—
86D3×D5—1234no—
87C2×C52—3691no—
88C5×D5—3691no—
89C5×D5C3⋊D12311yescharacteristic, direct product factor
90C32×C5—22no—
91C32×C5D5×D4111yescharacteristic, complemented
92C32×C5C2×C5×D4111yescharacteristic, complemented
93C41C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
94C2×C3⋊D3—2051noHall
95C2×C3×C5—54no—
96D15—1234no—
97C3×D5C5×D12314yescomplemented
98C5×D3—6154no—
99C5×D3—1234no—
100C5×D3—1234no—
101C5×D3—2468no—
102C52C2×C3⋊D12311yescharacteristic, complemented, Sylow
103C22×C5—18451no—
104C2×D5—3691no—
105C2×C32—51no—
106C3⋊D3—411no—
107C3⋊D3—2051no—
108C3×C5—28no—
109C3×C5D5×D12314yescomplemented
110C3×C5C2×C5×D12314yescomplemented
111C2×D3—6154no—
112C2×C5—51no—
113C2×C5—18451no—
114C2×C5—3691no—
115C2×C5—3691no—
116C2×C5—7382no—
117D5—3691no—
118D5C5×C3⋊D12311yescharacteristic, direct product factor
119C32C5×D5×D4111yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—6154no—
122D3—1234no—
123C5—22no—
124C5D5×C3⋊D12311yescharacteristic, direct product factor
125C5C2×C5×C3⋊D12311yescharacteristic, complemented
126C22—18451noSylow
127C3C5×D5×D12314yescomplemented
128C2—51no—
129C2—18451no—
130C2—3691no—
subgroupG/H
center, hypercenterC5D5×C3⋊D123
commutator, cosocle, hypocenterC32×C5×C41C22×C5
FrattiniC1G
Fitting, socleC32×C52×C41C22
LCSG ▷ C32×C5×C41
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C41C2semidirect
2. C52×C3⋊D123C2semidirect
3. C5×C3⋊D615C2semidirect
5. C32×C52×C41C22semidirect
7. D5×C3⋊D123C5direct (N × H)
10. C3×C5×D5×C41D3semidirect
12. C3⋊D615C2×C5semidirect
15. C5×C3⋊D123D5direct (N × H)
16. C5×C3⋊D123C2×C5semidirect
17. C32×D5×C41C2×C5semidirect
19. C3×C52×C41C2×D3semidirect
23. C5×D5×C41C3⋊D3semidirect
26. C32×C5×C41C2×D5semidirect
27. C32×C5×C41C22×C5semidirect
35. C3×D5×C41C5×D3semidirect
36. C52×C41C2×C3⋊D3semidirect
42. C3⋊D123C5×D5direct (N × H)
44. C3×C5×C41D3×D5semidirect
45. C3×C5×C41C2×C5×D3semidirect
49. C32×C5×D5D41semidirect
56. D5×C41C5×C3⋊D3semidirect
57. C32×C41C2×C5×D5semidirect
62. C32×C52C2×D41semidirect
64. C5×C41D5×C3⋊D3semidirect
65. C5×C41C2×C5×C3⋊D3semidirect
71. C3×C5×D5D123semidirect
72. C3×C41C5×D3×D5semidirect
80. C32×D5C5×D41semidirect
84. C3×C52C2×D123semidirect
89. C5×D5C3⋊D123direct (N × H)
91. C32×C5D5×D41semidirect
92. C32×C5C2×C5×D41semidirect
93. C41C5×D5×C3⋊D3semidirect
97. C3×D5C5×D123semidirect
102. C52C2×C3⋊D123semidirect
109. C3×C5D5×D123semidirect
110. C3×C5C2×C5×D123semidirect
118. D5C5×C3⋊D123direct (N × H)
119. C32C5×D5×D41semidirect
124. C5D5×C3⋊D123direct (N × H)
125. C5C2×C5×C3⋊D123semidirect
127. C3C5×D5×D123semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C412
C52×C3⋊D1232
C5×C3⋊D6152
C5×D5×D1233
C2×C5×C3⋊D1235
D5×C3⋊D1235
C5×D5×C3⋊D341