Finite Group Databasebeta

← D5×C3⋊D615 #49147182

Subgroups — D5×C3⋊D615 #49147182

Order 36900.

288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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
2C5×C3⋊D615C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D205))C211yesmaximal, characteristic, complemented
4D5×D615—34nomaximal
5C32×C52×C41C2211yescharacteristic, complemented, Hall
6C2×C3⋊D615—51nomaximal
7D5×C3⋊D123—51nomaximal
8C3⋊(C5⋊D205)—34no—
9C5×D615—34no—
10C3×C5×D5×C41D314yescomplemented
11D5×D205—91noHall
12C3⋊D615—51no—
13C3⋊D615—51no—
14C3⋊D615—102no—
15C3⋊D615D511yescharacteristic, direct product factor
16C5×C3⋊D123—51no—
17C32×D5×C41D511yescharacteristic, complemented
18C2×C32×C5×C41—51no—
19C3×C52×C41C2×D314yescomplemented
20C2×D615—154no—
21D5×D123—154no—
22C5⋊D205—91no—
23C5×D205—91no—
24C5×D5×C41C3⋊D311yescharacteristic, complemented
25C32×C5×C41—22no—
26C32×C5×C41C2×D511yescharacteristic, complemented
27C32×C5×C41C2×D511yescharacteristic, complemented
28C2×C3⋊D123—251noHall
29C2×C3×C5×C41—54no—
30D615—34no—
31D615—154no—
32D615—154no—
33D615—308no—
34C5×D123—154no—
35C3×D5×C41D1514yescomplemented
36C52×C41C2×C3⋊D311yescharacteristic, complemented, Hall
37D5×C3⋊D15—411nomaximal, Hall
38C2×D205—451no—
39D5×D41—451no—
40C2×C32×C41—51no—
41C3⋊D123—51no—
42C3⋊D123—251no—
43C3×C5×C41—28no—
44C3×C5×C41D3×D514yescomplemented
45C3×C5×C41C2×D1514yescomplemented
46C2×D123—754no—
47C3⋊(C3⋊(C5⋊D5))—411no—
48C5×C3⋊D15—411no—
49C32×C5×D5D4111yescharacteristic, complemented
50C2×C5×C41—51no—
51D205—91no—
52D205—451no—
53D205—451no—
54D205—902no—
55C5×D41—451no—
56D5×C41C3⋊D1511yescharacteristic, complemented
57C32×C41D5211yescharacteristic, complemented, Hall
58D5×D15—1234no—
59C2×C3×C41—54no—
60D123—154no—
61D123—754no—
62C32×C52C2×D4111yescharacteristic, complemented, Hall
63C5×C41—22no—
64C5×C41D5×C3⋊D311yescharacteristic, complemented
65C5×C41C2×C3⋊D1511yescharacteristic, complemented
66C2×C3⋊D15—2051no—
67D5×C3⋊D3—2051no—
68C2×D41—2251noHall
69C3⋊(C5⋊D5)—1234no—
70C5×D15—1234no—
71C3×C5×D5D12314yescomplemented
72C3×C41D5×D1514yescomplemented
73D52—3691noHall
74C2×C32×C5—51no—
75C3⋊D15—411no—
76C3⋊D15—4102no—
77C3⋊D15—2051no—
78C3⋊D15—2051no—
79C5×C3⋊D3—2051no—
80C32×D5D20511yescharacteristic, complemented
81C2×C41—51no—
82D41—451no—
83D41—2251no—
84C3×C52C2×D12314yescomplemented
85C2×D15—6154no—
86D3×D5—6154no—
87C5⋊D5—3691no—
88C5×D5—3691no—
89C5×D5C3⋊D12311yescharacteristic, complemented
90C32×C5—22no—
91C32×C5D5×D4111yescharacteristic, complemented
92C32×C5C2×D20511yescharacteristic, complemented
93C41D5×C3⋊D1511yescharacteristic, complemented, Sylow
94C2×C3⋊D3—10251noHall
95C2×C3×C5—54no—
96D15—6154no—
97D15—6154no—
98D15—1234no—
99D15—12308no—
100C3×D5D61514yescomplemented
101C5×D3—6154no—
102C52C2×C3⋊D12311yescharacteristic, complemented, Sylow
103C2×D5—18451no—
104C2×D5—18451no—
105C2×C32—51no—
106C3⋊D3—10251no—
107C3⋊D3—2051no—
108C3×C5—28no—
109C3×C5D5×D12314yescomplemented
110C3×C5C2×D61514yescomplemented
111C2×D3—30754no—
112C2×C5—51no—
113C2×C5—18451no—
114D5—18451no—
115D5—18451no—
116D5—36902no—
117D5—3691no—
118D5C3⋊D61511yescharacteristic, direct product factor
119C32D5×D20511yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—30754no—
122D3—6154no—
123C5—22no—
124C5D5×C3⋊D12311yescharacteristic, complemented
125C5C2×C3⋊D61511yescharacteristic, complemented
126C22—92251noSylow
127C3D5×D61514yescomplemented
128C2—51no—
129C2—92251no—
130C2—18451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C41C22
LCSG ▷ C32×C52×C41
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C41C2semidirect
2. C5×C3⋊D615C2semidirect
3. C3⋊(C3⋊(C5⋊D205))C2semidirect
5. C32×C52×C41C22semidirect
10. C3×C5×D5×C41D3semidirect
15. C3⋊D615D5direct (N × H)
17. C32×D5×C41D5semidirect
19. C3×C52×C41C2×D3semidirect
24. C5×D5×C41C3⋊D3semidirect
26. C32×C5×C41C2×D5semidirect
27. C32×C5×C41C2×D5semidirect
35. C3×D5×C41D15semidirect
36. C52×C41C2×C3⋊D3semidirect
44. C3×C5×C41D3×D5semidirect
45. C3×C5×C41C2×D15semidirect
49. C32×C5×D5D41semidirect
56. D5×C41C3⋊D15semidirect
57. C32×C41D52semidirect
62. C32×C52C2×D41semidirect
64. C5×C41D5×C3⋊D3semidirect
65. C5×C41C2×C3⋊D15semidirect
71. C3×C5×D5D123semidirect
72. C3×C41D5×D15semidirect
80. C32×D5D205semidirect
84. C3×C52C2×D123semidirect
89. C5×D5C3⋊D123semidirect
91. C32×C5D5×D41semidirect
92. C32×C5C2×D205semidirect
93. C41D5×C3⋊D15semidirect
100. C3×D5D615semidirect
102. C52C2×C3⋊D123semidirect
109. C3×C5D5×D123semidirect
110. C3×C5C2×D615semidirect
118. D5C3⋊D615direct (N × H)
119. C32D5×D205semidirect
124. C5D5×C3⋊D123semidirect
125. C5C2×C3⋊D615semidirect
127. C3D5×D615semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C412
C5×C3⋊D6152
C3⋊(C3⋊(C5⋊D205))2
D5×D6153
C2×C3⋊D6155
D5×C3⋊D1235
D5×C3⋊D1541