Finite Group Databasebeta

← C3⋊D15×D205 #49147183

Subgroups — C3⋊D15×D205 #49147183

Order 36900.

288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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×D205C211yesmaximal, characteristic, complemented
2C5×C41×C3⋊D15C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D205))C211yesmaximal, characteristic, complemented
4D15×D205—34nomaximal
5C32×C52×C41C2211yescharacteristic, complemented, Hall
6C3⋊D3×D205—51nomaximal
7D41×C3⋊D15—51nomaximal
8C3⋊(C5⋊D205)—34no—
9C5×D15×C41—34no—
10C3×C5×D205D314yescomplemented
11D5×D205—91noHall
12C3⋊D615—51no—
13C3⋊D615—51no—
14C3⋊D615—102no—
15C41×C3⋊D15D511yescharacteristic, complemented
16C5×C3⋊D3×C41—51no—
17C32×D205D511yescharacteristic, complemented
18C32×C5×D41—51no—
19C3×C52×C41C2×D314yescomplemented
20D3×D205—154no—
21D15×D41—154no—
22C5⋊D205—91no—
23C5×D205C3⋊D311yescharacteristic, complemented
24C5×D5×C41—91no—
25C32×C5×C41—22no—
26C32×C5×C41C2×D511yescharacteristic, complemented
27C32×C5×C41C2×D511yescharacteristic, complemented
28C3⋊D3×D41—251noHall
29D615—154no—
30D615—154no—
31D615—308no—
32D15×C41—34no—
33C5×D3×C41—154no—
34C3×D205D1514yescomplemented
35C3×C5×D41—54no—
36C52×C41C2×C3⋊D311yescharacteristic, complemented, Hall
37D5×C3⋊D15—411nomaximal, Hall
38C2×D205—451no—
39D5×D41—451no—
40C3⋊D123—251no—
41C3⋊D3×C41—51no—
42C32×D41—51no—
43C3×C5×C41—28no—
44C3×C5×C41D3×D514yescomplemented
45C3×C5×C41C2×D1514yescomplemented
46D3×D41—754no—
47C3⋊(C3⋊(C5⋊D5))—411no—
48C5×C3⋊D15D4111yescharacteristic, complemented
49C32×C5×D5—411no—
50C2×C5×C41—451no—
51D205—451no—
52D205—451no—
53D205—902no—
54D205C3⋊D1511yescharacteristic, direct product factor
55C5×D41—51no—
56D5×C41—91no—
57C32×C41D5211yescharacteristic, complemented, Hall
58D5×D15—1234no—
59D123—754no—
60C3×D41—54no—
61D3×C41—154no—
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—34no—
71C3×C5×D5—414no—
72C3×C41D5×D1514yescomplemented
73D52—3691noHall
74C2×C32×C5—2051no—
75C3⋊D15—4102no—
76C3⋊D15—2051no—
77C3⋊D15—2051no—
78C3⋊D15D20511yescharacteristic, direct product factor
79C5×C3⋊D3—51no—
80C32×D5—411no—
81C2×C41—451no—
82D41—51no—
83D41—2251no—
84C3×C52D3×D4114yescomplemented
85C2×D15—6154no—
86D3×D5—6154no—
87C5⋊D5—3691no—
88C5×D5—91no—
89C5×D5—411no—
90C32×C5—22no—
91C32×C5D5×D4111yescharacteristic, complemented
92C32×C5C2×D20511yescharacteristic, complemented
93C41D5×C3⋊D1511yescharacteristic, complemented, Sylow
94C2×C3⋊D3—10251noHall
95C2×C3×C5—2054no—
96D15—34no—
97D15—6154no—
98D15—6154no—
99D15—12308no—
100C3×D5—414no—
101C5×D3—154no—
102C52C3⋊D3×D4111yescharacteristic, complemented, Sylow
103C2×D5—18451no—
104C2×D5—18451no—
105C2×C32—2051no—
106C3⋊D3—10251no—
107C3⋊D3—51no—
108C3×C5—28no—
109C3×C5D15×D4114yescomplemented
110C3×C5D3×D20514yescomplemented
111C2×D3—30754no—
112C2×C5—451no—
113C2×C5—2051no—
114D5—91no—
115D5—411no—
116D5—18451no—
117D5—18451no—
118D5—36902no—
119C32D5×D20511yescharacteristic, complemented, Sylow
120C2×C3—2054no—
121D3—30754no—
122D3—154no—
123C5—22no—
124C5D41×C3⋊D1511yescharacteristic, complemented
125C5C3⋊D3×D20511yescharacteristic, complemented
126C22—92251noSylow
127C3D15×D20514yescomplemented
128C2—92251no—
129C2—451no—
130C2—2051no—
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×D205C2semidirect
2. C5×C41×C3⋊D15C2semidirect
3. C3⋊(C3⋊(C5⋊D205))C2semidirect
5. C32×C52×C41C22semidirect
10. C3×C5×D205D3semidirect
15. C41×C3⋊D15D5semidirect
17. C32×D205D5semidirect
19. C3×C52×C41C2×D3semidirect
23. C5×D205C3⋊D3semidirect
26. C32×C5×C41C2×D5semidirect
27. C32×C5×C41C2×D5semidirect
34. C3×D205D15semidirect
36. C52×C41C2×C3⋊D3semidirect
44. C3×C5×C41D3×D5semidirect
45. C3×C5×C41C2×D15semidirect
48. C5×C3⋊D15D41semidirect
54. D205C3⋊D15direct (N × H)
57. C32×C41D52semidirect
62. C32×C52C2×D41semidirect
64. C5×C41D5×C3⋊D3semidirect
65. C5×C41C2×C3⋊D15semidirect
72. C3×C41D5×D15semidirect
78. C3⋊D15D205direct (N × H)
84. C3×C52D3×D41semidirect
91. C32×C5D5×D41semidirect
92. C32×C5C2×D205semidirect
93. C41D5×C3⋊D15semidirect
102. C52C3⋊D3×D41semidirect
109. C3×C5D15×D41semidirect
110. C3×C5D3×D205semidirect
119. C32D5×D205semidirect
124. C5D41×C3⋊D15semidirect
125. C5C3⋊D3×D205semidirect
127. C3D15×D205semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D2052
C5×C41×C3⋊D152
C3⋊(C3⋊(C5⋊D205))2
D15×D2053
C3⋊D3×D2055
D41×C3⋊D155
D5×C3⋊D1541