Finite Group Databasebeta

← D5×C3⋊D285 #30685914

Subgroups — D5×C3⋊D285 #30685914

Order 17100.

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
1C3⋊(C3⋊(C5⋊D95))C211yesmaximal, characteristic, complemented
2C5×C3⋊D285C211yesmaximal, characteristic, complemented
3C32×C5×D5×C19C211yesmaximal, characteristic, complemented
4D5×D285—34nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6C2×C3⋊D285—51nomaximal
7D5×C3⋊D57—51nomaximal
8C3⋊(C5⋊D95)—34no—
9C5×D285—34no—
10C3×C5×D5×C19D314yescomplemented
11D5×D95—91noHall
12C2×C32×C5×C19—51no—
13C3⋊D285—51no—
14C3⋊D285—51no—
15C3⋊D285—102no—
16C3⋊D285D511yescharacteristic, direct product factor
17C5×C3⋊D57—51no—
18C32×D5×C19D511yescharacteristic, complemented
19C3×C52×C19C2×D314yescomplemented
20C2×D285—154no—
21D5×D57—154no—
22C5⋊D95—91no—
23C5×D95—91no—
24C5×D5×C19C3⋊D311yescharacteristic, complemented
25D5×C3⋊D15—191nomaximal, Hall
26C32×C5×C19—22no—
27C32×C5×C19C2×D511yescharacteristic, complemented
28C32×C5×C19C2×D511yescharacteristic, complemented
29C2×C3⋊D57—251noHall
30C2×C3×C5×C19—54no—
31D285—34no—
32D285—154no—
33D285—154no—
34D285—308no—
35C5×D57—154no—
36C3×D5×C19D1514yescomplemented
37C52×C19C2×C3⋊D311yescharacteristic, complemented, Hall
38C3⋊(C3⋊(C5⋊D5))—191no—
39C5×C3⋊D15—191no—
40C32×C5×D5D1911yescharacteristic, complemented
41C2×D95—451no—
42D5×D19—451no—
43C2×C32×C19—51no—
44C3⋊D57—51no—
45C3⋊D57—251no—
46D5×D15—574no—
47C3×C5×C19—28no—
48C3×C5×C19D3×D514yescomplemented
49C3×C5×C19C2×D1514yescomplemented
50C2×D57—754no—
51C32×C52C2×D1911yescharacteristic, complemented, Hall
52C2×C5×C19—51no—
53D95—91no—
54D95—451no—
55D95—451no—
56D95—902no—
57C5×D19—451no—
58D5×C19C3⋊D1511yescharacteristic, complemented
59C2×C3⋊D15—951no—
60D5×C3⋊D3—951no—
61C32×C19D5211yescharacteristic, complemented, Hall
62C3⋊(C5⋊D5)—574no—
63C5×D15—574no—
64C3×C5×D5D5714yescomplemented
65C2×C3×C19—54no—
66D57—154no—
67D57—754no—
68D52—1711noHall
69C5×C19—22no—
70C5×C19D5×C3⋊D311yescharacteristic, complemented
71C5×C19C2×C3⋊D1511yescharacteristic, complemented
72C2×C32×C5—51no—
73C3⋊D15—191no—
74C3⋊D15—951no—
75C3⋊D15—951no—
76C3⋊D15—1902no—
77C5×C3⋊D3—951no—
78C32×D5D9511yescharacteristic, complemented
79C2×D19—2251noHall
80C3×C52C2×D5714yescomplemented
81C2×D15—2854no—
82D3×D5—2854no—
83C3×C19D5×D1514yescomplemented
84C5⋊D5—1711no—
85C5×D5—1711no—
86C5×D5C3⋊D5711yescharacteristic, complemented
87C32×C5—22no—
88C32×C5D5×D1911yescharacteristic, complemented
89C32×C5C2×D9511yescharacteristic, complemented
90C2×C19—51no—
91D19—451no—
92D19—2251no—
93C2×C3⋊D3—4751noHall
94C2×C3×C5—54no—
95D15—2854no—
96D15—2854no—
97D15—574no—
98D15—5708no—
99C3×D5D28514yescomplemented
100C5×D3—2854no—
101C52C2×C3⋊D5711yescharacteristic, complemented, Sylow
102C2×D5—8551no—
103C2×D5—8551no—
104C19D5×C3⋊D1511yescharacteristic, complemented, Sylow
105C2×C32—51no—
106C3⋊D3—951no—
107C3⋊D3—4751no—
108C3×C5—28no—
109C3×C5D5×D5714yescomplemented
110C3×C5C2×D28514yescomplemented
111C2×D3—14254no—
112C2×C5—51no—
113C2×C5—8551no—
114D5—8551no—
115D5—8551no—
116D5—1711no—
117D5—17102no—
118D5C3⋊D28511yescharacteristic, direct product factor
119C32D5×D9511yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—2854no—
122D3—14254no—
123C5—22no—
124C5D5×C3⋊D5711yescharacteristic, complemented
125C5C2×C3⋊D28511yescharacteristic, complemented
126C22—42751noSylow
127C3D5×D28514yescomplemented
128C2—51no—
129C2—8551no—
130C2—42751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C19C22
LCSG ▷ C32×C52×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(C5⋊D95))C2semidirect
2. C5×C3⋊D285C2semidirect
3. C32×C5×D5×C19C2semidirect
5. C32×C52×C19C22semidirect
10. C3×C5×D5×C19D3semidirect
16. C3⋊D285D5direct (N × H)
18. C32×D5×C19D5semidirect
19. C3×C52×C19C2×D3semidirect
24. C5×D5×C19C3⋊D3semidirect
27. C32×C5×C19C2×D5semidirect
28. C32×C5×C19C2×D5semidirect
36. C3×D5×C19D15semidirect
37. C52×C19C2×C3⋊D3semidirect
40. C32×C5×D5D19semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19C2×D15semidirect
51. C32×C52C2×D19semidirect
58. D5×C19C3⋊D15semidirect
61. C32×C19D52semidirect
64. C3×C5×D5D57semidirect
70. C5×C19D5×C3⋊D3semidirect
71. C5×C19C2×C3⋊D15semidirect
78. C32×D5D95semidirect
80. C3×C52C2×D57semidirect
83. C3×C19D5×D15semidirect
86. C5×D5C3⋊D57semidirect
88. C32×C5D5×D19semidirect
89. C32×C5C2×D95semidirect
99. C3×D5D285semidirect
101. C52C2×C3⋊D57semidirect
104. C19D5×C3⋊D15semidirect
109. C3×C5D5×D57semidirect
110. C3×C5C2×D285semidirect
118. D5C3⋊D285direct (N × H)
119. C32D5×D95semidirect
124. C5D5×C3⋊D57semidirect
125. C5C2×C3⋊D285semidirect
127. C3D5×D285semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D95))2
C5×C3⋊D2852
C32×C5×D5×C192
D5×D2853
C2×C3⋊D2855
D5×C3⋊D575
D5×C3⋊D1519