Finite Group Databasebeta

← #30685919

Subgroups — #30685919

Order 17100.

288 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C5×C3⋊D285C211yesmaximal, characteristic, complemented
2C5×C19×C3⋊D15C211yesmaximal, characteristic, complemented
3C32×C5⋊D95C211yesmaximal, characteristic, complemented
4D15⋊D95—34nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6D95⋊(C3⋊D3)—51nomaximal
7C3⋊D3×D95—51nomaximal
8C5×D285—34no—
9C5×C19×D15—34no—
10C3×C5⋊D95D314yescomplemented
11D5×D95—91noHall
12C3⋊D285D511yescharacteristic, complemented
13C19×C3⋊D15D511yescharacteristic, complemented
14C5×C3⋊D57—51no—
15C5×C3⋊D3×C19—51no—
16C32×D95—51no—
17C32×D95—51no—
18C32×D95—102no—
19C3×C52×C19C2×D314yescomplemented
20D15⋊D19—154no—
21D3×D95—154no—
22C5⋊D95C3⋊D311yescharacteristic, complemented
23C5×D95—91no—
24C5×D5×C19—91no—
25#11744719—191nomaximal, Hall
26C32×C5×C19—22no—
27C32×C5×C19C2×D511yescharacteristic, complemented
28C32×C5×C19C2×D511yescharacteristic, complemented
29C3⋊D3×D19—251noHall
30D285—34no—
31C19×D15—34no—
32C5×D57—154no—
33C5×D3×C19—154no—
34C3×D95—54no—
35C3×D95—54no—
36C3×D95—108no—
37C52×C19C2×C3⋊D311yescharacteristic, complemented, Hall
38C5×C3⋊D15—191no—
39C5×C3⋊D15D1911yescharacteristic, complemented
40C32×C5⋊D5—191no—
41C2×D95—451no—
42D5×D19—451no—
43C3⋊D57—51no—
44C3⋊D3×C19—51no—
45C32×D19—251no—
46D15⋊D5—574no—
47C3×C5×C19—28no—
48C3×C5×C19D3×D514yescomplemented
49C3×C5×C19D3×D514yescomplemented
50D3×D19—754no—
51C32×C52C2×D1911yescharacteristic, complemented, Hall
52C2×C5×C19—451no—
53D95—51no—
54D95—51no—
55D95—91no—
56D95—102no—
57C5×D19—451no—
58D5×C19—91no—
59D5×C3⋊D3—951no—
60D5×C3⋊D3—951no—
61C32×C19D5211yescharacteristic, complemented, Hall
62C5×D15—34no—
63C5×D15—574no—
64C3×C5⋊D5—194no—
65D57—154no—
66C3×D19—254no—
67D3×C19—154no—
68D52—1711noHall
69C5×C19—22no—
70C5×C19D5×C3⋊D311yescharacteristic, complemented
71C5×C19D5×C3⋊D311yescharacteristic, complemented
72C3⋊D15—191no—
73C3⋊D15D9511yescharacteristic, complemented
74C5×C3⋊D3—51no—
75C5×C3⋊D3—951no—
76C32×D5—951no—
77C32×D5—951no—
78C32×D5—1902no—
79C2×D19—2251noHall
80C3×C52D3×D1914yescomplemented
81D3×D5—2854no—
82D3×D5—2854no—
83C3×C19D15⋊D514yescomplemented
84C5⋊D5—191no—
85C5×D5—91no—
86C5×D5—1711no—
87C32×C5—22no—
88C32×C5D5×D1911yescharacteristic, complemented
89C32×C5C2×D9511yescharacteristic, complemented
90C2×C19—451no—
91D19—251no—
92D19—451no—
93C2×C3⋊D3—4751noHall
94D15—34no—
95D15—574no—
96C3×D5—954no—
97C3×D5—954no—
98C3×D5—1908no—
99C5×D3—154no—
100C5×D3—2854no—
101C52C3⋊D3×D1911yescharacteristic, complemented, Sylow
102C2×D5—8551no—
103C2×D5—8551no—
104C19#1174471911yescharacteristic, complemented, Sylow
105C2×C32—4751no—
106C3⋊D3—51no—
107C3⋊D3—951no—
108C3×C5—28no—
109C3×C5D3×D9514yescomplemented
110C3×C5D15⋊D1914yescomplemented
111C2×D3—14254no—
112C2×C5—451no—
113C2×C5—8551no—
114D5—91no—
115D5—951no—
116D5—951no—
117D5—1711no—
118D5—1902no—
119C32D5×D9511yescharacteristic, complemented, Sylow
120C2×C3—4754no—
121D3—154no—
122D3—2854no—
123C5—22no—
124C5C3⋊D3×D9511yescharacteristic, complemented
125C5D95⋊(C3⋊D3)11yescharacteristic, complemented
126C22—42751noSylow
127C3D15⋊D9514yescomplemented
128C2—451no—
129C2—8551no—
130C2—4751no—
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. C5×C3⋊D285C2semidirect
2. C5×C19×C3⋊D15C2semidirect
3. C32×C5⋊D95C2semidirect
5. C32×C52×C19C22semidirect
10. C3×C5⋊D95D3semidirect
12. C3⋊D285D5semidirect
13. C19×C3⋊D15D5semidirect
19. C3×C52×C19C2×D3semidirect
22. C5⋊D95C3⋊D3semidirect
27. C32×C5×C19C2×D5semidirect
28. C32×C5×C19C2×D5semidirect
37. C52×C19C2×C3⋊D3semidirect
39. C5×C3⋊D15D19semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19D3×D5semidirect
51. C32×C52C2×D19semidirect
61. C32×C19D52semidirect
70. C5×C19D5×C3⋊D3semidirect
71. C5×C19D5×C3⋊D3semidirect
73. C3⋊D15D95semidirect
80. C3×C52D3×D19semidirect
83. C3×C19D15⋊D5semidirect
88. C32×C5D5×D19semidirect
89. C32×C5C2×D95semidirect
101. C52C3⋊D3×D19semidirect
104. C19#11744719semidirect
109. C3×C5D3×D95semidirect
110. C3×C5D15⋊D19semidirect
119. C32D5×D95semidirect
124. C5C3⋊D3×D95semidirect
125. C5D95⋊(C3⋊D3)semidirect
127. C3D15⋊D95semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2852
C5×C19×C3⋊D152
C32×C5⋊D952
D15⋊D953
D95⋊(C3⋊D3)5
C3⋊D3×D955
#1174471919