Finite Group Databasebeta

← C5×D5×C3⋊D3×C31 #42124949

Subgroups — C5×D5×C3⋊D3×C31 #42124949

Order 27900.

288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 88 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×C31C211yesmaximal, characteristic, complemented
2C52×C3⋊D3×C31C211yesmaximal, characteristic, complemented
3C5×C31×C3⋊D15C211yesmaximal, characteristic, complemented
4C5×D3×D5×C31—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C2×C5×C3⋊D3×C31—51nomaximal
7D5×C3⋊D3×C31C511yesmaximal, characteristic, direct product factor
8C5×D15×C31—34no—
9C52×D3×C31—34no—
10C3×C5×D5×C31D314yescomplemented
11C2×C5×D5×C31—91noHall
12C31×C3⋊D15C2×C511yescharacteristic, complemented
13C5×C3⋊D3×C31—22no—
14C5×C3⋊D3×C31—51no—
15C5×C3⋊D3×C31D511yescharacteristic, direct product factor
16C5×C3⋊D3×C31C2×C511yescharacteristic, complemented
17C32×D5×C31C2×C511yescharacteristic, complemented
18C2×C32×C5×C31—51no—
19C3×C52×C31C2×D314yescomplemented
20C2×C5×D3×C31—154no—
21D3×D5×C31—34no—
22C2×C52×C31—91no—
23C5×D5×C31—91no—
24C5×D5×C31C3⋊D311yescharacteristic, direct product factor
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C22×C511yescharacteristic, complemented
28C2×C3⋊D3×C31—51noHall
29C2×C3×C5×C31—54no—
30D15×C31—34no—
31C5×D3×C31—34no—
32C5×D3×C31—34no—
33C5×D3×C31—68no—
34C5×D3×C31—154no—
35C3×D5×C31C5×D314yescomplemented
36C5×D5×C3⋊D3C3111yesmaximal, characteristic, direct product factor, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38C22×C5×C31—451no—
39C2×D5×C31—91no—
40C2×C32×C31—51no—
41C3⋊D3×C31—51no—
42C3⋊D3×C31C5×D511yescharacteristic, direct product factor
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×C5×D314yescomplemented
46C5×C3⋊D15C2×C3111yescharacteristic, complemented
47C52×C3⋊D3C2×C3111yescharacteristic, complemented
48C32×C5×D5C2×C3111yescharacteristic, complemented
49C2×D3×C31—154no—
50C2×C5×C31—51no—
51C2×C5×C31—91no—
52C2×C5×C31—91no—
53C2×C5×C31—182no—
54C2×C5×C31—451no—
55D5×C31—91no—
56D5×C31C5×C3⋊D311yescharacteristic, direct product factor
57C5×D3×D5—34no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C22×C3111yescharacteristic, complemented, Hall
60C2×C3×C31—54no—
61D3×C31—34no—
62D3×C31—154no—
63C2×C5×C3⋊D3—51no—
64D5×C3⋊D3C5×C3111yescharacteristic, direct product factor
65C5×C31—22no—
66C5×C31D5×C3⋊D311yescharacteristic, direct product factor
67C5×C31C2×C5×C3⋊D311yescharacteristic, complemented
68C5×D15—34no—
69C52×D3—34no—
70C3×C5×D5D3×C3114yescomplemented
71C22×C31—451noHall
72C2×C5×D5—91noHall
73C3×C31C5×D3×D514yescomplemented
74C2×C32×C5—51no—
75C3⋊D15C2×C5×C3111yescharacteristic, complemented
76C5×C3⋊D3—22no—
77C5×C3⋊D3—51no—
78C5×C3⋊D3D5×C3111yescharacteristic, direct product factor
79C5×C3⋊D3C2×C5×C3111yescharacteristic, complemented
80C32×D5C2×C5×C3111yescharacteristic, complemented
81C3×C52C2×D3×C3114yescomplemented
82C2×C31—51no—
83C2×C31—91no—
84C2×C31—451no—
85C2×C5×D3—154no—
86D3×D5—34no—
87C2×C52—91no—
88C5×D5—91no—
89C5×D5C3⋊D3×C3111yescharacteristic, direct product factor
90C32×C5—22no—
91C32×C5C2×D5×C3111yescharacteristic, complemented
92C32×C5C22×C5×C3111yescharacteristic, complemented
93C2×C3⋊D3—51noHall
94C31C5×D5×C3⋊D311yescharacteristic, direct product factor, Sylow
95C2×C3×C5—54no—
96D15—34no—
97C3×D5C5×D3×C3114yescomplemented
98C5×D3—34no—
99C5×D3—34no—
100C5×D3—68no—
101C5×D3—154no—
102C52C2×C3⋊D3×C3111yescharacteristic, complemented, Sylow
103C22×C5—451no—
104C2×D5—91no—
105C2×C32—51no—
106C3⋊D3—51no—
107C3⋊D3C5×D5×C3111yescharacteristic, direct product factor
108C3×C5—28no—
109C3×C5D3×D5×C3114yescomplemented
110C3×C5C2×C5×D3×C3114yescomplemented
111C2×D3—154no—
112C2×C5—51no—
113C2×C5—91no—
114C2×C5—91no—
115C2×C5—182no—
116C2×C5—451no—
117D5—91no—
118D5C5×C3⋊D3×C3111yescharacteristic, direct product factor
119C32C2×C5×D5×C3111yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—34no—
122D3—154no—
123C5—22no—
124C5D5×C3⋊D3×C3111yescharacteristic, direct product factor
125C5C2×C5×C3⋊D3×C3111yescharacteristic, complemented
126C22—451noSylow
127C3C5×D3×D5×C3114yescomplemented
128C2—51no—
129C2—91no—
130C2—451no—
subgroupG/H
center, hypercenterC5×C31D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C22×C5×C31
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5
UCSC1 ◁ C5×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C31C2semidirect
2. C52×C3⋊D3×C31C2semidirect
3. C5×C31×C3⋊D15C2semidirect
5. C32×C52×C31C22semidirect
7. D5×C3⋊D3×C31C5direct (N × H)
10. C3×C5×D5×C31D3semidirect
12. C31×C3⋊D15C2×C5semidirect
15. C5×C3⋊D3×C31D5direct (N × H)
16. C5×C3⋊D3×C31C2×C5semidirect
17. C32×D5×C31C2×C5semidirect
19. C3×C52×C31C2×D3semidirect
24. C5×D5×C31C3⋊D3direct (N × H)
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C22×C5semidirect
35. C3×D5×C31C5×D3semidirect
36. C5×D5×C3⋊D3C31direct (N × H)
37. C52×C31C2×C3⋊D3semidirect
42. C3⋊D3×C31C5×D5direct (N × H)
44. C3×C5×C31D3×D5semidirect
45. C3×C5×C31C2×C5×D3semidirect
46. C5×C3⋊D15C2×C31semidirect
47. C52×C3⋊D3C2×C31semidirect
48. C32×C5×D5C2×C31semidirect
56. D5×C31C5×C3⋊D3direct (N × H)
58. C32×C31C2×C5×D5semidirect
59. C32×C52C22×C31semidirect
64. D5×C3⋊D3C5×C31direct (N × H)
66. C5×C31D5×C3⋊D3direct (N × H)
67. C5×C31C2×C5×C3⋊D3semidirect
70. C3×C5×D5D3×C31semidirect
73. C3×C31C5×D3×D5semidirect
75. C3⋊D15C2×C5×C31semidirect
78. C5×C3⋊D3D5×C31direct (N × H)
79. C5×C3⋊D3C2×C5×C31semidirect
80. C32×D5C2×C5×C31semidirect
81. C3×C52C2×D3×C31semidirect
89. C5×D5C3⋊D3×C31direct (N × H)
91. C32×C5C2×D5×C31semidirect
92. C32×C5C22×C5×C31semidirect
94. C31C5×D5×C3⋊D3direct (N × H)
97. C3×D5C5×D3×C31semidirect
102. C52C2×C3⋊D3×C31semidirect
107. C3⋊D3C5×D5×C31direct (N × H)
109. C3×C5D3×D5×C31semidirect
110. C3×C5C2×C5×D3×C31semidirect
118. D5C5×C3⋊D3×C31direct (N × H)
119. C32C2×C5×D5×C31semidirect
124. C5D5×C3⋊D3×C31direct (N × H)
125. C5C2×C5×C3⋊D3×C31semidirect
127. C3C5×D3×D5×C31semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C312
C52×C3⋊D3×C312
C5×C31×C3⋊D152
C5×D3×D5×C313
C2×C5×C3⋊D3×C315
D5×C3⋊D3×C315
C5×D5×C3⋊D331