Finite Group Databasebeta

← C5×C3⋊D3×D203 #49141636

Subgroups — C5×C3⋊D3×D203 #49141636

Order 36540.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×D203C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×C3⋊D609C211yesmaximal, characteristic, complemented
4C5×D3×D203—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C3⋊D3×D203C511yesmaximal, characteristic, direct product factor, Hall
7C5×D609—34no—
8C5×D3×C7×C29—34no—
9C3×C5×D203D314yescomplemented
10C5×C3⋊D3×D29—71nomaximal, Hall
11C2×C5×D203—91noHall
12C3⋊D609C2×C511yescharacteristic, complemented
13C7×C3⋊D3×C29C2×C511yescharacteristic, complemented
14C32×D203C2×C511yescharacteristic, complemented
15C3×C5×C7×C29C2×D314yescomplemented
16C5×C3⋊D87—71no—
17C5×C3⋊D3×C29D711yescharacteristic, complemented
18C32×C5×D29—71no—
19D3×D203—34no—
20C5×D203—91no—
21C5×D203C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C22×C511yescharacteristic, complemented, Hall
24C5×D3×D29—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26C5×D7×C3⋊D3—291nomaximal, Hall
27D609—34no—
28D3×C7×C29—34no—
29C3×D203C5×D314yescomplemented
30C3⋊D3×D29—71noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C5×D87—214no—
33C5×D3×C29—34no—
34C3×C5×D29—74no—
35C2×D203—91noHall
36C5×C3⋊D21—291no—
37C5×C7×C3⋊D3D2911yescharacteristic, complemented
38C32×C5×D7—291no—
39C3×C7×C29C2×C5×D314yescomplemented
40C2×C5×D29—631noHall
41C3⋊D87—71no—
42C3⋊D3×C29C5×D711yescharacteristic, complemented
43C32×D29—71no—
44C3×C5×C29D3×D714yescomplemented
45C5×D3×D7—874no—
46C2×C7×C29—91no—
47D203—91no—
48D203C5×C3⋊D311yescharacteristic, direct product factor
49D3×D29—214no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52C5×D29—71no—
53C5×D29—631no—
54C32×C29C2×C5×D711yescharacteristic, complemented, Hall
55D7×C3⋊D3—291noHall
56C5×D21—874no—
57C5×D3×C7—34no—
58C3×C5×D7—294no—
59C7×C29C2×C5×C3⋊D311yescharacteristic, complemented, Hall
60C2×C5×C3⋊D3—2031noHall
61D87—214no—
62C3×D29—74no—
63D3×C29—34no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65C2×C5×D7—2611noHall
66C3⋊D21—291no—
67C7×C3⋊D3C5×D2911yescharacteristic, complemented
68C32×D7—291no—
69C2×D29—631noHall
70C3×C5×C7D3×D2914yescomplemented
71C2×C32×C5—2031no—
72C5×C3⋊D3—2031no—
73C5×C3⋊D3D20311yescharacteristic, direct product factor
74C3×C29C5×D3×D714yescomplemented
75D3×D7—874no—
76C2×C5×C7—91no—
77C5×D7—2611no—
78C5×D7—291no—
79C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
80C2×C5×D3—6094no—
81C2×C29—91no—
82D29—71no—
83D29—631no—
84C32×C5C2×D20311yescharacteristic, complemented, Hall
85D21—874no—
86C3×D7—294no—
87D3×C7—34no—
88C2×C3⋊D3—2031noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90C2×C3×C5—2034no—
91C5×D3—34no—
92C5×D3—6094no—
93C29C5×D7×C3⋊D311yescharacteristic, complemented, Sylow
94C2×D7—2611noHall
95C3×C7C5×D3×D2914yescomplemented
96C22×C5—18271noHall
97C2×C32—2031no—
98C3⋊D3—2031no—
99C3⋊D3C5×D20311yescharacteristic, direct product factor
100C3×C5D3×D20314yescomplemented
101C2×C7—91no—
102D7—2611no—
103D7—291no—
104C2×D3—6094no—
105C2×C5—91no—
106C2×C5—18271no—
107C2×C5—2031no—
108C32C2×C5×D20311yescharacteristic, complemented, Sylow
109C7C5×C3⋊D3×D2911yescharacteristic, complemented, Sylow
110C2×C3—2034no—
111D3—34no—
112D3—6094no—
113C5C3⋊D3×D20311yescharacteristic, direct product factor, Sylow
114C22—18271noSylow
115C3C5×D3×D20314yescomplemented
116C2—91no—
117C2—18271no—
118C2—2031no—
subgroupG/H
center, hypercenterC5C3⋊D3×D203
commutator, cosocle, hypocenterC32×C7×C29C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C7×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D203C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
3. C5×C3⋊D609C2semidirect
5. C32×C5×C7×C29C22semidirect
6. C3⋊D3×D203C5direct (N × H)
9. C3×C5×D203D3semidirect
12. C3⋊D609C2×C5semidirect
13. C7×C3⋊D3×C29C2×C5semidirect
14. C32×D203C2×C5semidirect
15. C3×C5×C7×C29C2×D3semidirect
17. C5×C3⋊D3×C29D7semidirect
21. C5×D203C3⋊D3direct (N × H)
23. C32×C7×C29C22×C5semidirect
25. C32×C5×C29C2×D7semidirect
29. C3×D203C5×D3semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
37. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29C2×C5×D3semidirect
42. C3⋊D3×C29C5×D7semidirect
44. C3×C5×C29D3×D7semidirect
48. D203C5×C3⋊D3direct (N × H)
50. C32×C5×C7C2×D29semidirect
54. C32×C29C2×C5×D7semidirect
59. C7×C29C2×C5×C3⋊D3semidirect
64. C5×C29D7×C3⋊D3semidirect
67. C7×C3⋊D3C5×D29semidirect
70. C3×C5×C7D3×D29semidirect
73. C5×C3⋊D3D203direct (N × H)
74. C3×C29C5×D3×D7semidirect
79. C32×C7C2×C5×D29semidirect
84. C32×C5C2×D203semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29C5×D7×C3⋊D3semidirect
95. C3×C7C5×D3×D29semidirect
99. C3⋊D3C5×D203direct (N × H)
100. C3×C5D3×D203semidirect
108. C32C2×C5×D203semidirect
109. C7C5×C3⋊D3×D29semidirect
113. C5C3⋊D3×D203direct (N × H)
115. C3C5×D3×D203semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D2032
C5×C7×C3⋊D3×C292
C5×C3⋊D6092
C5×D3×D2033
C3⋊D3×D2035
C5×C3⋊D3×D297
C5×D7×C3⋊D329