Finite Group Databasebeta

← C7×D5×C3⋊D3×C23 #44394643

Subgroups — C7×D5×C3⋊D3×C23 #44394643

Order 28980.

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

normal subgroups only

This group has 240 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×C7×D5×C23C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C23C211yesmaximal, characteristic, complemented
3C7×C23×C3⋊D15C211yesmaximal, characteristic, complemented
4D3×C7×D5×C23—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C2×C7×C3⋊D3×C23—51nomaximal, Hall
7C7×C23×D15—34no—
8C5×D3×C7×C23—34no—
9C3×C7×D5×C23D314yescomplemented
10D5×C3⋊D3×C23C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C23—91noHall
12C7×C3⋊D3×C23—51no—
13C7×C3⋊D3×C23D511yescharacteristic, direct product factor
14C2×C32×C7×C23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C23×C3⋊D15C2×C711yescharacteristic, complemented
17C5×C3⋊D3×C23C2×C711yescharacteristic, complemented
18C32×D5×C23C2×C711yescharacteristic, complemented
19C2×D3×C7×C23—154no—
20C2×C5×C7×C23—91no—
21C7×D5×C23—91no—
22C7×D5×C23C3⋊D311yescharacteristic, direct product factor
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D3×D5×C23—34no—
25C7×D5×C3⋊D3C2311yesmaximal, characteristic, direct product factor, Hall
26C32×C5×C23C22×C711yescharacteristic, complemented, Hall
27C2×C3×C7×C23—54no—
28D3×C7×C23—34no—
29D3×C7×C23—154no—
30C2×C3⋊D3×C23—51noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32C23×D15—34no—
33C5×D3×C23—34no—
34C3×D5×C23D3×C714yescomplemented
35C22×C7×C23—451noHall
36C7×C3⋊D15C2×C2311yescharacteristic, complemented
37C5×C7×C3⋊D3C2×C2311yescharacteristic, complemented
38C32×C7×D5C2×C2311yescharacteristic, complemented
39C3×C7×C23D3×D514yescomplemented
40C2×D5×C23—91noHall
41D3×C7×D5—34no—
42C2×C32×C23—51no—
43C3⋊D3×C23—51no—
44C3⋊D3×C23C7×D511yescharacteristic, direct product factor
45C3×C5×C23C2×D3×C714yescomplemented
46C2×C7×C23—51no—
47C2×C7×C23—91no—
48C2×C7×C23—451no—
49C32×C5×C7C22×C2311yescharacteristic, complemented, Hall
50C2×D3×C23—154no—
51C2×C7×C3⋊D3—51noHall
52C2×C5×C23—91no—
53D5×C23—91no—
54D5×C23C7×C3⋊D311yescharacteristic, direct product factor
55C7×D15—34no—
56C5×D3×C7—34no—
57C3×C7×D5D3×C2314yescomplemented
58C32×C23C2×C7×D511yescharacteristic, complemented, Hall
59D5×C3⋊D3C7×C2311yescharacteristic, direct product factor, Hall
60C7×C23D5×C3⋊D311yescharacteristic, direct product factor, Hall
61C2×C7×D5—91noHall
62C2×C3×C23—54no—
63D3×C23—34no—
64D3×C23—154no—
65C2×C32×C7—51no—
66C7×C3⋊D3—51no—
67C7×C3⋊D3D5×C2311yescharacteristic, direct product factor
68C5×C23C2×C7×C3⋊D311yescharacteristic, complemented, Hall
69C3×C5×C7C2×D3×C2314yescomplemented
70C22×C23—451noHall
71C3⋊D15C2×C7×C2311yescharacteristic, complemented
72C5×C3⋊D3C2×C7×C2311yescharacteristic, complemented
73C32×D5C2×C7×C2311yescharacteristic, complemented
74C2×D3×C7—154no—
75C2×C5×C7—91no—
76C7×D5—91no—
77C7×D5C3⋊D3×C2311yescharacteristic, direct product factor
78C3×C23D3×C7×D514yescomplemented
79C32×C7C2×D5×C2311yescharacteristic, complemented, Hall
80D3×D5—34no—
81C2×C23—51no—
82C2×C23—91no—
83C2×C23—451no—
84C32×C5C22×C7×C2311yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86D3×C7—34no—
87D3×C7—154no—
88C2×C3⋊D3—51noHall
89C5×C7C2×C3⋊D3×C2311yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5D3×C7×C2314yescomplemented
92C5×D3—34no—
93C22×C7—451noHall
94C23C7×D5×C3⋊D311yescharacteristic, direct product factor, Sylow
95C3×C7D3×D5×C2314yescomplemented
96C2×D5—91noHall
97C2×C32—51no—
98C3⋊D3—51no—
99C3⋊D3C7×D5×C2311yescharacteristic, direct product factor
100C3×C5C2×D3×C7×C2314yescomplemented
101C2×C7—51no—
102C2×C7—91no—
103C2×C7—451no—
104C2×D3—154no—
105C2×C5—91no—
106D5—91no—
107D5C7×C3⋊D3×C2311yescharacteristic, direct product factor
108C32C2×C7×D5×C2311yescharacteristic, complemented, Sylow
109C7D5×C3⋊D3×C2311yescharacteristic, direct product factor, Sylow
110C2×C3—54no—
111D3—34no—
112D3—154no—
113C5C2×C7×C3⋊D3×C2311yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C2314yescomplemented
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C23D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C22×C7×C23
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C32×C5
UCSC1 ◁ C7×C23

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C23C2semidirect
2. C5×C7×C3⋊D3×C23C2semidirect
3. C7×C23×C3⋊D15C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C7×D5×C23D3semidirect
10. D5×C3⋊D3×C23C7direct (N × H)
13. C7×C3⋊D3×C23D5direct (N × H)
15. C3×C5×C7×C23C2×D3semidirect
16. C23×C3⋊D15C2×C7semidirect
17. C5×C3⋊D3×C23C2×C7semidirect
18. C32×D5×C23C2×C7semidirect
22. C7×D5×C23C3⋊D3direct (N × H)
23. C32×C7×C23C2×D5semidirect
25. C7×D5×C3⋊D3C23direct (N × H)
26. C32×C5×C23C22×C7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
34. C3×D5×C23D3×C7semidirect
36. C7×C3⋊D15C2×C23semidirect
37. C5×C7×C3⋊D3C2×C23semidirect
38. C32×C7×D5C2×C23semidirect
39. C3×C7×C23D3×D5semidirect
44. C3⋊D3×C23C7×D5direct (N × H)
45. C3×C5×C23C2×D3×C7semidirect
49. C32×C5×C7C22×C23semidirect
54. D5×C23C7×C3⋊D3direct (N × H)
57. C3×C7×D5D3×C23semidirect
58. C32×C23C2×C7×D5semidirect
59. D5×C3⋊D3C7×C23direct (N × H)
60. C7×C23D5×C3⋊D3direct (N × H)
67. C7×C3⋊D3D5×C23direct (N × H)
68. C5×C23C2×C7×C3⋊D3semidirect
69. C3×C5×C7C2×D3×C23semidirect
71. C3⋊D15C2×C7×C23semidirect
72. C5×C3⋊D3C2×C7×C23semidirect
73. C32×D5C2×C7×C23semidirect
77. C7×D5C3⋊D3×C23direct (N × H)
78. C3×C23D3×C7×D5semidirect
79. C32×C7C2×D5×C23semidirect
84. C32×C5C22×C7×C23semidirect
89. C5×C7C2×C3⋊D3×C23semidirect
91. C3×D5D3×C7×C23semidirect
94. C23C7×D5×C3⋊D3direct (N × H)
95. C3×C7D3×D5×C23semidirect
99. C3⋊D3C7×D5×C23direct (N × H)
100. C3×C5C2×D3×C7×C23semidirect
107. D5C7×C3⋊D3×C23direct (N × H)
108. C32C2×C7×D5×C23semidirect
109. C7D5×C3⋊D3×C23direct (N × H)
113. C5C2×C7×C3⋊D3×C23semidirect
115. C3D3×C7×D5×C23semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C232
C5×C7×C3⋊D3×C232
C7×C23×C3⋊D152
D3×C7×D5×C233
C2×C7×C3⋊D3×C235
D5×C3⋊D3×C237
C7×D5×C3⋊D323