Finite Group Databasebeta

← D5×C23×C3⋊D21 #44394647

Subgroups — D5×C23×C3⋊D21 #44394647

Order 28980.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×C23×C3⋊D21C211yesmaximal, characteristic, complemented
3C23×C3⋊D105C211yesmaximal, characteristic, complemented
4D5×C23×D21—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C2×C23×C3⋊D21—51nomaximal, Hall
7C23×D105—34no—
8C5×C23×D21—34no—
9C3×C7×D5×C23D314yescomplemented
10D5×C3⋊D3×C23—71nomaximal, Hall
11D5×D7×C23—91noHall
12C23×C3⋊D21—51no—
13C23×C3⋊D21D511yescharacteristic, direct product factor
14C2×C32×C7×C23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C23×C3⋊D15—71no—
17C5×C3⋊D3×C23—71no—
18C32×D5×C23D711yescharacteristic, complemented
19C2×C23×D21—154no—
20C23×D35—91no—
21C7×D5×C23C3⋊D311yescharacteristic, complemented
22C5×D7×C23—91no—
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D3×D5×C23—214no—
25D5×C3⋊D21C2311yesmaximal, characteristic, direct product factor, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27C2×C3×C7×C23—54no—
28C23×D21—34no—
29C23×D21—154no—
30C2×C3⋊D3×C23—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32C23×D15—214no—
33C5×D3×C23—214no—
34C3×D5×C23D2114yescomplemented
35C2×D7×C23—451noHall
36C3⋊D105C2×C2311yescharacteristic, complemented
37C5×C3⋊D21C2×C2311yescharacteristic, complemented
38C32×C7×D5C2×C2311yescharacteristic, complemented
39C3×C7×C23D3×D514yescomplemented
40C2×D5×C23—631noHall
41D5×D21—34no—
42C2×C32×C23—51no—
43C3⋊D3×C23—71no—
44C3⋊D3×C23—351no—
45C3×C5×C23C2×D2114yescomplemented
46C2×C7×C23—51no—
47D7×C23—91no—
48D7×C23—451no—
49C32×C5×C7C22×C2311yescharacteristic, complemented, Hall
50C2×D3×C23—1054no—
51C2×C3⋊D21—51noHall
52C2×C5×C23—631no—
53D5×C23—631no—
54D5×C23C3⋊D2111yescharacteristic, direct product factor
55D105—34no—
56C5×D21—34no—
57C3×C7×D5D3×C2314yescomplemented
58C32×C23D5×D711yescharacteristic, complemented, Hall
59D5×C3⋊D3—71noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61D5×D7—91noHall
62C2×C3×C23—54no—
63D3×C23—214no—
64D3×C23—1054no—
65C2×C32×C7—51no—
66C3⋊D21—51no—
67C3⋊D21D5×C2311yescharacteristic, direct product factor
68C5×C23C2×C3⋊D2111yescharacteristic, complemented, Hall
69C3×C5×C7C2×D3×C2314yescomplemented
70C22×C23—3151noHall
71C3⋊D15—71no—
72C5×C3⋊D3—71no—
73C32×D5D7×C2311yescharacteristic, complemented
74C2×D21—154no—
75D35—91no—
76C5×D7—91no—
77C7×D5C3⋊D3×C2311yescharacteristic, complemented
78C3×C23D5×D2114yescomplemented
79C32×C7C2×D5×C2311yescharacteristic, complemented, Hall
80D3×D5—214no—
81C2×C23—51no—
82C2×C23—3151no—
83C2×C23—631no—
84C32×C5C2×D7×C2311yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86D21—34no—
87D21—154no—
88C2×C3⋊D3—351noHall
89C5×C7C2×C3⋊D3×C2311yescharacteristic, complemented, Hall
90D15—214no—
91C3×D5C23×D2114yescomplemented
92C5×D3—214no—
93C2×D7—451noHall
94C23D5×C3⋊D2111yescharacteristic, direct product factor, Sylow
95C3×C7D3×D5×C2314yescomplemented
96C2×D5—631noHall
97C2×C32—51no—
98C3⋊D3—71no—
99C3⋊D3—351no—
100C3×C5C2×C23×D2114yescomplemented
101C2×C7—51no—
102D7—91no—
103D7—451no—
104C2×D3—1054no—
105C2×C5—631no—
106D5—631no—
107D5C23×C3⋊D2111yescharacteristic, direct product factor
108C32D5×D7×C2311yescharacteristic, complemented, Sylow
109C7D5×C3⋊D3×C2311yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—214no—
112D3—1054no—
113C5C2×C23×C3⋊D2111yescharacteristic, complemented, Sylow
114C22—3151noSylow
115C3D5×C23×D2114yescomplemented
116C2—51no—
117C2—3151no—
118C2—631no—
subgroupG/H
center, hypercenterC23D5×C3⋊D21
commutator, cosocle, hypocenterC32×C5×C7C22×C23
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C23C2semidirect
2. C5×C23×C3⋊D21C2semidirect
3. C23×C3⋊D105C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C7×D5×C23D3semidirect
13. C23×C3⋊D21D5direct (N × H)
15. C3×C5×C7×C23C2×D3semidirect
18. C32×D5×C23D7semidirect
21. C7×D5×C23C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
25. D5×C3⋊D21C23direct (N × H)
26. C32×C5×C23C2×D7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
34. C3×D5×C23D21semidirect
36. C3⋊D105C2×C23semidirect
37. C5×C3⋊D21C2×C23semidirect
38. C32×C7×D5C2×C23semidirect
39. C3×C7×C23D3×D5semidirect
45. C3×C5×C23C2×D21semidirect
49. C32×C5×C7C22×C23semidirect
54. D5×C23C3⋊D21direct (N × H)
57. C3×C7×D5D3×C23semidirect
58. C32×C23D5×D7semidirect
60. C7×C23D5×C3⋊D3semidirect
67. C3⋊D21D5×C23direct (N × H)
68. C5×C23C2×C3⋊D21semidirect
69. C3×C5×C7C2×D3×C23semidirect
73. C32×D5D7×C23semidirect
77. C7×D5C3⋊D3×C23semidirect
78. C3×C23D5×D21semidirect
79. C32×C7C2×D5×C23semidirect
84. C32×C5C2×D7×C23semidirect
89. C5×C7C2×C3⋊D3×C23semidirect
91. C3×D5C23×D21semidirect
94. C23D5×C3⋊D21direct (N × H)
95. C3×C7D3×D5×C23semidirect
100. C3×C5C2×C23×D21semidirect
107. D5C23×C3⋊D21direct (N × H)
108. C32D5×D7×C23semidirect
109. C7D5×C3⋊D3×C23semidirect
113. C5C2×C23×C3⋊D21semidirect
115. C3D5×C23×D21semidirect

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×C23×C3⋊D212
C23×C3⋊D1052
D5×C23×D213
C2×C23×C3⋊D215
D5×C3⋊D3×C237
D5×C3⋊D2123