Finite Group Databasebeta

← C3⋊D3×D805 #44394653

Subgroups — C3⋊D3×D805 #44394653

Order 28980.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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×D805C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C23C211yesmaximal, characteristic, complemented
3C3⋊D2415C211yesmaximal, characteristic, complemented
4D3×D805—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C3⋊D3×D161—51nomaximal, Hall
7D2415—34no—
8C5×D3×C7×C23—34no—
9C3×D805D314yescomplemented
10C3⋊D3×D115—71nomaximal, Hall
11C2×D805—91noHall
12C3⋊D483—51no—
13C7×C3⋊D3×C23D511yescharacteristic, complemented
14C32×D161—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C3⋊D345—71no—
17C5×C3⋊D3×C23D711yescharacteristic, complemented
18C32×D115—71no—
19D3×D161—154no—
20C2×C5×C7×C23—91no—
21D805—91no—
22D805C3⋊D311yescharacteristic, direct product factor
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D3×D115—214no—
25C3⋊D3×D35—231nomaximal, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27D483—154no—
28D3×C7×C23—34no—
29C3×D161—54no—
30C3⋊D3×D23—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32D345—214no—
33C5×D3×C23—34no—
34C3×D115—74no—
35C2×D161—451noHall
36C3⋊D105—231no—
37C5×C7×C3⋊D3D2311yescharacteristic, complemented
38C32×D35—231no—
39C3×C7×C23D3×D514yescomplemented
40C2×D115—631noHall
41D3×D35—694no—
42C3⋊D69—351no—
43C3⋊D3×C23D3511yescharacteristic, complemented
44C32×D23—351no—
45C3×C5×C23D3×D714yescomplemented
46C2×C7×C23—91no—
47D161—51no—
48D161—451no—
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50D3×D23—1054no—
51D7×C3⋊D3—1151noHall
52C2×C5×C23—91no—
53D115—71no—
54D115—631no—
55D105—694no—
56C5×D3×C7—34no—
57C3×D35—234no—
58C32×C23C2×D3511yescharacteristic, complemented, Hall
59D5×C3⋊D3—1611noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61C2×D35—2071noHall
62D69—1054no—
63C3×D23—354no—
64D3×C23—34no—
65C3⋊D21—1151no—
66C7×C3⋊D3D11511yescharacteristic, complemented
67C32×D7—1151no—
68C5×C23D7×C3⋊D311yescharacteristic, complemented, Hall
69C3×C5×C7D3×D2314yescomplemented
70C2×D23—3151noHall
71C3⋊D15—1611no—
72C5×C3⋊D3D16111yescharacteristic, complemented
73C32×D5—1611no—
74D3×D7—3454no—
75C2×C5×C7—91no—
76D35—231no—
77D35—2071no—
78C3×C23D3×D3514yescomplemented
79C32×C7C2×D11511yescharacteristic, complemented, Hall
80D3×D5—4834no—
81C2×C23—91no—
82D23—351no—
83D23—3151no—
84C32×C5C2×D16111yescharacteristic, complemented, Hall
85D21—3454no—
86C3×D7—1154no—
87D3×C7—34no—
88C2×C3⋊D3—8051noHall
89C5×C7C3⋊D3×D2311yescharacteristic, complemented, Hall
90D15—4834no—
91C3×D5—1614no—
92C5×D3—34no—
93C2×D7—10351noHall
94C23C3⋊D3×D3511yescharacteristic, complemented, Sylow
95C3×C7D3×D11514yescomplemented
96C2×D5—14491noHall
97C2×C32—8051no—
98C3⋊D3—8051no—
99C3⋊D3D80511yescharacteristic, direct product factor
100C3×C5D3×D16114yescomplemented
101C2×C7—91no—
102D7—10351no—
103D7—1151no—
104C2×D3—24154no—
105C2×C5—91no—
106D5—1611no—
107D5—14491no—
108C32C2×D80511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D11511yescharacteristic, complemented, Sylow
110C2×C3—8054no—
111D3—34no—
112D3—24154no—
113C5C3⋊D3×D16111yescharacteristic, complemented, Sylow
114C22—72451noSylow
115C3D3×D80514yescomplemented
116C2—91no—
117C2—8051no—
118C2—72451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×D805C2semidirect
2. C5×C7×C3⋊D3×C23C2semidirect
3. C3⋊D2415C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×D805D3semidirect
13. C7×C3⋊D3×C23D5semidirect
15. C3×C5×C7×C23C2×D3semidirect
17. C5×C3⋊D3×C23D7semidirect
22. D805C3⋊D3direct (N × H)
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C2×D7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
37. C5×C7×C3⋊D3D23semidirect
39. C3×C7×C23D3×D5semidirect
43. C3⋊D3×C23D35semidirect
45. C3×C5×C23D3×D7semidirect
49. C32×C5×C7C2×D23semidirect
58. C32×C23C2×D35semidirect
60. C7×C23D5×C3⋊D3semidirect
66. C7×C3⋊D3D115semidirect
68. C5×C23D7×C3⋊D3semidirect
69. C3×C5×C7D3×D23semidirect
72. C5×C3⋊D3D161semidirect
78. C3×C23D3×D35semidirect
79. C32×C7C2×D115semidirect
84. C32×C5C2×D161semidirect
89. C5×C7C3⋊D3×D23semidirect
94. C23C3⋊D3×D35semidirect
95. C3×C7D3×D115semidirect
99. C3⋊D3D805direct (N × H)
100. C3×C5D3×D161semidirect
108. C32C2×D805semidirect
109. C7C3⋊D3×D115semidirect
113. C5C3⋊D3×D161semidirect
115. C3D3×D805semidirect

Maximal subgroups

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

subgroupindex
C32×D8052
C5×C7×C3⋊D3×C232
C3⋊D24152
D3×D8053
C3⋊D3×D1615
C3⋊D3×D1157
C3⋊D3×D3523