Finite Group Databasebeta

← C3⋊D15×D161 #44394641

Subgroups — C3⋊D15×D161 #44394641

Order 28980.

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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×D161C211yesmaximal, characteristic, complemented
2C7×C23×C3⋊D15C211yesmaximal, characteristic, complemented
3C3⋊D2415C211yesmaximal, characteristic, complemented
4D15×D161—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6C3⋊D3×D161—51nomaximal, Hall
7D2415—34no—
8C7×C23×D15—34no—
9C3×C5×D161D314yescomplemented
10D23×C3⋊D15—71nomaximal, Hall
11D5×D161—91noHall
12C3⋊D483—51no—
13C7×C3⋊D3×C23—51no—
14C32×D161D511yescharacteristic, complemented
15C3×C5×C7×C23C2×D314yescomplemented
16C3⋊D345—71no—
17C23×C3⋊D15D711yescharacteristic, complemented
18C32×C5×D23—71no—
19D3×D161—154no—
20D805—91no—
21C7×D5×C23—91no—
22C5×D161C3⋊D311yescharacteristic, complemented
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D15×D23—214no—
25D7×C3⋊D15—231nomaximal, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27D483—154no—
28D3×C7×C23—154no—
29C3×D161D1514yescomplemented
30C3⋊D3×D23—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32D345—214no—
33C23×D15—34no—
34C3×C5×D23—74no—
35C2×D161—451noHall
36C3⋊D105—231no—
37C7×C3⋊D15D2311yescharacteristic, complemented
38C32×C5×D7—231no—
39C3×C7×C23C2×D1514yescomplemented
40D5×D23—631noHall
41D7×D15—694no—
42C3⋊D69—351no—
43C3⋊D3×C23—51no—
44C32×D23—71no—
45C3×C5×C23D3×D714yescomplemented
46C2×C7×C23—451no—
47D161—451no—
48D161C3⋊D1511yescharacteristic, direct product factor
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50D3×D23—1054no—
51D7×C3⋊D3—1151noHall
52D115—631no—
53C5×D23—71no—
54D5×C23—91no—
55D105—694no—
56C7×D15—34no—
57C3×C5×D7—234no—
58C32×C23D5×D711yescharacteristic, complemented, Hall
59C2×C3⋊D15—1611noHall
60C7×C23C2×C3⋊D1511yescharacteristic, complemented, Hall
61D5×D7—2071noHall
62D69—1054no—
63C3×D23—74no—
64D3×C23—154no—
65C3⋊D21—1151no—
66C7×C3⋊D3—51no—
67C32×D7—231no—
68C5×C23D7×C3⋊D311yescharacteristic, complemented, Hall
69C3×C5×C7D3×D2314yescomplemented
70C2×D23—3151noHall
71C2×C32×C5—1611no—
72C3⋊D15—1611no—
73C3⋊D15D16111yescharacteristic, direct product factor
74D3×D7—3454no—
75D35—2071no—
76C5×D7—231no—
77C7×D5—91no—
78C3×C23D7×D1514yescomplemented
79C32×C7D5×D2311yescharacteristic, complemented, Hall
80C2×D15—4834no—
81C2×C23—451no—
82D23—71no—
83D23—3151no—
84C32×C5C2×D16111yescharacteristic, complemented, Hall
85D21—3454no—
86C3×D7—234no—
87D3×C7—154no—
88C2×C3⋊D3—8051noHall
89C5×C7C3⋊D3×D2311yescharacteristic, complemented, Hall
90C2×C3×C5—1614no—
91D15—34no—
92D15—4834no—
93C2×D7—10351noHall
94C23D7×C3⋊D1511yescharacteristic, complemented, Sylow
95C3×C7D15×D2314yescomplemented
96C2×D5—14491noHall
97C2×C32—1611no—
98C3⋊D3—51no—
99C3⋊D3—8051no—
100C3×C5D3×D16114yescomplemented
101C2×C7—451no—
102D7—10351no—
103D7—231no—
104C2×D3—24154no—
105C2×C5—1611no—
106D5—91no—
107D5—14491no—
108C32D5×D16111yescharacteristic, complemented, Sylow
109C7D23×C3⋊D1511yescharacteristic, complemented, Sylow
110C2×C3—1614no—
111D3—154no—
112D3—24154no—
113C5C3⋊D3×D16111yescharacteristic, complemented, Sylow
114C22—72451noSylow
115C3D15×D16114yescomplemented
116C2—451no—
117C2—72451no—
118C2—1611no—
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×C5×D161C2semidirect
2. C7×C23×C3⋊D15C2semidirect
3. C3⋊D2415C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C5×D161D3semidirect
14. C32×D161D5semidirect
15. C3×C5×C7×C23C2×D3semidirect
17. C23×C3⋊D15D7semidirect
22. C5×D161C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C2×D7semidirect
29. C3×D161D15semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
37. C7×C3⋊D15D23semidirect
39. C3×C7×C23C2×D15semidirect
45. C3×C5×C23D3×D7semidirect
48. D161C3⋊D15direct (N × H)
49. C32×C5×C7C2×D23semidirect
58. C32×C23D5×D7semidirect
60. C7×C23C2×C3⋊D15semidirect
68. C5×C23D7×C3⋊D3semidirect
69. C3×C5×C7D3×D23semidirect
73. C3⋊D15D161direct (N × H)
78. C3×C23D7×D15semidirect
79. C32×C7D5×D23semidirect
84. C32×C5C2×D161semidirect
89. C5×C7C3⋊D3×D23semidirect
94. C23D7×C3⋊D15semidirect
95. C3×C7D15×D23semidirect
100. C3×C5D3×D161semidirect
108. C32D5×D161semidirect
109. C7D23×C3⋊D15semidirect
113. C5C3⋊D3×D161semidirect
115. C3D15×D161semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1612
C7×C23×C3⋊D152
C3⋊D24152
D15×D1613
C3⋊D3×D1615
D23×C3⋊D157
D7×C3⋊D1523