Finite Group Databasebeta

← C3⋊D15×D31⋊C5 #42124728

Subgroups — C3⋊D15×D31⋊C5 #42124728

Order 27900.

288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C3⋊D15×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented
2C3⋊(C3⋊(C5⋊(D31⋊C5)))C211yesmaximal, characteristic, complemented
3C32×C5×D31⋊C5C211yesmaximal, characteristic, complemented
4D15×D31⋊C5—34nomaximal
5C32×C5×ΓL(1,𝔽32)C2211yescharacteristic, complemented, Hall
6D31×C3⋊D15C511yesmaximal, characteristic, complemented
7C3⋊D3×D31⋊C5—51nomaximal
8D15×ΓL(1,𝔽32)—34no—
9C3⋊(C5⋊(D31⋊C5))—34no—
10C3×C5×D31⋊C5D314yescomplemented
11D5×D31⋊C5—91noHall
12C3⋊D465C2×C511yescharacteristic, complemented
13C31×C3⋊D15C2×C511yescharacteristic, complemented
14C32×C5×D31C2×C511yescharacteristic, complemented
15C3⋊D3×ΓL(1,𝔽32)—51no—
16C3⋊(C3⋊(D31⋊C5))—51no—
17C32×D31⋊C5—22no—
18C32×D31⋊C5D511yescharacteristic, complemented
19C3×C5×ΓL(1,𝔽32)C2×D314yescomplemented
20D15×D31—34no—
21D3×D31⋊C5—154no—
22C5⋊(D31⋊C5)—91no—
23D5×ΓL(1,𝔽32)—91no—
24C5×D31⋊C5C3⋊D311yescharacteristic, complemented
25C32×C5×C31C22×C511yescharacteristic, complemented
26C32×ΓL(1,𝔽32)—22no—
27C32×ΓL(1,𝔽32)C2×D511yescharacteristic, complemented
28C3⋊D3×D31—51noHall
29D465—34no—
30D15×C31—34no—
31C3×C5×D31C5×D314yescomplemented
32C3⋊(D31⋊C5)—154no—
33D3×ΓL(1,𝔽32)—154no—
34C3×D31⋊C5—28no—
35C3×D31⋊C5D1514yescomplemented
36C2×C5×C3⋊D15—311nomaximal, Hall
37C5×ΓL(1,𝔽32)C2×C3⋊D311yescharacteristic, complemented, Hall
38D5×D31—91no—
39C2×D31⋊C5—451no—
40C3⋊D93—51no—
41C3⋊D3×C31—51no—
42C32×D31C5×D511yescharacteristic, complemented
43C3×C5×C31C2×C5×D314yescomplemented
44C3×ΓL(1,𝔽32)—28no—
45C3×ΓL(1,𝔽32)C2×D1514yescomplemented
46C2×C32×C52—311no—
47C5×C3⋊D15—311no—
48C5×C3⋊D15—311no—
49D3×D31—154no—
50D155—91no—
51C5×D31C5×C3⋊D311yescharacteristic, complemented
52D5×C31—91no—
53C2×ΓL(1,𝔽32)—451no—
54D31⋊C5—22no—
55D31⋊C5—451no—
56D31⋊C5C3⋊D1511yescharacteristic, direct product factor
57C2×C5×D15—934no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52—311noHall
60D93—154no—
61C3×D31C5×D1514yescomplemented
62D3×C31—154no—
63C2×C3⋊D15—311no—
64C2×C5×C3⋊D3—1551no—
65C5×C31C2×C5×C3⋊D311yescharacteristic, complemented
66ΓL(1,𝔽32)—22no—
67ΓL(1,𝔽32)C2×C3⋊D1511yescharacteristic, complemented
68C2×C3×C52—314no—
69C5×D15—934no—
70C5×D15—934no—
71C2×D31—451noHall
72C2×C5×D5—2791noHall
73C3×C31C2×C5×D1514yescomplemented
74C2×C32×C5—311no—
75C2×C32×C5—311no—
76C2×C32×C5—622no—
77C3⋊D15—311no—
78C3⋊D15D31⋊C511yescharacteristic, direct product factor
79C5×C3⋊D3—1551no—
80C5×C3⋊D3—1551no—
81C3×C52—314no—
82C2×C31—451no—
83D31—451no—
84D31C5×C3⋊D1511yescharacteristic, complemented
85C2×D15—934no—
86C2×C5×D3—4654no—
87C2×C52—311no—
88C5×D5—2791no—
89C5×D5—2791no—
90C32×C5—311no—
91C32×C5—622no—
92C32×C5C2×D31⋊C511yescharacteristic, complemented
93C2×C3⋊D3—1551noHall
94C31C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
95C2×C3×C5—314no—
96C2×C3×C5—314no—
97C2×C3×C5—628no—
98D15—34no—
99D15—934no—
100C5×D3—4654no—
101C5×D3—4654no—
102C52—311noSylow
103C22×C5—13951no—
104C2×D5—2791no—
105C2×C32—311no—
106C3⋊D3—51no—
107C3⋊D3—1551no—
108C3×C5—314no—
109C3×C5—628no—
110C3×C5D3×D31⋊C514yescomplemented
111C2×D3—4654no—
112C2×C5—311no—
113C2×C5—311no—
114C2×C5—622no—
115C2×C5—13951no—
116C2×C5—13951no—
117D5—91no—
118D5—2791no—
119C32D5×D31⋊C511yescharacteristic, complemented, Sylow
120C2×C3—314no—
121D3—154no—
122D3—4654no—
123C5—311no—
124C5—622no—
125C5C3⋊D3×D31⋊C511yescharacteristic, complemented
126C22—13951noSylow
127C3D15×D31⋊C514yescomplemented
128C2—311no—
129C2—451no—
130C2—13951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C31C22×C5
LCSG ▷ C32×C5×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊D15×ΓL(1,𝔽32)C2semidirect
2. C3⋊(C3⋊(C5⋊(D31⋊C5)))C2semidirect
3. C32×C5×D31⋊C5C2semidirect
5. C32×C5×ΓL(1,𝔽32)C22semidirect
6. D31×C3⋊D15C5semidirect
10. C3×C5×D31⋊C5D3semidirect
12. C3⋊D465C2×C5semidirect
13. C31×C3⋊D15C2×C5semidirect
14. C32×C5×D31C2×C5semidirect
18. C32×D31⋊C5D5semidirect
19. C3×C5×ΓL(1,𝔽32)C2×D3semidirect
24. C5×D31⋊C5C3⋊D3semidirect
25. C32×C5×C31C22×C5semidirect
27. C32×ΓL(1,𝔽32)C2×D5semidirect
31. C3×C5×D31C5×D3semidirect
35. C3×D31⋊C5D15semidirect
37. C5×ΓL(1,𝔽32)C2×C3⋊D3semidirect
42. C32×D31C5×D5semidirect
43. C3×C5×C31C2×C5×D3semidirect
45. C3×ΓL(1,𝔽32)C2×D15semidirect
51. C5×D31C5×C3⋊D3semidirect
56. D31⋊C5C3⋊D15direct (N × H)
58. C32×C31C2×C5×D5semidirect
61. C3×D31C5×D15semidirect
65. C5×C31C2×C5×C3⋊D3semidirect
67. ΓL(1,𝔽32)C2×C3⋊D15semidirect
73. C3×C31C2×C5×D15semidirect
78. C3⋊D15D31⋊C5direct (N × H)
84. D31C5×C3⋊D15semidirect
92. C32×C5C2×D31⋊C5semidirect
94. C31C2×C5×C3⋊D15semidirect
110. C3×C5D3×D31⋊C5semidirect
119. C32D5×D31⋊C5semidirect
125. C5C3⋊D3×D31⋊C5semidirect
127. C3D15×D31⋊C5semidirect

Maximal subgroups

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

subgroupindex
C3⋊D15×ΓL(1,𝔽32)2
C3⋊(C3⋊(C5⋊(D31⋊C5)))2
C32×C5×D31⋊C52
D15×D31⋊C53
D31×C3⋊D155
C3⋊D3×D31⋊C55
C2×C5×C3⋊D1531