Finite Group Databasebeta

← C5×D5×C3⋊D93 #42124950

Subgroups — C5×D5×C3⋊D93 #42124950

Order 27900.

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

normal subgroups only

This group has 288 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×C5×D5×C31C211yesmaximal, characteristic, complemented
2C52×C3⋊D93C211yesmaximal, characteristic, complemented
3C5×C3⋊D465C211yesmaximal, characteristic, complemented
4C5×D5×D93—34nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C2×C5×C3⋊D93—51nomaximal
7D5×C3⋊D93C511yesmaximal, characteristic, direct product factor
8C5×D465—34no—
9C52×D93—34no—
10C3×C5×D5×C31D314yescomplemented
11C5×D5×D31—91noHall
12C3⋊D465C2×C511yescharacteristic, complemented
13C5×C3⋊D93—22no—
14C5×C3⋊D93—51no—
15C5×C3⋊D93D511yescharacteristic, direct product factor
16C5×C3⋊D93C2×C511yescharacteristic, complemented
17C32×D5×C31C2×C511yescharacteristic, complemented
18C2×C32×C5×C31—51no—
19C3×C52×C31C2×D314yescomplemented
20C2×C5×D93—154no—
21D5×D93—34no—
22C5×D155—91no—
23C5×D5×C31C3⋊D311yescharacteristic, complemented
24C52×D31—91no—
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C22×C511yescharacteristic, complemented
28C2×C3⋊D93—51noHall
29C2×C3×C5×C31—54no—
30D465—34no—
31C5×D93—34no—
32C5×D93—34no—
33C5×D93—68no—
34C5×D93—154no—
35C3×D5×C31C5×D314yescomplemented
36C5×D5×C3⋊D3—311nomaximal, Hall
37C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×C5×D31—451no—
39D5×D31—91no—
40C2×C32×C31—51no—
41C3⋊D93—51no—
42C3⋊D93C5×D511yescharacteristic, direct product factor
43C3×C5×C31—28no—
44C3×C5×C31D3×D514yescomplemented
45C3×C5×C31C2×C5×D314yescomplemented
46C5×C3⋊D15—311no—
47C52×C3⋊D3—311no—
48C32×C5×D5D3111yescharacteristic, complemented
49C2×D93—154no—
50C2×C5×C31—51no—
51D155—91no—
52C5×D31—91no—
53C5×D31—91no—
54C5×D31—182no—
55C5×D31—451no—
56D5×C31C5×C3⋊D311yescharacteristic, complemented
57C5×D3×D5—934no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60C2×C3×C31—54no—
61D93—34no—
62D93—154no—
63C2×C5×C3⋊D3—1551no—
64D5×C3⋊D3—311no—
65C5×C31—22no—
66C5×C31D5×C3⋊D311yescharacteristic, complemented
67C5×C31C2×C5×C3⋊D311yescharacteristic, complemented
68C5×D15—934no—
69C52×D3—934no—
70C3×C5×D5D9314yescomplemented
71C2×D31—451noHall
72C2×C5×D5—2791noHall
73C3×C31C5×D3×D514yescomplemented
74C2×C32×C5—51no—
75C3⋊D15—311no—
76C5×C3⋊D3—311no—
77C5×C3⋊D3—311no—
78C5×C3⋊D3—622no—
79C5×C3⋊D3—1551no—
80C32×D5C5×D3111yescharacteristic, complemented
81C3×C52C2×D9314yescomplemented
82C2×C31—51no—
83D31—91no—
84D31—451no—
85C2×C5×D3—4654no—
86D3×D5—934no—
87C2×C52—2791no—
88C5×D5—2791no—
89C5×D5C3⋊D9311yescharacteristic, direct product factor
90C32×C5—22no—
91C32×C5D5×D3111yescharacteristic, complemented
92C32×C5C2×C5×D3111yescharacteristic, complemented
93C2×C3⋊D3—1551noHall
94C31C5×D5×C3⋊D311yescharacteristic, complemented, Sylow
95C2×C3×C5—54no—
96D15—934no—
97C3×D5C5×D9314yescomplemented
98C5×D3—934no—
99C5×D3—934no—
100C5×D3—1868no—
101C5×D3—4654no—
102C52C2×C3⋊D9311yescharacteristic, complemented, Sylow
103C22×C5—13951no—
104C2×D5—2791no—
105C2×C32—51no—
106C3⋊D3—311no—
107C3⋊D3—1551no—
108C3×C5—28no—
109C3×C5D5×D9314yescomplemented
110C3×C5C2×C5×D9314yescomplemented
111C2×D3—4654no—
112C2×C5—51no—
113C2×C5—2791no—
114C2×C5—2791no—
115C2×C5—5582no—
116C2×C5—13951no—
117D5—2791no—
118D5C5×C3⋊D9311yescharacteristic, direct product factor
119C32C5×D5×D3111yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—934no—
122D3—4654no—
123C5—22no—
124C5D5×C3⋊D9311yescharacteristic, direct product factor
125C5C2×C5×C3⋊D9311yescharacteristic, complemented
126C22—13951noSylow
127C3C5×D5×D9314yescomplemented
128C2—51no—
129C2—2791no—
130C2—13951no—
subgroupG/H
center, hypercenterC5D5×C3⋊D93
commutator, cosocle, hypocenterC32×C5×C31C22×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C31C2semidirect
2. C52×C3⋊D93C2semidirect
3. C5×C3⋊D465C2semidirect
5. C32×C52×C31C22semidirect
7. D5×C3⋊D93C5direct (N × H)
10. C3×C5×D5×C31D3semidirect
12. C3⋊D465C2×C5semidirect
15. C5×C3⋊D93D5direct (N × H)
16. C5×C3⋊D93C2×C5semidirect
17. C32×D5×C31C2×C5semidirect
19. C3×C52×C31C2×D3semidirect
23. C5×D5×C31C3⋊D3semidirect
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C22×C5semidirect
35. C3×D5×C31C5×D3semidirect
37. C52×C31C2×C3⋊D3semidirect
42. C3⋊D93C5×D5direct (N × H)
44. C3×C5×C31D3×D5semidirect
45. C3×C5×C31C2×C5×D3semidirect
48. C32×C5×D5D31semidirect
56. D5×C31C5×C3⋊D3semidirect
58. C32×C31C2×C5×D5semidirect
59. C32×C52C2×D31semidirect
66. C5×C31D5×C3⋊D3semidirect
67. C5×C31C2×C5×C3⋊D3semidirect
70. C3×C5×D5D93semidirect
73. C3×C31C5×D3×D5semidirect
80. C32×D5C5×D31semidirect
81. C3×C52C2×D93semidirect
89. C5×D5C3⋊D93direct (N × H)
91. C32×C5D5×D31semidirect
92. C32×C5C2×C5×D31semidirect
94. C31C5×D5×C3⋊D3semidirect
97. C3×D5C5×D93semidirect
102. C52C2×C3⋊D93semidirect
109. C3×C5D5×D93semidirect
110. C3×C5C2×C5×D93semidirect
118. D5C5×C3⋊D93direct (N × H)
119. C32C5×D5×D31semidirect
124. C5D5×C3⋊D93direct (N × H)
125. C5C2×C5×C3⋊D93semidirect
127. C3C5×D5×D93semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C312
C52×C3⋊D932
C5×C3⋊D4652
C5×D5×D933
C2×C5×C3⋊D935
D5×C3⋊D935
C5×D5×C3⋊D331