Finite Group Databasebeta

← C52×D3×D93 #42124924

Subgroups — C52×D3×D93 #42124924

Order 27900.

352 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 128 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×C52×D3×C31C211yesmaximal, characteristic, complemented
2C3×C52×D93C211yesmaximal, characteristic, complemented
3C52×C3⋊D93C211yesmaximal, characteristic, complemented
4C2×C52×D93—31nomaximal
5C52×D3×D31—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C5×D3×D93C516yesmaximal, direct product factor
8C52×D93—31no—
9C52×D93—31no—
10C52×D93—61no—
11C52×D93D311yescharacteristic, direct product factor
12C52×D3×C31D311yescharacteristic, complemented
13C3×C52×D31—31no—
14C2×C3×C52×C31—31no—
15C2×C52×D31—91noHall
16C5×C3⋊D93C2×C516yescomplemented
17C3×C5×D93C2×C516yescomplemented
18C3×C5×D3×C31C2×C516yescomplemented
19C3×C52×C31—21no—
20C3×C52×C31C2×D311yescharacteristic, complemented
21C3×C52×C31C2×D311yescharacteristic, complemented
22C2×C5×D93—36no—
23C5×D3×D31—36no—
24C2×C52×C31—31no—
25C52×D31—31no—
26C52×D31—91no—
27C32×C5×C31C22×C516yescomplemented
28D3×D93C5211yescharacteristic, direct product factor, Hall
29C2×C3×C5×C31—36no—
30C5×D93—36no—
31C5×D93—36no—
32C5×D93—66no—
33C5×D93C5×D316yesdirect product factor
34C5×D3×C31C5×D316yescomplemented
35C3×C5×D31—36no—
36C52×D32—311nomaximal, Hall
37C52×C31D3211yescharacteristic, complemented, Hall
38C2×C5×D31—96no—
39C3⋊D93C2×C5211yescharacteristic, complemented
40C3×D93C2×C5211yescharacteristic, complemented
41C3×D3×C31C2×C5211yescharacteristic, complemented
42C3×C5×C31—26no—
43C3×C5×C31C2×C5×D316yescomplemented
44C3×C5×C31C2×C5×D316yescomplemented
45C52×C3⋊D3—311no—
46C3×C52×D3—311no—
47C3×C52×D3D3111yescharacteristic, complemented
48C2×D93—31no—
49D3×D31—31no—
50C2×C5×C31—36no—
51C5×D31—36no—
52C5×D31—96no—
53C2×C52×D3—931no—
54C2×C52×D3—931no—
55C32×C31C22×C5211yescharacteristic, complemented, Hall
56C32×C52C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—31no—
58D93—31no—
59D93—31no—
60D93—61no—
61D93C52×D311yescharacteristic, direct product factor
62C3×D31—31no—
63D3×C31C52×D311yescharacteristic, complemented
64C5×D32—316no—
65C5×C31C5×D3216yescomplemented
66C2×C3×C52—31no—
67C2×C3×C52—931no—
68C52×D3—311no—
69C52×D3—931no—
70C52×D3—931no—
71C52×D3—1861no—
72C52×D3D9311yescharacteristic, direct product factor
73C2×D31—91noHall
74C22×C52—2791noHall
75C3×C31—21no—
76C3×C31C2×C52×D311yescharacteristic, complemented
77C3×C31C2×C52×D311yescharacteristic, complemented
78C5×C3⋊D3—316no—
79C3×C5×D3—316no—
80C3×C5×D3C5×D3116yescomplemented
81C3×C52—21no—
82C3×C52D3×D3111yescharacteristic, complemented
83C3×C52C2×D9311yescharacteristic, complemented
84C2×C31—31no—
85D31—31no—
86D31—91no—
87C2×C5×D3—936no—
88C2×C5×D3—936no—
89C2×C52—31no—
90C2×C52—2791no—
91C2×C52—931no—
92C32×C5C2×C5×D3116yescomplemented
93D32—311noHall
94C31C52×D3211yescharacteristic, complemented, Sylow
95C2×C3×C5—36no—
96C2×C3×C5—936no—
97C5×D3—316no—
98C5×D3—936no—
99C5×D3—936no—
100C5×D3—1866no—
101C5×D3C5×D9316yesdirect product factor
102C52D3×D9311yescharacteristic, direct product factor, Sylow
103C22×C5—2796no—
104C3⋊D3—311no—
105C3×D3—311no—
106C3×D3C52×D3111yescharacteristic, complemented
107C3×C5—26no—
108C3×C5C5×D3×D3116yescomplemented
109C3×C5C2×C5×D9316yescomplemented
110C2×D3—931no—
111C2×D3—931no—
112C2×C5—36no—
113C2×C5—2796no—
114C2×C5—936no—
115C32C2×C52×D3111yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—931no—
118D3—311no—
119D3—931no—
120D3—931no—
121D3—1861no—
122D3C52×D9311yescharacteristic, direct product factor
123C5C5×D3×D9316yesdirect product factor
124C22—2791noSylow
125C3—21no—
126C3C52×D3×D3111yescharacteristic, complemented
127C3C2×C52×D9311yescharacteristic, complemented
128C2—31no—
129C2—2791no—
130C2—931no—
subgroupG/H
center, hypercenterC52D3×D93
commutator, cosocle, hypocenterC32×C31C22×C52
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C31
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×D3×C31C2semidirect
2. C3×C52×D93C2semidirect
3. C52×C3⋊D93C2semidirect
6. C32×C52×C31C22semidirect
7. C5×D3×D93C5direct (N × H)
11. C52×D93D3direct (N × H)
12. C52×D3×C31D3semidirect
16. C5×C3⋊D93C2×C5semidirect
17. C3×C5×D93C2×C5semidirect
18. C3×C5×D3×C31C2×C5semidirect
20. C3×C52×C31C2×D3semidirect
21. C3×C52×C31C2×D3semidirect
27. C32×C5×C31C22×C5semidirect
28. D3×D93C52direct (N × H)
33. C5×D93C5×D3direct (N × H)
34. C5×D3×C31C5×D3semidirect
37. C52×C31D32semidirect
39. C3⋊D93C2×C52semidirect
40. C3×D93C2×C52semidirect
41. C3×D3×C31C2×C52semidirect
43. C3×C5×C31C2×C5×D3semidirect
44. C3×C5×C31C2×C5×D3semidirect
47. C3×C52×D3D31semidirect
55. C32×C31C22×C52semidirect
56. C32×C52C2×D31semidirect
61. D93C52×D3direct (N × H)
63. D3×C31C52×D3semidirect
65. C5×C31C5×D32semidirect
72. C52×D3D93direct (N × H)
76. C3×C31C2×C52×D3semidirect
77. C3×C31C2×C52×D3semidirect
80. C3×C5×D3C5×D31semidirect
82. C3×C52D3×D31semidirect
83. C3×C52C2×D93semidirect
92. C32×C5C2×C5×D31semidirect
94. C31C52×D32semidirect
101. C5×D3C5×D93direct (N × H)
102. C52D3×D93direct (N × H)
106. C3×D3C52×D31semidirect
108. C3×C5C5×D3×D31semidirect
109. C3×C5C2×C5×D93semidirect
115. C32C2×C52×D31semidirect
122. D3C52×D93direct (N × H)
123. C5C5×D3×D93direct (N × H)
126. C3C52×D3×D31semidirect
127. C3C2×C52×D93semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D3×C312
C3×C52×D932
C52×C3⋊D932
C2×C52×D933
C52×D3×D313
C5×D3×D935
C52×D3231