Finite Group Databasebeta

← C2×C3×C52×D93 #42124986

Subgroups — C2×C3×C52×D93 #42124986

Order 27900.

352 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 176 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×D93C212yesmaximal, direct product factor
2C2×C32×C52×C31C211yesmaximal, characteristic, complemented
3C2×C3×C52×D31—31nomaximal
4C2×C52×D93C311yesmaximal, characteristic, direct product factor
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D93C516yesmaximal, direct product factor
7C52×D93C2×C312yesdirect product factor
8C3×C52×D31—32no—
9C2×C3×C52×C31—21no—
10C2×C3×C52×C31D311yescharacteristic, complemented
11C2×C3×C52×C31C2×C311yescharacteristic, complemented
12C2×C52×D31—31noHall
13C3×C5×D93C2×C5112yesdirect product factor
14C2×C32×C5×C31C2×C516yescomplemented
15C3×C52×C31—21no—
16C3×C52×C31C2×D311yescharacteristic, complemented
17C3×C52×C31C22×C311yescharacteristic, complemented
18C2×C5×D93C3×C516yesdirect product factor
19C2×C3×C5×D31—36no—
20C2×C52×C31C3×D311yescharacteristic, complemented
21C52×D31—32no—
22C32×C5×C31C22×C516yescomplemented
23C2×C3×D93C5211yescharacteristic, direct product factor, Hall
24C2×C3×C5×C31—26no—
25C2×C3×C5×C31C5×D316yescomplemented
26C2×C3×C5×C31C2×C3×C516yescomplemented
27C5×D93C2×C3×C5112yesdirect product factor
28C3×C5×D31—312no—
29C2×C3×C52×D3—311nomaximal, Hall
30C52×C31C2×C3×D311yescharacteristic, complemented, Hall
31C2×C5×D31—36no—
32C2×C32×C31C2×C5211yescharacteristic, complemented
33C3×D93C2×C5212yesdirect product factor
34C3×C5×C31—26no—
35C3×C5×C31C2×C5×D316yescomplemented
36C3×C5×C31C22×C3×C516yescomplemented
37C2×C32×C52D3111yescharacteristic, complemented
38C3×C52×D3—312no—
39C2×D93C3×C5211yescharacteristic, direct product factor
40C2×C3×D31—31no—
41C2×C5×C31C3×C5×D316yescomplemented
42C5×D31—312no—
43C22×C3×C52—931no—
44C2×C52×D3—311no—
45C32×C31C22×C5211yescharacteristic, complemented, Hall
46C32×C52C2×D3111yescharacteristic, complemented, Hall
47C2×C3×C31—21no—
48C2×C3×C31C52×D311yescharacteristic, complemented
49C2×C3×C31C2×C3×C5211yescharacteristic, complemented
50D93C2×C3×C5212yesdirect product factor
51C3×D31—32no—
52C2×C3×C5×D3—316no—
53C5×C31C2×C3×C5×D316yescomplemented
54C2×C3×C52—21no—
55C2×C3×C52—932no—
56C2×C3×C52C3×D3111yescharacteristic, complemented
57C2×C3×C52D9311yescharacteristic, direct product factor
58C52×D3—312no—
59C2×D31—31noHall
60C22×C52—931noHall
61C3×C31—21no—
62C3×C31C2×C52×D311yescharacteristic, complemented
63C3×C31C22×C3×C5211yescharacteristic, complemented
64C2×C32×C5C5×D3116yescomplemented
65C3×C5×D3—3112no—
66C3×C52—21no—
67C3×C52C2×C3×D3111yescharacteristic, complemented
68C3×C52C2×D9311yescharacteristic, direct product factor
69C2×C31C3×C52×D311yescharacteristic, complemented
70D31—32no—
71C22×C3×C5—936no—
72C2×C5×D3—316no—
73C2×C52—932no—
74C2×C52C3×D9311yescharacteristic, direct product factor
75C32×C5C2×C5×D3116yescomplemented
76C2×C3×D3—311noHall
77C31C2×C3×C52×D311yescharacteristic, complemented, Sylow
78C2×C3×C5—26no—
79C2×C3×C5—9312no—
80C2×C3×C5C3×C5×D3116yescomplemented
81C2×C3×C5C5×D9316yesdirect product factor
82C5×D3—3112no—
83C52C2×C3×D9311yescharacteristic, direct product factor, Sylow
84C22×C5—936no—
85C2×C32C52×D3111yescharacteristic, complemented
86C3×D3—312no—
87C3×C5—26no—
88C3×C5C2×C3×C5×D3116yescomplemented
89C3×C5C2×C5×D9316yesdirect product factor
90C22×C3—931no—
91C2×D3—311no—
92C2×C5—9312no—
93C2×C5C3×C5×D9316yesdirect product factor
94C32C2×C52×D3111yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—932no—
97C2×C3C3×C52×D3111yescharacteristic, complemented
98C2×C3C52×D9311yescharacteristic, direct product factor
99D3—312no—
100C5C2×C3×C5×D9316yesdirect product factor
101C22—931noSylow
102C3—21no—
103C3C2×C52×D9311yescharacteristic, direct product factor
104C3C2×C3×C52×D3111yescharacteristic, complemented
105C2—932no—
106C2C3×C52×D9311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C52D93
commutator, cosocle, hypocenterC3×C31C22×C3×C52
FrattiniC1G
Fitting, socleC2×C32×C52×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3×C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×D93C2direct (N × H)
2. C2×C32×C52×C31C2semidirect
4. C2×C52×D93C3direct (N × H)
5. C32×C52×C31C22semidirect
6. C2×C3×C5×D93C5direct (N × H)
7. C52×D93C2×C3direct (N × H)
10. C2×C3×C52×C31D3semidirect
11. C2×C3×C52×C31C2×C3semidirect
13. C3×C5×D93C2×C5direct (N × H)
14. C2×C32×C5×C31C2×C5semidirect
16. C3×C52×C31C2×D3semidirect
17. C3×C52×C31C22×C3semidirect
18. C2×C5×D93C3×C5direct (N × H)
20. C2×C52×C31C3×D3semidirect
22. C32×C5×C31C22×C5semidirect
23. C2×C3×D93C52direct (N × H)
25. C2×C3×C5×C31C5×D3semidirect
26. C2×C3×C5×C31C2×C3×C5semidirect
27. C5×D93C2×C3×C5direct (N × H)
30. C52×C31C2×C3×D3semidirect
32. C2×C32×C31C2×C52semidirect
33. C3×D93C2×C52direct (N × H)
35. C3×C5×C31C2×C5×D3semidirect
36. C3×C5×C31C22×C3×C5semidirect
37. C2×C32×C52D31semidirect
39. C2×D93C3×C52direct (N × H)
41. C2×C5×C31C3×C5×D3semidirect
45. C32×C31C22×C52semidirect
46. C32×C52C2×D31semidirect
48. C2×C3×C31C52×D3semidirect
49. C2×C3×C31C2×C3×C52semidirect
50. D93C2×C3×C52direct (N × H)
53. C5×C31C2×C3×C5×D3semidirect
56. C2×C3×C52C3×D31semidirect
57. C2×C3×C52D93direct (N × H)
62. C3×C31C2×C52×D3semidirect
63. C3×C31C22×C3×C52semidirect
64. C2×C32×C5C5×D31semidirect
67. C3×C52C2×C3×D31semidirect
68. C3×C52C2×D93direct (N × H)
69. C2×C31C3×C52×D3semidirect
74. C2×C52C3×D93direct (N × H)
75. C32×C5C2×C5×D31semidirect
77. C31C2×C3×C52×D3semidirect
80. C2×C3×C5C3×C5×D31semidirect
81. C2×C3×C5C5×D93direct (N × H)
83. C52C2×C3×D93direct (N × H)
85. C2×C32C52×D31semidirect
88. C3×C5C2×C3×C5×D31semidirect
89. C3×C5C2×C5×D93direct (N × H)
93. C2×C5C3×C5×D93direct (N × H)
94. C32C2×C52×D31semidirect
97. C2×C3C3×C52×D31semidirect
98. C2×C3C52×D93direct (N × H)
100. C5C2×C3×C5×D93direct (N × H)
103. C3C2×C52×D93direct (N × H)
104. C3C2×C3×C52×D31semidirect
106. C2C3×C52×D93direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×D932
C2×C32×C52×C312
C2×C3×C52×D313
C2×C52×D933
C2×C3×C5×D935
C2×C3×C52×D331