Finite Group Databasebeta

← C2×C3×D2775 #45685930

Subgroups — C2×C3×D2775 #45685930

Order 33300.

132 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 54 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×D2775C212yesmaximal, direct product factor
2C2×C32×C25×C37C211yesmaximal, characteristic, complemented
3C2×D2775C311yesmaximal, characteristic, direct product factor
4C2×C3×D925—31nomaximal
5C32×C25×C37C2211yescharacteristic, complemented, Hall
6C2×C3×D555—51nomaximal
7D2775C2×C312yesdirect product factor
8C3×D925—32no—
9C2×C3×C25×C37—21no—
10C2×C3×C25×C37D311yescharacteristic, complemented
11C2×C3×C25×C37C2×C311yescharacteristic, complemented
12C2×D925—31noHall
13C3×D555—52no—
14C2×C32×C5×C37D511yescharacteristic
15C3×C25×C37—21no—
16C3×C25×C37C2×D311yescharacteristic, complemented
17C3×C25×C37C22×C311yescharacteristic, complemented
18C2×D555—51no—
19C2×C3×D185—151no—
20C2×C25×C37C3×D311yescharacteristic, complemented
21D925—32no—
22C32×C5×C37C2×D511yescharacteristic
23C2×C3×D111—251noHall
24C2×C3×C5×C37—21no—
25C2×C3×C5×C37C3×D511yescharacteristic
26C2×C3×C5×C37D1511yescharacteristic
27D555—52no—
28C3×D185—152no—
29C25×C37C2×C3×D311yescharacteristic, complemented, Hall
30C2×C3×D75—371nomaximal, Hall
31C2×D185—151no—
32C2×C32×C37D2511yescharacteristic, complemented
33C3×D111—252no—
34C3×C5×C37—21no—
35C3×C5×C37C2×C3×D511yescharacteristic
36C3×C5×C37C2×D1511yescharacteristic
37C2×C32×C25D3711yescharacteristic, complemented
38C3×D75—372no—
39C2×D111—251no—
40C2×C3×D37—751no—
41C2×C5×C37C3×D1511yescharacteristic
42D185—152no—
43C32×C37C2×D2511yescharacteristic, complemented, Hall
44C2×D75—371no—
45C2×C3×D25—1111no—
46C32×C25C2×D3711yescharacteristic, complemented, Hall
47C2×C3×C37—21no—
48C2×C3×C37C3×D2511yescharacteristic, complemented
49C2×C3×C37D7511yescharacteristic, complemented
50D111—252no—
51C3×D37—752no—
52C5×C37C2×C3×D1511yescharacteristic
53C2×C3×D15—1851no—
54C2×C3×C25—21no—
55C2×C3×C25C3×D3711yescharacteristic, complemented
56C2×C3×C25D11111yescharacteristic, complemented
57D75—372no—
58C3×D25—1112no—
59C2×D37—751noHall
60C3×C37—21no—
61C3×C37C2×C3×D2511yescharacteristic, complemented
62C3×C37C2×D7511yescharacteristic, complemented
63C2×D25—1111noHall
64C2×C32×C5D18511yescharacteristic
65C3×D15—1852no—
66C3×C25—21no—
67C3×C25C2×C3×D3711yescharacteristic, complemented
68C3×C25C2×D11111yescharacteristic, complemented
69C2×C37C3×D7511yescharacteristic, complemented
70D37—752no—
71C2×D15—1851no—
72C2×C3×D5—5551no—
73C2×C25C3×D11111yescharacteristic, complemented
74D25—1112no—
75C32×C5C2×D18511yescharacteristic
76C37C2×C3×D7511yescharacteristic, complemented, Sylow
77C2×C3×D3—9251noHall
78C2×C3×C5—21no—
79C2×C3×C5C3×D18511yescharacteristic
80C2×C3×C5D55511yescharacteristic
81D15—1852no—
82C3×D5—5552no—
83C25C2×C3×D11111yescharacteristic, complemented, Sylow
84C2×D5—5551no—
85C2×C32D92511yescharacteristic, complemented
86C3×D3—9252no—
87C3×C5—21no—
88C3×C5C2×C3×D18511yescharacteristic
89C3×C5C2×D55511yescharacteristic
90C22×C3—27751no—
91C2×D3—9251no—
92C2×C5C3×D55511yescharacteristic
93D5—5552no—
94C32C2×D92511yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—27752no—
97C2×C3C3×D92511yescharacteristic, complemented
98C2×C3D277511yescharacteristic, direct product factor
99D3—9252no—
100C5C2×C3×D55511yescharacteristic
101C22—27751noSylow
102C3—21no—
103C3C2×C3×D92511yescharacteristic, complemented
104C3C2×D277511yescharacteristic, direct product factor
105C2—27752no—
106C2C3×D277511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D2775
commutator, cosocle, hypocenterC3×C25×C37C22×C3
FrattiniC5C2×C3×D555
FittingC2×C32×C25×C37C2
socleC2×C32×C5×C37D5
LCSG ▷ C3×C25×C37
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×D2775C2direct (N × H)
2. C2×C32×C25×C37C2semidirect
3. C2×D2775C3direct (N × H)
5. C32×C25×C37C22semidirect
7. D2775C2×C3direct (N × H)
10. C2×C3×C25×C37D3semidirect
11. C2×C3×C25×C37C2×C3semidirect
16. C3×C25×C37C2×D3semidirect
17. C3×C25×C37C22×C3semidirect
20. C2×C25×C37C3×D3semidirect
29. C25×C37C2×C3×D3semidirect
32. C2×C32×C37D25semidirect
37. C2×C32×C25D37semidirect
43. C32×C37C2×D25semidirect
46. C32×C25C2×D37semidirect
48. C2×C3×C37C3×D25semidirect
49. C2×C3×C37D75semidirect
55. C2×C3×C25C3×D37semidirect
56. C2×C3×C25D111semidirect
61. C3×C37C2×C3×D25semidirect
62. C3×C37C2×D75semidirect
67. C3×C25C2×C3×D37semidirect
68. C3×C25C2×D111semidirect
69. C2×C37C3×D75semidirect
73. C2×C25C3×D111semidirect
76. C37C2×C3×D75semidirect
83. C25C2×C3×D111semidirect
85. C2×C32D925semidirect
94. C32C2×D925semidirect
97. C2×C3C3×D925semidirect
98. C2×C3D2775direct (N × H)
103. C3C2×C3×D925semidirect
104. C3C2×D2775direct (N × H)
106. C2C3×D2775direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D27752
C2×C32×C25×C372
C2×D27753
C2×C3×D9253
C2×C3×D5555
C2×C3×D7537