Finite Group Databasebeta

← C2×C3×C25×D111 #45685932

Subgroups — C2×C3×C25×D111 #45685932

Order 33300.

132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 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×C25×D111C212yesmaximal, direct product factor
2C2×C32×C25×C37C211yesmaximal, characteristic, complemented
3C2×C25×D111C311yesmaximal, characteristic, direct product factor
4C2×C3×C25×D37—31nomaximal
5C32×C25×C37C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D111C511yesmaximal, characteristic
7C25×D111C2×C312yesdirect product factor
8C3×C25×D37—32no—
9C2×C3×C25×C37—21no—
10C2×C3×C25×C37D311yescharacteristic, complemented
11C2×C3×C25×C37C2×C311yescharacteristic, complemented
12C2×C25×D37—31noHall
13C3×C5×D111C2×C512yes—
14C2×C32×C5×C37C2×C511yescharacteristic
15C3×C25×C37—21no—
16C3×C25×C37C2×D311yescharacteristic, complemented
17C3×C25×C37C22×C311yescharacteristic, complemented
18C2×C5×D111C3×C511yescharacteristic
19C2×C3×C5×D37—31no—
20C2×C25×C37C3×D311yescharacteristic, complemented
21C25×D37—32no—
22C32×C5×C37C22×C511yescharacteristic
23C2×C3×D111C2511yescharacteristic, direct product factor, Hall
24C2×C3×C5×C37—21no—
25C2×C3×C5×C37C5×D311yescharacteristic
26C2×C3×C5×C37C2×C3×C511yescharacteristic
27C5×D111C2×C3×C512yes—
28C3×C5×D37—32no—
29C25×C37C2×C3×D311yescharacteristic, complemented, Hall
30C2×C3×D3×C25—371nomaximal, Hall
31C2×C5×D37—31no—
32C2×C32×C37C2×C2511yescharacteristic, complemented
33C3×D111C2×C2512yesdirect product factor
34C3×C5×C37—21no—
35C3×C5×C37C2×C5×D311yescharacteristic
36C3×C5×C37C22×C3×C511yescharacteristic
37C2×C32×C25D3711yescharacteristic, complemented
38C3×D3×C25—372no—
39C2×D111C3×C2511yescharacteristic, direct product factor
40C2×C3×D37—31no—
41C2×C5×C37C3×C5×D311yescharacteristic
42C5×D37—32no—
43C32×C37C22×C2511yescharacteristic, complemented, Hall
44C22×C3×C25—1111no—
45C2×D3×C25—371no—
46C32×C25C2×D3711yescharacteristic, complemented, Hall
47C2×C3×C37—21no—
48C2×C3×C37D3×C2511yescharacteristic, complemented
49C2×C3×C37C2×C3×C2511yescharacteristic, complemented
50D111C2×C3×C2512yesdirect product factor
51C3×D37—32no—
52C5×C37C2×C3×C5×D311yescharacteristic
53C2×C3×C5×D3—371no—
54C2×C3×C25—21no—
55C2×C3×C25—1112no—
56C2×C3×C25C3×D3711yescharacteristic, complemented
57C2×C3×C25D11111yescharacteristic, direct product factor
58D3×C25—372no—
59C2×D37—31noHall
60C3×C37—21no—
61C3×C37C2×D3×C2511yescharacteristic, complemented
62C3×C37C22×C3×C2511yescharacteristic, complemented
63C22×C25—1111noHall
64C2×C32×C5C5×D3711yescharacteristic
65C3×C5×D3—372no—
66C3×C25—21no—
67C3×C25C2×C3×D3711yescharacteristic, complemented
68C3×C25C2×D11111yescharacteristic, direct product factor
69C2×C37C3×D3×C2511yescharacteristic, complemented
70D37—32no—
71C22×C3×C5—1111no—
72C2×C5×D3—371no—
73C2×C25—1112no—
74C2×C25C3×D11111yescharacteristic, direct product factor
75C32×C5C2×C5×D3711yescharacteristic
76C37C2×C3×D3×C2511yescharacteristic, complemented, Sylow
77C2×C3×D3—371noHall
78C2×C3×C5—21no—
79C2×C3×C5—1112no—
80C2×C3×C5C3×C5×D3711yescharacteristic
81C2×C3×C5C5×D11111yescharacteristic
82C5×D3—372no—
83C25C2×C3×D11111yescharacteristic, direct product factor, Sylow
84C22×C5—1111no—
85C2×C32C25×D3711yescharacteristic, complemented
86C3×D3—372no—
87C3×C5—21no—
88C3×C5C2×C3×C5×D3711yescharacteristic
89C3×C5C2×C5×D11111yescharacteristic
90C22×C3—1111no—
91C2×D3—371no—
92C2×C5—1112no—
93C2×C5C3×C5×D11111yescharacteristic
94C32C2×C25×D3711yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—1112no—
97C2×C3C3×C25×D3711yescharacteristic, complemented
98C2×C3C25×D11111yescharacteristic, direct product factor
99D3—372no—
100C5C2×C3×C5×D11111yescharacteristic
101C22—1111noSylow
102C3—21no—
103C3C2×C3×C25×D3711yescharacteristic, complemented
104C3C2×C25×D11111yescharacteristic, direct product factor
105C2—1112no—
106C2C3×C25×D11111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C25D111
commutator, hypocenterC3×C37C22×C3×C25
FrattiniC5C2×C3×C5×D111
FittingC2×C32×C25×C37C2
socleC2×C32×C5×C37C2×C5
prime radicalC2×C3×C5×D111C5
cosocleC3×C5×C37C22×C3×C5
LCSG ▷ C3×C37
UCSC1 ◁ C2×C3×C25

Complements

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

NH ≅ G/Ntype
1. C3×C25×D111C2direct (N × H)
2. C2×C32×C25×C37C2semidirect
3. C2×C25×D111C3direct (N × H)
5. C32×C25×C37C22semidirect
7. C25×D111C2×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
23. C2×C3×D111C25direct (N × H)
29. C25×C37C2×C3×D3semidirect
32. C2×C32×C37C2×C25semidirect
33. C3×D111C2×C25direct (N × H)
37. C2×C32×C25D37semidirect
39. C2×D111C3×C25direct (N × H)
43. C32×C37C22×C25semidirect
46. C32×C25C2×D37semidirect
48. C2×C3×C37D3×C25semidirect
49. C2×C3×C37C2×C3×C25semidirect
50. D111C2×C3×C25direct (N × H)
56. C2×C3×C25C3×D37semidirect
57. C2×C3×C25D111direct (N × H)
61. C3×C37C2×D3×C25semidirect
62. C3×C37C22×C3×C25semidirect
67. C3×C25C2×C3×D37semidirect
68. C3×C25C2×D111direct (N × H)
69. C2×C37C3×D3×C25semidirect
74. C2×C25C3×D111direct (N × H)
76. C37C2×C3×D3×C25semidirect
83. C25C2×C3×D111direct (N × H)
85. C2×C32C25×D37semidirect
94. C32C2×C25×D37semidirect
97. C2×C3C3×C25×D37semidirect
98. C2×C3C25×D111direct (N × H)
103. C3C2×C3×C25×D37semidirect
104. C3C2×C25×D111direct (N × H)
106. C2C3×C25×D111direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C25×D1112
C2×C32×C25×C372
C2×C25×D1113
C2×C3×C25×D373
C2×C3×C5×D1115
C2×C3×D3×C2537