Finite Group Databasebeta

← C3×#26012924 #45686427

Subgroups — C3×#26012924 #45686427

Order 33300.

224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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×C37×C5⋊D5C211yesmaximal, characteristic, complemented
2C3×C5×D555C212yesmaximal, complemented
3#26012924C311yesmaximal, characteristic, direct product factor
4C3×(C5⋊D5)⋊D37—31nomaximal
5C32×C52×C37C2211yescharacteristic, complemented, Hall
6C3×D5×D111—52nomaximal
7C5×D555C2×C312yescomplemented
8C3×C37×C5⋊D5—21no—
9C3×C37×C5⋊D5D311yescharacteristic, complemented
10C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
11C3×C5×D185—32no—
12(C5⋊D5)⋊D37—31noHall
13C3×D555D512yescomplemented
14C3×C5×D111—52no—
15C32×D5×C37—52no—
16C32×D5×C37—102no—
17C3×C52×C37—21no—
18C3×C52×C37C2×D311yescharacteristic, complemented
19C3×C52×C37C22×C311yescharacteristic, complemented
20D5×D111—52no—
21C3×D5×D37—152no—
22C37×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D185—32no—
24C32×C5×C37—22no—
25C32×C5×C37C2×D512yescomplemented
26C2×C3×D111—251noHall
27D555C3×D512yescomplemented
28C5×D111—52no—
29C3×D185—32no—
30C3×D5×C37—52no—
31C3×D5×C37—52no—
32C3×D5×C37—102no—
33C3×D5×C37—102no—
34C3×D5×C37—102no—
35C3×D5×C37—104no—
36C3×C5×D37—152no—
37C52×C37C2×C3×D311yescharacteristic, complemented, Hall
38C3×D15⋊D5—371nomaximal, Hall
39D5×D37—152no—
40C2×C32×C37—251no—
41C3×D111—52no—
42C3×C5×C37—24no—
43C3×C5×C37—22no—
44C3×C5×C37—22no—
45C3×C5×C37—22no—
46C3×C5×C37D3×D512yescomplemented
47C3×C5×C37C2×C3×D512yescomplemented
48C3×C5×D15—372no—
49C32×C5⋊D5D3711yescharacteristic, complemented
50C2×D111—251no—
51C2×C3×D37—751no—
52D185—32no—
53C5×D37—152no—
54D5×C37—52no—
55D5×C37—102no—
56C32×C37D5211yescharacteristic, complemented, Hall
57D15⋊D5—371no—
58C3×D52—1111no—
59C32×C52C2×D3711yescharacteristic, complemented, Hall
60C2×C3×C37—251no—
61C2×C3×C37—251no—
62C2×C3×C37—501no—
63D111—52no—
64C3×D37—152no—
65C5×C37—22no—
66C5×C37C3×D3×D512yescomplemented
67C3×D3×D5—1852no—
68C5×D15—372no—
69C3×C5⋊D5—21no—
70C3×C5⋊D5C3×D3711yescharacteristic, complemented
71C3×C5⋊D5D11111yescharacteristic, complemented
72C3×C5×D5—1112no—
73C2×D37—751noHall
74C3×C37—21no—
75C3×C37C3×D5211yescharacteristic, complemented
76C3×C37D15⋊D511yescharacteristic, complemented
77D52—1111noHall
78C3×D15—372no—
79C3×C5×D3—1852no—
80C32×D5—52no—
81C32×D5—102no—
82C3×C52—21no—
83C3×C52C2×C3×D3711yescharacteristic, complemented
84C3×C52C2×D11111yescharacteristic, complemented
85C2×C37—251no—
86D37—152no—
87C2×C3×D5—5552no—
88D3×D5—1852no—
89C5⋊D5C3×D11111yescharacteristic, complemented
90C5×D5—1112no—
91C32×C5—22no—
92C32×C5D5×D3712yescomplemented
93C37C3×D15⋊D511yescharacteristic, complemented, Sylow
94C2×C3×D3—9251noHall
95C2×C3×C5—5552no—
96D15—372no—
97C3×D5—52no—
98C3×D5—52no—
99C3×D5—102no—
100C3×D5—102no—
101C3×D5—102no—
102C3×D5—104no—
103C3×D5—1112no—
104C5×D3—1852no—
105C52C2×C3×D11111yescharacteristic, complemented, Sylow
106C2×D5—5552no—
107C2×C32—251no—
108C3×D3—1852no—
109C3×C5—24no—
110C3×C5—22no—
111C3×C5—22no—
112C3×C5—22no—
113C3×C5C3×D5×D3712yescomplemented
114C3×C5D5×D11112yescomplemented
115C22×C3—27751no—
116C2×D3—9251no—
117C2×C5—5552no—
118D5—52no—
119D5—102no—
120D5—1112no—
121C32(C5⋊D5)⋊D3711yescharacteristic, complemented, Sylow
122C2×C3—251no—
123C2×C3—251no—
124C2×C3—5552no—
125C2×C3—501no—
126D3—1852no—
127C5—22no—
128C5C3×D5×D11112yescomplemented
129C22—27751noSylow
130C3—21no—
131C3C3×(C5⋊D5)⋊D3711yescharacteristic, complemented
132C3#2601292411yescharacteristic, direct product factor
133C2—251no—
134C2—5552no—
subgroupG/H
center, hypercenterC3#26012924
commutator, cosocle, hypocenterC3×C52×C37C22×C3
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C3×C52×C37
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C37×C5⋊D5C2semidirect
2. C3×C5×D555C2semidirect
3. #26012924C3direct (N × H)
5. C32×C52×C37C22semidirect
7. C5×D555C2×C3semidirect
9. C3×C37×C5⋊D5D3semidirect
10. C3×C37×C5⋊D5C2×C3semidirect
13. C3×D555D5semidirect
18. C3×C52×C37C2×D3semidirect
19. C3×C52×C37C22×C3semidirect
22. C37×C5⋊D5C3×D3semidirect
25. C32×C5×C37C2×D5semidirect
27. D555C3×D5semidirect
37. C52×C37C2×C3×D3semidirect
46. C3×C5×C37D3×D5semidirect
47. C3×C5×C37C2×C3×D5semidirect
49. C32×C5⋊D5D37semidirect
56. C32×C37D52semidirect
59. C32×C52C2×D37semidirect
66. C5×C37C3×D3×D5semidirect
70. C3×C5⋊D5C3×D37semidirect
71. C3×C5⋊D5D111semidirect
75. C3×C37C3×D52semidirect
76. C3×C37D15⋊D5semidirect
83. C3×C52C2×C3×D37semidirect
84. C3×C52C2×D111semidirect
89. C5⋊D5C3×D111semidirect
92. C32×C5D5×D37semidirect
93. C37C3×D15⋊D5semidirect
105. C52C2×C3×D111semidirect
113. C3×C5C3×D5×D37semidirect
114. C3×C5D5×D111semidirect
121. C32(C5⋊D5)⋊D37semidirect
128. C5C3×D5×D111semidirect
131. C3C3×(C5⋊D5)⋊D37semidirect
132. C3#26012924direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C37×C5⋊D52
C3×C5×D5552
#260129243
C3×(C5⋊D5)⋊D373
C3×D5×D1115
C3×D15⋊D537