Finite Group Databasebeta

← C9×D5×D185 #45686017

Subgroups — C9×D5×D185 #45686017

Order 33300.

144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C9×C5⋊D185C211yesmaximal, characteristic, complemented
2C5×C9×D185C211yesmaximal, characteristic, complemented
3C5×C9×D5×C37C211yesmaximal, characteristic, complemented
4C3×D5×D185C311yesmaximal, characteristic
5C52×C9×C37C2211yescharacteristic, complemented, Hall
6C2×C9×D185—51nomaximal
7C9×D5×D37—51nomaximal
8C3×C5⋊D185C2×C311yescharacteristic
9C3×C5×D185C2×C311yescharacteristic
10C3×C5×D5×C37C2×C311yescharacteristic
11D5×D185C911yescharacteristic, direct product factor, Hall
12C9×D185—51no—
13C9×D185—51no—
14C9×D185—102no—
15C9×D185D511yescharacteristic, direct product factor
16C9×D5×C37D511yescharacteristic, complemented
17C5×C9×D37—51no—
18C2×C5×C9×C37—51no—
19C3×C52×C37C22×C311yescharacteristic
20C2×C3×D185—51no—
21C3×D5×D37—51no—
22C5⋊D185C2×C911yescharacteristic, complemented
23C5×D185C2×C911yescharacteristic, complemented
24C5×D5×C37C2×C911yescharacteristic, complemented
25C5×C9×C37—22no—
26C5×C9×C37C2×D511yescharacteristic, complemented
27C5×C9×C37C2×D511yescharacteristic, complemented
28C2×C9×D37—251noHall
29C2×C3×C5×C37—51no—
30C3×D185—51no—
31C3×D185—51no—
32C3×D185—102no—
33C3×D185C3×D511yescharacteristic
34C3×D5×C37C3×D511yescharacteristic
35C3×C5×D37—51no—
36C52×C37C22×C911yescharacteristic, complemented, Hall
37C9×D52—371nomaximal, Hall
38C2×D185—51no—
39D5×D37—51no—
40C2×C9×C37—51no—
41C9×D37—51no—
42C9×D37—251no—
43C3×C5×C37—22no—
44C3×C5×C37C2×C3×D511yescharacteristic
45C3×C5×C37C2×C3×D511yescharacteristic
46C9×C5⋊D5—371no—
47C5×C9×D5—371no—
48C5×C9×D5D3711yescharacteristic, complemented
49C2×C3×D37—251no—
50C2×C5×C37—51no—
51D185—51no—
52D185—51no—
53D185—102no—
54D185C9×D511yescharacteristic, direct product factor
55C5×D37—51no—
56D5×C37C9×D511yescharacteristic, complemented
57C9×C37D5211yescharacteristic, complemented, Hall
58C3×D52—371no—
59C52×C9C2×D3711yescharacteristic, complemented, Hall
60C2×C3×C37—51no—
61C3×D37—51no—
62C3×D37—251no—
63C5×C37—22no—
64C5×C37C2×C9×D511yescharacteristic, complemented
65C5×C37C2×C9×D511yescharacteristic, complemented
66C2×C9×D5—1851no—
67C2×C9×D5—1851no—
68C3×C5⋊D5—371no—
69C3×C5×D5—371no—
70C3×C5×D5C3×D3711yescharacteristic
71C2×D37—251noHall
72C3×C37C3×D5211yescharacteristic
73D52—371noHall
74C2×C5×C9—51no—
75C2×C5×C9—1851no—
76C9×D5—371no—
77C9×D5—3702no—
78C9×D5—1851no—
79C9×D5—1851no—
80C9×D5D18511yescharacteristic, direct product factor
81C3×C52C2×C3×D3711yescharacteristic
82C2×C37—51no—
83D37—51no—
84D37—251no—
85C2×C3×D5—1851no—
86C2×C3×D5—1851no—
87C5⋊D5—371no—
88C5×D5—371no—
89C5×D5C9×D3711yescharacteristic, complemented
90C5×C9—22no—
91C5×C9D5×D3711yescharacteristic, complemented
92C5×C9C2×D18511yescharacteristic, complemented
93C37C9×D5211yescharacteristic, complemented, Sylow
94C22×C9—9251noHall
95C2×C3×C5—51no—
96C2×C3×C5—1851no—
97C3×D5—371no—
98C3×D5—3702no—
99C3×D5—1851no—
100C3×D5—1851no—
101C3×D5C3×D18511yescharacteristic
102C52C2×C9×D3711yescharacteristic, complemented, Sylow
103C2×D5—1851no—
104C2×D5—1851no—
105C2×C9—51no—
106C2×C9—9251no—
107C2×C9—1851no—
108C3×C5—22no—
109C3×C5C3×D5×D3711yescharacteristic
110C3×C5C2×C3×D18511yescharacteristic
111C22×C3—9251no—
112C2×C5—51no—
113C2×C5—1851no—
114D5—371no—
115D5—3702no—
116D5—1851no—
117D5—1851no—
118D5C9×D18511yescharacteristic, direct product factor
119C9D5×D18511yescharacteristic, direct product factor, Sylow
120C2×C3—51no—
121C2×C3—9251no—
122C2×C3—1851no—
123C5—22no—
124C5C9×D5×D3711yescharacteristic, complemented
125C5C2×C9×D18511yescharacteristic, complemented
126C22—9251noSylow
127C3C3×D5×D18511yescharacteristic
128C2—51no—
129C2—9251no—
130C2—1851no—
subgroupG/H
center, hypercenterC9D5×D185
commutator, hypocenterC52×C37C22×C9
FrattiniC3C3×D5×D185
FittingC52×C9×C37C22
socle, cosocleC3×C52×C37C22×C3
prime radicalC3×D5×D185C3
LCSG ▷ C52×C37
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×C5⋊D185C2semidirect
2. C5×C9×D185C2semidirect
3. C5×C9×D5×C37C2semidirect
5. C52×C9×C37C22semidirect
11. D5×D185C9direct (N × H)
15. C9×D185D5direct (N × H)
16. C9×D5×C37D5semidirect
22. C5⋊D185C2×C9semidirect
23. C5×D185C2×C9semidirect
24. C5×D5×C37C2×C9semidirect
26. C5×C9×C37C2×D5semidirect
27. C5×C9×C37C2×D5semidirect
36. C52×C37C22×C9semidirect
48. C5×C9×D5D37semidirect
54. D185C9×D5direct (N × H)
56. D5×C37C9×D5semidirect
57. C9×C37D52semidirect
59. C52×C9C2×D37semidirect
64. C5×C37C2×C9×D5semidirect
65. C5×C37C2×C9×D5semidirect
80. C9×D5D185direct (N × H)
89. C5×D5C9×D37semidirect
91. C5×C9D5×D37semidirect
92. C5×C9C2×D185semidirect
93. C37C9×D52semidirect
102. C52C2×C9×D37semidirect
118. D5C9×D185direct (N × H)
119. C9D5×D185direct (N × H)
124. C5C9×D5×D37semidirect
125. C5C2×C9×D185semidirect

Maximal subgroups

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

subgroupindex
C9×C5⋊D1852
C5×C9×D1852
C5×C9×D5×C372
C3×D5×D1853
C2×C9×D1855
C9×D5×D375
C9×D5237