Finite Group Databasebeta

← C5×(C3⋊D3)⋊D185 #45686451

Subgroups — C5×(C3⋊D3)⋊D185 #45686451

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
1C3×C5×D555C212yesmaximal, complemented
2C52×C3⋊D3×C37C211yesmaximal, characteristic, complemented
3C5×D3×D185—32nomaximal
4C32×C52×C37C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D185C511yesmaximal, characteristic, direct product factor
6C5×(C3⋊D3)⋊D37—51nomaximal
7C5×D555D312yescomplemented
8C52×D3×C37—32no—
9C52×D3×C37—61no—
10C3×C5×D185—32no—
11C2×C5×D185—91noHall
12C5×C3⋊D3×C37—22no—
13C5×C3⋊D3×C37D511yescharacteristic, complemented
14C5×C3⋊D3×C37C2×C511yescharacteristic, complemented
15C3×D555C2×C512yescomplemented
16C3×C5×D111—52no—
17C3×C52×C37—21no—
18C3×C52×C37C2×D312yescomplemented
19D3×D185—32no—
20C5×D3×D37—152no—
21C2×C52×C37—91no—
22C5×D185—32no—
23C32×C5×C37—22no—
24C32×C5×C37C2×D511yescharacteristic, complemented
25C32×C5×C37C22×C511yescharacteristic, complemented
26(C3⋊D3)⋊D37—51noHall
27D555C5×D312yescomplemented
28C5×D111—52no—
29C5×D3×C37—32no—
30C5×D3×C37—32no—
31C5×D3×C37—64no—
32C5×D3×C37—61no—
33C5×D3×C37—61no—
34C5×D3×C37—64no—
35C3×D185—32no—
36C3×C5×D37—152no—
37C52×C37D3211yescharacteristic, complemented, Hall
38C5×(C3⋊D3)⋊D5—371nomaximal, Hall
39C2×D185—91no—
40C2×C5×D37—451no—
41C3⋊D3×C37C5×D511yescharacteristic, complemented
42C3×D111—52no—
43C3×C5×C37—24no—
44C3×C5×C37—24no—
45C3×C5×C37—21no—
46C3×C5×C37—21no—
47C3×C5×C37D3×D512yescomplemented
48C3×C5×C37C2×C5×D312yescomplemented
49C52×C3⋊D3D3711yescharacteristic, complemented
50C3×C5×D15—372no—
51D3×D37—152no—
52C2×C5×C37—91no—
53C2×C5×C37—91no—
54C2×C5×C37—182no—
55D185—32no—
56C5×D37—152no—
57C32×C37C2×C5×D511yescharacteristic, complemented, Hall
58C5×D3×D5—1112no—
59C32×C52C2×D3711yescharacteristic, complemented, Hall
60D111—52no—
61C3×D37—152no—
62D3×C37—32no—
63D3×C37—61no—
64C5×C37—22no—
65C5×C37C5×D3211yescharacteristic, complemented
66C5×C37(C3⋊D3)⋊D511yescharacteristic, complemented
67(C3⋊D3)⋊D5—371no—
68C5×D32—1851no—
69C5×D15—372no—
70C52×D3—32no—
71C52×D3—61no—
72C3×C5×D5—1112no—
73C2×D37—451noHall
74C3×C37—21no—
75C3×C37C5×D3×D512yescomplemented
76C2×C5×D5—3331noHall
77C5×C3⋊D3—22no—
78C5×C3⋊D3C5×D3711yescharacteristic, complemented
79C5×C3⋊D3D18511yescharacteristic, complemented
80C3×D15—372no—
81C3×C5×D3—1852no—
82C3×C52—21no—
83C3×C52D3×D3712yescomplemented
84C2×C37—91no—
85D37—152no—
86C2×C5×D3—5552no—
87D3×D5—1112no—
88C2×C52—91no—
89C5×D5—1112no—
90C32×C5—22no—
91C32×C5C2×C5×D3711yescharacteristic, complemented
92C32×C5C2×D18511yescharacteristic, complemented
93C37C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
94D32—1851noHall
95C2×C3×C5—5552no—
96D15—372no—
97C3×D5—1112no—
98C5×D3—32no—
99C5×D3—32no—
100C5×D3—64no—
101C5×D3—61no—
102C5×D3—61no—
103C5×D3—64no—
104C5×D3—1852no—
105C52(C3⋊D3)⋊D3711yescharacteristic, complemented, Sylow
106C22×C5—16651no—
107C2×D5—3331no—
108C3⋊D3C5×D18511yescharacteristic, complemented
109C3×D3—1852no—
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5C5×D3×D3712yescomplemented
115C3×C5D3×D18512yescomplemented
116C2×D3—5552no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—182no—
120C2×C5—5552no—
121D5—1112no—
122C32C2×C5×D18511yescharacteristic, complemented, Sylow
123C2×C3—5552no—
124D3—32no—
125D3—61no—
126D3—1852no—
127C5—22no—
128C5C5×(C3⋊D3)⋊D3711yescharacteristic, complemented
129C5(C3⋊D3)⋊D18511yescharacteristic, direct product factor
130C22—16651noSylow
131C3—21no—
132C3C5×D3×D18512yescomplemented
133C2—91no—
134C2—5552no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D185
commutator, cosocle, hypocenterC32×C5×C37C22×C5
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C32×C5×C37
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D555C2semidirect
2. C52×C3⋊D3×C37C2semidirect
4. C32×C52×C37C22semidirect
5. (C3⋊D3)⋊D185C5direct (N × H)
7. C5×D555D3semidirect
13. C5×C3⋊D3×C37D5semidirect
14. C5×C3⋊D3×C37C2×C5semidirect
15. C3×D555C2×C5semidirect
18. C3×C52×C37C2×D3semidirect
24. C32×C5×C37C2×D5semidirect
25. C32×C5×C37C22×C5semidirect
27. D555C5×D3semidirect
37. C52×C37D32semidirect
41. C3⋊D3×C37C5×D5semidirect
47. C3×C5×C37D3×D5semidirect
48. C3×C5×C37C2×C5×D3semidirect
49. C52×C3⋊D3D37semidirect
57. C32×C37C2×C5×D5semidirect
59. C32×C52C2×D37semidirect
65. C5×C37C5×D32semidirect
66. C5×C37(C3⋊D3)⋊D5semidirect
75. C3×C37C5×D3×D5semidirect
78. C5×C3⋊D3C5×D37semidirect
79. C5×C3⋊D3D185semidirect
83. C3×C52D3×D37semidirect
91. C32×C5C2×C5×D37semidirect
92. C32×C5C2×D185semidirect
93. C37C5×(C3⋊D3)⋊D5semidirect
105. C52(C3⋊D3)⋊D37semidirect
108. C3⋊D3C5×D185semidirect
114. C3×C5C5×D3×D37semidirect
115. C3×C5D3×D185semidirect
122. C32C2×C5×D185semidirect
128. C5C5×(C3⋊D3)⋊D37semidirect
129. C5(C3⋊D3)⋊D185direct (N × H)
132. C3C5×D3×D185semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D5552
C52×C3⋊D3×C372
C5×D3×D1853
(C3⋊D3)⋊D1855
C5×(C3⋊D3)⋊D375
C5×(C3⋊D3)⋊D537