Finite Group Databasebeta

← C5×(C3⋊D3)⋊D145 #39908169

Subgroups — C5×(C3⋊D3)⋊D145 #39908169

Order 26100.

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×D435C212yesmaximal, complemented
2C52×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×D3×D145—32nomaximal
4C32×C52×C29C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D145C511yesmaximal, characteristic, direct product factor
6C5×(C3⋊D3)⋊D29—51nomaximal
7C5×D435D312yescomplemented
8C52×D3×C29—32no—
9C52×D3×C29—61no—
10C3×C5×D145—32no—
11C2×C5×D145—91noHall
12C5×C3⋊D3×C29—22no—
13C5×C3⋊D3×C29D511yescharacteristic, complemented
14C5×C3⋊D3×C29C2×C511yescharacteristic, complemented
15C3×D435C2×C512yescomplemented
16C3×C5×D87—52no—
17C3×C52×C29—21no—
18C3×C52×C29C2×D312yescomplemented
19D3×D145—32no—
20C5×D3×D29—152no—
21C2×C52×C29—91no—
22C5×D145—32no—
23C32×C5×C29—22no—
24C32×C5×C29C2×D511yescharacteristic, complemented
25C32×C5×C29C22×C511yescharacteristic, complemented
26(C3⋊D3)⋊D29—51noHall
27C5×(C3⋊D3)⋊D5—291nomaximal, Hall
28D435C5×D312yescomplemented
29C5×D87—52no—
30C5×D3×C29—32no—
31C5×D3×C29—32no—
32C5×D3×C29—61no—
33C5×D3×C29—61no—
34C5×D3×C29—64no—
35C5×D3×C29—64no—
36C3×D145—32no—
37C3×C5×D29—152no—
38C52×C29D3211yescharacteristic, complemented, Hall
39C2×D145—91no—
40C2×C5×D29—451no—
41C3⋊D3×C29C5×D511yescharacteristic, complemented
42C3×D87—52no—
43C52×C3⋊D3D2911yescharacteristic, complemented
44C3×C5×D15—292no—
45C3×C5×C29—24no—
46C3×C5×C29—24no—
47C3×C5×C29—21no—
48C3×C5×C29—21no—
49C3×C5×C29D3×D512yescomplemented
50C3×C5×C29C2×C5×D312yescomplemented
51D3×D29—152no—
52C5×D3×D5—872no—
53C2×C5×C29—91no—
54C2×C5×C29—91no—
55C2×C5×C29—182no—
56D145—32no—
57C5×D29—152no—
58C32×C29C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60(C3⋊D3)⋊D5—291no—
61C5×D32—1451no—
62D87—52no—
63C3×D29—152no—
64D3×C29—32no—
65D3×C29—61no—
66C5×D15—292no—
67C52×D3—32no—
68C52×D3—61no—
69C3×C5×D5—872no—
70C5×C29—22no—
71C5×C29C5×D3211yescharacteristic, complemented
72C5×C29(C3⋊D3)⋊D511yescharacteristic, complemented
73C2×D29—451noHall
74C2×C5×D5—2611noHall
75C5×C3⋊D3—22no—
76C5×C3⋊D3C5×D2911yescharacteristic, complemented
77C5×C3⋊D3D14511yescharacteristic, complemented
78C3×D15—292no—
79C3×C5×D3—1452no—
80C3×C29—21no—
81C3×C29C5×D3×D512yescomplemented
82C3×C52—21no—
83C3×C52D3×D2912yescomplemented
84C2×C5×D3—4352no—
85D3×D5—872no—
86C2×C29—91no—
87D29—152no—
88C2×C52—91no—
89C5×D5—872no—
90C32×C5—22no—
91C32×C5C2×C5×D2911yescharacteristic, complemented
92C32×C5C2×D14511yescharacteristic, complemented
93D32—1451noHall
94C2×C3×C5—4352no—
95D15—292no—
96C3×D5—872no—
97C5×D3—32no—
98C5×D3—32no—
99C5×D3—64no—
100C5×D3—61no—
101C5×D3—61no—
102C5×D3—64no—
103C5×D3—1452no—
104C29C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
105C52(C3⋊D3)⋊D2911yescharacteristic, complemented, Sylow
106C22×C5—13051no—
107C2×D5—2611no—
108C3⋊D3C5×D14511yescharacteristic, complemented
109C3×D3—1452no—
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5C5×D3×D2912yescomplemented
115C3×C5D3×D14512yescomplemented
116C2×D3—4352no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—182no—
120C2×C5—4352no—
121D5—872no—
122C32C2×C5×D14511yescharacteristic, complemented, Sylow
123C2×C3—4352no—
124D3—32no—
125D3—61no—
126D3—1452no—
127C5—22no—
128C5C5×(C3⋊D3)⋊D2911yescharacteristic, complemented
129C5(C3⋊D3)⋊D14511yescharacteristic, direct product factor
130C22—13051noSylow
131C3—21no—
132C3C5×D3×D14512yescomplemented
133C2—91no—
134C2—4352no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D145
commutator, cosocle, hypocenterC32×C5×C29C22×C5
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D435C2semidirect
2. C52×C3⋊D3×C29C2semidirect
4. C32×C52×C29C22semidirect
5. (C3⋊D3)⋊D145C5direct (N × H)
7. C5×D435D3semidirect
13. C5×C3⋊D3×C29D5semidirect
14. C5×C3⋊D3×C29C2×C5semidirect
15. C3×D435C2×C5semidirect
18. C3×C52×C29C2×D3semidirect
24. C32×C5×C29C2×D5semidirect
25. C32×C5×C29C22×C5semidirect
28. D435C5×D3semidirect
38. C52×C29D32semidirect
41. C3⋊D3×C29C5×D5semidirect
43. C52×C3⋊D3D29semidirect
49. C3×C5×C29D3×D5semidirect
50. C3×C5×C29C2×C5×D3semidirect
58. C32×C29C2×C5×D5semidirect
59. C32×C52C2×D29semidirect
71. C5×C29C5×D32semidirect
72. C5×C29(C3⋊D3)⋊D5semidirect
76. C5×C3⋊D3C5×D29semidirect
77. C5×C3⋊D3D145semidirect
81. C3×C29C5×D3×D5semidirect
83. C3×C52D3×D29semidirect
91. C32×C5C2×C5×D29semidirect
92. C32×C5C2×D145semidirect
104. C29C5×(C3⋊D3)⋊D5semidirect
105. C52(C3⋊D3)⋊D29semidirect
108. C3⋊D3C5×D145semidirect
114. C3×C5C5×D3×D29semidirect
115. C3×C5D3×D145semidirect
122. C32C2×C5×D145semidirect
128. C5C5×(C3⋊D3)⋊D29semidirect
129. C5(C3⋊D3)⋊D145direct (N × H)
132. C3C5×D3×D145semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4352
C52×C3⋊D3×C292
C5×D3×D1453
(C3⋊D3)⋊D1455
C5×(C3⋊D3)⋊D295
C5×(C3⋊D3)⋊D529