Finite Group Databasebeta

← C2×C5×#15690150 #44477704

Subgroups — C2×C5×#15690150 #44477704

Order 30420.

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

normal subgroups only

This group has 192 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
1C2×C5×#13095200C211yesmaximal, characteristic, complemented
2C5×#15690150C211yesmaximal, characteristic, direct product factor
3C5×#15690150C211yesmaximal, characteristic, direct product factor
4C2×C3×C5×C13×D13C311yesmaximal, characteristic
5C5×#13095200C2211yescharacteristic, complemented, Hall
6C2×#15690150C511yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C13×D13C2×C311yescharacteristic
8C3×C5×C13×D13C2×C311yescharacteristic
9C2×C3×C5×C132C2×C311yescharacteristic
10C2×C5×C13×D13C911yescharacteristic, complemented, Hall
11C2×#13095200C2×C511yescharacteristic, complemented
12#15690150C2×C511yescharacteristic, direct product factor
13#15690150C2×C511yescharacteristic, direct product factor
14C3×C5×C132C22×C311yescharacteristic
15C22×C5×C13⋊C9—131nomaximal
16C2×C5×D13⋊C9—131nomaximal
17C2×C3×C13×D13C3×C511yescharacteristic
18C2×C5×C132C2×C911yescharacteristic, complemented
19C5×C13×D13C2×C911yescharacteristic, complemented
20C5×C13×D13C2×C911yescharacteristic, complemented
21#13095200C22×C511yescharacteristic, complemented, Hall
22C2×C5×C13⋊C9—131no—
23C2×C5×C13⋊C9—131no—
24C2×C5×C13⋊C9—131no—
25C2×C5×C13⋊C9—131no—
26C2×C5×C13⋊C9—266no—
27C5×D13⋊C9—131no—
28C5×D13⋊C9—131no—
29C2×C3×C132C2×C3×C511yescharacteristic
30C3×C13×D13C2×C3×C511yescharacteristic
31C3×C13×D13C2×C3×C511yescharacteristic
32C5×C132C22×C911yescharacteristic, complemented, Hall
33C22×C3×C5×C13—391no—
34C2×C3×C5×D13C13⋊C311yescharacteristic
35C2×C13×D13C5×C911yescharacteristic, complemented, Hall
36C5×C13⋊C9—131no—
37C5×C13⋊C9—131no—
38C5×C13⋊C9—266no—
39C3×C132C22×C3×C511yescharacteristic
40C22×C13⋊C9—131no—
41C2×D13⋊C9—131no—
42C2×C3×C5×C13—26no—
43C2×C3×C5×C13—131no—
44C2×C3×C5×C13—391no—
45C2×C3×C5×C13D13⋊C311yescharacteristic
46C2×C3×C5×C13C2×C13⋊C311yescharacteristic
47C3×C5×D13C2×C13⋊C311yescharacteristic
48C3×C5×D13C2×C13⋊C311yescharacteristic
49C2×C132C2×C5×C911yescharacteristic, complemented
50C13×D13C2×C5×C911yescharacteristic, complemented
51C13×D13C2×C5×C911yescharacteristic, complemented
52C22×C5×C13—391no—
53C2×C5×D13C13⋊C911yescharacteristic, complemented
54C2×C13⋊C9—131no—
55C2×C13⋊C9—131no—
56C2×C13⋊C9—131no—
57C2×C13⋊C9—131no—
58C2×C13⋊C9—266no—
59D13⋊C9—131no—
60D13⋊C9—131no—
61C3×C5×C13—26no—
62C3×C5×C13C2×D13⋊C311yescharacteristic
63C3×C5×C13C22×C13⋊C311yescharacteristic
64C22×C5×C9—1691noHall
65C132C22×C5×C911yescharacteristic, complemented, Sylow
66C22×C3×C13—391no—
67C2×C3×D13C5×C13⋊C311yescharacteristic
68C2×C5×C13—26no—
69C2×C5×C13—131no—
70C2×C5×C13—391no—
71C2×C5×C13D13⋊C911yescharacteristic, complemented
72C2×C5×C13C2×C13⋊C911yescharacteristic, complemented
73C5×D13C2×C13⋊C911yescharacteristic, complemented
74C5×D13C2×C13⋊C911yescharacteristic, complemented
75C13⋊C9—131no—
76C13⋊C9—131no—
77C13⋊C9—266no—
78C2×C5×C9—1691no—
79C2×C5×C9—1691no—
80C2×C5×C9—1691no—
81C2×C3×C13—26no—
82C2×C3×C13—391no—
83C2×C3×C13—391no—
84C2×C3×C13C5×D13⋊C311yescharacteristic
85C2×C3×C13C2×C5×C13⋊C311yescharacteristic
86C3×D13C2×C5×C13⋊C311yescharacteristic
87C3×D13C2×C5×C13⋊C311yescharacteristic
88C5×C13—26no—
89C5×C13C2×D13⋊C911yescharacteristic, complemented
90C5×C13C22×C13⋊C911yescharacteristic, complemented
91C22×C3×C5—391no—
92C22×C13—391no—
93C2×D13C5×C13⋊C911yescharacteristic, complemented
94C5×C9—1691noHall
95C3×C13—26no—
96C3×C13C2×C5×D13⋊C311yescharacteristic
97C3×C13C22×C5×C13⋊C311yescharacteristic
98C22×C9—1691noHall
99C2×C3×C5—391no—
100C2×C3×C5—391no—
101C2×C3×C5#1175981711yescharacteristic
102C2×C13—26no—
103C2×C13—391no—
104C2×C13—391no—
105C2×C13C5×D13⋊C911yescharacteristic, complemented
106C2×C13C2×C5×C13⋊C911yescharacteristic, complemented
107D13C2×C5×C13⋊C911yescharacteristic, complemented
108D13C2×C5×C13⋊C911yescharacteristic, complemented
109C22×C5—391noHall
110C2×C9—1691no—
111C2×C9—1691no—
112C2×C9—1691no—
113C3×C5C2×#1175981711yescharacteristic
114C13—26no—
115C13C2×C5×D13⋊C911yescharacteristic, complemented
116C13C22×C5×C13⋊C911yescharacteristic, complemented
117C22×C3—391no—
118C2×C5—391no—
119C2×C5—391no—
120C2×C5#1569015011yescharacteristic, direct product factor
121C9—1691noSylow
122C2×C3—391no—
123C2×C3—391no—
124C2×C3C5×#1175981711yescharacteristic
125C5C2×#1569015011yescharacteristic, direct product factor, Sylow
126C22—391noSylow
127C3C2×C5×#1175981711yescharacteristic
128C2—391no—
129C2—391no—
130C2C5×#1569015011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5#11759817
commutator, hypocenterC132C22×C5×C9
FrattiniC3C2×C5×#11759817
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×C13×D13C3
cosocleC3×C132C22×C3×C5
LCSG ▷ C132
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#13095200C2semidirect
2. C5×#15690150C2direct (N × H)
3. C5×#15690150C2direct (N × H)
5. C5×#13095200C22semidirect
6. C2×#15690150C5direct (N × H)
10. C2×C5×C13×D13C9semidirect
11. C2×#13095200C2×C5semidirect
12. #15690150C2×C5direct (N × H)
13. #15690150C2×C5direct (N × H)
18. C2×C5×C132C2×C9semidirect
19. C5×C13×D13C2×C9semidirect
20. C5×C13×D13C2×C9semidirect
21. #13095200C22×C5semidirect
32. C5×C132C22×C9semidirect
35. C2×C13×D13C5×C9semidirect
49. C2×C132C2×C5×C9semidirect
50. C13×D13C2×C5×C9semidirect
51. C13×D13C2×C5×C9semidirect
53. C2×C5×D13C13⋊C9semidirect
65. C132C22×C5×C9semidirect
71. C2×C5×C13D13⋊C9semidirect
72. C2×C5×C13C2×C13⋊C9semidirect
73. C5×D13C2×C13⋊C9semidirect
74. C5×D13C2×C13⋊C9semidirect
89. C5×C13C2×D13⋊C9semidirect
90. C5×C13C22×C13⋊C9semidirect
93. C2×D13C5×C13⋊C9semidirect
105. C2×C13C5×D13⋊C9semidirect
106. C2×C13C2×C5×C13⋊C9semidirect
107. D13C2×C5×C13⋊C9semidirect
108. D13C2×C5×C13⋊C9semidirect
115. C13C2×C5×D13⋊C9semidirect
116. C13C22×C5×C13⋊C9semidirect
120. C2×C5#15690150direct (N × H)
125. C5C2×#15690150direct (N × H)
130. C2C5×#15690150direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#130952002
C5×#156901502
C2×C3×C5×C13×D133
C2×#156901505
C22×C5×C13⋊C913
C2×C5×D13⋊C913