Finite Group Databasebeta

← C5×#13109896⋊C2 #30655003

Subgroups — C5×#13109896⋊C2 #30655003

Order 16380.

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

normal subgroups only

This group has 120 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
1C5×#13109902C211yesmaximal, characteristic, complemented
2C5×#13109900C211yesmaximal, characteristic, complemented
3C5×#13109896C211yesmaximal, characteristic, complemented
4C3×C5×D7×D13C311yesmaximal, characteristic
5C5×#11717941C2211yescharacteristic, complemented, Hall
6#13109896⋊C2C511yesmaximal, characteristic, direct product factor, Hall
7C3×C5×D91C2×C311yescharacteristic
8C3×C5×C13×D7C2×C311yescharacteristic
9C3×C5×C7×D13C2×C311yescharacteristic
10C2×C5×D13⋊C9—71nomaximal, Hall
11C5×D7×D13C911yescharacteristic, complemented, Hall
12#13109902C2×C511yescharacteristic, complemented
13#13109900C2×C511yescharacteristic, complemented
14#13109896C2×C511yescharacteristic, complemented
15C3×C5×C7×C13C22×C311yescharacteristic
16C2×C5×D7⋊C9—131nomaximal, Hall
17C2×C5×C13⋊C9—71no—
18C5×D13⋊C9—71no—
19C5×D13⋊C9—71no—
20C3×D7×D13C3×C511yescharacteristic
21C5×D91C2×C911yescharacteristic, complemented
22C5×C13×D7C2×C911yescharacteristic, complemented
23C5×C7×D13C2×C911yescharacteristic, complemented
24#11717941C22×C511yescharacteristic, complemented, Hall
25C2×C3×C5×D13—211no—
26C2×C5×C7⋊C9—131no—
27C5×D7⋊C9—131no—
28C5×D7⋊C9—131no—
29C5×C13⋊C9—71noHall
30C3×D91C2×C3×C511yescharacteristic
31C3×C13×D7C2×C3×C511yescharacteristic
32C3×C7×D13C2×C3×C511yescharacteristic
33C2×D13⋊C9—71noHall
34C5×C7×C13C22×C911yescharacteristic, complemented, Hall
35C2×C3×C5×D7—391no—
36C2×C3×C5×C13—211no—
37C3×C5×D13—211no—
38C3×C5×D13AGL(1,𝔽7)11yescharacteristic
39D7×D13C5×C911yescharacteristic, complemented, Hall
40C5×C7⋊C9—131noHall
41C3×C7×C13C22×C3×C511yescharacteristic
42C2×C5×D13—211noHall
43C2×D7⋊C9—131noHall
44C2×C13⋊C9—71no—
45D13⋊C9—71no—
46D13⋊C9—71no—
47C2×C3×C5×C7—391no—
48C3×C5×D7—391no—
49C3×C5×D7D13⋊C311yescharacteristic
50C3×C5×C13C2×AGL(1,𝔽7)11yescharacteristic
51D91C2×C5×C911yescharacteristic, complemented
52C7×D13C2×C5×C911yescharacteristic, complemented
53C13×D7C2×C5×C911yescharacteristic, complemented
54C22×C5×C9—911noHall
55C2×C3×D13—211no—
56C2×C5×D7—391noHall
57C2×C5×C13—211no—
58C5×D13—211no—
59C5×D13D7⋊C911yescharacteristic, complemented
60C2×C7⋊C9—131no—
61D7⋊C9—131no—
62D7⋊C9—131no—
63C13⋊C9—71noHall
64C3×C5×C7C2×D13⋊C311yescharacteristic
65C7×C13C22×C5×C911yescharacteristic, complemented, Hall
66C2×C5×C9—911no—
67C2×C5×C9—911no—
68C2×C5×C9—911no—
69C2×C3×D7—391no—
70C2×C3×C13—211no—
71C3×D13—211no—
72C3×D13C5×AGL(1,𝔽7)11yescharacteristic
73C2×C5×C7—391no—
74C5×D7—391no—
75C5×D7D13⋊C911yescharacteristic, complemented
76C5×C13C2×D7⋊C911yescharacteristic, complemented, Hall
77C7⋊C9—131noHall
78C22×C3×C5—2731no—
79C2×D13—211noHall
80C5×C9—911noHall
81C2×C3×C7—391no—
82C3×D7—391no—
83C3×D7C5×D13⋊C311yescharacteristic
84C3×C13C2×C5×AGL(1,𝔽7)11yescharacteristic
85C22×C9—911noHall
86C5×C7C2×D13⋊C911yescharacteristic, complemented, Hall
87C2×C3×C5—2731no—
88C2×C3×C5—211no—
89C2×C3×C5—391no—
90C2×D7—391noHall
91C2×C13—211no—
92D13—211no—
93D13C5×D7⋊C911yescharacteristic, complemented
94C3×C7C2×C5×D13⋊C311yescharacteristic
95C22×C5—2731noHall
96C2×C9—911no—
97C2×C9—911no—
98C2×C9—911no—
99C3×C5#10587716⋊C211yescharacteristic
100C2×C7—391no—
101D7—391no—
102D7C5×D13⋊C911yescharacteristic, complemented
103C13C2×C5×D7⋊C911yescharacteristic, complemented, Sylow
104C22×C3—2731no—
105C2×C5—2731no—
106C2×C5—211no—
107C2×C5—391no—
108C9—911noSylow
109C7C2×C5×D13⋊C911yescharacteristic, complemented, Sylow
110C2×C3—2731no—
111C2×C3—211no—
112C2×C3—391no—
113C5#13109896⋊C211yescharacteristic, direct product factor, Sylow
114C22—2731noSylow
115C3C5×#10587716⋊C211yescharacteristic
116C2—2731no—
117C2—211no—
118C2—391no—
subgroupG/H
center, hypercenterC3×C5#10587716⋊C2
commutator, hypocenterC7×C13C22×C5×C9
FrattiniC3C5×#10587716⋊C2
Fitting, socleC3×C5×C7×C13C22×C3
prime radicalC3×C5×D7×D13C3
cosocleC3×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C5×#13109902C2semidirect
2. C5×#13109900C2semidirect
3. C5×#13109896C2semidirect
5. C5×#11717941C22semidirect
6. #13109896⋊C2C5direct (N × H)
11. C5×D7×D13C9semidirect
12. #13109902C2×C5semidirect
13. #13109900C2×C5semidirect
14. #13109896C2×C5semidirect
21. C5×D91C2×C9semidirect
22. C5×C13×D7C2×C9semidirect
23. C5×C7×D13C2×C9semidirect
24. #11717941C22×C5semidirect
34. C5×C7×C13C22×C9semidirect
39. D7×D13C5×C9semidirect
51. D91C2×C5×C9semidirect
52. C7×D13C2×C5×C9semidirect
53. C13×D7C2×C5×C9semidirect
59. C5×D13D7⋊C9semidirect
65. C7×C13C22×C5×C9semidirect
75. C5×D7D13⋊C9semidirect
76. C5×C13C2×D7⋊C9semidirect
86. C5×C7C2×D13⋊C9semidirect
93. D13C5×D7⋊C9semidirect
102. D7C5×D13⋊C9semidirect
103. C13C2×C5×D7⋊C9semidirect
109. C7C2×C5×D13⋊C9semidirect
113. C5#13109896⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#131099022
C5×#131099002
C5×#131098962
C3×C5×D7×D133
#13109896⋊C25
C2×C5×D13⋊C97
C2×C5×D7⋊C913