Finite Group Databasebeta

← C5×C3⋊#11763979 #30655412

Subgroups — C5×C3⋊#11763979 #30655412

Order 16380.

112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 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×C7×D13⋊C3C211yesmaximal, characteristic
2C5×C3⋊(C7⋊#261)C311yesmaximal, characteristic, complemented
3C5×#11763979—31nomaximal
4C3×C5×C7×C13⋊C3C411yescharacteristic, complemented, Hall
5C3⋊#11763979C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×D13⋊C3—21no—
7C5×C7×D13⋊C3D311yescharacteristic
8C3×C5×C7×D13C2×C311yescharacteristic
9C5×C3⋊AGL(1,𝔽13)—71nomaximal, Hall
10C5×C7⋊#261—31noHall
11C3×C7×D13⋊C3C2×C511yescharacteristic
12C3×C5×C7×C13C3×C411yescharacteristic, complemented
13C5×C7×C13⋊C3—21no—
14C5×C7×C13⋊C3Dic311yescharacteristic, complemented
15C3×C5×Dic21—131nomaximal, Hall
16C3×C5×D13⋊C3D711yescharacteristic
17C3⋊(C7⋊#261)C3×C511yescharacteristic, complemented
18#11763979—31no—
19C5×C7×D13C3×D311yescharacteristic
20C3×C7×C13⋊C3C4×C511yescharacteristic, complemented, Hall
21C5×C3⋊#261—71no—
22C5×AGL(1,𝔽13)—211no—
23C2×C32×C5×C7—131no—
24C3×C5×C13⋊C3Dic711yescharacteristic, complemented, Hall
25C3×C7×D13C2×C3×C511yescharacteristic
26C7×D13⋊C3—21no—
27C7×D13⋊C3C5×D311yescharacteristic
28C3⋊AGL(1,𝔽13)—71noHall
29C5×C7×C13C3×Dic311yescharacteristic, complemented, Hall
30C5×Dic21—131no—
31C3×C5×Dic7—391no—
32C3×C5×D13C3×D711yescharacteristic
33C5×D13⋊C3—21no—
34C5×D13⋊C3D2111yescharacteristic
35C7⋊#261—31noHall
36C32×C5×C7—131noHall
37C3×C7×C13C3×C4×C511yescharacteristic, complemented
38C7×C13⋊C3—21no—
39C7×C13⋊C3C5×Dic311yescharacteristic, complemented
40C5×#261—211noHall
41C3×Dic21—131noHall
42C3×D13⋊C3C5×D711yescharacteristic
43C2×C3×C5×C7—131no—
44C2×C3×C5×C7—131no—
45C2×C3×C5×C7—261no—
46C3×C5×C13C3×Dic711yescharacteristic, complemented
47C5×C13⋊C3—21no—
48C5×C13⋊C3Dic2111yescharacteristic, complemented
49C7×D13C3×C5×D311yescharacteristic
50C3×C5×Dic3—911noHall
51C3⋊#261—71no—
52AGL(1,𝔽13)—211no—
53C5×Dic7—391noHall
54C5×D13C3×D2111yescharacteristic
55C2×C32×C7—131no—
56C3×C13⋊C3C5×Dic711yescharacteristic, complemented, Hall
57C3×C5×C7—131no—
58C3×C5×C7—261no—
59C3×C5×C7AGL(1,𝔽13)11yescharacteristic, complemented
60C7×C13C3×C5×Dic311yescharacteristic, complemented, Hall
61C2×C32×C5—131no—
62Dic21—131no—
63C3×Dic7—391no—
64C3×D13C3×C5×D711yescharacteristic
65D13⋊C3—21no—
66D13⋊C3C5×D2111yescharacteristic
67C2×C5×C7—131no—
68C5×C13C3×Dic2111yescharacteristic, complemented, Hall
69C32×C7—131noHall
70C3×C4×C5—2731no—
71C5×Dic3—911no—
72#261—211noHall
73C32×C5—131noHall
74C2×C3×C7—131no—
75C2×C3×C7—131no—
76C2×C3×C7—261no—
77C3×C13C3×C5×Dic711yescharacteristic, complemented
78C13⋊C3—21no—
79C13⋊C3C5×Dic2111yescharacteristic, complemented
80C3×Dic3—911noHall
81C5×C7C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Hall
82C2×C3×C5—131no—
83C2×C3×C5—131no—
84C2×C3×C5—261no—
85Dic7—391noHall
86D13C3×C5×D2111yescharacteristic
87C3×C7—131no—
88C3×C7—261no—
89C3×C7C5×AGL(1,𝔽13)11yescharacteristic, complemented
90C4×C5—2731noHall
91C2×C32—131no—
92C3×C5—131no—
93C3×C5—261no—
94C3×C5#1176397911yescharacteristic, complemented
95C2×C7—131no—
96C13C3×C5×Dic2111yescharacteristic, complemented, Sylow
97C3×C4—2731no—
98Dic3—911no—
99C2×C5—131no—
100C32—131noSylow
101C7C5×C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
102C2×C3—131no—
103C2×C3—131no—
104C2×C3—261no—
105C5C3⋊#1176397911yescharacteristic, direct product factor, Sylow
106C4—2731noSylow
107C3—131no—
108C3—261no—
109C3C5×#1176397911yescharacteristic, complemented
110C2—131no—
subgroupG/H
center, hypercenterC5C3⋊#11763979
commutator, hypocenterC3×C7×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13⋊C3C2
cosocleC3×C7×D13C2×C3×C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
2. C5×C3⋊(C7⋊#261)C3semidirect
4. C3×C5×C7×C13⋊C3C4semidirect
5. C3⋊#11763979C5direct (N × H)
12. C3×C5×C7×C13C3×C4semidirect
14. C5×C7×C13⋊C3Dic3semidirect
17. C3⋊(C7⋊#261)C3×C5semidirect
20. C3×C7×C13⋊C3C4×C5semidirect
24. C3×C5×C13⋊C3Dic7semidirect
29. C5×C7×C13C3×Dic3semidirect
37. C3×C7×C13C3×C4×C5semidirect
39. C7×C13⋊C3C5×Dic3semidirect
46. C3×C5×C13C3×Dic7semidirect
48. C5×C13⋊C3Dic21semidirect
56. C3×C13⋊C3C5×Dic7semidirect
59. C3×C5×C7AGL(1,𝔽13)semidirect
60. C7×C13C3×C5×Dic3semidirect
68. C5×C13C3×Dic21semidirect
77. C3×C13C3×C5×Dic7semidirect
79. C13⋊C3C5×Dic21semidirect
81. C5×C7C3⋊AGL(1,𝔽13)semidirect
89. C3×C7C5×AGL(1,𝔽13)semidirect
94. C3×C5#11763979semidirect
96. C13C3×C5×Dic21semidirect
101. C7C5×C3⋊AGL(1,𝔽13)semidirect
105. C5C3⋊#11763979direct (N × H)
109. C3C5×#11763979semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D13⋊C32
C5×C3⋊(C7⋊#261)3
C5×#117639793
C3⋊#117639795
C5×C3⋊AGL(1,𝔽13)7
C3×C5×Dic2113