Finite Group Databasebeta

← C3×C3⋊(C7⋊#63120) #30655649

Subgroups — C3×C3⋊(C7⋊#63120) #30655649

Order 16380.

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

normal subgroups only

This group has 112 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
1C32×C7×D5×C13C211yesmaximal, characteristic
2C3⋊(C7⋊#63120)C311yesmaximal, characteristic, direct product factor
3C3×C7⋊#63120—31nomaximal
4C32×C5×C7×C13C411yescharacteristic, complemented, Hall
5C3×Dic273—51nomaximal, Hall
6C3×C7×D5×C13—21no—
7C3×C7×D5×C13D311yescharacteristic
8C3×C7×D5×C13C2×C311yescharacteristic
9C3×C3⋊#63120—71nomaximal, Hall
10C7⋊#63120—31noHall
11C2×C32×C7×C13—51no—
12C3×C5×C7×C13—21no—
13C3×C5×C7×C13Dic311yescharacteristic, complemented
14C3×C5×C7×C13C3×C411yescharacteristic, complemented
15C3×C3⋊(C7⋊AGL(1,𝔽5))—131nomaximal, Hall
16C32×D5×C13D711yescharacteristic
17Dic273—51no—
18C3×Dic91—151no—
19C7×D5×C13C3×D311yescharacteristic
20C32×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C3⋊#63120—71no—
22C3×#63120—211no—
23C32×C7×D5D1311yescharacteristic
24C32×C5×C13Dic711yescharacteristic, complemented, Hall
25C2×C3×C7×C13—51no—
26C2×C3×C7×C13—51no—
27C2×C3×C7×C13—101no—
28C3×Dic39—351noHall
29C5×C7×C13C3×Dic311yescharacteristic, complemented, Hall
30C3⋊(C7⋊AGL(1,𝔽5))—131no—
31C3×C7⋊AGL(1,𝔽5)—391no—
32C3×D5×C13—21no—
33C3×D5×C13C3×D711yescharacteristic
34C3×D5×C13D2111yescharacteristic
35Dic91—151noHall
36C32×C5×C7Dic1311yescharacteristic, complemented, Hall
37C3×C7×C13—21no—
38C3×C7×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented
39C3×C7×C13ΓL(1,𝔽16)11yescharacteristic, complemented
40#63120—211noHall
41C3×Dic21—651noHall
42C2×C32×C13—51no—
43C3×C7×D5—21no—
44C3×C7×D5C3×D1311yescharacteristic
45C3×C7×D5D3911yescharacteristic
46C3×C5×C13—21no—
47C3×C5×C13C3×Dic711yescharacteristic, complemented
48C3×C5×C13Dic2111yescharacteristic, complemented
49C2×C7×C13—51no—
50C3×ΓL(1,𝔽16)—911noHall
51Dic39—351no—
52C3×Dic13—1051no—
53C7⋊AGL(1,𝔽5)—391noHall
54D5×C13C3×D2111yescharacteristic
55C2×C32×C7—51no—
56C32×C13C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
57C3×C5×C7—21no—
58C3×C5×C7C3×Dic1311yescharacteristic, complemented
59C3×C5×C7Dic3911yescharacteristic, complemented
60C7×C13C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
61C32×D5D9111yescharacteristic
62Dic21—651no—
63C3×Dic7—1951no—
64C2×C3×C13—51no—
65C2×C3×C13—51no—
66C2×C3×C13—101no—
67C7×D5C3×D3911yescharacteristic
68C5×C13C3×Dic2111yescharacteristic, complemented, Hall
69C32×C7#6312011yescharacteristic, complemented, Hall
70ΓL(1,𝔽16)—911no—
71C3×AGL(1,𝔽5)—2731no—
72Dic13—1051noHall
73C32×C5Dic9111yescharacteristic, complemented, Hall
74C2×C3×C7—51no—
75C2×C3×C7—51no—
76C2×C3×C7—101no—
77C3×C13—21no—
78C3×C13C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
79C3×C13C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
80C3×Dic3—4551noHall
81C5×C7C3×Dic3911yescharacteristic, complemented, Hall
82C3×D5—21no—
83C3×D5C3×D9111yescharacteristic
84C3×D5D27311yescharacteristic
85Dic7—1951noHall
86C2×C13—51no—
87C3×C7—21no—
88C3×C7C3×#6312011yescharacteristic, complemented
89C3×C7C3⋊#6312011yescharacteristic, complemented
90AGL(1,𝔽5)—2731noHall
91C2×C32—51no—
92C3×C5—21no—
93C3×C5C3×Dic9111yescharacteristic, complemented
94C3×C5Dic27311yescharacteristic, complemented
95C2×C7—51no—
96C13C3×C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
97C3×C4—13651no—
98Dic3—4551no—
99D5C3×D27311yescharacteristic
100C32C7⋊#6312011yescharacteristic, complemented, Sylow
101C7C3×C3⋊#6312011yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—51no—
104C2×C3—101no—
105C5C3×Dic27311yescharacteristic, complemented, Sylow
106C4—13651noSylow
107C3—21no—
108C3C3×C7⋊#6312011yescharacteristic, complemented
109C3C3⋊(C7⋊#63120)11yescharacteristic, direct product factor
110C2—51no—
subgroupG/H
center, hypercenterC3C3⋊(C7⋊#63120)
commutator, hypocenterC3×C5×C7×C13C3×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C7×D5×C13C2
cosocleC3×C7×D5×C13C2×C3
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C7⋊#63120)C3direct (N × H)
4. C32×C5×C7×C13C4semidirect
13. C3×C5×C7×C13Dic3semidirect
14. C3×C5×C7×C13C3×C4semidirect
20. C32×C7×C13AGL(1,𝔽5)semidirect
24. C32×C5×C13Dic7semidirect
29. C5×C7×C13C3×Dic3semidirect
36. C32×C5×C7Dic13semidirect
38. C3×C7×C13C3×AGL(1,𝔽5)semidirect
39. C3×C7×C13ΓL(1,𝔽16)semidirect
47. C3×C5×C13C3×Dic7semidirect
48. C3×C5×C13Dic21semidirect
56. C32×C13C7⋊AGL(1,𝔽5)semidirect
58. C3×C5×C7C3×Dic13semidirect
59. C3×C5×C7Dic39semidirect
60. C7×C13C3×ΓL(1,𝔽16)semidirect
68. C5×C13C3×Dic21semidirect
69. C32×C7#63120semidirect
73. C32×C5Dic91semidirect
78. C3×C13C3×C7⋊AGL(1,𝔽5)semidirect
79. C3×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
81. C5×C7C3×Dic39semidirect
88. C3×C7C3×#63120semidirect
89. C3×C7C3⋊#63120semidirect
93. C3×C5C3×Dic91semidirect
94. C3×C5Dic273semidirect
96. C13C3×C3⋊(C7⋊AGL(1,𝔽5))semidirect
100. C32C7⋊#63120semidirect
101. C7C3×C3⋊#63120semidirect
105. C5C3×Dic273semidirect
108. C3C3×C7⋊#63120semidirect
109. C3C3⋊(C7⋊#63120)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D5×C132
C3⋊(C7⋊#63120)3
C3×C7⋊#631203
C3×Dic2735
C3×C3⋊#631207
C3×C3⋊(C7⋊AGL(1,𝔽5))13