Finite Group Databasebeta

← C3⋊#19129734 #30655432

Subgroups — C3⋊#19129734 #30655432

Order 16380.

112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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×D5×#63271C211yesmaximal, characteristic
2C13×C3⋊(C7⋊AGL(1,𝔽5))C311yesmaximal, characteristic, complemented
3#19129734—31nomaximal
4C3×C5×#63271C411yescharacteristic, complemented, Hall
5C3⋊#11763962—51nomaximal, Hall
6D5×#63271—21no—
7D5×#63271D311yescharacteristic
8C3×C7×D5×C13C2×C311yescharacteristic
9C13⋊C3×ΓL(1,𝔽16)—71nomaximal, Hall
10C13×C7⋊AGL(1,𝔽5)—31noHall
11C2×C3×#63271—51no—
12C3×C5×C7×C13C3×C411yescharacteristic, complemented
13C5×#63271—21no—
14C5×#63271Dic311yescharacteristic, complemented
15C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))—131nomaximal, Hall
16C3×D5×C13⋊C3—141no—
17C13×Dic21—51no—
18#11763962—151no—
19C7×D5×C13C3×D311yescharacteristic
20C3×#63271AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C13×ΓL(1,𝔽16)—71no—
22AGL(1,𝔽5)×C13⋊C3—211no—
23C3×D5×ΓL(1,𝔽8)—131no—
24C3×C5×C13⋊C3—141noHall
25C2×C3×C7×C13—51no—
26C2×#63271—51no—
27C2×#63271—101no—
28Dic3×C13⋊C3—351noHall
29C5×C7×C13C3×Dic311yescharacteristic, complemented, Hall
30C3⋊(C7⋊AGL(1,𝔽5))C13⋊C311yescharacteristic, complemented
31ΓL(1,𝔽8)⋊AGL(1,𝔽5)—391no—
32C3×D5×C13AGL(1,𝔽7)11yescharacteristic
33D5×C13⋊C3—141no—
34D5×C13⋊C3—141no—
35C13×Dic7—151noHall
36C3×C5×ΓL(1,𝔽8)—131noHall
37C3×C7×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented
38#63271—21no—
39#63271ΓL(1,𝔽16)11yescharacteristic, complemented
40C13×AGL(1,𝔽5)—211noHall
41C3⋊(ΓL(1,𝔽8)⋊C4)—651noHall
42C2×C3×C13⋊C3—701no—
43C3×C7×D5C2×C13⋊C311yescharacteristic
44D5×ΓL(1,𝔽8)—131no—
45D5×ΓL(1,𝔽8)—261no—
46C3×C5×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
47C5×C13⋊C3—141no—
48C5×C13⋊C3—141no—
49C2×C7×C13—51no—
50C3×ΓL(1,𝔽16)—911noHall
51Dic3×C13—351no—
52C4×C13⋊C3—1051no—
53C7⋊AGL(1,𝔽5)—31noHall
54D5×C13C3⋊AGL(1,𝔽7)11yescharacteristic
55C2×C3×ΓL(1,𝔽8)—651no—
56C3×C13⋊C3—141noHall
57C3×C5×C7C4×C13⋊C311yescharacteristic, complemented
58C5×ΓL(1,𝔽8)—131no—
59C5×ΓL(1,𝔽8)—261no—
60C7×C13C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
61C32×D5—1821no—
62Dic21—51no—
63ΓL(1,𝔽8)⋊C4—1951no—
64C2×C3×C13—51no—
65C2×C13⋊C3—701no—
66C2×C13⋊C3—701no—
67C7×D5D3×C13⋊C311yescharacteristic
68C5×C13C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Hall
69C3×ΓL(1,𝔽8)—131noHall
70ΓL(1,𝔽16)—71no—
71C3×AGL(1,𝔽5)—2731no—
72C4×C13—1051noHall
73C32×C5—1821noHall
74C2×C3×C7—51no—
75C2×ΓL(1,𝔽8)—651no—
76C2×ΓL(1,𝔽8)—1301no—
77C3×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
78C13⋊C3—141no—
79C13⋊C3—141no—
80C3×Dic3—4551noHall
81C5×C7Dic3×C13⋊C311yescharacteristic, complemented, Hall
82C3×D5—1821no—
83C3×D5—1821no—
84C3×D5#1058772111yescharacteristic
85Dic7—151noHall
86C2×C13—51no—
87C3×C7AGL(1,𝔽5)×C13⋊C311yescharacteristic, complemented
88ΓL(1,𝔽8)—131no—
89ΓL(1,𝔽8)—261no—
90AGL(1,𝔽5)—211noHall
91C2×C32—9101no—
92C3×C5—1821no—
93C3×C5—1821no—
94C3×C5#1176396211yescharacteristic, complemented
95C2×C7—51no—
96C13C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
97C3×C4—13651no—
98Dic3—351no—
99D5C3⋊#1058772111yescharacteristic
100C32—1821noSylow
101C7C13⋊C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—9101no—
104C2×C3—9101no—
105C5C3⋊#1176396211yescharacteristic, complemented, Sylow
106C4—1051noSylow
107C3—1821no—
108C3—1821no—
109C3#1912973411yescharacteristic, complemented
110C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C13C3×C4
prime radicalC3×D5×#63271C2
cosocleC3×C7×D5×C13C2×C3
LCSG ▷ C3×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. C13×C3⋊(C7⋊AGL(1,𝔽5))C3semidirect
4. C3×C5×#63271C4semidirect
12. C3×C5×C7×C13C3×C4semidirect
14. C5×#63271Dic3semidirect
20. C3×#63271AGL(1,𝔽5)semidirect
29. C5×C7×C13C3×Dic3semidirect
30. C3⋊(C7⋊AGL(1,𝔽5))C13⋊C3semidirect
37. C3×C7×C13C3×AGL(1,𝔽5)semidirect
39. #63271ΓL(1,𝔽16)semidirect
46. C3×C5×C13ΓL(1,𝔽8)⋊C4semidirect
57. C3×C5×C7C4×C13⋊C3semidirect
60. C7×C13C3×ΓL(1,𝔽16)semidirect
68. C5×C13C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
77. C3×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
81. C5×C7Dic3×C13⋊C3semidirect
87. C3×C7AGL(1,𝔽5)×C13⋊C3semidirect
94. C3×C5#11763962semidirect
96. C13C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))semidirect
101. C7C13⋊C3×ΓL(1,𝔽16)semidirect
105. C5C3⋊#11763962semidirect
109. C3#19129734semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#632712
C13×C3⋊(C7⋊AGL(1,𝔽5))3
#191297343
C3⋊#117639625
C13⋊C3×ΓL(1,𝔽16)7
C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5))13