Finite Group Databasebeta

← C3⋊#27130893 #49137447

Subgroups — C3⋊#27130893 #49137447

Order 36300.

364 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 92 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×#10597243C211yesmaximal, characteristic
2#27130893—31nomaximal, Hall
3C3×C5×#10597243C411yescharacteristic, complemented, Hall
4C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))C511yesmaximal, characteristic, complemented
5C3⋊#14559051—51nomaximal
6D5×#10597243D311yescharacteristic
7C3×D5×C112C2×C511yescharacteristic
8C2×C3×#10597243—51no—
9C3⋊((C11⋊C5)⋊AGL(1,𝔽5))—113nomaximal
10C3⋊((C11⋊C5)⋊AGL(1,𝔽5))—119nomaximal
11C5×#10597243Dic311yescharacteristic, complemented, Hall
12C11⋊(C11⋊AGL(1,𝔽5))—31no—
13#14559051—151no—
14C3×C5×C112C4×C511yescharacteristic, complemented
15C3×#10597243—41no—
16C3×#10597243AGL(1,𝔽5)11yescharacteristic, complemented
17C3×D5×C11⋊C5—223no—
18C3×D5×C11⋊C5—229no—
19C3⋊(C11⋊Dic11)—51noHall
20D5×C112C5×D311yescharacteristic
21C2×#10597243—51no—
22(C11⋊C5)⋊AGL(1,𝔽5)—333no—
23(C11⋊C5)⋊AGL(1,𝔽5)—339no—
24C3×C5×C11⋊C5—223no—
25C3×C5×C11⋊C5—229no—
26C2×C3×C112—51no—
27C3⋊(C11⋊AGL(1,𝔽5))—113no—
28C3⋊(C11⋊AGL(1,𝔽5))—119no—
29C3⋊(Dic11⋊C5)—553no—
30C3⋊(Dic11⋊C5)—559no—
31C5×C112C5×Dic311yescharacteristic, complemented
32#10597243—41no—
33#10597243ΓL(1,𝔽16)11yescharacteristic, complemented
34D5×C11⋊C5—223no—
35D5×C11⋊C5—229no—
36C11⋊Dic11—151noHall
37C3×C112C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C3×D5×C11AGL(1,𝔽11)13yes—
39C3×D5×C11AGL(1,𝔽11)19yes—
40C2×C3×C11⋊C5—553no—
41C2×C3×C11⋊C5—1109no—
42C5×ΓL(1,𝔽16)—1211noHall
43C5×C11⋊C5—223no—
44C5×C11⋊C5—229no—
45C2×C112—51no—
46C11⋊AGL(1,𝔽5)—333no—
47C11⋊AGL(1,𝔽5)—339no—
48Dic11⋊C5—1653no—
49Dic11⋊C5—1659no—
50C3×C5×C11Dic11⋊C513yescomplemented
51C3×C5×C11Dic11⋊C519yescomplemented
52C3×C11⋊C5—113no—
53C3×C11⋊C5—229no—
54C3×C11⋊C5—443no—
55C3×C11⋊C5—449no—
56C3×C5×D5—2421no—
57Dic33—553no—
58Dic33—559no—
59C112C5×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
60D5×C11C3⋊AGL(1,𝔽11)13yes—
61D5×C11C3⋊AGL(1,𝔽11)19yes—
62C2×C11⋊C5—1103no—
63C2×C11⋊C5—1109no—
64C5×AGL(1,𝔽5)—3631noHall
65C3×C52—2421noHall
66C2×C3×C11—53no—
67C2×C3×C11—59no—
68ΓL(1,𝔽16)—1211no—
69C5×Dic3—6051no—
70C5×C11C3⋊(Dic11⋊C5)13yescomplemented
71C5×C11C3⋊(Dic11⋊C5)19yescomplemented
72C11⋊C5—223no—
73C11⋊C5—229no—
74C11⋊C5—443no—
75C11⋊C5—449no—
76C5×D5—2421no—
77Dic11—1653no—
78Dic11—1659no—
79C3×C11(C11⋊C5)⋊AGL(1,𝔽5)13yescomplemented
80C3×C11(C11⋊C5)⋊AGL(1,𝔽5)19yescomplemented
81C2×C3×C5—12101no—
82C3×D5#1192589211yescharacteristic
83C52—2421noSylow
84C2×C11—53no—
85C2×C11—59no—
86AGL(1,𝔽5)—3631no—
87C4×C5—18151no—
88C3×C5—4841no—
89C3×C5—2421no—
90C3×C5#1455905111yescharacteristic, complemented
91Dic3—6051noHall
92C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))13yescomplemented
93C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))19yescomplemented
94C2×C5—12101no—
95D5C3⋊#1192589211yescharacteristic
96C2×C3—51no—
97C5—4841no—
98C5—2421no—
99C5C3⋊#1455905111yescharacteristic, complemented
100C4—18151noSylow
101C3#2713089311yescharacteristic, complemented, Sylow
102C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C112C4×C5
prime radicalC3×D5×#10597243C2
cosocleC3×D5×C112C2×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C5×#10597243C4semidirect
4. C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))C5semidirect
11. C5×#10597243Dic3semidirect
14. C3×C5×C112C4×C5semidirect
16. C3×#10597243AGL(1,𝔽5)semidirect
31. C5×C112C5×Dic3semidirect
33. #10597243ΓL(1,𝔽16)semidirect
37. C3×C112C5×AGL(1,𝔽5)semidirect
50. C3×C5×C11Dic11⋊C5semidirect
51. C3×C5×C11Dic11⋊C5semidirect
59. C112C5×ΓL(1,𝔽16)semidirect
70. C5×C11C3⋊(Dic11⋊C5)semidirect
71. C5×C11C3⋊(Dic11⋊C5)semidirect
79. C3×C11(C11⋊C5)⋊AGL(1,𝔽5)semidirect
80. C3×C11(C11⋊C5)⋊AGL(1,𝔽5)semidirect
90. C3×C5#14559051semidirect
92. C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))semidirect
93. C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))semidirect
99. C5C3⋊#14559051semidirect
101. C3#27130893semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#105972432
#271308933
C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))5
C3⋊#145590515
C3⋊((C11⋊C5)⋊AGL(1,𝔽5))11