Finite Group Databasebeta

← C3⋊#27130896 #49137448

Subgroups — C3⋊#27130896 #49137448

Order 36300.

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

normal subgroups only

This group has 204 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×#10597243C211yesmaximal, characteristic
2#27130896—31nomaximal, Hall
3C3×C5×#10597243C411yescharacteristic, complemented, Hall
4C11×C3⋊(C11⋊AGL(1,𝔽5))C511yesmaximal, characteristic, complemented
5C3⋊#14559054—51nomaximal
6D5×#10597243D311yescharacteristic
7C3×D5×C112C2×C511yescharacteristic
8C2×C3×#10597243—51no—
9C11⋊C5×ΓL(1,𝔽16)—111nomaximal
10C3⋊((C11⋊C5)⋊AGL(1,𝔽5))—111nomaximal
11C5×#10597243Dic311yescharacteristic, complemented, Hall
12C11×C11⋊AGL(1,𝔽5)—31no—
13#14559054—151no—
14C3×C5×C112C4×C511yescharacteristic, complemented
15C3×#10597243—41no—
16C3×#10597243AGL(1,𝔽5)11yescharacteristic, complemented
17C3×D5×C11⋊C5—111no—
18C3×D5×C11⋊C5—225no—
19C3×D5×C11⋊C5—221no—
20C11×Dic33—51noHall
21D5×C112C5×D311yescharacteristic
22C2×#10597243—51no—
23(C11⋊C5)⋊AGL(1,𝔽5)—331no—
24AGL(1,𝔽5)×C11⋊C5—331no—
25C3×C5×C11⋊C5—111no—
26C3×C5×C11⋊C5—225no—
27C3×C5×C11⋊C5—221no—
28C2×C3×C112—51no—
29C3⋊(C11⋊AGL(1,𝔽5))C11⋊C511yescharacteristic, complemented
30C11×ΓL(1,𝔽16)—111no—
31C3⋊(Dic11⋊C5)—551no—
32Dic3×C11⋊C5—551no—
33C5×C112C5×Dic311yescharacteristic, complemented
34#10597243—41no—
35#10597243ΓL(1,𝔽16)11yescharacteristic, complemented
36D5×C11⋊C5—111no—
37D5×C11⋊C5—225no—
38D5×C11⋊C5—221no—
39C11×Dic11—151noHall
40C3×C112C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
41C3×D5×C11—25no—
42C3×D5×C11AGL(1,𝔽11)11yescharacteristic
43C3×D5×C11C2×C11⋊C511yescharacteristic
44C2×C3×C11⋊C5—551no—
45C2×C3×C11⋊C5—1101no—
46C2×C3×C11⋊C5—1105no—
47C5×ΓL(1,𝔽16)—1211noHall
48C5×C11⋊C5—111no—
49C5×C11⋊C5—225no—
50C5×C11⋊C5—221no—
51C2×C112—51no—
52C11⋊AGL(1,𝔽5)—31no—
53C11×AGL(1,𝔽5)—331no—
54C4×C11⋊C5—1651no—
55Dic11⋊C5—1651no—
56C3×C5×C11—25no—
57C3×C5×C11Dic11⋊C511yescharacteristic, complemented
58C3×C5×C11C4×C11⋊C511yescharacteristic, complemented
59C3×C11⋊C5—111no—
60C3×C11⋊C5—225no—
61C3×C11⋊C5—221no—
62C3×C11⋊C5—4410no—
63C3×C11⋊C5—441no—
64C3×C11⋊C5—441no—
65C3×C5×D5—2421no—
66Dic33—51no—
67C11×Dic3—551no—
68C112C5×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
69D5×C11—25no—
70D5×C11D3×C11⋊C511yescharacteristic
71D5×C11C3⋊AGL(1,𝔽11)11yescharacteristic
72C2×C11⋊C5—551no—
73C2×C11⋊C5—1101no—
74C2×C11⋊C5—1105no—
75C5×AGL(1,𝔽5)—3631noHall
76C3×C52—2421noHall
77C2×C3×C11—51no—
78C2×C3×C11—51no—
79C2×C3×C11—105no—
80ΓL(1,𝔽16)—111no—
81C5×Dic3—6051no—
82C5×C11—25no—
83C5×C11Dic3×C11⋊C511yescharacteristic, complemented
84C5×C11C3⋊(Dic11⋊C5)11yescharacteristic, complemented
85C11⋊C5—111no—
86C11⋊C5—225no—
87C11⋊C5—221no—
88C11⋊C5—4410no—
89C11⋊C5—441no—
90C11⋊C5—441no—
91C5×D5—2421no—
92C4×C11—1651no—
93Dic11—151no—
94C3×C11—25no—
95C3×C11AGL(1,𝔽5)×C11⋊C511yescharacteristic, complemented
96C3×C11(C11⋊C5)⋊AGL(1,𝔽5)11yescharacteristic, complemented
97C2×C3×C5—12101no—
98C3×D5#1192589511yescharacteristic
99C52—2421noSylow
100C2×C11—51no—
101C2×C11—51no—
102C2×C11—105no—
103AGL(1,𝔽5)—331no—
104C4×C5—18151no—
105C3×C5—4841no—
106C3×C5—2421no—
107C3×C5#1455905411yescharacteristic, complemented
108Dic3—551noHall
109C11—25no—
110C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))11yescharacteristic, complemented
111C11C11⋊C5×ΓL(1,𝔽16)11yescharacteristic, complemented
112C2×C5—12101no—
113D5C3⋊#1192589511yescharacteristic
114C2×C3—51no—
115C5—4841no—
116C5—2421no—
117C5C3⋊#1455905411yescharacteristic, complemented
118C4—1651noSylow
119C3#2713089611yescharacteristic, complemented, Sylow
120C2—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. C11×C3⋊(C11⋊AGL(1,𝔽5))C5semidirect
11. C5×#10597243Dic3semidirect
14. C3×C5×C112C4×C5semidirect
16. C3×#10597243AGL(1,𝔽5)semidirect
29. C3⋊(C11⋊AGL(1,𝔽5))C11⋊C5semidirect
33. C5×C112C5×Dic3semidirect
35. #10597243ΓL(1,𝔽16)semidirect
40. C3×C112C5×AGL(1,𝔽5)semidirect
57. C3×C5×C11Dic11⋊C5semidirect
58. C3×C5×C11C4×C11⋊C5semidirect
68. C112C5×ΓL(1,𝔽16)semidirect
83. C5×C11Dic3×C11⋊C5semidirect
84. C5×C11C3⋊(Dic11⋊C5)semidirect
95. C3×C11AGL(1,𝔽5)×C11⋊C5semidirect
96. C3×C11(C11⋊C5)⋊AGL(1,𝔽5)semidirect
107. C3×C5#14559054semidirect
110. C11C3⋊((C11⋊C5)⋊AGL(1,𝔽5))semidirect
111. C11C11⋊C5×ΓL(1,𝔽16)semidirect
117. C5C3⋊#14559054semidirect
119. C3#27130896semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#105972432
#271308963
C11×C3⋊(C11⋊AGL(1,𝔽5))5
C3⋊#145590545
C11⋊C5×ΓL(1,𝔽16)11
C3⋊((C11⋊C5)⋊AGL(1,𝔽5))11