Finite Group Databasebeta

← C5×C3⋊#14559056 #49137258

Subgroups — C5×C3⋊#14559056 #49137258

Order 36300.

200 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C3×C5×#10597244C211yesmaximal, characteristic
2C5×#14559056—31nomaximal, Hall
3C3×C5×#10597244C411yescharacteristic, complemented, Hall
4C5×C11×Dic33C511yesmaximal, characteristic, complemented
5C3⋊#14559056C515yesmaximal, direct product factor
6C2×C5×#10597244D311yescharacteristic
7C2×C3×#10597244C2×C515yes—
8C2×C3×C5×C112C2×C511yescharacteristic
9C5×C3⋊(Dic11⋊C5)—111nomaximal
10C5×Dic3×C11⋊C5—111nomaximal
11C5×#10597244Dic311yescharacteristic, complemented, Hall
12C5×C11×Dic11—31no—
13#14559056—35no—
14C3×C5×C112C4×C511yescharacteristic, complemented
15C3×#10597244C4×C515yescomplemented
16C2×C3×C5×C11⋊C5—111no—
17C2×C3×C5×C11⋊C5—111no—
18C11×Dic33C5211yescharacteristic, complemented, Hall
19C2×C5×C112C5×D311yescharacteristic
20C2×#10597244C5×D315yes—
21C4×C5×C11⋊C5—331no—
22C5×Dic11⋊C5—331no—
23C3×C5×C11⋊C5—111no—
24C3×C5×C11⋊C5—111no—
25C2×C3×C112C2×C5211yescharacteristic
26C5×Dic33C11⋊C511yescharacteristic, complemented
27C5×C11×Dic3—551no—
28C3⋊(Dic11⋊C5)—115no—
29Dic3×C11⋊C5—115no—
30C5×C112C5×Dic311yescharacteristic, complemented
31#10597244C5×Dic315yescomplemented
32C2×C5×C11⋊C5—111no—
33C2×C5×C11⋊C5—111no—
34C11×Dic11—31noHall
35C3×C112C4×C5211yescharacteristic, complemented, Hall
36C2×C3×C5×C11—101no—
37C2×C3×C5×C11AGL(1,𝔽11)11yescharacteristic
38C2×C3×C5×C11C2×C11⋊C511yescharacteristic
39C2×C3×C11⋊C5—115no—
40C2×C3×C11⋊C5—115no—
41C52×Dic3—1211noHall
42C5×C11⋊C5—111no—
43C5×C11⋊C5—111no—
44C2×C112C52×D311yescharacteristic
45C4×C5×C11—1651no—
46C5×Dic11—31no—
47C4×C11⋊C5—335no—
48Dic11⋊C5—335no—
49C3×C5×C11—101no—
50C3×C5×C11Dic11⋊C511yescharacteristic, complemented
51C3×C5×C11C4×C11⋊C511yescharacteristic, complemented
52C3×C11⋊C5—115no—
53C3×C11⋊C5—115no—
54C2×C3×C52—1211no—
55Dic33C5×C11⋊C511yescharacteristic, complemented
56C11×Dic3—551no—
57C112C52×Dic311yescharacteristic, complemented, Sylow
58C2×C5×C11—101no—
59C2×C5×C11D3×C11⋊C511yescharacteristic
60C2×C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic
61C2×C11⋊C5—115no—
62C2×C11⋊C5—115no—
63C4×C52—3631noHall
64C3×C52—1211noHall
65C2×C3×C11—101no—
66C2×C3×C11C5×AGL(1,𝔽11)11yescharacteristic
67C2×C3×C11C2×C5×C11⋊C511yescharacteristic
68C5×Dic3—551no—
69C5×Dic3—1215no—
70C5×C11—101no—
71C5×C11Dic3×C11⋊C511yescharacteristic, complemented
72C5×C11C3⋊(Dic11⋊C5)11yescharacteristic, complemented
73C11⋊C5—115no—
74C11⋊C5—115no—
75C2×C52—1211no—
76C4×C11—1651no—
77Dic11—31no—
78C3×C11—101no—
79C3×C11C5×Dic11⋊C511yescharacteristic, complemented
80C3×C11C4×C5×C11⋊C511yescharacteristic, complemented
81C2×C3×C5—1215no—
82C2×C3×C5#1192589711yescharacteristic
83C52—1211noSylow
84C2×C11—101no—
85C2×C11C5×D3×C11⋊C511yescharacteristic
86C2×C11C5×C3⋊AGL(1,𝔽11)11yescharacteristic
87C4×C5—331no—
88C4×C5—3635no—
89C3×C5—1215no—
90C3×C5#1455905611yescharacteristic, complemented
91Dic3—551noHall
92C11—101no—
93C11C5×Dic3×C11⋊C511yescharacteristic, complemented
94C11C5×C3⋊(Dic11⋊C5)11yescharacteristic, complemented
95C2×C5—1215no—
96C2×C5C3⋊#1192589711yescharacteristic
97C2×C3C5×#1192589711yescharacteristic
98C5—1215no—
99C5C3⋊#1455905611yescharacteristic, direct product factor
100C4—331noSylow
101C3C5×#1455905611yescharacteristic, complemented, Sylow
102C2C5×C3⋊#1192589711yescharacteristic
subgroupG/H
center, hypercenterC2×C5C3⋊#11925897
commutator, hypocenterC3×C112C4×C52
FrattiniC2C5×C3⋊#11925897
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×#10597244C2
cosocleC2×C3×C112C2×C52
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
3. C3×C5×#10597244C4semidirect
4. C5×C11×Dic33C5semidirect
5. C3⋊#14559056C5direct (N × H)
11. C5×#10597244Dic3semidirect
14. C3×C5×C112C4×C5semidirect
15. C3×#10597244C4×C5semidirect
18. C11×Dic33C52semidirect
26. C5×Dic33C11⋊C5semidirect
30. C5×C112C5×Dic3semidirect
31. #10597244C5×Dic3semidirect
35. C3×C112C4×C52semidirect
50. C3×C5×C11Dic11⋊C5semidirect
51. C3×C5×C11C4×C11⋊C5semidirect
55. Dic33C5×C11⋊C5semidirect
57. C112C52×Dic3semidirect
71. C5×C11Dic3×C11⋊C5semidirect
72. C5×C11C3⋊(Dic11⋊C5)semidirect
79. C3×C11C5×Dic11⋊C5semidirect
80. C3×C11C4×C5×C11⋊C5semidirect
90. C3×C5#14559056semidirect
93. C11C5×Dic3×C11⋊C5semidirect
94. C11C5×C3⋊(Dic11⋊C5)semidirect
99. C5C3⋊#14559056direct (N × H)
101. C3C5×#14559056semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#105972442
C5×#145590563
C5×C11×Dic335
C3⋊#145590565
C5×C3⋊(Dic11⋊C5)11
C5×Dic3×C11⋊C511