Finite Group Databasebeta

← C5×C3⋊#14559049 #49137265

Subgroups — C5×C3⋊#14559049 #49137265

Order 36300.

120 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 26 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×#10597245C211yesmaximal, characteristic
2C5×#14559049—31nomaximal, Hall
3C3×C5×#10597245C411yescharacteristic, complemented, Hall
4C5×C11×Dic33—51nomaximal
5C3⋊#14559049C511yesmaximal, characteristic, direct product factor
6C2×C5×#10597245D311yescharacteristic
7C2×C3×#10597245—22no—
8C2×C3×#10597245C2×C511yescharacteristic
9C2×C3×C5×C112D511yescharacteristic
10C5×#10597245Dic311yescharacteristic, complemented, Hall
11C5×C11×Dic11—151no—
12#14559049—31no—
13C3×C5×C112Dic511yescharacteristic, complemented
14C3×#10597245—22no—
15C3×#10597245C4×C511yescharacteristic, complemented
16C2×C3×C5×C11⋊C5—221no—
17C11×Dic33—51noHall
18C2×C5×C112D1511yescharacteristic
19C2×#10597245—22no—
20C2×#10597245C5×D311yescharacteristic
21C3×C5×C11⋊C5—221no—
22C2×C3×C112C5×D511yescharacteristic
23C5×Dic33—51no—
24C5×C11×Dic3—551no—
25C5×C112Dic1511yescharacteristic, complemented
26#10597245—22no—
27#10597245C5×Dic311yescharacteristic, complemented
28C2×C5×C11⋊C5—221no—
29C11×Dic11—151noHall
30C3×C112C5×Dic511yescharacteristic, complemented, Hall
31C2×C3×C5×C11—21no—
32C2×C3×C5×C11—101no—
33C2×C3×C5×C11—101no—
34C2×C3×C11⋊C5—224no—
35C2×C3×C11⋊C5—221no—
36C5×Dic15—1211nomaximal, Hall
37C5×C11⋊C5—221no—
38C2×C112C5×D1511yescharacteristic
39C4×C5×C11—1651no—
40C5×Dic11—151no—
41C3×C5×C11—21no—
42C3×C5×C11—101no—
43C3×C5×C11—101no—
44C3×C11⋊C5—224no—
45C3×C11⋊C5—221no—
46C2×C3×C52—2421no—
47Dic33—51no—
48C11×Dic3—551no—
49C112C5×Dic1511yescharacteristic, complemented, Sylow
50C2×C5×C11—21no—
51C2×C5×C11—101no—
52C2×C5×C11—101no—
53C2×C11⋊C5—221no—
54C2×C11⋊C5—224no—
55C5×Dic5—3631noHall
56C3×C52—2421noHall
57C2×C3×C11—21no—
58C2×C3×C11—101no—
59C2×C3×C11—101no—
60Dic15—1211no—
61C5×Dic3—551no—
62C5×C11—21no—
63C5×C11—101no—
64C5×C11—101no—
65C11⋊C5—221no—
66C11⋊C5—224no—
67C2×C52—1211no—
68C4×C11—1651no—
69Dic11—151no—
70C3×C11—21no—
71C3×C11—101no—
72C3×C11—101no—
73C2×C3×C5—2421no—
74C2×C3×C5—2422no—
75C2×C3×C5#1192589011yescharacteristic
76C52—1211noSylow
77C2×C11—21no—
78C2×C11—101no—
79C2×C11—101no—
80C4×C5—1651no—
81Dic5—3631no—
82C3×C5—2421no—
83C3×C5—2422no—
84C3×C5#1455904911yescharacteristic, complemented
85Dic3—551noHall
86C11—21no—
87C11—101no—
88C11—101no—
89C2×C5—1211no—
90C2×C5—2422no—
91C2×C5C3⋊#1192589011yescharacteristic
92C2×C3C5×#1192589011yescharacteristic
93C5—1211no—
94C5—2422no—
95C5C3⋊#1455904911yescharacteristic, direct product factor
96C4—1651noSylow
97C3C5×#1455904911yescharacteristic, complemented, Sylow
98C2C5×C3⋊#1192589011yescharacteristic
subgroupG/H
center, hypercenterC2×C5C3⋊#11925890
commutator, hypocenterC3×#10597245C4×C5
FrattiniC2C5×C3⋊#11925890
Fitting, socleC2×C3×C5×C112D5
prime radicalC2×C3×C5×#10597245C2
cosocleC2×C3×#10597245C2×C5
LCSG ▷ C3×#10597245
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
3. C3×C5×#10597245C4semidirect
5. C3⋊#14559049C5direct (N × H)
10. C5×#10597245Dic3semidirect
13. C3×C5×C112Dic5semidirect
15. C3×#10597245C4×C5semidirect
25. C5×C112Dic15semidirect
27. #10597245C5×Dic3semidirect
30. C3×C112C5×Dic5semidirect
49. C112C5×Dic15semidirect
84. C3×C5#14559049semidirect
95. C5C3⋊#14559049direct (N × H)
97. C3C5×#14559049semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#105972452
C5×#145590493
C5×C11×Dic335
C3⋊#145590495
C5×Dic15121