Finite Group Databasebeta

← C5×D3×#11925890 #49137414

Subgroups — C5×D3×#11925890 #49137414

Order 36300.

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

normal subgroups only

This group has 168 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
1C5×C3⋊#11925890C211yesmaximal, characteristic, complemented
2C5×D3×#10597245C211yesmaximal, characteristic, complemented
3C3×C5×#11925890C211yesmaximal, characteristic, complemented
4C2×C5×#11925890—31nomaximal, Hall
5C3×C5×#10597245C2211yescharacteristic, complemented, Hall
6C5×D3×C11×D11—51nomaximal
7D3×#11925890C511yesmaximal, characteristic, direct product factor
8C2×C5×#10597245—31no—
9C5×#11925890—31no—
10C5×#11925890D311yescharacteristic, direct product factor
11C5×C11×D33—51no—
12C5×D3×C112D511yescharacteristic, complemented
13C3×C5×C11×D11—51no—
14C3⋊#11925890C2×C511yescharacteristic, complemented
15D3×#10597245—22no—
16D3×#10597245C2×C511yescharacteristic, complemented
17C3×#11925890C2×C511yescharacteristic, complemented
18C5×#10597245C2×D311yescharacteristic, complemented, Hall
19C2×C5×C11×D11—151no—
20C2×#11925890—31no—
21C3×C5×C112C2×D511yescharacteristic, complemented
22C3×#10597245—22no—
23C3×#10597245C22×C511yescharacteristic, complemented
24C5×D3×C11⋊C5—221no—
25D3×C11×D11—51noHall
26C2×C5×C112—31no—
27C5×C11×D11—51no—
28C5×C11×D11—151no—
29C2×#10597245—31no—
30C2×#10597245—62no—
31#11925890—31no—
32#11925890C5×D311yescharacteristic, direct product factor
33C3×C5×C11⋊C5—221no—
34C11×D33—51no—
35D3×C112C5×D511yescharacteristic, complemented
36C3×C11×D11—51no—
37C2×C5×D3×C11—551no—
38C5×D3×D11—51no—
39C5×C112D3×D511yescharacteristic, complemented
40#10597245—22no—
41#10597245C2×C5×D311yescharacteristic, complemented
42C2×C5×C11⋊C5—661no—
43C2×C11×D11—151noHall
44C3×C112C2×C5×D511yescharacteristic, complemented, Hall
45C2×C3×C5×C11—551no—
46C5×D33—51no—
47C5×D3×C11—21no—
48C5×D3×C11—101no—
49C5×D3×C11—101no—
50C5×D3×C11—551no—
51C3×C5×D11—51no—
52D3×C11⋊C5—224no—
53D3×C11⋊C5—221no—
54C5×D3×D5—1211nomaximal, Hall
55C5×C11⋊C5—221no—
56C2×C112—31no—
57C11×D11—51no—
58C11×D11—151no—
59C22×C5×C11—1651no—
60C2×C5×D11—151no—
61C3×C5×C11—21no—
62C3×C5×C11—101no—
63C3×C5×C11—101no—
64C3×C11⋊C5—224no—
65C3×C11⋊C5—221no—
66C5×D15—1211no—
67C52×D3—2421no—
68C3×C5×D5—1211no—
69C2×D3×C11—551no—
70D3×D11—51no—
71C112C5×D3×D511yescharacteristic, complemented, Sylow
72C2×C5×C11—61no—
73C2×C5×C11—301no—
74C2×C5×C11—301no—
75C2×C5×C11—551no—
76C2×C5×C11—1651no—
77C5×D11—51no—
78C5×D11—151no—
79C2×C11⋊C5—661no—
80C2×C11⋊C5—664no—
81C2×C5×D5—3631noHall
82C3×C52—2421noHall
83C2×C3×C11—551no—
84D33—51no—
85C3×D11—51no—
86D3×C11—21no—
87D3×C11—101no—
88D3×C11—101no—
89D3×C11—551no—
90C2×C5×D3—551no—
91D3×D5—1211no—
92C5×C11—21no—
93C5×C11—101no—
94C5×C11—101no—
95C11⋊C5—224no—
96C11⋊C5—221no—
97C2×C52—7261no—
98C5×D5—3631no—
99C5×D5—1211no—
100C22×C11—1651no—
101C2×D11—151no—
102C3×C11—21no—
103C3×C11—101no—
104C3×C11—101no—
105C2×C3×C5—551no—
106D15—1211no—
107C3×D5—1211no—
108C5×D3—551no—
109C5×D3—2421no—
110C5×D3—2422no—
111C5×D3#1192589011yescharacteristic, direct product factor
112C52—2421noSylow
113C2×C11—61no—
114C2×C11—151no—
115C2×C11—151no—
116C2×C11—551no—
117C2×C11—1651no—
118D11—51no—
119D11—151no—
120C22×C5—1651no—
121C2×D5—3631no—
122C3×C5—2421no—
123C3×C5—2422no—
124C3×C5C2×#1192589011yescharacteristic, complemented
125C2×D3—551noHall
126C11—21no—
127C11—51no—
128C11—51no—
129C2×C5—31no—
130C2×C5—551no—
131C2×C5—1651no—
132C2×C5—7261no—
133C2×C5—7262no—
134D5—3631no—
135D5—1211no—
136C2×C3—551no—
137D3—551no—
138D3C5×#1192589011yescharacteristic, direct product factor
139C5—2421no—
140C5—2422no—
141C5D3×#1192589011yescharacteristic, direct product factor
142C22—1651noSylow
143C3C2×C5×#1192589011yescharacteristic, complemented, Sylow
144C2—31no—
145C2—551no—
146C2—1651no—
subgroupG/H
center, hypercenterC5D3×#11925890
commutator, cosocle, hypocenterC3×#10597245C22×C5
FrattiniC1G
Fitting, socleC3×C5×C112C2×D5
LCSG ▷ C3×#10597245
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊#11925890C2semidirect
2. C5×D3×#10597245C2semidirect
3. C3×C5×#11925890C2semidirect
5. C3×C5×#10597245C22semidirect
7. D3×#11925890C5direct (N × H)
10. C5×#11925890D3direct (N × H)
12. C5×D3×C112D5semidirect
14. C3⋊#11925890C2×C5semidirect
16. D3×#10597245C2×C5semidirect
17. C3×#11925890C2×C5semidirect
18. C5×#10597245C2×D3semidirect
21. C3×C5×C112C2×D5semidirect
23. C3×#10597245C22×C5semidirect
32. #11925890C5×D3direct (N × H)
35. D3×C112C5×D5semidirect
39. C5×C112D3×D5semidirect
41. #10597245C2×C5×D3semidirect
44. C3×C112C2×C5×D5semidirect
71. C112C5×D3×D5semidirect
111. C5×D3#11925890direct (N × H)
124. C3×C5C2×#11925890semidirect
138. D3C5×#11925890direct (N × H)
141. C5D3×#11925890direct (N × H)
143. C3C2×C5×#11925890semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊#119258902
C5×D3×#105972452
C3×C5×#119258902
C2×C5×#119258903
C5×D3×C11×D115
D3×#119258905
C5×D3×D5121