Finite Group Databasebeta

← C5×#20300106 #49137749

Subgroups — C5×#20300106 #49137749

Order 36300.

352 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 50 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×C52×C11⋊D11C211yesmaximal, characteristic, complemented
2C5×C11×D165C212yesmaximal, complemented
3C5×D55⋊D11—31nomaximal, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5#20300106C511yesmaximal, characteristic, direct product factor
6C5×D33⋊D11—51nomaximal
7C5×C11×D55—32no—
8C52×C11⋊D11D311yescharacteristic, complemented
9C11×D165C2×C512yescomplemented
10C5×C11×D33—52no—
11C3×C5×C11⋊D11—22no—
12C3×C5×C11⋊D11D511yescharacteristic, complemented
13C3×C5×C11⋊D11C2×C511yescharacteristic, complemented
14C5×D11×D15—112nomaximal
15C52×C112C2×D311yescharacteristic, complemented, Hall
16D55⋊D11—31no—
17C5×D112—151no—
18C3×C5×C112—22no—
19C3×C5×C112C2×D511yescharacteristic, complemented
20C3×C5×C112C22×C511yescharacteristic, complemented
21C5×D165D1112yescomplemented
22C5×C11×D15—112no—
23C3×C52×D11—112no—
24C3×C52×D11—225no—
25D33⋊D11—51noHall
26C11×D55—32no—
27C5×C11⋊D11—22no—
28C5×C11⋊D11C5×D311yescharacteristic, complemented
29C5×C11⋊D11D1511yescharacteristic, complemented
30C5×C11×D11—152no—
31C5×D5×D11—332no—
32C3×C52×C11—25no—
33C3×C52×C11C2×D1112yescomplemented
34C11×D33—52no—
35C3×C11⋊D11C5×D511yescharacteristic, complemented
36D11×D15—112no—
37C5×D3×D11—552no—
38C5×C112—22no—
39C5×C112C2×C5×D311yescharacteristic, complemented
40C5×C112C2×D1511yescharacteristic, complemented
41C5×D55—32no—
42C5×D5×C11—332no—
43C52×D11—112no—
44C52×D11—225no—
45D112—151noHall
46C3×C112C2×C5×D511yescharacteristic, complemented, Hall
47D165C5×D1112yescomplemented
48C11×D15—112no—
49C5×D33—52no—
50C5×D3×C11—552no—
51C3×C5×D11—112no—
52C3×C5×D11—112no—
53C3×C5×D11—224no—
54C3×C5×D11—225no—
55C3×C5×D11—225no—
56C3×C5×D11—2220no—
57C2×C5×D15—1211noHall
58C52×C11—25no—
59C52×C11D3×D1112yescomplemented
60C11⋊D11C5×D1511yescharacteristic, complemented
61C11×D11—152no—
62C2×C5×D11—1652no—
63D5×D11—332no—
64C3×C5×C11—220no—
65C3×C5×C11—24no—
66C3×C5×C11—25no—
67C3×C5×C11—25no—
68C3×C5×C11D5×D1112yescomplemented
69C3×C5×C11C2×C5×D1112yescomplemented
70C2×C3×C52—1211no—
71C5×D15—112no—
72D3×D11—552no—
73C112C2×C5×D1511yescharacteristic, complemented, Sylow
74C2×C5×C11—1652no—
75D55—32no—
76C5×D11—112no—
77C5×D11—112no—
78C5×D11—152no—
79C5×D11—225no—
80C5×D11—225no—
81C5×D11—224no—
82C5×D11—2220no—
83D5×C11—332no—
84C2×C5×D5—3631noHall
85C3×C52D11211yescharacteristic, complemented, Hall
86D33—52no—
87C3×D11—112no—
88C3×D11—225no—
89D3×C11—552no—
90C2×D15—1211no—
91C2×C5×D3—6051no—
92C5×C11—220no—
93C5×C11—24no—
94C5×C11—25no—
95C5×C11—25no—
96C5×C11C5×D3×D1112yescomplemented
97C5×C11D11×D1512yescomplemented
98C2×C52—1211no—
99C5×D5—332no—
100C2×D11—1652no—
101C3×C11—25no—
102C3×C11C5×D5×D1112yescomplemented
103C2×C3×C5—1211no—
104C2×C3×C5—1211no—
105C2×C3×C5—2422no—
106D15—112no—
107C5×D3—552no—
108C52D33⋊D1111yescharacteristic, complemented, Sylow
109C2×C11—1652no—
110D11—112no—
111D11—152no—
112D11—225no—
113C22×C5—18151no—
114C2×D5—3631no—
115C3×C5—22no—
116C3×C5C5×D11211yescharacteristic, complemented
117C3×C5D55⋊D1111yescharacteristic, complemented
118C2×D3—6051noHall
119C11—25no—
120C11C5×D11×D1512yescomplemented
121C2×C5—1211no—
122C2×C5—1211no—
123C2×C5—1652no—
124C2×C5—2422no—
125D5—332no—
126C2×C3—1211no—
127D3—552no—
128C5—22no—
129C5C5×D33⋊D1111yescharacteristic, complemented
130C5#2030010611yescharacteristic, direct product factor
131C22—18151noSylow
132C3C5×D55⋊D1111yescharacteristic, complemented, Sylow
133C2—1211no—
134C2—1652no—
subgroupG/H
center, hypercenterC5#20300106
commutator, cosocle, hypocenterC3×C5×C112C22×C5
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C3×C5×C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11⋊D11C2semidirect
2. C5×C11×D165C2semidirect
4. C3×C52×C112C22semidirect
5. #20300106C5direct (N × H)
8. C52×C11⋊D11D3semidirect
9. C11×D165C2×C5semidirect
12. C3×C5×C11⋊D11D5semidirect
13. C3×C5×C11⋊D11C2×C5semidirect
15. C52×C112C2×D3semidirect
19. C3×C5×C112C2×D5semidirect
20. C3×C5×C112C22×C5semidirect
21. C5×D165D11semidirect
28. C5×C11⋊D11C5×D3semidirect
29. C5×C11⋊D11D15semidirect
33. C3×C52×C11C2×D11semidirect
35. C3×C11⋊D11C5×D5semidirect
39. C5×C112C2×C5×D3semidirect
40. C5×C112C2×D15semidirect
46. C3×C112C2×C5×D5semidirect
47. D165C5×D11semidirect
59. C52×C11D3×D11semidirect
60. C11⋊D11C5×D15semidirect
68. C3×C5×C11D5×D11semidirect
69. C3×C5×C11C2×C5×D11semidirect
73. C112C2×C5×D15semidirect
85. C3×C52D112semidirect
96. C5×C11C5×D3×D11semidirect
97. C5×C11D11×D15semidirect
102. C3×C11C5×D5×D11semidirect
108. C52D33⋊D11semidirect
116. C3×C5C5×D112semidirect
117. C3×C5D55⋊D11semidirect
120. C11C5×D11×D15semidirect
129. C5C5×D33⋊D11semidirect
130. C5#20300106direct (N × H)
132. C3C5×D55⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11⋊D112
C5×C11×D1652
C5×D55⋊D113
#203001065
C5×D33⋊D115
C5×D11×D1511