Finite Group Databasebeta

← C3×C5×D55⋊D11 #49137711

Subgroups — C3×C5×D55⋊D11 #49137711

Order 36300.

352 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 60 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
2C3×C5×C11×D55C212yesmaximal, complemented
3C5×D55⋊D11C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C112C2211yescharacteristic, complemented, Hall
5C3×D55⋊D11C511yesmaximal, characteristic, direct product factor
6C3×C5×D112—51nomaximal
7C5×C11×D55C2×C312yescomplemented
8C52×C11⋊D11C2×C311yescharacteristic, complemented
9C3×C11×D55C2×C512yescomplemented
10C3×C5×C11⋊D11—22no—
11C3×C5×C11⋊D11D511yescharacteristic, complemented
12C3×C5×C11⋊D11C2×C511yescharacteristic, complemented
13C3×C5×C11×D11—52no—
14C3×C5×D5×D11—112nomaximal
15C52×C112C22×C311yescharacteristic, complemented, Hall
16D55⋊D11C3×C511yescharacteristic, direct product factor
17C5×D112—51no—
18C3×C5×C112—22no—
19C3×C5×C112C2×D511yescharacteristic, complemented
20C3×C5×C112C22×C511yescharacteristic, complemented
21C3×C5×D55D1112yescomplemented
22C3×C5×D5×C11—112no—
23C3×C52×D11—112no—
24C3×C52×D11—225no—
25C3×D112—51noHall
26C11×D55C2×C3×C512yescomplemented
27C5×C11⋊D11—22no—
28C5×C11⋊D11C3×D511yescharacteristic, complemented
29C5×C11⋊D11C2×C3×C511yescharacteristic, complemented
30C5×C11×D11—52no—
31C5×D5×D11—112no—
32C3×C52×C11—25no—
33C3×C52×C11C2×D1112yescomplemented
34C3×C11⋊D11C5×D511yescharacteristic, complemented
35C3×C11×D11—52no—
36C2×C3×C5×D11—552no—
37C3×D5×D11—112no—
38C5×C112—22no—
39C5×C112C2×C3×D511yescharacteristic, complemented
40C5×C112C22×C3×C511yescharacteristic, complemented
41C5×D55C3×D1112yescomplemented
42C5×D5×C11—112no—
43C52×D11—112no—
44C52×D11—225no—
45D112—51noHall
46C3×C112C2×C5×D511yescharacteristic, complemented, Hall
47C2×C3×C5×C11—552no—
48C3×D55C5×D1112yescomplemented
49C3×D5×C11—112no—
50C3×C5×D11—52no—
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×C3×C5×D5—1211noHall
58C52×C11—25no—
59C52×C11C2×C3×D1112yescomplemented
60C11⋊D11C3×C5×D511yescharacteristic, complemented
61C11×D11—52no—
62C2×C5×D11—552no—
63D5×D11—112no—
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—
71C3×C5×D5—112no—
72C2×C3×D11—552no—
73C112C2×C3×C5×D511yescharacteristic, complemented, Sylow
74C2×C5×C11—552no—
75D55C3×C5×D1112yescomplemented
76C5×D11—52no—
77C5×D11—112no—
78C5×D11—112no—
79C5×D11—225no—
80C5×D11—225no—
81C5×D11—224no—
82C5×D11—2220no—
83D5×C11—112no—
84C2×C5×D5—1211noHall
85C3×C52D11211yescharacteristic, complemented, Hall
86C2×C3×C11—552no—
87C3×D11—52no—
88C3×D11—112no—
89C3×D11—225no—
90C22×C3×C5—6051no—
91C2×C3×D5—1211no—
92C5×C11—220no—
93C5×C11—24no—
94C5×C11—25no—
95C5×C11—25no—
96C5×C11C3×D5×D1112yescomplemented
97C5×C11C2×C3×C5×D1112yescomplemented
98C2×C52—1211no—
99C5×D5—112no—
100C2×D11—552no—
101C3×C11—25no—
102C3×C11C5×D5×D1112yescomplemented
103C2×C3×C5—552no—
104C2×C3×C5—1211no—
105C2×C3×C5—1211no—
106C2×C3×C5—2422no—
107C3×D5—112no—
108C52C3×D11211yescharacteristic, complemented, Sylow
109C2×C11—552no—
110D11—52no—
111D11—112no—
112D11—225no—
113C22×C5—6051no—
114C2×D5—1211no—
115C3×C5—22no—
116C3×C5C5×D11211yescharacteristic, complemented
117C3×C5D55⋊D1111yescharacteristic, direct product factor
118C22×C3—6051noHall
119C11—25no—
120C11C3×C5×D5×D1112yescomplemented
121C2×C5—552no—
122C2×C5—1211no—
123C2×C5—1211no—
124C2×C5—2422no—
125D5—112no—
126C2×C3—552no—
127C2×C3—1211no—
128C5—22no—
129C5C3×C5×D11211yescharacteristic, complemented
130C5C3×D55⋊D1111yescharacteristic, direct product factor
131C22—6051noSylow
132C3C5×D55⋊D1111yescharacteristic, direct product factor, Sylow
133C2—552no—
134C2—1211no—
subgroupG/H
center, hypercenterC3×C5D55⋊D11
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C5×C112
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11⋊D11C2semidirect
2. C3×C5×C11×D55C2semidirect
3. C5×D55⋊D11C3direct (N × H)
4. C3×C52×C112C22semidirect
5. C3×D55⋊D11C5direct (N × H)
7. C5×C11×D55C2×C3semidirect
8. C52×C11⋊D11C2×C3semidirect
9. C3×C11×D55C2×C5semidirect
11. C3×C5×C11⋊D11D5semidirect
12. C3×C5×C11⋊D11C2×C5semidirect
15. C52×C112C22×C3semidirect
16. D55⋊D11C3×C5direct (N × H)
19. C3×C5×C112C2×D5semidirect
20. C3×C5×C112C22×C5semidirect
21. C3×C5×D55D11semidirect
26. C11×D55C2×C3×C5semidirect
28. C5×C11⋊D11C3×D5semidirect
29. C5×C11⋊D11C2×C3×C5semidirect
33. C3×C52×C11C2×D11semidirect
34. C3×C11⋊D11C5×D5semidirect
39. C5×C112C2×C3×D5semidirect
40. C5×C112C22×C3×C5semidirect
41. C5×D55C3×D11semidirect
46. C3×C112C2×C5×D5semidirect
48. C3×D55C5×D11semidirect
59. C52×C11C2×C3×D11semidirect
60. C11⋊D11C3×C5×D5semidirect
68. C3×C5×C11D5×D11semidirect
69. C3×C5×C11C2×C5×D11semidirect
73. C112C2×C3×C5×D5semidirect
75. D55C3×C5×D11semidirect
85. C3×C52D112semidirect
96. C5×C11C3×D5×D11semidirect
97. C5×C11C2×C3×C5×D11semidirect
102. C3×C11C5×D5×D11semidirect
108. C52C3×D112semidirect
116. C3×C5C5×D112semidirect
117. C3×C5D55⋊D11direct (N × H)
120. C11C3×C5×D5×D11semidirect
129. C5C3×C5×D112semidirect
130. C5C3×D55⋊D11direct (N × H)
132. C3C5×D55⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C11⋊D112
C3×C5×C11×D552
C5×D55⋊D113
C3×D55⋊D115
C3×C5×D1125
C3×C5×D5×D1111