Finite Group Databasebeta

← C2×C3×C5×C22⋊D5 #11925684

Subgroups — C2×C3×C5×C22⋊D5 #11925684

Order 1200.

280 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C23×C3×C52C211yesmaximal, characteristic, complemented
2C22×C3×C5×D5C211yesmaximal, characteristic, complemented
3C3×C5×C22⋊D5C214yesmaximal, direct product factor
4C2×C3×C5×Dic5C211yesmaximal, characteristic, complemented
5C2×C5×C22⋊D5C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C52—22no—
7C22×C3×C52C2211yescharacteristic
8C22×C3×C52C2212yescomplemented
9C2×C3×C5×D5—22no—
10C2×C3×C5×D5C2212yescomplemented
11C3×C5×Dic5C2212yescomplemented
12C2×C3×C5×D4—51nomaximal
13C2×C3×C22⋊D5C511yesmaximal, characteristic, direct product factor
14C23×C52C2×C311yescharacteristic, complemented
15C22×C5×D5C2×C311yescharacteristic, complemented
16C5×C22⋊D5C2×C314yesdirect product factor
17C2×C5×Dic5C2×C311yescharacteristic, complemented
18C2×C3×C52—22no—
19C2×C3×C52D412yescomplemented
20C2×C3×C52C2311yescharacteristic
21C3×C5×D5—22no—
22C23×C3×C5—22no—
23C23×C3×C5—51no—
24C23×C3×C5D511yescharacteristic, complemented
25C23×C3×C5C2×C511yescharacteristic, complemented
26C22×C3×D5C2×C511yescharacteristic, complemented
27C3×C5×D4—54no—
28C2×C3×C4×C5—51no—
29C3×C22⋊D5C2×C514yesdirect product factor
30C2×C3×Dic5C2×C511yescharacteristic, complemented
31C22×C52—22no—
32C22×C52C22×C311yescharacteristic
33C22×C52C22×C312yescomplemented
34C2×C5×D5—22no—
35C2×C5×D5C22×C312yescomplemented
36C5×Dic5C22×C312yescomplemented
37C2×C5×D4—51no—
38C2×C22⋊D5C3×C511yescharacteristic, direct product factor
39C3×C52C2×D411yescharacteristic, complemented, Hall
40C22×C3×C5—28no—
41C22×C3×C5—22no—
42C22×C3×C5—22no—
43C22×C3×C5—22no—
44C22×C3×C5—24no—
45C22×C3×C5—52no—
46C22×C3×C5—102no—
47C22×C3×C5C2×D511yescharacteristic
48C22×C3×C5C2×D512yescomplemented
49C22×C3×C5C22×C511yescharacteristic
50C22×C3×C5C22×C512yescomplemented
51C2×C3×D5—22no—
52C2×C3×D5C22×C512yescomplemented
53C3×C4×C5—52no—
54C3×Dic5C22×C512yescomplemented
55C2×C52—22no—
56C2×C52C3×D412yescomplemented
57C2×C52C23×C311yescharacteristic
58C5×D5—22no—
59C2×C3×D4—51noHall
60C23×C5—22no—
61C23×C5—51no—
62C23×C5C3×D511yescharacteristic, complemented
63C23×C5C2×C3×C511yescharacteristic, complemented
64C22×D5C2×C3×C511yescharacteristic, complemented
65C5×D4—54no—
66C2×C4×C5—51no—
67C22⋊D5C2×C3×C514yesdirect product factor
68C2×Dic5C2×C3×C511yescharacteristic, complemented
69C2×C3×C5—28no—
70C2×C3×C5—22no—
71C2×C3×C5—22no—
72C2×C3×C5—24no—
73C2×C3×C5—22no—
74C2×C3×C5—102no—
75C2×C3×C5C22⋊D512yesdirect product factor
76C2×C3×C5C5×D412yescomplemented
77C2×C3×C5C22×D511yescharacteristic
78C2×C3×C5C23×C511yescharacteristic
79C3×D5—22no—
80C52C2×C3×D411yescharacteristic, complemented, Sylow
81C23×C3—51no—
82C23×C3C5×D511yescharacteristic, complemented
83C3×D4—54no—
84C2×C3×C4—51no—
85C22×C5—28no—
86C22×C5—22no—
87C22×C5—22no—
88C22×C5—22no—
89C22×C5—24no—
90C22×C5—52no—
91C22×C5—102no—
92C22×C5C2×C3×D511yescharacteristic
93C22×C5C2×C3×D512yescomplemented
94C22×C5C22×C3×C511yescharacteristic
95C22×C5C22×C3×C512yescomplemented
96C2×D5—22no—
97C2×D5C22×C3×C512yescomplemented
98C4×C5—52no—
99Dic5C22×C3×C512yescomplemented
100C2×D4—51noSylow
101C3×C5—22no—
102C3×C5C2×C22⋊D511yescharacteristic, direct product factor
103C3×C5C2×C5×D411yescharacteristic, complemented
104C22×C3—22no—
105C22×C3—52no—
106C22×C3—102no—
107C22×C3C2×C5×D511yescharacteristic
108C22×C3C2×C5×D512yescomplemented
109C3×C4—52no—
110C2×C5—28no—
111C2×C5—22no—
112C2×C5—22no—
113C2×C5—24no—
114C2×C5—22no—
115C2×C5—102no—
116C2×C5C3×C22⋊D512yesdirect product factor
117C2×C5C3×C5×D412yescomplemented
118C2×C5C22×C3×D511yescharacteristic
119C2×C5C23×C3×C511yescharacteristic
120D5—22no—
121C23—51no—
122C23C3×C5×D511yescharacteristic, complemented
123D4—54no—
124C2×C4—51no—
125C2×C3—22no—
126C2×C3—102no—
127C2×C3C5×C22⋊D512yesdirect product factor
128C2×C3C22×C5×D511yescharacteristic
129C5—22no—
130C5C2×C3×C22⋊D511yescharacteristic, direct product factor
131C5C2×C3×C5×D411yescharacteristic, complemented
132C22—22no—
133C22—52no—
134C22—102no—
135C22C2×C3×C5×D511yescharacteristic
136C22C2×C3×C5×D512yescomplemented
137C4—52no—
138C3C2×C5×C22⋊D511yescharacteristic, direct product factor, Sylow
139C2—22no—
140C2—102no—
141C2C3×C5×C22⋊D512yesdirect product factor
142C2C22×C3×C5×D511yescharacteristic
subgroupG/H
centerC22×C3×C5C2×D5
commutator, cosocleC2×C5C23×C3×C5
FrattiniC2C22×C3×C5×D5
FittingC23×C3×C52C2
socleC22×C3×C52C22
hypercenterC23×C3×C5D5
hypocenterC5C2×C3×C5×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C5 ◁ C23×C3×C5

Complements

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

NH ≅ G/Ntype
1. C23×C3×C52C2semidirect
2. C22×C3×C5×D5C2semidirect
3. C3×C5×C22⋊D5C2direct (N × H)
4. C2×C3×C5×Dic5C2semidirect
5. C2×C5×C22⋊D5C3direct (N × H)
8. C22×C3×C52C22semidirect
10. C2×C3×C5×D5C22semidirect
11. C3×C5×Dic5C22semidirect
13. C2×C3×C22⋊D5C5direct (N × H)
14. C23×C52C2×C3semidirect
15. C22×C5×D5C2×C3semidirect
16. C5×C22⋊D5C2×C3direct (N × H)
17. C2×C5×Dic5C2×C3semidirect
19. C2×C3×C52D4semidirect
24. C23×C3×C5D5semidirect
25. C23×C3×C5C2×C5semidirect
26. C22×C3×D5C2×C5semidirect
29. C3×C22⋊D5C2×C5direct (N × H)
30. C2×C3×Dic5C2×C5semidirect
33. C22×C52C22×C3semidirect
35. C2×C5×D5C22×C3semidirect
36. C5×Dic5C22×C3semidirect
38. C2×C22⋊D5C3×C5direct (N × H)
39. C3×C52C2×D4semidirect
48. C22×C3×C5C2×D5semidirect
50. C22×C3×C5C22×C5semidirect
52. C2×C3×D5C22×C5semidirect
54. C3×Dic5C22×C5semidirect
56. C2×C52C3×D4semidirect
62. C23×C5C3×D5semidirect
63. C23×C5C2×C3×C5semidirect
64. C22×D5C2×C3×C5semidirect
67. C22⋊D5C2×C3×C5direct (N × H)
68. C2×Dic5C2×C3×C5semidirect
75. C2×C3×C5C22⋊D5direct (N × H)
76. C2×C3×C5C5×D4semidirect
80. C52C2×C3×D4semidirect
82. C23×C3C5×D5semidirect
93. C22×C5C2×C3×D5semidirect
95. C22×C5C22×C3×C5semidirect
97. C2×D5C22×C3×C5semidirect
99. Dic5C22×C3×C5semidirect
102. C3×C5C2×C22⋊D5direct (N × H)
103. C3×C5C2×C5×D4semidirect
108. C22×C3C2×C5×D5semidirect
116. C2×C5C3×C22⋊D5direct (N × H)
117. C2×C5C3×C5×D4semidirect
122. C23C3×C5×D5semidirect
127. C2×C3C5×C22⋊D5direct (N × H)
130. C5C2×C3×C22⋊D5direct (N × H)
131. C5C2×C3×C5×D4semidirect
136. C22C2×C3×C5×D5semidirect
138. C3C2×C5×C22⋊D5direct (N × H)
141. C2C3×C5×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C522
C22×C3×C5×D52
C3×C5×C22⋊D52
C2×C3×C5×Dic52
C2×C5×C22⋊D53
C2×C3×C5×D45
C2×C3×C22⋊D55