Finite Group Databasebeta

← C3×C5×D4×D5 #11925679

Subgroups — C3×C5×D4×D5 #11925679

Order 1200.

248 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C22×C3×C5×D5C212yesmaximal, complemented
2C3×C52×D4C211yesmaximal, characteristic, complemented
3C3×C5×C22⋊D5C212yesmaximal, complemented
4C3×C5×D20C211yesmaximal, characteristic, complemented
5C3×C4×C5×D5C211yesmaximal, characteristic, complemented
6C5×D4×D5C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C52C2212yescomplemented
8C2×C3×C5×D5—24no—
9C2×C3×C5×D5C2211yescharacteristic
10C2×C3×C5×D5C2212yescomplemented
11C3×C4×C52C2211yescharacteristic, complemented
12C3×C5×Dic5C2211yescharacteristic, complemented
13C2×C3×C5×D4—51nomaximal
14C3×D4×D5C511yesmaximal, characteristic, direct product factor
15C22×C5×D5C2×C312yescomplemented
16C52×D4C2×C311yescharacteristic, complemented
17C5×C22⋊D5C2×C312yescomplemented
18C5×D20C2×C311yescharacteristic, complemented
19C4×C5×D5C2×C311yescharacteristic, complemented
20C2×C3×C52—22no—
21C2×C3×C52C2311yescharacteristic
22C3×C5×D5—22no—
23C3×C5×D5D412yesdirect product factor
24C23×C3×C5—52no—
25C22×C3×D5C2×C512yescomplemented
26C3×C5×D4—22no—
27C3×C5×D4—52no—
28C3×C5×D4—51no—
29C3×C5×D4D511yescharacteristic, direct product factor
30C3×C5×D4C2×C511yescharacteristic, complemented
31C2×C3×C4×C5—51no—
32C3×C22⋊D5C2×C512yescomplemented
33C3×D20C2×C511yescharacteristic, complemented
34C3×C4×D5C2×C511yescharacteristic, complemented
35C22×C52C22×C312yescomplemented
36C2×C5×D5—24no—
37C2×C5×D5C22×C311yescharacteristic
38C2×C5×D5C22×C312yescomplemented
39C4×C52C22×C311yescharacteristic, complemented
40C5×Dic5C22×C311yescharacteristic, complemented
41C2×C5×D4—51no—
42D4×D5C3×C511yescharacteristic, direct product factor
43C3×C52C2×D411yescharacteristic, complemented, Hall
44C22×C3×C5—24no—
45C22×C3×C5—51no—
46C22×C3×C5—52no—
47C22×C3×C5—104no—
48C22×C3×C5C2×D512yescomplemented
49C22×C3×C5C22×C512yescomplemented
50C2×C3×D5—24no—
51C2×C3×D5C22×C511yescharacteristic
52C2×C3×D5C22×C512yescomplemented
53C3×C4×C5—22no—
54C3×C4×C5—51no—
55C3×C4×C5C2×D511yescharacteristic, complemented
56C3×C4×C5C22×C511yescharacteristic, complemented
57C3×Dic5C22×C511yescharacteristic, complemented
58C2×C52—22no—
59C2×C52C23×C311yescharacteristic
60C5×D5—22no—
61C5×D5C3×D412yesdirect product factor
62C2×C3×D4—51noHall
63C23×C5—52no—
64C22×D5C2×C3×C512yescomplemented
65C5×D4—22no—
66C5×D4—52no—
67C5×D4—51no—
68C5×D4C3×D511yescharacteristic, direct product factor
69C5×D4C2×C3×C511yescharacteristic, complemented
70C2×C4×C5—51no—
71C22⋊D5C2×C3×C512yescomplemented
72D20C2×C3×C511yescharacteristic, complemented
73C4×D5C2×C3×C511yescharacteristic, complemented
74C2×C3×C5—22no—
75C2×C3×C5—22no—
76C2×C3×C5—22no—
77C2×C3×C5—44no—
78C2×C3×C5—52no—
79C2×C3×C5—102no—
80C2×C3×C5C22×D511yescharacteristic
81C2×C3×C5C23×C511yescharacteristic
82C3×D5—22no—
83C3×D5C5×D412yesdirect product factor
84C52C2×C3×D411yescharacteristic, complemented, Sylow
85C23×C3—52no—
86C3×D4—52no—
87C3×D4—51no—
88C3×D4C5×D511yescharacteristic, direct product factor
89C2×C3×C4—51no—
90C22×C5—24no—
91C22×C5—51no—
92C22×C5—52no—
93C22×C5—104no—
94C22×C5C2×C3×D512yescomplemented
95C22×C5C22×C3×C512yescomplemented
96C2×D5—24no—
97C2×D5C22×C3×C511yescharacteristic
98C2×D5C22×C3×C512yescomplemented
99C4×C5—22no—
100C4×C5—51no—
101C4×C5C2×C3×D511yescharacteristic, complemented
102C4×C5C22×C3×C511yescharacteristic, complemented
103Dic5C22×C3×C511yescharacteristic, complemented
104C2×D4—51noSylow
105C3×C5—22no—
106C3×C5D4×D511yescharacteristic, direct product factor
107C3×C5C2×C5×D411yescharacteristic, complemented
108C22×C3—51no—
109C22×C3—52no—
110C22×C3—104no—
111C22×C3C2×C5×D512yescomplemented
112C3×C4—51no—
113C3×C4C2×C5×D511yescharacteristic, complemented
114C2×C5—22no—
115C2×C5—22no—
116C2×C5—22no—
117C2×C5—44no—
118C2×C5—52no—
119C2×C5—102no—
120C2×C5C22×C3×D511yescharacteristic
121C2×C5C23×C3×C511yescharacteristic
122D5—22no—
123D5C3×C5×D412yesdirect product factor
124C23—52no—
125D4—52no—
126D4—51no—
127D4C3×C5×D511yescharacteristic, direct product factor
128C2×C4—51no—
129C2×C3—22no—
130C2×C3—52no—
131C2×C3—102no—
132C2×C3C22×C5×D511yescharacteristic
133C5—22no—
134C5C3×D4×D511yescharacteristic, direct product factor
135C5C2×C3×C5×D411yescharacteristic, complemented
136C22—51no—
137C22—52no—
138C22—104no—
139C22C2×C3×C5×D512yescomplemented
140C4—51no—
141C4C2×C3×C5×D511yescharacteristic, complemented
142C3C5×D4×D511yescharacteristic, direct product factor, Sylow
143C2—22no—
144C2—52no—
145C2—102no—
146C2C22×C3×C5×D511yescharacteristic
subgroupG/H
centerC2×C3×C5C22×D5
commutator, cosocleC2×C5C23×C3×C5
FrattiniC2C22×C3×C5×D5
FittingC3×C52×D4C2
socleC2×C3×C52C23
hypercenterC3×C5×D4D5
hypocenterC5C2×C3×C5×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C5 ◁ C3×C5×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×D5C2semidirect
2. C3×C52×D4C2semidirect
3. C3×C5×C22⋊D5C2semidirect
4. C3×C5×D20C2semidirect
5. C3×C4×C5×D5C2semidirect
6. C5×D4×D5C3direct (N × H)
7. C22×C3×C52C22semidirect
10. C2×C3×C5×D5C22semidirect
11. C3×C4×C52C22semidirect
12. C3×C5×Dic5C22semidirect
14. C3×D4×D5C5direct (N × H)
15. C22×C5×D5C2×C3semidirect
16. C52×D4C2×C3semidirect
17. C5×C22⋊D5C2×C3semidirect
18. C5×D20C2×C3semidirect
19. C4×C5×D5C2×C3semidirect
23. C3×C5×D5D4direct (N × H)
25. C22×C3×D5C2×C5semidirect
29. C3×C5×D4D5direct (N × H)
30. C3×C5×D4C2×C5semidirect
32. C3×C22⋊D5C2×C5semidirect
33. C3×D20C2×C5semidirect
34. C3×C4×D5C2×C5semidirect
35. C22×C52C22×C3semidirect
38. C2×C5×D5C22×C3semidirect
39. C4×C52C22×C3semidirect
40. C5×Dic5C22×C3semidirect
42. D4×D5C3×C5direct (N × H)
43. C3×C52C2×D4semidirect
48. C22×C3×C5C2×D5semidirect
49. C22×C3×C5C22×C5semidirect
52. C2×C3×D5C22×C5semidirect
55. C3×C4×C5C2×D5semidirect
56. C3×C4×C5C22×C5semidirect
57. C3×Dic5C22×C5semidirect
61. C5×D5C3×D4direct (N × H)
64. C22×D5C2×C3×C5semidirect
68. C5×D4C3×D5direct (N × H)
69. C5×D4C2×C3×C5semidirect
71. C22⋊D5C2×C3×C5semidirect
72. D20C2×C3×C5semidirect
73. C4×D5C2×C3×C5semidirect
83. C3×D5C5×D4direct (N × H)
84. C52C2×C3×D4semidirect
88. C3×D4C5×D5direct (N × H)
94. C22×C5C2×C3×D5semidirect
95. C22×C5C22×C3×C5semidirect
98. C2×D5C22×C3×C5semidirect
101. C4×C5C2×C3×D5semidirect
102. C4×C5C22×C3×C5semidirect
103. Dic5C22×C3×C5semidirect
106. C3×C5D4×D5direct (N × H)
107. C3×C5C2×C5×D4semidirect
111. C22×C3C2×C5×D5semidirect
113. C3×C4C2×C5×D5semidirect
123. D5C3×C5×D4direct (N × H)
127. D4C3×C5×D5direct (N × H)
134. C5C3×D4×D5direct (N × H)
135. C5C2×C3×C5×D4semidirect
139. C22C2×C3×C5×D5semidirect
141. C4C2×C3×C5×D5semidirect
142. C3C5×D4×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D52
C3×C52×D42
C3×C5×C22⋊D52
C3×C5×D202
C3×C4×C5×D52
C5×D4×D53
C2×C3×C5×D45
C3×D4×D55