Finite Group Databasebeta

← C2×C3×#4099 #11755851

Subgroups — C2×C3×#4099 #11755851

Order 960.

1324 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 318 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
1C25×C3×C5C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊D5C213yesmaximal, complemented
3C3×#4099C218yesmaximal, direct product factor
4C2×C3×C22⋊Dic5C213yesmaximal, complemented
5C2×#4099C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×C5—212no—
7C24×C3×C5C2213yes—
8C24×C3×C5C2214yescomplemented
9C23×C3×D5C2211yescharacteristic, complemented
10C2×C3×C22⋊D5—212no—
11C2×C3×C22⋊D5C22112yescomplemented
12C22×C3×Dic5C2213yescomplemented
13C3×C22⋊Dic5C22112yescomplemented
14C2×C3×#120—51nomaximal, Hall
15C25×C5C2×C311yescharacteristic, complemented
16C22×C22⋊D5C2×C313yescomplemented
17#4099C2×C318yesdirect product factor
18C2×C22⋊Dic5C2×C313yescomplemented
19C23×C3×C5—232no—
20C23×C3×C5—212no—
21C23×C3×C5—224no—
22C23×C3×C5D4112yescomplemented
23C23×C3×C5C2316yes—
24C23×C3×C5C2311yescharacteristic
25C22×C3×D5—26no—
26C22×C3×D5C2312yescomplemented
27C3×C22⋊D5—224no—
28C2×C3×Dic5—26no—
29C2×C3×Dic5C2316yescomplemented
30C25×C3D511yescharacteristic, complemented
31C22×C3×D4—53no—
32C3×#120—58no—
33C2×C3×C22⋊C4—53no—
34C24×C5—212no—
35C24×C5C22×C313yes—
36C24×C5C22×C314yescomplemented
37C23×D5C22×C311yescharacteristic, complemented
38C2×C22⋊D5—212no—
39C2×C22⋊D5C22×C3112yescomplemented
40C22×Dic5C22×C313yescomplemented
41C22⋊Dic5C22×C3112yescomplemented
42C2×#120—51noSylow
43C22×C3×C5—232no—
44C22×C3×C5—224no—
45C22×C3×C5—212no—
46C22×C3×C5C2×D416yes—
47C22×C3×C5C2×D4112yescomplemented
48C22×C3×C5C2411yescharacteristic
49C2×C3×D5—26no—
50C2×C3×D5—44no—
51C3×Dic5—26no—
52C24×C3—212no—
53C24×C3—51no—
54C24×C3C2×D513yes—
55C24×C3C2×D514yescomplemented
56C2×C3×D4—512no—
57C2×C3×D4—1012no—
58C22×C3×C4—53no—
59C3×C22⋊C4—512no—
60C23×C5—232no—
61C23×C5—212no—
62C23×C5—224no—
63C23×C5C3×D4112yescomplemented
64C23×C5C23×C316yes—
65C23×C5C23×C311yescharacteristic
66C22×D5—26no—
67C22×D5C23×C312yescomplemented
68C22⋊D5—224no—
69C2×Dic5—26no—
70C2×Dic5C23×C316yescomplemented
71C25C3×D511yescharacteristic, complemented
72C22×D4—53no—
73#120—58no—
74C2×C22⋊C4—53no—
75C2×C3×C5—212no—
76C2×C3×C5#12014yescomplemented
77C2×C3×C5C22×D413yes—
78C3×D5—42no—
79C23×C3—232no—
80C23×C3—212no—
81C23×C3—224no—
82C23×C3—52no—
83C23×C3—106no—
84C23×C3C22⋊D5112yescomplemented
85C23×C3C22×D516yes—
86C23×C3C22×D511yescharacteristic
87C3×D4—1024no—
88C2×C3×C4—56no—
89C2×C3×C4—106no—
90C22×C5—232no—
91C22×C5—224no—
92C22×C5—212no—
93C22×C5C2×C3×D416yes—
94C22×C5C2×C3×D4112yescomplemented
95C22×C5C24×C311yescharacteristic
96C2×D5—26no—
97C2×D5—44no—
98Dic5—26no—
99C24—212no—
100C24—51no—
101C24C2×C3×D513yes—
102C24C2×C3×D514yescomplemented
103C2×D4—512no—
104C2×D4—1012no—
105C22×C4—53no—
106C22⋊C4—512no—
107C3×C5C2×#12011yescharacteristic, complemented, Hall
108C22×C3—232no—
109C22×C3—224no—
110C22×C3—212no—
111C22×C3—106no—
112C22×C3—204no—
113C22×C3C2×C22⋊D516yes—
114C22×C3C2×C22⋊D5112yescomplemented
115C22×C3C23×D511yescharacteristic
116C3×C4—106no—
117C2×C5—212no—
118C2×C5C3×#12014yescomplemented
119C2×C5C22×C3×D413yes—
120D5—42no—
121C23—232no—
122C23—212no—
123C23—224no—
124C23—52no—
125C23—106no—
126C23C3×C22⋊D5112yescomplemented
127C23C22×C3×D516yes—
128C23C22×C3×D511yescharacteristic
129D4—1024no—
130C2×C4—56no—
131C2×C4—106no—
132C2×C3—212no—
133C2×C3—202no—
134C2×C3#409914yesdirect product factor
135C2×C3C22×C22⋊D513yes—
136C5C2×C3×#12011yescharacteristic, complemented, Sylow
137C22—232no—
138C22—224no—
139C22—212no—
140C22—106no—
141C22—204no—
142C22C2×C3×C22⋊D516yes—
143C22C2×C3×C22⋊D5112yescomplemented
144C22C23×C3×D511yescharacteristic
145C4—106no—
146C3C2×#409911yescharacteristic, direct product factor, Sylow
147C2—212no—
148C2—202no—
149C2C3×#409914yesdirect product factor
150C2C22×C3×C22⋊D513yes—
subgroupG/H
centerC23×C3C22×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC25×C3×C5C2
socleC23×C3×C5C23
hypercenterC25×C3D5
hypocenterC5C2×C3×#120
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C25×C3

Complements

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

NH ≅ G/Ntype
1. C25×C3×C5C2semidirect
2. C22×C3×C22⋊D5C2semidirect
3. C3×#4099C2direct (N × H)
4. C2×C3×C22⋊Dic5C2semidirect
5. C2×#4099C3direct (N × H)
8. C24×C3×C5C22semidirect
9. C23×C3×D5C22semidirect
11. C2×C3×C22⋊D5C22semidirect
12. C22×C3×Dic5C22semidirect
13. C3×C22⋊Dic5C22semidirect
15. C25×C5C2×C3semidirect
16. C22×C22⋊D5C2×C3semidirect
17. #4099C2×C3direct (N × H)
18. C2×C22⋊Dic5C2×C3semidirect
22. C23×C3×C5D4semidirect
26. C22×C3×D5C23semidirect
29. C2×C3×Dic5C23semidirect
30. C25×C3D5semidirect
36. C24×C5C22×C3semidirect
37. C23×D5C22×C3semidirect
39. C2×C22⋊D5C22×C3semidirect
40. C22×Dic5C22×C3semidirect
41. C22⋊Dic5C22×C3semidirect
47. C22×C3×C5C2×D4semidirect
55. C24×C3C2×D5semidirect
63. C23×C5C3×D4semidirect
67. C22×D5C23×C3semidirect
70. C2×Dic5C23×C3semidirect
71. C25C3×D5semidirect
76. C2×C3×C5#120semidirect
84. C23×C3C22⋊D5semidirect
94. C22×C5C2×C3×D4semidirect
102. C24C2×C3×D5semidirect
107. C3×C5C2×#120semidirect
114. C22×C3C2×C22⋊D5semidirect
118. C2×C5C3×#120semidirect
126. C23C3×C22⋊D5semidirect
134. C2×C3#4099direct (N × H)
136. C5C2×C3×#120semidirect
143. C22C2×C3×C22⋊D5semidirect
146. C3C2×#4099direct (N × H)
149. C2C3×#4099direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C52
C22×C3×C22⋊D52
C3×#40992
C2×C3×C22⋊Dic52
C2×#40993
C2×C3×#1205