Finite Group Databasebeta

← C2×C4×#6036 #13105937

Subgroups — C2×C4×#6036 #13105937

Order 1600.

1232 conjugacy classes of subgroups; only the 384 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 384 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×C4×C5⋊D5C211yesmaximal, characteristic
2C22×#6036C212yesmaximal
3C2×C4×C5×Dic5C212yesmaximal, complemented
4C2×Dic52C212yesmaximal, complemented
5C4×#6036C218yesmaximal, direct product factor
6C23×C5⋊D5C2211yescharacteristic
7C22×C4×C52C2211yescharacteristic
8C22×#1039C2211yescharacteristic
9C2×C4×C5⋊D5C418yescomplemented
10C2×C4×C5⋊D5C2214yes—
11C22×C5×Dic5C2214yes—
12C2×#6036C4116yesdirect product factor
13C2×#6036C2218yes—
14C4×C5×Dic5C2218yescomplemented
15Dic52C2218yescomplemented
16C2×C42×D5—52nomaximal
17C23×C52C2311yescharacteristic
18C22×C5⋊D5C2×C418yes—
19C22×C5⋊D5C2×C414yes—
20C22×C5⋊D5C2312yes—
21C2×C4×C52C2×C414yescomplemented
22C2×C4×C52C2312yes—
23C2×#1039C2×C414yescomplemented
24C2×#1039C2312yes—
25C4×C5⋊D5C2×C4116yescomplemented
26C2×C5×Dic5C2×C4116yescomplemented
27C2×C5×Dic5C2318yes—
28#6036C2×C4132yesdirect product factor
29C22×C4×D5—52no—
30C22×C4×D5—54no—
31C22×C4×D5—102no—
32C2×C42×C5—52no—
33C2×C4×Dic5—54no—
34C2×C4×Dic5D512yescomplemented
35C42×D5—516no—
36C22×C52C22×C414yes—
37C22×C52C22×C412yes—
38C22×C52C2411yescharacteristic
39C2×C5⋊D5C42116yescomplemented
40C2×C5⋊D5C22×C418yes—
41C2×C5⋊D5C22×C414yes—
42C4×C52C22×C414yescomplemented
43#1039C22×C414yescomplemented
44C5×Dic5C22×C4116yescomplemented
45C23×D5—52no—
46C23×D5—102no—
47C22×C4×C5—22no—
48C22×C4×C5—54no—
49C22×C4×C5C2×D512yes—
50C22×Dic5—52no—
51C22×Dic5—102no—
52C22×Dic5C2×D514yes—
53C2×C4×D5—516no—
54C2×C4×D5—58no—
55C2×C4×D5—532no—
56C2×C4×D5—516no—
57C2×C4×D5—1016no—
58C2×C4×D5—108no—
59C42×C5—58no—
60C4×Dic5—516no—
61C4×Dic5C2×D518yescomplemented
62C22×C42—251noSylow
63C2×C52C2×C4214yescomplemented
64C2×C52C23×C412yes—
65C2×C52C23×C411yescharacteristic
66C5⋊D5C2×C4218yescomplemented
67C23×C5—22no—
68C23×C5C22×D512yes—
69C22×D5—516no—
70C22×D5—58no—
71C22×D5—54no—
72C22×D5—108no—
73C22×D5—1016no—
74C22×D5—104no—
75C2×C4×C5—28no—
76C2×C4×C5—24no—
77C2×C4×C5—516no—
78C2×C4×C5—58no—
79C2×C4×C5C4×D518yescomplemented
80C2×C4×C5C22×D514yes—
81C2×Dic5—58no—
82C2×Dic5—54no—
83C2×Dic5—108no—
84C2×Dic5—104no—
85C2×Dic5C4×D5116yescomplemented
86C2×Dic5C22×D518yes—
87C4×D5—532no—
88C4×D5—564no—
89C4×D5—1032no—
90C23×C4—252no—
91C23×C4—251no—
92C2×C42—52no—
93C2×C42—258no—
94C2×C42—252no—
95C52C22×C4211yescharacteristic, complemented, Sylow
96C22×C5—28no—
97C22×C5—24no—
98C22×C5—22no—
99C22×C5C2×C4×D518yes—
100C22×C5C2×C4×D514yes—
101C22×C5C23×D512yes—
102C2×D5—516no—
103C2×D5—58no—
104C2×D5—532no—
105C2×D5—1032no—
106C2×D5—108no—
107C2×D5—1016no—
108C4×C5—28no—
109C4×C5—516no—
110C4×C5C2×C4×D518yescomplemented
111Dic5—58no—
112Dic5—108no—
113Dic5C2×C4×D5116yescomplemented
114C24—251no—
115C22×C4—54no—
116C22×C4—258no—
117C22×C4—2516no—
118C22×C4—251no—
119C22×C4—258no—
120C22×C4—254no—
121C22×C4D5211yescharacteristic
122C42—58no—
123C42—258no—
124C2×C5—24no—
125C2×C5—22no—
126C2×C5—28no—
127C2×C5C42×D518yescomplemented
128C2×C5C22×C4×D514yes—
129C2×C5C22×C4×D512yes—
130D5—516no—
131D5—1016no—
132C23—258no—
133C23—254no—
134C23—252no—
135C23C2×D5211yescharacteristic
136C2×C4—516no—
137C2×C4—58no—
138C2×C4—2532no—
139C2×C4—254no—
140C2×C4—252no—
141C2×C4—2516no—
142C2×C4#603614yesdirect product factor
143C2×C4C2×D5212yes—
144C5—22no—
145C5C2×C42×D512yescomplemented
146C22—258no—
147C22—254no—
148C22—2516no—
149C22C4×D5214yes—
150C22C2×#603612yes—
151C22C22×D5211yescharacteristic
152C4—516no—
153C4—254no—
154C4C2×#603614yesdirect product factor
155C2—258no—
156C2C4×#603614yesdirect product factor
157C2C2×C4×D5212yes—
158C2C22×#603611yescharacteristic
subgroupG/H
center, hypercenterC22×C4D52
commutator, hypocenterC52C22×C42
FrattiniC22C22×D52
FittingC22×C4×C52C22
socleC23×C52C23
prime radicalC23×C5⋊D5C22
cosocleC22×C52C24
LCSG ▷ C52
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C5×Dic5C2semidirect
4. C2×Dic52C2semidirect
5. C4×#6036C2direct (N × H)
9. C2×C4×C5⋊D5C4semidirect
12. C2×#6036C4direct (N × H)
14. C4×C5×Dic5C22semidirect
15. Dic52C22semidirect
21. C2×C4×C52C2×C4semidirect
23. C2×#1039C2×C4semidirect
25. C4×C5⋊D5C2×C4semidirect
26. C2×C5×Dic5C2×C4semidirect
28. #6036C2×C4direct (N × H)
34. C2×C4×Dic5D5semidirect
39. C2×C5⋊D5C42semidirect
42. C4×C52C22×C4semidirect
43. #1039C22×C4semidirect
44. C5×Dic5C22×C4semidirect
61. C4×Dic5C2×D5semidirect
63. C2×C52C2×C42semidirect
66. C5⋊D5C2×C42semidirect
79. C2×C4×C5C4×D5semidirect
85. C2×Dic5C4×D5semidirect
95. C52C22×C42semidirect
110. C4×C5C2×C4×D5semidirect
113. Dic5C2×C4×D5semidirect
127. C2×C5C42×D5semidirect
142. C2×C4#6036direct (N × H)
145. C5C2×C42×D5semidirect
154. C4C2×#6036direct (N × H)
156. C2C4×#6036direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5⋊D52
C22×#60362
C2×C4×C5×Dic52
C2×Dic522
C4×#60362
C2×C42×D55