Finite Group Databasebeta

← #13017430

Subgroups — #13017430

Order 1280.

810 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 132 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×#4036C211yesmaximal, characteristic
2#10604902C212yesmaximal
3C2×#64913C214yesmaximal
4C22×C5×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic5C411yescharacteristic
6C22×C4⋊Dic5C2212yes—
7C22×#683C412yes—
8C22×C4×Dic5C2211yescharacteristic
9C2×#4036—28no—
10C2×#4036—24no—
11C2×C22⋊#170C2214yes—
12#64918—24no—
13#64913—28no—
14#8306—51nomaximal, Sylow
15C23×C4×C5C2×C412yes—
16C23×C4×C5C2×C411yescharacteristic
17C23×Dic5C2×C411yescharacteristic
18C23×Dic5C2×C412yes—
19C23×Dic5C2311yescharacteristic
20C22×#170—24no—
21C2×C5×C4⋊C4—24no—
22C2×C5×C4⋊C4—22no—
23C2×C4⋊Dic5—22no—
24C2×C4⋊Dic5—24no—
25C2×C4⋊Dic5—24no—
26C2×C4⋊Dic5—24no—
27C2×C4⋊Dic5D418yes—
28C2×#683—24no—
29C2×#683—24no—
30C2×#683—24no—
31C2×C4×Dic5—24no—
32C2×C4×Dic5D414yes—
33#4036—232no—
34C22⋊#170—28no—
35C22×#125—51no—
36#1817—52no—
37C2×#324—54no—
38C24×C5C22×C411yescharacteristic
39C22×C4×C5—22no—
40C22×C4×C5—24no—
41C22×C4×C5—22no—
42C22×C4×C5—22no—
43C22×C4×C5—28no—
44C22×C4×C5C22⋊C414yes—
45C22×C4×C5C22⋊C412yes—
46C22×Dic5—22no—
47C22×Dic5—22no—
48C22×Dic5—22no—
49C22×Dic5—24no—
50C22×Dic5—42no—
51C22×Dic5—44no—
52C22×Dic5C22⋊C412yes—
53C22×Dic5C22⋊C414yes—
54C22×Dic5C2×D412yes—
55C22×Dic5C2×D414yes—
56C2×#170—48no—
57C2×#170—44no—
58C5×C4⋊C4—28no—
59C4⋊Dic5—28no—
60C4⋊Dic5—216no—
61#683—216no—
62C4×Dic5—28no—
63C2×#125—104no—
64C2×#125—108no—
65C22×C4⋊C4—52no—
66C22×C4⋊C4—52no—
67C22×C4⋊C4—51no—
68C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
69C22×C42—51no—
70C2×C22⋊C8—54no—
71#336—104no—
72#324—108no—
73C23×C5—22no—
74C23×C5—22no—
75C23×C5C2×C22⋊C412yes—
76C23×C5C2×C22⋊C411yescharacteristic
77C23×C5#13114yes—
78C2×C4×C5—28no—
79C2×C4×C5—22no—
80C2×C4×C5—22no—
81C2×C4×C5—24no—
82C2×C4×C5—28no—
83C2×C4×C5—44no—
84C2×C4×C5—44no—
85C2×C4×C5#10114yes—
86C2×Dic5—24no—
87C2×Dic5—22no—
88C2×Dic5—24no—
89C2×Dic5—24no—
90C2×Dic5—44no—
91C2×Dic5—44no—
92C2×Dic5—44no—
93C2×Dic5—44no—
94C2×Dic5—44no—
95C2×Dic5#12014yes—
96#170—84no—
97C23×C4—51no—
98C23×C4—51no—
99C23×C4—52no—
100C23×C4C2×AGL(1,𝔽5)12yes—
101C23×C4C2×AGL(1,𝔽5)11yescharacteristic
102C22×C8—104no—
103#125—1032no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—58no—
107C2×C4⋊C4—104no—
108C2×C4⋊C4—104no—
109C2×C4⋊C4—104no—
110C2×C4⋊C4—104no—
111C2×C4⋊C4—104no—
112C2×C4⋊C4—104no—
113C2×C4⋊C4—102no—
114C2×C42—54no—
115C2×C42—104no—
116C22⋊C8—108no—
117C22×C5—28no—
118C22×C5—22no—
119C22×C5—22no—
120C22×C5#37911yescharacteristic
121C22×C5#40814yes—
122C22×C5#40812yes—
123C22×C5#41012yes—
124C22×C5C2×#10112yes—
125C4×C5—24no—
126C4×C5—44no—
127Dic5—24no—
128Dic5—42no—
129Dic5—44no—
130C24C22×AGL(1,𝔽5)11yescharacteristic
131C22×C4—22no—
132C22×C4—24no—
133C22×C4—28no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—52no—
137C22×C4—54no—
138C22×C4—52no—
139C22×C4—54no—
140C22×C4—104no—
141C22×C4—102no—
142C22×C4—102no—
143C22×C4—102no—
144C22×C4—202no—
145C22×C4—204no—
146C22×C4C22⋊AGL(1,𝔽5)14yes—
147C22×C4C22⋊AGL(1,𝔽5)12yes—
148C2×C8—204no—
149C2×C8—208no—
150C4⋊C4—28no—
151C4⋊C4—1016no—
152C4⋊C4—1016no—
153C4⋊C4—108no—
154C42—108no—
155C2×C5—24no—
156C2×C5#147014yes—
157C2×C5#178011yescharacteristic
158C2×C5#178211yescharacteristic
159C2×C5#178411yescharacteristic
160C23—22no—
161C23—22no—
162C23#413114yes—
163C23C2×C22⋊AGL(1,𝔽5)12yes—
164C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
165C2×C4—28no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—28no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—54no—
173C2×C4—104no—
174C2×C4—102no—
175C2×C4—104no—
176C2×C4—104no—
177C2×C4—204no—
178C2×C4—204no—
179C2×C4—204no—
180C2×C4—204no—
181C2×C4—204no—
182C2×C4#400514yes—
183C8—404no—
184C5#830611yescharacteristic, complemented, Sylow
185C22—28no—
186C22—22no—
187C22—22no—
188C22C2×#400512yes—
189C22#6577514yes—
190C22#6577612yes—
191C22#6578512yes—
192C22#6580011yescharacteristic
193C4—24no—
194C4—44no—
195C4—104no—
196C4—202no—
197C4—204no—
198C2—24no—
199C2#1060429814yes—
200C2#1060490511yescharacteristic
201C2#1060494511yescharacteristic
202C2#1060498111yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutator, prime radicalC24×C5C22×C4
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
cosocleC23×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8306
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
184. C5#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#40362
#106049022
C2×#649132
#83065