Finite Group Databasebeta

← #13014635

Subgroups — #13014635

Order 1280.

550 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 128 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
1#10613957C211yesmaximal, characteristic
2C4×C22⋊#170C212yesmaximal
3#10598714C214yesmaximal, complemented
4C2×C5×#117C411yescharacteristic
5C2×#4072C411yescharacteristic
6C22×C4×Dic5C2211yescharacteristic
7C2×C22⋊#170—22no—
8C2×C4×#170—22no—
9#65262C412yes—
10#65262C2212yes—
11#65235—22no—
12C4×#683—22no—
13#64918C2214yes—
14#7564—51nomaximal, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×Dic5D412yes—
17C22×#170—24no—
18C5×#117—42no—
19C2×C5×C4⋊C4C2×C412yes—
20C2×C5×C22⋊C4—21no—
21C2×C42×C5—21no—
22C2×C22⋊Dic5—21no—
23#4072—22no—
24#4072C814yescomplemented
25C2×C4⋊Dic5C2×C412yes—
26C2×#683—22no—
27C2×#683—22no—
28C2×C4×Dic5—21no—
29C2×C4×Dic5—42no—
30C2×C4×Dic5C2×C411yescharacteristic
31C2×C4×Dic5D412yes—
32C2×C4×Dic5C2311yescharacteristic
33C22⋊#170—28no—
34C4×#170—44no—
35#3963—22no—
36#3963—22no—
37#2296—51no—
38C4×C22⋊C8—52no—
39#1271—54no—
40C24×C5C22⋊C411yescharacteristic
41C22×C4×C5—22no—
42C22×C4×C5—22no—
43C22×C4×C5—22no—
44C22×C4×C5C22⋊C411yescharacteristic
45C22×C4×C5C2×C812yes—
46C22×C4×C5M1612yes—
47C22×C4×C5C22×C411yescharacteristic
48C22×Dic5—22no—
49C22×Dic5—24no—
50C22×Dic5—24no—
51C22×Dic5—42no—
52C22×Dic5C22⋊C412yes—
53C22×Dic5C2×D412yes—
54C2×#170—28no—
55C2×#170—44no—
56C2×#170—44no—
57C5×C4⋊C4—42no—
58C5×C22⋊C4—42no—
59C42×C5—42no—
60C22⋊Dic5—24no—
61C4⋊Dic5—22no—
62C4⋊Dic5C2×C814yes—
63#683—44no—
64#683—44no—
65C4×Dic5—24no—
66C4×Dic5—24no—
67C4×Dic5—41no—
68C4×Dic5—41no—
69C2×#117—51no—
70C2×#117AGL(1,𝔽5)11yescharacteristic
71C22×C42—51no—
72C2×C22⋊C8—102no—
73C2×C4×C8—102no—
74#389—52no—
75#389—52no—
76#385—102no—
77C4×C4⋊C4—102no—
78#336—54no—
79C23×C5—21no—
80C23×C5—21no—
81C23×C5—22no—
82C23×C5—22no—
83C23×C5C22⋊C812yes—
84C23×C5C2×C22⋊C411yescharacteristic
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—24no—
88C2×C4×C5—24no—
89C2×C4×C5—42no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5C22⋊C812yes—
93C2×C4×C5#9912yes—
94C2×C4×C5#10112yes—
95C2×C4×C5C22×C811yescharacteristic
96C2×C4×C5C2×M1611yescharacteristic
97C2×Dic5—22no—
98C2×Dic5—22no—
99C2×Dic5—22no—
100C2×Dic5—22no—
101C2×Dic5—24no—
102C2×Dic5—48no—
103C2×Dic5—42no—
104C2×Dic5—42no—
105C2×Dic5#10414yes—
106C2×Dic5#13514yes—
107#170—48no—
108C23×C4—52no—
109C23×C4C2×AGL(1,𝔽5)11yescharacteristic
110C22×C8—104no—
111#117—42no—
112#117—54no—
113#117—102no—
114C2×C4⋊C4—52no—
115C2×C4⋊C4—102no—
116C2×C4⋊C4—102no—
117C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—101no—
120C2×C42—21no—
121C2×C42—52no—
122C2×C42—51no—
123C2×C42—51no—
124C2×C42—101no—
125C2×C42—202no—
126C22⋊C8—108no—
127C4×C8—204no—
128#95—102no—
129#95—102no—
130C22×C5—22no—
131C22×C5—24no—
132C22×C5—41no—
133C22×C5—42no—
134C22×C5—41no—
135C22×C5C2×C22⋊C811yescharacteristic
136C22×C5C2×#9911yescharacteristic
137C22×C5C2×#10111yescharacteristic
138C22×C5#41612yes—
139C22×C5C2×#10412yes—
140C4×C5—21no—
141C4×C5—21no—
142C4×C5—82no—
143C4×C5#32414yes—
144Dic5—24no—
145Dic5—24no—
146Dic5—44no—
147C24C22⋊AGL(1,𝔽5)11yescharacteristic
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—52no—
152C22×C4—52no—
153C22×C4—104no—
154C22×C4—104no—
155C22×C4—102no—
156C22×C4—202no—
157C22×C4D5⋊C812yes—
158C22×C4#70012yes—
159C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
160C22×C4C22×AGL(1,𝔽5)11yescharacteristic
161C2×C8—108no—
162C2×C8—204no—
163C2×C8—204no—
164C4⋊C4—42no—
165C4⋊C4—54no—
166C4⋊C4—102no—
167C4⋊C4—204no—
168C4⋊C4—204no—
169C22⋊C4—42no—
170C22⋊C4—104no—
171C42—42no—
172C42—104no—
173C42—104no—
174C42—201no—
175C42—201no—
176C2×C5—42no—
177C2×C5C2×#32411yescharacteristic
178C2×C5#147612yes—
179C2×C5#150112yes—
180C2×C5#152611yescharacteristic
181C2×C5#154411yescharacteristic
182C23—22no—
183C23—22no—
184C23—21no—
185C23—21no—
186C23#400312yes—
187C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—54no—
196C2×C4—54no—
197C2×C4—102no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—104no—
202C2×C4—208no—
203C2×C4—202no—
204C2×C4—202no—
205C2×C4#400312yes—
206C2×C4#400512yes—
207C2×C4#401112yes—
208C2×C4C2×D5⋊C811yescharacteristic
209C2×C4C2×#70011yescharacteristic
210C8—208no—
211C5#756411yescharacteristic, complemented, Sylow
212C22—24no—
213C22—22no—
214C22—41no—
215C22—41no—
216C22—42no—
217C22C2×#400311yescharacteristic
218C22C2×#400511yescharacteristic
219C22D5⋊#10412yes—
220C22#6579412yes—
221C22C2×#401111yescharacteristic
222C4—21no—
223C4—21no—
224C4—82no—
225C4—104no—
226C4—104no—
227C4—204no—
228C4#6491414yes—
229C2—42no—
230C2#1060435011yescharacteristic
231C2#1060435912yes—
232C2#1060436311yescharacteristic
233C2C2×#6491411yescharacteristic
234C2#1060498912yes—
subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5#7564
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #10598714C2semidirect
24. #4072C8semidirect
211. C5#7564semidirect

Maximal subgroups

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

subgroupindex
#106139572
C4×C22⋊#1702
#105987142
#75645