Finite Group Databasebeta

← #13018091

Subgroups — #13018091

Order 1280.

778 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 104 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×#4035C211yesmaximal, characteristic
2#10604908C212yesmaximal
3#10604882C212yesmaximal
4#10604881C212yesmaximal
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic5C2211yescharacteristic
7C22×#683C411yescharacteristic
8C22×#683C411yescharacteristic
9C22×#683C2211yescharacteristic
10C22×#683C2211yescharacteristic
11C22×C4×Dic5C411yescharacteristic
12C2×#4035—24no—
13C2×#4035—24no—
14C2×#4035—24no—
15#65798C2214yes—
16#64919—24no—
17#64914—24no—
18#64913—24no—
19#8554—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×Dic5C2×C411yescharacteristic
24C23×Dic5C2×C411yescharacteristic
25C23×Dic5C2×C411yescharacteristic
26C23×Dic5C2311yescharacteristic
27C2×#704—24no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C4⋊Dic5—22no—
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5D414yes—
34C2×#683—22no—
35C2×#683—22no—
36C2×#683—22no—
37C2×#683—22no—
38C2×#683—22no—
39C2×#683—22no—
40C2×#683—22no—
41C2×#683—22no—
42C2×#683—22no—
43C2×#683—22no—
44C2×#683D414yes—
45C2×#683D414yes—
46C2×C4×Dic5—22no—
47C2×C4×Dic5—22no—
48C2×C4×Dic5—22no—
49#4035—232no—
50C22⋊#170—24no—
51C22⋊#170—24no—
52C22×#125—51no—
53#1821—52no—
54#1463—52no—
55#1463—52no—
56C24×C5C22×C411yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5C22⋊C412yes—
67C22×C4×C5C22⋊C412yes—
68C22×C4×C5C22⋊C412yes—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—24no—
72C22×Dic5—21no—
73C22×Dic5—21no—
74C22×Dic5—21no—
75C22×Dic5—21no—
76C22×Dic5—42no—
77C22×Dic5—42no—
78C22×Dic5—42no—
79C22×Dic5C22⋊C412yes—
80C22×Dic5C22⋊C412yes—
81C22×Dic5C22⋊C412yes—
82C22×Dic5C2×D412yes—
83C22×Dic5C2×D412yes—
84C22×Dic5C2×D412yes—
85#704—48no—
86C2×#170—44no—
87C5×C4⋊C4—28no—
88C4⋊Dic5—28no—
89#683—28no—
90#683—28no—
91#683—28no—
92#683—28no—
93C4×Dic5—28no—
94C2×#125—104no—
95C2×#125—104no—
96C2×#125—104no—
97C22×C4⋊C4—51no—
98C22×C4⋊C4—51no—
99C22×C4⋊C4—51no—
100C22×C4⋊C4—51no—
101C22×C4⋊C4—51no—
102C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
103C22×C42—51no—
104#407—54no—
105#343—104no—
106#324—104no—
107#324—104no—
108C23×C5—22no—
109C23×C5—22no—
110C23×C5—22no—
111C23×C5C2×C22⋊C411yescharacteristic
112C23×C5C2×C22⋊C411yescharacteristic
113C23×C5C2×C22⋊C411yescharacteristic
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—22no—
117C2×C4×C5—24no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×Dic5—24no—
127C2×Dic5—24no—
128C2×Dic5—22no—
129C2×Dic5—24no—
130C2×Dic5—22no—
131C2×Dic5—22no—
132C2×Dic5—22no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5#10114yes—
142C2×Dic5#12014yes—
143#170—84no—
144C23×C4—51no—
145C23×C4—51no—
146C23×C4—51no—
147C23×C4—51no—
148C23×C4C2×AGL(1,𝔽5)11yescharacteristic
149C23×C4C2×AGL(1,𝔽5)11yescharacteristic
150C23×C4C2×AGL(1,𝔽5)11yescharacteristic
151C2×M16—104no—
152#125—1032no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—54no—
157C2×C4⋊C4—54no—
158C2×C4⋊C4—54no—
159C2×C4⋊C4—102no—
160C2×C4⋊C4—102no—
161C2×C4⋊C4—102no—
162C2×C4⋊C4—102no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4—102no—
165C2×C4⋊C4—102no—
166C2×C4⋊C4—102no—
167C2×C4⋊C4—102no—
168C2×C4⋊C4—102no—
169C2×C4⋊C4—102no—
170C2×C4⋊C4—102no—
171C2×C42—102no—
172C2×C42—102no—
173C2×C42—102no—
174C22⋊C8—104no—
175C22⋊C8—104no—
176C22×C5—28no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—21no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5#37911yescharacteristic
184C22×C5#41012yes—
185C22×C5C2×#10112yes—
186C22×C5#41312yes—
187C4×C5—42no—
188C4×C5—42no—
189C4×C5—42no—
190Dic5—24no—
191Dic5—24no—
192Dic5—42no—
193Dic5—42no—
194C24C22×AGL(1,𝔽5)11yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—52no—
205C22×C4—52no—
206C22×C4—52no—
207C22×C4—52no—
208C22×C4—52no—
209C22×C4—52no—
210C22×C4—104no—
211C22×C4—101no—
212C22×C4—101no—
213C22×C4—101no—
214C22×C4—101no—
215C22×C4—101no—
216C22×C4—101no—
217C22×C4—202no—
218C22×C4—202no—
219C22×C4—202no—
220C22×C4C22⋊AGL(1,𝔽5)12yes—
221C22×C4C22⋊AGL(1,𝔽5)12yes—
222C22×C4C22⋊AGL(1,𝔽5)12yes—
223M16—208no—
224C2×C8—204no—
225C4⋊C4—28no—
226C4⋊C4—108no—
227C4⋊C4—108no—
228C4⋊C4—108no—
229C4⋊C4—108no—
230C4⋊C4—108no—
231C42—108no—
232C2×C5—22no—
233C2×C5—22no—
234C2×C5—22no—
235C2×C5#178211yescharacteristic
236C2×C5#178411yescharacteristic
237C2×C5#178511yescharacteristic
238C23—22no—
239C23—22no—
240C23—22no—
241C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
242C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
243C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—54no—
257C2×C4—54no—
258C2×C4—104no—
259C2×C4—104no—
260C2×C4—102no—
261C2×C4—104no—
262C2×C4—102no—
263C2×C4—102no—
264C2×C4—102no—
265C2×C4—202no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4—202no—
273C8—404no—
274C5#855411yescharacteristic, complemented, Sylow
275C22—28no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#6574512yes—
283C22#6577712yes—
284C22D5⋊#10112yes—
285C22#6580011yescharacteristic
286C4—42no—
287C4—42no—
288C4—42no—
289C4—104no—
290C4—104no—
291C4—202no—
292C4—202no—
293C2—22no—
294C2—22no—
295C2—22no—
296C2#1060489111yescharacteristic
297C2#1060495111yescharacteristic
298C2#1060498611yescharacteristic
subgroupG/H
centerC22#65800
commutator, prime radicalC24×C5C22×C4
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC22×C5#379
cosocleC23×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8554
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
274. C5#8554semidirect

Maximal subgroups

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

subgroupindex
C22×#40352
#106049082
#106048822
#106048812
#85545