Finite Group Databasebeta

← #11996974

Subgroups — #11996974

Order 1280.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C5×#2983C211yesmaximal, characteristic
2#10614208C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10601607C212yesmaximal
5#10598240C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4016C2211yescharacteristic
8C5×#446—24no—
9C5×#432—21no—
10C5×#432C2212yes—
11C5×#431—21no—
12#65519C411yescharacteristic
13#65519C411yescharacteristic
14#65273—21no—
15#65273—21no—
16#65266C411yescharacteristic
17#65265C411yescharacteristic
18C4×C4⋊Dic5C2211yescharacteristic
19#65222—21no—
20#65222—21no—
21#65215C2212yes—
22#64748—21no—
23#64748—21no—
24#64685—24no—
25#9450—51nomaximal, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C4×C5×Q8—22no—
28C4×C5×Q8—22no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C42×C5C2311yescharacteristic
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×#683—21no—
39C2×#683—21no—
40C2×#683—21no—
41C2×#683—21no—
42C2×C4×Dic5C2×C411yescharacteristic
43C2×C4×Dic5C2×C411yescharacteristic
44#4016—22no—
45#4016—22no—
46C5×C4⋊C8—22no—
47C5×C4⋊C8—22no—
48C5×C4⋊C8—22no—
49C5×C22⋊C8—22no—
50C5×#97—22no—
51C5×#97D414yes—
52C4×C5×C8—22no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3963—21no—
58#3963—21no—
59#3963—21no—
60C22⋊#168—22no—
61C4⋊#168—22no—
62#3935—22no—
63#2983D511yescharacteristic
64#2565—51no—
65#1534—52no—
66#1467—51no—
67#1285—52no—
68C2×C5×Q8—22no—
69C2×C5×Q8—22no—
70C2×C5×Q8—41no—
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×Dic5—21no—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C2×C5×C8—24no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C42×C5—21no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—21no—
90C42×C5C2×D412yes—
91C42×C5#4112yes—
92C4⋊Dic5—22no—
93C4⋊Dic5—22no—
94C4⋊Dic5—42no—
95#683—42no—
96#683—42no—
97#683—41no—
98#683—42no—
99#683—41no—
100C4×Dic5—41no—
101C4×Dic5—41no—
102C2×#168—42no—
103C2×#125—51no—
104C2×C4×Q8C2×D511yescharacteristic
105#446—24no—
106#432—21no—
107#432—52no—
108#432C2×D512yes—
109#431—21no—
110#398—101no—
111#398—101no—
112#391—51no—
113#391—51no—
114#387—101no—
115#387—101no—
116#384—51no—
117#382—51no—
118C4×C4⋊C4—51no—
119#330—104no—
120#324—101no—
121#324—101no—
122C23×C5C2×C22⋊C411yescharacteristic
123C5×Q8—44no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5#10112yes—
138C2×C4×C5C4×D412yes—
139C2×C4×C5#12011yescharacteristic
140C2×C4×C5#12112yes—
141C2×C4×C5#12311yescharacteristic
142C2×Dic5—22no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—42no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C5×C8—44no—
154#168—82no—
155C22×Q8C4×D511yescharacteristic
156#125—102no—
157#125—102no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—101no—
163C2×C4⋊C4—101no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—101no—
166C2×C4⋊C4—101no—
167C2×C4⋊C4C4×D511yescharacteristic
168C2×C4⋊C4D2011yescharacteristic
169C2×C4⋊C4D2011yescharacteristic
170C2×C42—51no—
171C2×C42—51no—
172C2×C42C22⋊D511yescharacteristic
173C2×C42C22⋊D511yescharacteristic
174C2×C42C22×D511yescharacteristic
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—102no—
179C22⋊C8—22no—
180C22⋊C8—102no—
181#97—22no—
182#97—102no—
183#97C22⋊D514yes—
184C4×C8—22no—
185#95—101no—
186#95—101no—
187#95—101no—
188#95—101no—
189#95—101no—
190#95—101no—
191#95—101no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5#38611yescharacteristic
195C22×C5C2×#10111yescharacteristic
196C22×C5#41311yescharacteristic
197C4×C5—22no—
198C4×C5—22no—
199C4×C5—22no—
200C4×C5—21no—
201C4×C5—21no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C5—41no—
205Dic5—42no—
206Dic5—81no—
207Dic5—81no—
208Dic5—81no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—41no—
212C22×C4—101no—
213C22×C4—101no—
214C22×C4—101no—
215C22×C4—101no—
216C22×C4#68511yescharacteristic
217C22×C4#68511yescharacteristic
218C22×C4#68511yescharacteristic
219C22×C4#68511yescharacteristic
220C22×C4C2×C4×D511yescharacteristic
221C22×C4C2×D2011yescharacteristic
222C22×C4C2×C22⋊D511yescharacteristic
223C2×C8—24no—
224C2×C8—202no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—102no—
229C4⋊C4—102no—
230C4⋊C4—202no—
231C4⋊C4—202no—
232C4⋊C4—202no—
233C4⋊C4—201no—
234C4⋊C4—201no—
235C4⋊C4—202no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—201no—
241C42—201no—
242C42#70912yes—
243C42C2×C22⋊D512yes—
244C2×C5—21no—
245C2×C5—21no—
246C2×C5#188411yescharacteristic
247C2×C5#190111yescharacteristic
248C2×C5#191211yescharacteristic
249C23C2×#68511yescharacteristic
250Q8—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—102no—
265C2×C4—201no—
266C2×C4—201no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—201no—
270C2×C4—201no—
271C2×C4—202no—
272C2×C4—201no—
273C2×C4—201no—
274C2×C4—201no—
275C2×C4#395612yes—
276C2×C4C4×C22⋊D512yes—
277C2×C4#407511yescharacteristic
278C2×C4#407612yes—
279C2×C4#409911yescharacteristic
280C8—44no—
281C8—402no—
282C5#945011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22#6542111yescharacteristic
286C22C2×#395611yescharacteristic
287C22#6550211yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—202no—
297C4—401no—
298C4—401no—
299C4—401no—
300C2—21no—
301C2—21no—
302C2#1060245611yescharacteristic
303C2#1060279611yescharacteristic
304C2#1060281411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2983C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2983D5
hypocenterC5#9450
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
282. C5#9450semidirect

Maximal subgroups

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

subgroupindex
C5×#29832
#106142082
#106024182
#106016072
#105982402
#94505