Finite Group Databasebeta

← #11996975

Subgroups — #11996975

Order 1280.

424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2565C211yesmaximal, characteristic
2#10614167C211yesmaximal, characteristic
3#10602529C212yesmaximal
4#10602418C211yesmaximal, characteristic
5#10598112C212yesmaximal
6C2×C5×#125C2211yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#398—21no—
9C5×#398—21no—
10C5×#391C411yescharacteristic
11C5×#391C411yescharacteristic
12C5×#387—21no—
13C5×#387—21no—
14C5×#384C411yescharacteristic
15C5×#382C411yescharacteristic
16C4×C5×C4⋊C4C2211yescharacteristic
17#65313—24no—
18#65215—21no—
19#65215C2212yes—
20#65215C2212yes—
21#65214—21no—
22#64763—24no—
23#64748—21no—
24#64748—21no—
25#9450—51nomaximal, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C5×#125—22no—
28C5×#125—22no—
29C4×C5×Q8—22no—
30C4×C5×Q8—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5C2311yescharacteristic
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C22⋊#168—22no—
54C22⋊#168—22no—
55C4⋊#168—22no—
56C4⋊#168—22no—
57C4⋊#168—22no—
58C4⋊#168—22no—
59#3935—22no—
60#3935—22no—
61#3935D414yes—
62C4×#168—22no—
63#2983—51no—
64#2565D511yescharacteristic
65#1534—52no—
66#1467—51no—
67#1285—52no—
68C2×C5×Q8—22no—
69C2×C5×Q8—22no—
70C2×C5×Q8—41no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C5×C4⋊C4—22no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—42no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—42no—
92C5×C4⋊C4—41no—
93C42×C5—21no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—21no—
97C42×C5—41no—
98C42×C5—41no—
99C42×C5C2×D412yes—
100C42×C5#4112yes—
101C2×#168—24no—
102C2×#168—42no—
103C2×#125C2×D511yescharacteristic
104C2×C4×Q8C2×D511yescharacteristic
105#446—104no—
106#432—52no—
107#432—52no—
108#432—101no—
109#431—101no—
110#398—21no—
111#398—21no—
112#391Dic511yescharacteristic
113#391Dic511yescharacteristic
114#387—21no—
115#387—21no—
116#384Dic511yescharacteristic
117#382Dic511yescharacteristic
118C4×C4⋊C4C2×D511yescharacteristic
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—22no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—42no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5#10112yes—
149C2×C4×C5C4×D412yes—
150C2×C4×C5#12011yescharacteristic
151C2×C4×C5#12112yes—
152C2×C4×C5#12311yescharacteristic
153#168—44no—
154#168—82no—
155C22×Q8C2×Dic511yescharacteristic
156#125—22no—
157#125—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×Dic511yescharacteristic
166C2×C4⋊C4C2×Dic511yescharacteristic
167C2×C4⋊C4C2×Dic511yescharacteristic
168C2×C4⋊C4C22⋊D511yescharacteristic
169C2×C4⋊C4C22⋊D511yescharacteristic
170C2×C42C2×Dic511yescharacteristic
171C2×C42C2×Dic511yescharacteristic
172C2×C42C22⋊D511yescharacteristic
173C2×C42C22⋊D511yescharacteristic
174C2×C42C22×D511yescharacteristic
175C4⋊C8—102no—
176C4⋊C8—102no—
177C4⋊C8—102no—
178C4⋊C8—102no—
179C22⋊C8—102no—
180C22⋊C8—102no—
181#97—54no—
182#97—102no—
183#97—102no—
184C4×C8—102no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
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—42no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—41no—
206C4×C5—81no—
207C4×C5—81no—
208C4×C5—81no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C22⋊Dic511yescharacteristic
217C22×C4C22⋊Dic511yescharacteristic
218C22×C4C22⋊Dic511yescharacteristic
219C22×C4C22⋊Dic511yescharacteristic
220C22×C4C22×Dic511yescharacteristic
221C22×C4C2×C22⋊D511yescharacteristic
222C22×C4C2×C22⋊D511yescharacteristic
223C2×C8—104no—
224C2×C8—202no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—41no—
241C42—41no—
242C42D4×D512yes—
243C42#71112yes—
244C2×C5—21no—
245C2×C5—21no—
246C2×C5#188411yescharacteristic
247C2×C5#190111yescharacteristic
248C2×C5#191211yescharacteristic
249C23C2×C22⋊Dic511yescharacteristic
250Q8—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4#396812yes—
276C2×C4D4×Dic512yes—
277C2×C4#408111yescharacteristic
278C2×C4#408311yescharacteristic
279C2×C4#408512yes—
280C8—204no—
281C8—402no—
282C5#945011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22#6550911yescharacteristic
286C22C2×#396811yescharacteristic
287C22#6552611yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1060249111yescharacteristic
303C2#1060261011yescharacteristic
304C2#1060265711yescharacteristic
subgroupG/H
centerC22#65509
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2565C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2565D5
hypocenterC5#9450
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2565

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×#25652
#106141672
#106025292
#106024182
#105981122
#94505