Finite Group Databasebeta

← #12008947

Subgroups — #12008947

Order 1280.

424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2563C211yesmaximal, characteristic
2#10602395C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10598123C214yesmaximal, complemented
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×D4C2211yescharacteristic
7C5×#393—21no—
8C5×#393—21no—
9C5×#390C412yes—
10C5×#382C2212yes—
11C5×#380—21no—
12C5×#380—21no—
13C4×C5×C4⋊C4C411yescharacteristic
14#65496—21no—
15C2×C22⋊#168—21no—
16#64748C2212yes—
17#64748C2212yes—
18#64745—21no—
19#64745—21no—
20#11569—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×C5×D4C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C5×C4⋊Q8—41no—
26C5×C4⋊Q8—41no—
27C4×C5×D4—41no—
28C4×C5×D4—41no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C412yes—
32C2×C5×C4⋊C4C2311yescharacteristic
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—22no—
35C2×C5×C22⋊C4D411yescharacteristic
36C2×C5×C22⋊C4D411yescharacteristic
37C2×C42×C5C2×C412yes—
38C2×C42×C5C2×C411yescharacteristic
39C2×#681—41no—
40C22×#168—41no—
41C5×#95—21no—
42C5×#95—22no—
43C5×#95—22no—
44C22⋊#168—22no—
45C22⋊#168—22no—
46C22⋊#168—41no—
47C22⋊#168—41no—
48#2563D511yescharacteristic
49#1465—51no—
50#1459—51no—
51#1324—54no—
52C24×C5C22⋊C411yescharacteristic
53C24×C5C22⋊C411yescharacteristic
54C2×C5×Q8—42no—
55C2×C5×Q8—82no—
56C2×C5×D4—22no—
57C2×C5×D4—22no—
58C2×C5×D4—41no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C5×C4⋊C4—41no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—41no—
77C5×C22⋊C4—41no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—82no—
80C5×C22⋊C4—82no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—24no—
84#681—82no—
85C2×#168—42no—
86C2×#168—42no—
87C2×#168—82no—
88C2×C4⋊Q8Dic511yescharacteristic
89C2×C4×D4C2×D511yescharacteristic
90#407—101no—
91C2×C22⋊C8—101no—
92#393—21no—
93#393—21no—
94#390Dic512yes—
95#382C2×D512yes—
96#380—21no—
97#380—21no—
98C4×C4⋊C4Dic511yescharacteristic
99#324—52no—
100#324—52no—
101#323—101no—
102#323—101no—
103C23×C5—21no—
104C23×C5—21no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—41no—
111C23×C5—41no—
112C23×C5#10112yes—
113C23×C5C2×C22⋊C411yescharacteristic
114C5×Q8—84no—
115C5×D4—44no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—22no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5—42no—
132C2×C4×C5—42no—
133C2×C4×C5—81no—
134C2×C4×C5—81no—
135C2×C4×C5#9911yescharacteristic
136C2×C4×C5#9911yescharacteristic
137C2×C4×C5#13112yes—
138#168—82no—
139#168—82no—
140C22×Q8—21no—
141C22×D4C2×Dic511yescharacteristic
142C23×C4C22⋊D511yescharacteristic
143C23×C4C22⋊D511yescharacteristic
144C2×M16—201no—
145C22×C8—201no—
146C4⋊Q8—41no—
147C4⋊Q8—41no—
148C4×D4—41no—
149C4×D4—41no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4C2×Dic512yes—
153C2×C4⋊C4C22×D511yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4C22⋊D511yescharacteristic
157C2×C22⋊C4C22⋊D511yescharacteristic
158C2×C42C2×Dic512yes—
159C2×C42C2×Dic511yescharacteristic
160C22⋊C8—102no—
161C22⋊C8—102no—
162C22⋊C8—201no—
163C22⋊C8—201no—
164#95—21no—
165#95—22no—
166#95—22no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—22no—
170C22×C5—42no—
171C22×C5—42no—
172C22×C5—41no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5—81no—
178C22×C5—81no—
179C22×C5#40811yescharacteristic
180C22×C5C2×#9911yescharacteristic
181C22×C5C2×#10111yescharacteristic
182C4×C5—21no—
183C4×C5—22no—
184C4×C5—41no—
185C4×C5—41no—
186C4×C5—41no—
187C4×C5—82no—
188C4×C5—82no—
189C4×C5#35412yes—
190C24C22⋊Dic511yescharacteristic
191C24C22⋊Dic511yescharacteristic
192C2×Q8—42no—
193C2×Q8—82no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—41no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4C22⋊Dic511yescharacteristic
206C22×C4C22⋊Dic511yescharacteristic
207C22×C4C22×Dic511yescharacteristic
208C22×C4C2×C22⋊D511yescharacteristic
209C22×C4C2×C22⋊D511yescharacteristic
210M16—402no—
211C2×C8—202no—
212C2×C8—202no—
213C2×C8—402no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—82no—
222C22⋊C4—82no—
223C42—21no—
224C42—21no—
225C42—24no—
226C2×C5—21no—
227C2×C5—21no—
228C2×C5—42no—
229C2×C5—81no—
230C2×C5#147211yescharacteristic
231C2×C5C2×#35411yescharacteristic
232C2×C5#213411yescharacteristic
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23#396812yes—
243C23C2×C22⋊Dic511yescharacteristic
244Q8—84no—
245D4—44no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4#396611yescharacteristic
266C2×C4#396611yescharacteristic
267C2×C4#409412yes—
268C8—402no—
269C8—402no—
270C5#1156911yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C2×#396611yescharacteristic
284C22C2×#396811yescharacteristic
285C22#6552311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4#6476112yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1060248411yescharacteristic
299C2C2×#6476111yescharacteristic
300C2#1060265511yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2563C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2563D5
hypocenterC5#11569
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
4. #10598123C2semidirect
270. C5#11569semidirect

Maximal subgroups

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

subgroupindex
C5×#25632
#106023952
#106023932
#105981232
#115695