Finite Group Databasebeta

← #12008951

Subgroups — #12008951

Order 1280.

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

normal subgroups only

This group has 480 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×#2542C211yesmaximal, characteristic
2#10602395C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10598126C214yesmaximal, complemented
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C5×C22⋊Q8—21no—
7C2×C5×C22⋊Q8—21no—
8C2×C4×C5×D4C2211yescharacteristic
9C5×#399—21no—
10C5×#399—21no—
11C5×#390C412yes—
12C5×#384C2212yes—
13C4×C5×C4⋊C4C411yescharacteristic
14#65496—21no—
15C2×C22⋊#168—21no—
16#64748C2212yes—
17#64748C2212yes—
18#64745—21no—
19#64745—21no—
20#11570—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×C5×D4C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C5×C4⋊Q8—41no—
26C5×C4⋊Q8—41no—
27C5×C22⋊Q8—44no—
28C5×C22⋊Q8—44no—
29C4×C5×D4—41no—
30C4×C5×D4—41no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4C2×C412yes—
36C2×C5×C4⋊C4C2311yescharacteristic
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4—22no—
39C2×C5×C22⋊C4D411yescharacteristic
40C2×C5×C22⋊C4D411yescharacteristic
41C2×C42×C5C2×C412yes—
42C2×C42×C5C2×C411yescharacteristic
43C2×#681—41no—
44C22×#168—41no—
45C5×#95—21no—
46C22⋊#168—22no—
47C22⋊#168—22no—
48C22⋊#168—41no—
49C22⋊#168—41no—
50#2542D511yescharacteristic
51#1465—51no—
52#1459—51no—
53#1325—54no—
54C24×C5C22⋊C411yescharacteristic
55C24×C5C22⋊C411yescharacteristic
56C2×C5×Q8—42no—
57C2×C5×Q8—42no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×D4—22no—
61C2×C5×D4—22no—
62C2×C5×D4—41no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—42no—
70C22×C4×C5—42no—
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C5×C4⋊C4—24no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—42no—
79C5×C4⋊C4—44no—
80C5×C4⋊C4—44no—
81C5×C4⋊C4—42no—
82C5×C22⋊C4—41no—
83C5×C22⋊C4—41no—
84C5×C22⋊C4—44no—
85C5×C22⋊C4—44no—
86C42×C5—21no—
87C42×C5—21no—
88C42×C5—24no—
89#681—82no—
90C2×#168—42no—
91C2×#168—42no—
92C2×#168—82no—
93C2×C4⋊Q8Dic511yescharacteristic
94C2×C22⋊Q8—21no—
95C2×C22⋊Q8—21no—
96C2×C4×D4C2×D511yescharacteristic
97#407—101no—
98C2×C22⋊C8—101no—
99#399—21no—
100#399—21no—
101#390Dic512yes—
102#384C2×D512yes—
103C4×C4⋊C4Dic511yescharacteristic
104#324—52no—
105#324—52no—
106#323—101no—
107#323—101no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5#10112yes—
118C23×C5C2×C22⋊C411yescharacteristic
119C5×Q8—82no—
120C5×Q8—82no—
121C5×D4—44no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—22no—
125C2×C4×C5—24no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5—42no—
132C2×C4×C5—42no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—42no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—81no—
140C2×C4×C5—81no—
141C2×C4×C5#9911yescharacteristic
142C2×C4×C5#9911yescharacteristic
143C2×C4×C5#13112yes—
144#168—82no—
145#168—82no—
146C22×Q8—21no—
147C22×D4C2×Dic511yescharacteristic
148C23×C4C22⋊D511yescharacteristic
149C23×C4C22⋊D511yescharacteristic
150C2×M16—201no—
151C22×C8—201no—
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C22⋊Q8—44no—
155C22⋊Q8—44no—
156C4×D4—41no—
157C4×D4—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C2×Dic512yes—
163C2×C4⋊C4C22×D511yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4C22⋊D511yescharacteristic
167C2×C22⋊C4C22⋊D511yescharacteristic
168C2×C42C2×Dic512yes—
169C2×C42C2×Dic511yescharacteristic
170C22⋊C8—102no—
171C22⋊C8—102no—
172C22⋊C8—201no—
173C22⋊C8—201no—
174#95—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—22no—
178C22×C5—42no—
179C22×C5—42no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—41no—
185C22×C5—81no—
186C22×C5—81no—
187C22×C5#40811yescharacteristic
188C22×C5C2×#9911yescharacteristic
189C22×C5C2×#10111yescharacteristic
190C4×C5—21no—
191C4×C5—22no—
192C4×C5—44no—
193C4×C5—41no—
194C4×C5—41no—
195C4×C5—41no—
196C4×C5—82no—
197C4×C5#35312yes—
198C24C22⋊Dic511yescharacteristic
199C24C22⋊Dic511yescharacteristic
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—41no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C22⋊Dic511yescharacteristic
216C22×C4C22⋊Dic511yescharacteristic
217C22×C4C22×Dic511yescharacteristic
218C22×C4C2×C22⋊D511yescharacteristic
219C22×C4C2×C22⋊D511yescharacteristic
220M16—402no—
221C2×C8—202no—
222C2×C8—202no—
223C2×C8—402no—
224C4⋊C4—24no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—44no—
228C4⋊C4—44no—
229C4⋊C4—42no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—44no—
233C22⋊C4—44no—
234C42—21no—
235C42—21no—
236C42—24no—
237C2×C5—21no—
238C2×C5—21no—
239C2×C5—42no—
240C2×C5—81no—
241C2×C5#147211yescharacteristic
242C2×C5C2×#35311yescharacteristic
243C2×C5#213511yescharacteristic
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#396812yes—
254C23C2×C22⋊Dic511yescharacteristic
255Q8—82no—
256Q8—82no—
257D4—44no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4#396611yescharacteristic
278C2×C4#396611yescharacteristic
279C2×C4#409412yes—
280C8—402no—
281C8—402no—
282C5#1157011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C2×#396611yescharacteristic
296C22C2×#396811yescharacteristic
297C22#6552311yescharacteristic
298C4—21no—
299C4—22no—
300C4—44no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4#6476512yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1060248411yescharacteristic
311C2C2×#6476511yescharacteristic
312C2#1060266611yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2542C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2542D5
hypocenterC5#11570
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
4. #10598126C2semidirect
282. C5#11570semidirect

Maximal subgroups

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

subgroupindex
C5×#25422
#106023952
#106023932
#105981262
#115705