Finite Group Databasebeta

← #11986332

Subgroups — #11986332

Order 1280.

422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 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×#1463C211yesmaximal, characteristic
2#10602357C211yesmaximal, characteristic
3#10602355C211yesmaximal, characteristic
4C22×C5×C4⋊C4C2211yescharacteristic
5C22×C4×Dic5C411yescharacteristic
6C5×#407—21no—
7C2×#3963—21no—
8C2×#3963—21no—
9C2×#3963C411yescharacteristic
10#65496—21no—
11C5×#324—21no—
12C5×#324C412yescomplemented
13#64750—21no—
14#64750C412yescomplemented
15#7215—51nomaximal, Sylow
16C23×C4×C5C2×C411yescharacteristic
17C23×C4×C5D411yescharacteristic
18C23×C4×C5D411yescharacteristic
19C23×Dic5—21no—
20C23×Dic5—21no—
21C2×C5×M16—41no—
22C2×C5×C4⋊C4—41no—
23C2×C5×C4⋊C4—41no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C4⋊C4Q811yescharacteristic
28C2×C4×Dic5—41no—
29C2×C4×Dic5—42no—
30C2×#681—22no—
31C5×C22⋊C8—22no—
32C5×C22⋊C8—41no—
33#3963—24no—
34#3963—42no—
35#3963—41no—
36C22⋊#168—41no—
37C22⋊#168—41no—
38#1821—51no—
39#1463D511yescharacteristic
40#1436—51no—
41C24×C5C22⋊C411yescharacteristic
42C22×C4×C5—21no—
43C22×C4×C5—21no—
44C22×C4×C5—21no—
45C22×C4×C5—21no—
46C22×C4×C5—21no—
47C22×C4×C5—21no—
48C22×C4×C5—22no—
49C22×C4×C5—41no—
50C22×C4×C5—41no—
51C22×C4×C5—41no—
52C22×C4×C5—41no—
53C22×C4×C5—41no—
54C22×C4×C5C4211yescharacteristic
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C4⋊C411yescharacteristic
58C22×C4×C5C4⋊C411yescharacteristic
59C22×C4×C5C4⋊C411yescharacteristic
60C22×Dic5—22no—
61C22×Dic5—22no—
62C22×Dic5—22no—
63C22×Dic5—22no—
64C22×Dic5—41no—
65C22×Dic5—41no—
66C22×Dic5—41no—
67C22×Dic5—41no—
68C22×Dic5—41no—
69C22×Dic5—41no—
70C22×Dic5—41no—
71C22×Dic5—41no—
72C22×Dic5—41no—
73C22×Dic5—41no—
74C5×M16—81no—
75C5×M16—81no—
76C2×C5×C8—42no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C4×Dic5—42no—
82C4×Dic5—42no—
83#681—42no—
84#681—42no—
85C2×#168—42no—
86C22×C4⋊C4C2×D511yescharacteristic
87C22×C42—51no—
88#407—21no—
89#407—101no—
90C2×#95—51no—
91C2×#95—101no—
92C2×#95—101no—
93#343—52no—
94#343—101no—
95#324—21no—
96#324Dic512yescomplemented
97C23×C5—21no—
98C23×C5—21no—
99C23×C5—21no—
100C23×C5—21no—
101C23×C5—21no—
102C23×C5—21no—
103C23×C5#9511yescharacteristic
104C23×C5#9911yescharacteristic
105C23×C5#9911yescharacteristic
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—81no—
127C2×C4×C5#10412yes—
128C2×Dic5—24no—
129C2×Dic5—42no—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—81no—
139C2×Dic5—81no—
140C2×Dic5—81no—
141C2×Dic5—81no—
142C5×C8—82no—
143#168—82no—
144C23×C4—101no—
145C23×C4—101no—
146C23×C4C4×D511yescharacteristic
147C23×C4D2011yescharacteristic
148C23×C4C22⋊D511yescharacteristic
149C2×M16—41no—
150C2×M16—102no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4Dic1011yescharacteristic
154C2×C4⋊C4C4×D511yescharacteristic
155C2×C4⋊C4C2×Dic511yescharacteristic
156C2×C4⋊C4C22⋊D511yescharacteristic
157C2×C42—201no—
158C2×C42—202no—
159C22⋊C8—22no—
160C22⋊C8—41no—
161C22⋊C8—201no—
162C22⋊C8—201no—
163#95—104no—
164#95—201no—
165#95—202no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5H(3,ℤ/4)11yescharacteristic
181C22×C5#33911yescharacteristic
182C22×C5#34211yescharacteristic
183C22×C5AΣL(1,𝔽16)11yescharacteristic
184C22×C5#35211yescharacteristic
185C22×C5#35511yescharacteristic
186C22×C5#35611yescharacteristic
187C4×C5—22no—
188C4×C5—41no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193Dic5—44no—
194Dic5—82no—
195C24#68511yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—102no—
209C22×C4—102no—
210C22×C4—102no—
211C22×C4—102no—
212C22×C4—201no—
213C22×C4—201no—
214C22×C4—201no—
215C22×C4—201no—
216C22×C4—201no—
217C22×C4—201no—
218C22×C4—201no—
219C22×C4—201no—
220C22×C4—201no—
221C22×C4—201no—
222C22×C4C4×Dic511yescharacteristic
223C22×C4#68311yescharacteristic
224C22×C4#68311yescharacteristic
225C22×C4C4⋊Dic511yescharacteristic
226C22×C4#68511yescharacteristic
227C22×C4C22⋊Dic511yescharacteristic
228M16—81no—
229M16—81no—
230M16—202no—
231M16—202no—
232C2×C8—42no—
233C2×C8—202no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C42—202no—
239C42—202no—
240C2×C5—21no—
241C2×C5—21no—
242C2×C5—21no—
243C2×C5—21no—
244C2×C5—21no—
245C2×C5—21no—
246C2×C5#128411yescharacteristic
247C2×C5#139011yescharacteristic
248C2×C5#139411yescharacteristic
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23#393811yescharacteristic
256C23#393811yescharacteristic
257C23#396311yescharacteristic
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—104no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4—202no—
285C2×C4—202no—
286C2×C4—202no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4—401no—
292C2×C4—401no—
293C2×C4#395712yes—
294C8—82no—
295C8—402no—
296C5#721511yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#6469111yescharacteristic
312C22#6469211yescharacteristic
313C22#6469711yescharacteristic
314C22#6469811yescharacteristic
315C22#6474711yescharacteristic
316C22#6477511yescharacteristic
317C22#6477711yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—204no—
325C4—402no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1059817311yescharacteristic
333C2#1059818511yescharacteristic
334C2#1059819011yescharacteristic
subgroupG/H
centerC22#64747
commutatorC22×C4×C5C42
FrattiniC22×C4⋊C4C2×D5
FittingC5×#1463C2
socleC22×C5#342
prime radicalC24×C5C22⋊C4
cosocleC22×C5×C4⋊C4C22
hypercenter#1463D5
hypocenterC5#7215
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
12. C5×#324C4semidirect
14. #64750C4semidirect
96. #324Dic5semidirect
296. C5#7215semidirect

Maximal subgroups

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

subgroupindex
C5×#14632
#106023572
#106023552
#72155