Finite Group Databasebeta

← #11986605

Subgroups — #11986605

Order 1280.

342 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 71 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×#1870C211yesmaximal, characteristic
2#10602412C211yesmaximal, characteristic
3#10602396C211yesmaximal, characteristic
4C22×C5×M16C411yescharacteristic, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×C5×C22⋊C8—21no—
7C2×C5×C22⋊C8C411yescharacteristic, complemented
8C2×#3966C412yes—
9#65501—21no—
10#65215—21no—
11C5×#336—21no—
12#64746—21no—
13#64745—21no—
14#64745C412yescomplemented
15#7320—51nomaximal, Sylow
16C22×C5×D4C2×C411yescharacteristic
17C23×C4×C5C2×C411yescharacteristic
18C23×C4×C5D411yescharacteristic
19C2×C5×M16—42no—
20C2×C5×M16—41no—
21C22×C5×C8—21no—
22C22×C5×C8—21no—
23C4×C5×D4—41no—
24C4×C5×D4—41no—
25C2×C5×C4⋊C4Q811yescharacteristic
26C2×C5×C22⋊C4C2×C411yescharacteristic
27C2×C5×C22⋊C4D411yescharacteristic
28C2×C42×C5D411yescharacteristic
29C2×C22⋊Dic5—22no—
30C2×C4⋊Dic5—41no—
31C5×C22⋊C8—42no—
32C5×C22⋊C8—41no—
33#3966—42no—
34#3963—41no—
35C22⋊#168—22no—
36C4⋊#168—41no—
37#3935—41no—
38#1870D511yescharacteristic
39#1799—51no—
40#1466—51no—
41C24×C5C4211yescharacteristic
42C24×C5C22⋊C411yescharacteristic
43C2×C5×D4—21no—
44C2×C5×D4—21no—
45C2×C5×D4—41no—
46C2×C5×D4—41no—
47C22×C4×C5—21no—
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5—41no—
52C22×C4×C5—41no—
53C22×C4×C5—41no—
54C22×C4×C5—41no—
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C4⋊C411yescharacteristic
58C22×C4×C5C4⋊C411yescharacteristic
59C22×C4×C5C4⋊C411yescharacteristic
60C22×Dic5—42no—
61C5×M16—42no—
62C5×M16—42no—
63C2×C5×C8—22no—
64C2×C5×C8—41no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C2×C5×C8—41no—
68C2×C5×C8—41no—
69C5×C4⋊C4—41no—
70C5×C22⋊C4—41no—
71C5×C22⋊C4—41no—
72C42×C5—21no—
73C42×C5—21no—
74C22⋊Dic5—42no—
75C22⋊Dic5—42no—
76C4⋊Dic5—81no—
77C4⋊Dic5—81no—
78C2×#168—42no—
79C22×M16Dic511yescharacteristic, complemented
80C2×C4×D4C2×D511yescharacteristic
81#432—101no—
82C2×#99—52no—
83C2×C22⋊C8—21no—
84C2×C22⋊C8Dic511yescharacteristic, complemented
85#380—101no—
86#342—101no—
87#336—21no—
88#323—52no—
89#323—101no—
90C23×C5—21no—
91C23×C5—21no—
92C23×C5—21no—
93C23×C5—21no—
94C23×C5—21no—
95C23×C5—41no—
96C23×C5—41no—
97C23×C5—41no—
98C23×C5—41no—
99C23×C5#9511yescharacteristic
100C23×C5#10011yescharacteristic
101C23×C5#10111yescharacteristic
102C5×D4—42no—
103C5×D4—42no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
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—42no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—81no—
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#9911yescharacteristic
123C2×Dic5—82no—
124C2×Dic5—82no—
125C2×Dic5—82no—
126C5×C8—42no—
127C5×C8—81no—
128#168—82no—
129C22×D4C4×D511yescharacteristic
130C23×C4C2×Dic511yescharacteristic
131C23×C4C22⋊D511yescharacteristic
132C2×M16—42no—
133C2×M16—41no—
134C22×C8—21no—
135C22×C8—21no—
136C4×D4—41no—
137C4×D4—41no—
138C2×C4⋊C4—201no—
139C2×C4⋊C4Dic1011yescharacteristic
140C2×C22⋊C4—102no—
141C2×C22⋊C4C4×D511yescharacteristic
142C2×C22⋊C4D2011yescharacteristic
143C2×C42C22⋊D511yescharacteristic
144C4⋊C8—201no—
145#99—202no—
146C22⋊C8—42no—
147C22⋊C8—41no—
148C22⋊C8—102no—
149#97—201no—
150#95—201no—
151C22×C5—21no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5—41no—
156C22×C5—41no—
157C22×C5—41no—
158C22×C5—41no—
159C22×C5—41no—
160C22×C5—41no—
161C22×C5—41no—
162C22×C5—81no—
163C22×C5—81no—
164C22×C5—81no—
165C22×C5#34211yescharacteristic
166C22×C5#34311yescharacteristic
167C22×C5#34411yescharacteristic
168C4×C5—21no—
169C4×C5—41no—
170C4×C5—41no—
171C4×C5—41no—
172C4×C5—41no—
173C4×C5AΣL(1,𝔽16)11yescharacteristic
174C4×C5#35211yescharacteristic
175Dic5—162no—
176C24C4×Dic511yescharacteristic
177C24#68511yescharacteristic
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—202no—
191C22×C4#68311yescharacteristic
192C22×C4#68311yescharacteristic
193C22×C4C4⋊Dic511yescharacteristic
194C22×C4#68511yescharacteristic
195C22×C4C22⋊Dic511yescharacteristic
196M16—42no—
197M16—42no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—202no—
205C4⋊C4—41no—
206C4⋊C4—401no—
207C4⋊C4—401no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—202no—
211C22⋊C4—202no—
212C42—21no—
213C42—21no—
214C2×C5—21no—
215C2×C5—21no—
216C2×C5—41no—
217C2×C5—41no—
218C2×C5—81no—
219C2×C5#130511yescharacteristic
220C2×C5#139011yescharacteristic
221C2×C5#139111yescharacteristic
222C23—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23#395511yescharacteristic
232C23#395611yescharacteristic
233C23#396311yescharacteristic
234D4—42no—
235D4—42no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—402no—
254C2×C4—402no—
255C2×C4—402no—
256C2×C4#396611yescharacteristic
257C2×C4#396611yescharacteristic
258C8—42no—
259C8—81no—
260C8—402no—
261C5#732011yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22#6474611yescharacteristic
277C22#6477411yescharacteristic
278C22#6477911yescharacteristic
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—802no—
285C4#6475611yescharacteristic
286C4#6475911yescharacteristic
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2—81no—
292C2#1059812811yescharacteristic
293C2#1059817511yescharacteristic
294C2#1059818211yescharacteristic
subgroupG/H
centerC22#64746
commutatorC24×C5C42
FrattiniC2×C4×D4C2×D5
FittingC5×#1870C2
socleC22×C5#342
prime radicalC22×C5×D4C2×C4
cosocleC2×C4×C5×D4C22
hypercenter#1870D5
hypocenterC5#7320
LCSG ▷ C24×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
4. C22×C5×M16C4semidirect
7. C2×C5×C22⋊C8C4semidirect
14. #64745C4semidirect
79. C22×M16Dic5semidirect
84. C2×C22⋊C8Dic5semidirect
261. C5#7320semidirect

Maximal subgroups

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

subgroupindex
C5×#18702
#106024122
#106023962
#73205