Finite Group Databasebeta

← #13023279

Subgroups — #13023279

Order 1280.

460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C4×#4082C211yesmaximal, characteristic
2#10604161C212yesmaximal, complemented
3#10598823C212yesmaximal
4#10598710C212yesmaximal, complemented
5C2×C4×C5×D4C411yescharacteristic
6C2×#4082C411yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8#65754—22no—
9#65510C2211yescharacteristic
10C4×C22⋊Dic5—22no—
11#65266C2211yescharacteristic
12#65263C411yescharacteristic
13#65234—22no—
14C42×Dic5C411yescharacteristic
15#64914—22no—
16#64913C2214yes—
17#11476—51nomaximal, Sylow
18C22×C5×D4C2×C411yescharacteristic
19C23×C4×C5—21no—
20C22×Dic10C2×C411yescharacteristic
21C4×C5×D4—41no—
22C4×C5×D4—41no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C5×C22⋊C4—21no—
25C2×C42×C5C2×C411yescharacteristic
26C2×C22⋊Dic5—22no—
27C2×C22⋊Dic5—22no—
28#4082—22no—
29#4082C814yescomplemented
30C2×C4⋊Dic5C2311yescharacteristic
31C2×#683D412yes—
32C2×C4×Dic5—21no—
33C2×C4×Dic5—21no—
34C2×C4×Dic5C2×C411yescharacteristic
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D412yes—
37C4×Dic10—41no—
38C4×Dic10—41no—
39C22⋊#170—24no—
40#4004—42no—
41C4×#170—42no—
42#3963—22no—
43#3963—22no—
44C4×#124—51no—
45#1461—52no—
46#1324—52no—
47#1318—52no—
48C24×C5—21no—
49C2×C5×D4—21no—
50C2×C5×D4—41no—
51C2×C5×D4—41no—
52C2×C5×D4C2×C812yes—
53C22×C4×C5—21no—
54C22×C4×C5—44no—
55C22×C4×C5—41no—
56C22×C4×C5—41no—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C22×Dic5—21no—
61C22×Dic5—21no—
62C22×Dic5C22⋊C412yes—
63C22×Dic5C2×D412yes—
64C2×Dic10—41no—
65C2×Dic10—41no—
66C2×Dic10C2×C812yes—
67C2×Dic10M1612yes—
68C2×#170—44no—
69C5×C4⋊C4—41no—
70C5×C22⋊C4—42no—
71C42×C5—21no—
72C42×C5—21no—
73C22⋊Dic5—28no—
74C22⋊Dic5—44no—
75C4⋊Dic5—41no—
76#683—42no—
77C4×Dic5—22no—
78C4×Dic5—22no—
79C4×Dic5—21no—
80C4×Dic5—42no—
81C4×Dic5—42no—
82C4×Dic5—41no—
83C4×Dic5C2×C812yes—
84C2×#124—51no—
85C2×C4×Q8—51no—
86C2×C4×D4AGL(1,𝔽5)11yescharacteristic
87#431—102no—
88#391—51no—
89#390—51no—
90#388—102no—
91#382—51no—
92C4×C22⋊C4—102no—
93C43—51no—
94#324—54no—
95#324—102no—
96C23×C5—22no—
97C23×C5—42no—
98C23×C5—42no—
99C23×C5—41no—
100C23×C5—41no—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×D4—42no—
103C5×D4—42no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—22no—
107C2×C4×C5—21no—
108C2×C4×C5—41no—
109C2×C4×C5—42no—
110C2×C4×C5—41no—
111C2×C4×C5—82no—
112C2×C4×C5—82no—
113C2×C4×C5#9911yescharacteristic
114C2×C4×C5#9911yescharacteristic
115C2×C4×C5C22×C811yescharacteristic
116C2×C4×C5C2×M1611yescharacteristic
117C2×Dic5—22no—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—22no—
122C2×Dic5—41no—
123C2×Dic5—41no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5—42no—
127C2×Dic5C22⋊C814yes—
128Dic10—42no—
129Dic10—42no—
130#170—84no—
131C22×Q8—51no—
132C22×D4C2×AGL(1,𝔽5)11yescharacteristic
133C23×C4—21no—
134#124—54no—
135#124—102no—
136C4×Q8—201no—
137C4×Q8—201no—
138C4×D4—41no—
139C4×D4—41no—
140C2×C4⋊C4—52no—
141C2×C4⋊C4—51no—
142C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
143C2×C22⋊C4—21no—
144C2×C22⋊C4—102no—
145C2×C22⋊C4—102no—
146C2×C42—51no—
147C2×C42—52no—
148C2×C42—51no—
149C2×C42—101no—
150C2×C42—101no—
151C2×C42C2×AGL(1,𝔽5)11yescharacteristic
152C4⋊C8—202no—
153C22⋊C8—104no—
154C4×C8—202no—
155#95—102no—
156#95—102no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5—44no—
160C22×C5—42no—
161C22×C5—82no—
162C22×C5—81no—
163C22×C5—81no—
164C22×C5C2×C22⋊C811yescharacteristic
165C22×C5C2×#9911yescharacteristic
166C22×C5#41311yescharacteristic
167C4×C5—21no—
168C4×C5—21no—
169C4×C5—21no—
170C4×C5—41no—
171C4×C5—81no—
172C4×C5#35512yes—
173Dic5—24no—
174Dic5—42no—
175Dic5—42no—
176Dic5—42no—
177C24—21no—
178C2×Q8—52no—
179C2×Q8—52no—
180C2×Q8—201no—
181C2×Q8—201no—
182C2×D4—21no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4D5⋊C812yes—
186C22×C4—21no—
187C22×C4—44no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—52no—
191C22×C4—52no—
192C22×C4—101no—
193C22×C4—101no—
194C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
195C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C22×C4C22×AGL(1,𝔽5)11yescharacteristic
197C2×C8—204no—
198C4⋊C4—41no—
199C4⋊C4—202no—
200C4⋊C4—201no—
201C22⋊C4—42no—
202C22⋊C4—108no—
203C22⋊C4—204no—
204C42—21no—
205C42—21no—
206C42—52no—
207C42—101no—
208C42—102no—
209C42—102no—
210C42—201no—
211C42—202no—
212C42—202no—
213C2×C5—21no—
214C2×C5—21no—
215C2×C5—82no—
216C2×C5#145911yescharacteristic
217C2×C5#212611yescharacteristic
218C2×C5C2×#35511yescharacteristic
219C23—22no—
220C23—42no—
221C23—42no—
222C23—41no—
223C23—41no—
224C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
225Q8—202no—
226Q8—202no—
227D4—42no—
228D4—42no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—54no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—102no—
240C2×C4—102no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—201no—
245C2×C4—201no—
246C2×C4—201no—
247C2×C4—201no—
248C2×C4—202no—
249C2×C4#401111yescharacteristic
250C2×C4#401111yescharacteristic
251C2×C4C2×D5⋊C811yescharacteristic
252C2×C4D5⋊M1611yescharacteristic
253C8—404no—
254C5#1147611yescharacteristic, complemented, Sylow
255C22—21no—
256C22—21no—
257C22—44no—
258C22—42no—
259C22—82no—
260C22—81no—
261C22—81no—
262C22D5⋊(C22⋊C8)11yescharacteristic
263C22#6576111yescharacteristic
264C22C2×#401111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—81no—
270C4—104no—
271C4—202no—
272C4—202no—
273C4—202no—
274C4#6492312yes—
275C2—21no—
276C2—21no—
277C2—82no—
278C2#1060487811yescharacteristic
279C2C2×#6492311yescharacteristic
280C2#1060499611yescharacteristic
subgroupG/H
centerC2×C4#4011
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C4⋊Dic5C23
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5#11476
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #10604161C2semidirect
4. #10598710C2semidirect
29. #4082C8semidirect
254. C5#11476semidirect

Maximal subgroups

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

subgroupindex
C4×#40822
#106041612
#105988232
#105987102
#114765