Finite Group Databasebeta

← #13019192

Subgroups — #13019192

Order 1280.

510 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#10617522C211yesmaximal, characteristic
2Dic5×C4⋊Q8C211yesmaximal, characteristic
3#10604976C211yesmaximal, characteristic
4#10604967C212yesmaximal
5#10598696C212yesmaximal
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×Q8×Dic5C2211yescharacteristic
8C2×Q8×Dic5C2211yescharacteristic
9#65788—24no—
10#65757—22no—
11#65748C2212yes—
12#65748C2212yes—
13#65519C411yescharacteristic
14#65519C411yescharacteristic
15#65274—22no—
16C4⋊C4×Dic5—22no—
17#65224C411yescharacteristic
18C42×Dic5C2211yescharacteristic
19Q8⋊#170—24no—
20#64913—22no—
21#8962—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×C5×Q8C2×C411yescharacteristic
24C5×C4⋊Q8—22no—
25C5×C4⋊Q8—22no—
26C2×C5×C4⋊C4—22no—
27C2×C42×C5C2×C411yescharacteristic
28Q8×Dic5—22no—
29Q8×Dic5—22no—
30Q8×Dic5—22no—
31Q8×Dic5—22no—
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5D412yes—
37C2×C4×Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D412yes—
42C2×C4×Dic5C2311yescharacteristic
43C22⋊#170—22no—
44C22⋊#170—22no—
45#4004—24no—
46#4002—24no—
47C4⋊#170—22no—
48C4⋊#170D414yes—
49C4×#170—22no—
50C4×#170—22no—
51#3963—22no—
52#3963—22no—
53#2983—51no—
54C4×C4⋊Q8—51no—
55#1479—52no—
56#1461—51no—
57#1276—52no—
58C2×C5×Q8—22no—
59C2×C5×Q8—21no—
60C2×C5×Q8—21no—
61C2×C5×Q8—21no—
62C2×C5×Q8—22no—
63C2×C5×Q8—22no—
64C2×C5×Q8—22no—
65C2×C5×Q8M1612yes—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C22⋊C412yes—
69C22×C4×C5C22×C411yescharacteristic
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5C22⋊C412yes—
73C22×Dic5C2×D411yescharacteristic
74C22×Dic5C2×D411yescharacteristic
75C2×#170—24no—
76C2×#170—42no—
77C5×C4⋊C4—28no—
78C42×C5—21no—
79C42×C5M1612yes—
80C4⋊Dic5—22no—
81C4⋊Dic5—24no—
82C4⋊Dic5—22no—
83C4⋊Dic5—44no—
84C4⋊Dic5—42no—
85C4×Dic5—24no—
86C4×Dic5—22no—
87C4×Dic5—22no—
88C4×Dic5—22no—
89C4×Dic5—42no—
90C4×Dic5—41no—
91C4×Dic5—41no—
92C4×Dic5C2×D412yes—
93C4×Dic5#4112yes—
94C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
95C2×C4×Q8—51no—
96C2×C4×Q8—51no—
97#446—104no—
98#432—102no—
99#431—52no—
100#431—52no—
101#391—51no—
102#391—51no—
103#389—102no—
104#384—51no—
105C4×C4⋊C4—102no—
106C43—51no—
107Q8⋊C8—104no—
108#324—102no—
109C23×C5C2×C22⋊C411yescharacteristic
110C5×Q8—24no—
111C5×Q8—42no—
112C5×Q8—42no—
113C5×Q8—42no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—22no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5C4×D412yes—
124C2×C4×C5C2×M1611yescharacteristic
125C2×C4×C5C2×M1611yescharacteristic
126C2×C4×C5#13112yes—
127C2×Dic5—22no—
128C2×Dic5—22no—
129C2×Dic5—22no—
130C2×Dic5—41no—
131C2×Dic5—41no—
132C2×Dic5—41no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—41no—
136C2×Dic5#12011yescharacteristic
137C2×Dic5#12112yes—
138C2×Dic5#12311yescharacteristic
139#170—44no—
140#170—82no—
141C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
142C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4×Q8—102no—
146C4×Q8—102no—
147C4×Q8—102no—
148C4×Q8—102no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—52no—
151C2×C4⋊C4—51no—
152C2×C4⋊C4—51no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—102no—
155C2×C42—51no—
156C2×C42—52no—
157C2×C42—51no—
158C2×C42—101no—
159C2×C42—101no—
160C2×C42—101no—
161C2×C42C2×AGL(1,𝔽5)11yescharacteristic
162C4⋊C8—54no—
163C4⋊C8—102no—
164C4⋊C8—104no—
165C22⋊C8—102no—
166C22⋊C8—102no—
167#97—104no—
168C4×C8—102no—
169C4×C8—102no—
170#95—102no—
171#95—102no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5#38611yescharacteristic
175C22×C5#40711yescharacteristic
176C22×C5#40811yescharacteristic
177C4×C5—24no—
178C4×C5—42no—
179C4×C5—42no—
180C4×C5#43512yes—
181C4×C5#43612yes—
182Dic5—22no—
183Dic5—21no—
184Dic5—42no—
185Dic5—42no—
186Dic5—81no—
187Dic5#45612yes—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8#70412yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—52no—
201C22×C4—101no—
202C22×C4—101no—
203C22×C4C22⋊AGL(1,𝔽5)12yes—
204C22×C4C22×AGL(1,𝔽5)11yescharacteristic
205C2×C8—104no—
206C2×C8—202no—
207C4⋊C4—28no—
208C4⋊C4—104no—
209C4⋊C4—102no—
210C4⋊C4—102no—
211C4⋊C4—204no—
212C4⋊C4—202no—
213C42—21no—
214C42—52no—
215C42—52no—
216C42—102no—
217C42—102no—
218C42—104no—
219C42—102no—
220C42—202no—
221C42—201no—
222C42—201no—
223C42#70412yes—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5#187011yescharacteristic
227C2×C5#188411yescharacteristic
228C2×C5#188611yescharacteristic
229C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
230Q8—24no—
231Q8—42no—
232Q8—42no—
233Q8—42no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—51no—
244C2×C4—51no—
245C2×C4—52no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—201no—
250C2×C4—201no—
251C2×C4—201no—
252C2×C4—202no—
253C2×C4—202no—
254C2×C4—201no—
255C2×C4#413112yes—
256C2×C4D4×AGL(1,𝔽5)12yes—
257C2×C4C2×#70411yescharacteristic
258C2×C4C2×#70411yescharacteristic
259C8—204no—
260C8—402no—
261C5#896211yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22#6577511yescharacteristic
265C22#6577911yescharacteristic
266C22#6579811yescharacteristic
267C4—24no—
268C4—42no—
269C4—42no—
270C4—52no—
271C4—101no—
272C4—102no—
273C4—202no—
274C4—202no—
275C4—401no—
276C4#6577312yes—
277C4#6577412yes—
278C2—21no—
279C2—21no—
280C2#1060467011yescharacteristic
281C2#1060467611yescharacteristic
282C2#1060494711yescharacteristic
subgroupG/H
centerC22#65779
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#8962
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
261. C5#8962semidirect

Maximal subgroups

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

subgroupindex
#106175222
Dic5×C4⋊Q82
#106049762
#106049672
#105986962
#89625