Finite Group Databasebeta

← #13019554

Subgroups — #13019554

Order 1280.

498 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 116 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#10617521C211yesmaximal, characteristic
2#10608216C211yesmaximal, characteristic
3#10604976C211yesmaximal, characteristic
4#10604271C212yesmaximal
5#10598695C212yesmaximal
6C2×Q8×Dic5C2211yescharacteristic
7C2×#4090C411yescharacteristic
8C2×#4033C2211yescharacteristic
9Q8×#170—24no—
10#65748—22no—
11#65748C2212yes—
12#65748C2212yes—
13C5×#391C411yescharacteristic
14#65266C411yescharacteristic
15#65221C2211yescharacteristic
16#65218C411yescharacteristic
17#64944—22no—
18#64941—22no—
19#64913—22no—
20#64872—24no—
21#9100—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×Dic10C2×C411yescharacteristic
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C42×C5C2×C411yescharacteristic
26Q8×Dic5—22no—
27Q8×Dic5—22no—
28#4090—22no—
29#4090C814yescomplemented
30C2×C4⋊Dic5C2×C411yescharacteristic
31C2×C4⋊Dic5D412yes—
32C2×#683—22no—
33C2×#683—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D412yes—
37C2×C4×Dic5C2311yescharacteristic
38#4033—22no—
39#4033—22no—
40C22⋊#170—22no—
41C22⋊#170—22no—
42C4⋊#170—24no—
43C4⋊#170—22no—
44C4⋊#170—22no—
45C4×#170—24no—
46C4×#170—22no—
47C4×#170D414yes—
48C5×#95—22no—
49#3963—22no—
50#3963—22no—
51#3963—21no—
52#3963—21no—
53#2982—51no—
54#2327—51no—
55#1479—52no—
56#1461—51no—
57#1274—52no—
58C2×C5×Q8—22no—
59C2×C5×Q8—22no—
60C2×C5×Q8C2×C812yes—
61C2×C5×Q8M1612yes—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5C22⋊C412yes—
65C22×C4×C5C22×C411yescharacteristic
66C22×Dic5—21no—
67C22×Dic5—21no—
68C22×Dic5C22⋊C412yes—
69C22×Dic5C2×D411yescharacteristic
70C22×Dic5C2×D411yescharacteristic
71C2×Dic10—22no—
72C2×Dic10—22no—
73C2×Dic10—21no—
74C2×Dic10C2×C812yes—
75C2×#170—24no—
76C2×#170—42no—
77C5×C4⋊C4—22no—
78C42×C5—22no—
79C4⋊Dic5—22no—
80C4⋊Dic5—24no—
81#683—28no—
82#683—41no—
83#683—41no—
84C4×Dic5—21no—
85C4×Dic5—22no—
86C4×Dic5—22no—
87C4×Dic5—42no—
88C4×Dic5C2×C812yes—
89C4×Dic5C2×D412yes—
90C4×Dic5#4112yes—
91C2×C4⋊Q8—51no—
92C2×C4×Q8—51no—
93C2×C4×Q8—51no—
94C8×Q8—104no—
95#431—52no—
96#431—52no—
97#431—102no—
98#391—51no—
99#391AGL(1,𝔽5)11yescharacteristic
100#387—102no—
101#387—102no—
102#382—51no—
103#376—51no—
104Q8⋊C8—104no—
105#324—102no—
106C23×C5C2×C22⋊C411yescharacteristic
107C5×Q8—24no—
108C5×Q8—24no—
109C2×C4×C5—22no—
110C2×C4×C5—22no—
111C2×C4×C5—41no—
112C2×C4×C5—41no—
113C2×C4×C5—42no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5C22⋊C814yes—
117C2×C4×C5C4×D412yes—
118C2×C4×C5C22×C811yescharacteristic
119C2×C4×C5C2×M1611yescharacteristic
120C2×C4×C5#13112yes—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—22no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5—41no—
127C2×Dic5—41no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5#12011yescharacteristic
132C2×Dic5#12112yes—
133C2×Dic5#12311yescharacteristic
134Dic10—24no—
135Dic10—42no—
136#170—44no—
137#170—82no—
138C22×Q8—51no—
139C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
140C4⋊Q8—54no—
141C4⋊Q8—102no—
142C4×Q8—102no—
143C4×Q8—102no—
144C4×Q8—102no—
145C4×Q8—102no—
146C2×C4⋊C4—52no—
147C2×C4⋊C4—51no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4—101no—
150C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
151C2×C42—51no—
152C2×C42—51no—
153C2×C42—52no—
154C2×C42—101no—
155C2×C42C2×AGL(1,𝔽5)11yescharacteristic
156C4⋊C8—102no—
157C4⋊C8—102no—
158C4⋊C8—104no—
159C22⋊C8—102no—
160C22⋊C8—102no—
161C4×C8—54no—
162C4×C8—102no—
163C4×C8—104no—
164#95—22no—
165#95—101no—
166#95—101no—
167#95—102no—
168#95—102no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5#38611yescharacteristic
172C22×C5C2×C22⋊C811yescharacteristic
173C22×C5#40811yescharacteristic
174C4×C5—24no—
175C4×C5—81no—
176C4×C5—81no—
177C4×C5C8×D412yes—
178C4×C5#43512yes—
179Dic5—22no—
180Dic5—21no—
181Dic5—21no—
182Dic5—42no—
183Dic5—42no—
184Dic5—42no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—52no—
188C2×Q8—101no—
189C2×Q8—102no—
190C2×Q8—102no—
191C2×Q8D5⋊C812yes—
192C2×Q8#70012yes—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—52no—
198C22×C4—101no—
199C22×C4—101no—
200C22×C4C22⋊AGL(1,𝔽5)12yes—
201C22×C4C22×AGL(1,𝔽5)11yescharacteristic
202C2×C8—104no—
203C2×C8—202no—
204C4⋊C4—22no—
205C4⋊C4—104no—
206C4⋊C4—102no—
207C4⋊C4—108no—
208C4⋊C4—201no—
209C4⋊C4—201no—
210C42—22no—
211C42—52no—
212C42—52no—
213C42—52no—
214C42—102no—
215C42—102no—
216C42—101no—
217C42—202no—
218C2×C5—21no—
219C2×C5—21no—
220C2×C5#186911yescharacteristic
221C2×C5#190911yescharacteristic
222C2×C5#191211yescharacteristic
223C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
224Q8—24no—
225Q8—24no—
226Q8—104no—
227Q8—202no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—51no—
236C2×C4—51no—
237C2×C4—52no—
238C2×C4—102no—
239C2×C4—102no—
240C2×C4—102no—
241C2×C4—201no—
242C2×C4—201no—
243C2×C4—201no—
244C2×C4—201no—
245C2×C4—201no—
246C2×C4—201no—
247C2×C4—202no—
248C2×C4#400314yes—
249C2×C4C2×D5⋊C811yescharacteristic
250C2×C4C2×#70011yescharacteristic
251C2×C4#413112yes—
252C2×C4D4×AGL(1,𝔽5)12yes—
253C8—204no—
254C8—402no—
255C5#910011yescharacteristic, complemented, Sylow
256C22—21no—
257C22—21no—
258C22C2×#400311yescharacteristic
259C22#6577511yescharacteristic
260C22#6577911yescharacteristic
261C4—24no—
262C4—81no—
263C4—81no—
264C4—101no—
265C4—101no—
266C4—102no—
267C4—202no—
268C4—202no—
269C4—202no—
270C4#6569212yes—
271C4#6569312yes—
272C2—21no—
273C2—21no—
274C2#1060423311yescharacteristic
275C2#1060456511yescharacteristic
276C2#1060467711yescharacteristic
subgroupG/H
centerC22#65779
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#391C4
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#391AGL(1,𝔽5)
hypocenterC5#9100
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
29. #4090C8semidirect
255. C5#9100semidirect

Maximal subgroups

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

subgroupindex
#106175212
#106082162
#106049762
#106042712
#105986952
#91005