Finite Group Databasebeta

← #13020908

Subgroups — #13020908

Order 1280.

530 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 134 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#10608212C211yesmaximal, characteristic
2C2×Q8⋊#170C212yesmaximal
3C2×#64872C212yesmaximal
4#10604187C211yesmaximal, characteristic
5#10604173C211yesmaximal, characteristic
6C2×Q8×Dic5C2211yescharacteristic
7C2×#4090C411yescharacteristic
8C2×#4033C2211yescharacteristic
9C2×C4⋊#170C2212yes—
10C2×C4×#170C2212yes—
11C5×#391C411yescharacteristic
12#65265C411yescharacteristic
13C42×Dic5C2211yescharacteristic
14#65218C411yescharacteristic
15#64938—22no—
16#64936—22no—
17Q8⋊#170—24no—
18#64918—22no—
19#64918—22no—
20#64872—24no—
21#9641—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×Dic10C2×C411yescharacteristic
24C22×#170—22no—
25C22×#170—22no—
26C2×C5×C4⋊C4C2×C411yescharacteristic
27C2×C42×C5C2×C411yescharacteristic
28Q8×Dic5—22no—
29Q8×Dic5—22no—
30#4090—22no—
31#4090C814yescomplemented
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×#683—22no—
35C2×#683—22no—
36C2×#683—21no—
37C2×C4×Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5D412yes—
41C2×C4×Dic5D412yes—
42C2×C4×Dic5C2311yescharacteristic
43#4033—22no—
44#4033—22no—
45C4⋊#170—22no—
46C4⋊#170—22no—
47C4×#170—22no—
48C4×#170D414yes—
49C5×#95—22no—
50#3963—22no—
51C4×C4⋊Q8—51no—
52#1831—51no—
53#1744—51no—
54C2×Q8⋊C8—52no—
55C2×Q8⋊C8—52no—
56C2×C5×Q8—21no—
57C2×C5×Q8—22no—
58C2×C5×Q8—22no—
59C2×C5×Q8C2×C812yes—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5C22⋊C412yes—
63C22×C4×C5C22×C411yescharacteristic
64C22×Dic5—21no—
65C22×Dic5—21no—
66C22×Dic5C22⋊C412yes—
67C22×Dic5C2×D411yescharacteristic
68C22×Dic5C2×D411yescharacteristic
69C2×Dic10—22no—
70C2×Dic10—22no—
71C2×Dic10—21no—
72C2×Dic10C2×C812yes—
73C2×#170—24no—
74C2×#170—44no—
75C2×#170—42no—
76C2×#170—44no—
77C5×C4⋊C4—22no—
78C42×C5—22no—
79C4⋊Dic5—22no—
80C4⋊Dic5—42no—
81#683—28no—
82#683—44no—
83#683—42no—
84C4×Dic5—24no—
85C4×Dic5—42no—
86C4×Dic5—41no—
87C4×Dic5—41no—
88C4×Dic5—41no—
89C4×Dic5—41no—
90C4×Dic5C2×C812yes—
91C4×Dic5M1612yes—
92C4×Dic5C2×D412yes—
93C4×Dic5#4112yes—
94C2×C4⋊Q8—51no—
95C2×C4×Q8—51no—
96C2×C4×Q8—51no—
97C2×C4⋊C8—52no—
98C2×C4×C8—52no—
99#391—51no—
100#391AGL(1,𝔽5)11yescharacteristic
101#389—102no—
102#384—51no—
103C4×C4⋊C4—102no—
104C43—51no—
105#336—102no—
106#336—102no—
107Q8⋊C8—104no—
108Q8⋊C8—104no—
109C23×C5C2×C22⋊C411yescharacteristic
110C5×Q8—24no—
111C5×Q8—42no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—42no—
120C2×C4×C5C4×D412yes—
121C2×C4×C5C22×C811yescharacteristic
122C2×C4×C5C2×M1611yescharacteristic
123C2×C4×C5#13112yes—
124C2×Dic5—22no—
125C2×Dic5—22no—
126C2×Dic5—22no—
127C2×Dic5—22no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5—42no—
132C2×Dic5C22⋊C814yes—
133C2×Dic5#12112yes—
134C2×Dic5#12411yescharacteristic
135C2×Dic5#12711yescharacteristic
136C2×Dic5#13714yes—
137Dic10—24no—
138Dic10—42no—
139#170—44no—
140#170—82no—
141C22×Q8—51no—
142C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
143C22×C8—102no—
144C22×C8—102no—
145C4⋊Q8—54no—
146C4⋊Q8—102no—
147C4×Q8—102no—
148C4×Q8—102no—
149C4×Q8—102no—
150C4×Q8—102no—
151C2×C4⋊C4—51no—
152C2×C4⋊C4—102no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—102no—
156C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
157C2×C42—51no—
158C2×C42—51no—
159C2×C42—52no—
160C2×C42—52no—
161C2×C42—101no—
162C2×C42—101no—
163C2×C42C2×AGL(1,𝔽5)11yescharacteristic
164C4⋊C8—102no—
165C4⋊C8—102no—
166C4×C8—54no—
167C4×C8—102no—
168#95—22no—
169#95—102no—
170C22×C5#39011yescharacteristic
171C22×C5C2×C22⋊C811yescharacteristic
172C22×C5#40811yescharacteristic
173C22×C5#41912yes—
174C22×C5#42112yes—
175C4×C5—42no—
176C4×C5—42no—
177C4×C5—81no—
178C4×C5C8×D412yes—
179C4×C5#43612yes—
180Dic5—22no—
181Dic5—24no—
182Dic5—42no—
183Dic5—81no—
184Dic5#49112yes—
185Dic5#49712yes—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—52no—
190C2×Q8—101no—
191C2×Q8—102no—
192C2×Q8—102no—
193C2×Q8D5⋊C812yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—51no—
197C22×C4—51no—
198C22×C4—52no—
199C22×C4—101no—
200C22×C4—101no—
201C22×C4C22⋊AGL(1,𝔽5)12yes—
202C22×C4C22×AGL(1,𝔽5)11yescharacteristic
203C2×C8—104no—
204C2×C8—204no—
205C2×C8—202no—
206C2×C8—204no—
207C4⋊C4—22no—
208C4⋊C4—108no—
209C4⋊C4—102no—
210C4⋊C4—202no—
211C4⋊C4—202no—
212C4⋊C4—204no—
213C42—22no—
214C42—52no—
215C42—52no—
216C42—52no—
217C42—52no—
218C42—104no—
219C42—202no—
220C42—201no—
221C42—201no—
222C42—201no—
223C42—201no—
224C2×C5#147912yes—
225C2×C5#149712yes—
226C2×C5#195411yescharacteristic
227C2×C5#196011yescharacteristic
228C2×C5#196311yescharacteristic
229C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
230Q8—24no—
231Q8—42no—
232Q8—104no—
233Q8—202no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—51no—
243C2×C4—51no—
244C2×C4—54no—
245C2×C4—54no—
246C2×C4—52no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—102no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4—202no—
254C2×C4—201no—
255C2×C4C2×D5⋊C811yescharacteristic
256C2×C4D5⋊M1611yescharacteristic
257C2×C4#413112yes—
258C2×C4D4×AGL(1,𝔽5)12yes—
259C8—204no—
260C8—402no—
261C5#964111yescharacteristic, complemented, Sylow
262C22D5⋊(C22⋊C8)11yescharacteristic
263C22#6577511yescharacteristic
264C22#6578011yescharacteristic
265C22#6578212yes—
266C22#6579512yes—
267C4—42no—
268C4—42no—
269C4—52no—
270C4—52no—
271C4—81no—
272C4—102no—
273C4—104no—
274C4—202no—
275C4—401no—
276C4#6569212yes—
277C4#6569512yes—
278C2#1060424111yescharacteristic
279C2#1060443812yes—
280C2#1060451612yes—
281C2#1060456011yescharacteristic
282C2#1060467311yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#391C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#391AGL(1,𝔽5)
hypocenterC5#9641
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
31. #4090C8semidirect
261. C5#9641semidirect

Maximal subgroups

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

subgroupindex
#106082122
C2×Q8⋊#1702
C2×#648722
#106041872
#106041732
#96415