Finite Group Databasebeta

← #13021083

Subgroups — #13021083

Order 1280.

538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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#10614984C211yesmaximal, characteristic
2C2×#64931C214yesmaximal
3#10604186C211yesmaximal, characteristic
4#10604180C211yesmaximal, characteristic
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×#4090C412yes—
7C2×#4090C2212yes—
8C2×#4015C411yescharacteristic
9C2×#4004C2212yes—
10C2×#4004C2212yes—
11C2×#4002—21no—
12#65265—21no—
13#65265—21no—
14#65265—21no—
15#65265—21no—
16C42×Dic5C2211yescharacteristic
17#64931—28no—
18#64918—21no—
19#64918—21no—
20#64918—21no—
21#9702—51nomaximal, Sylow
22C22×C5×Q8C2×C412yes—
23C22×Dic10C2×C412yes—
24C22×#170—22no—
25C22×#170—22no—
26C5×C4⋊Q8—42no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C42×C5C2×C411yescharacteristic
30#4090—24no—
31#4090—24no—
32#4090—44no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×#683—22no—
36C2×#683—22no—
37C2×#683—22no—
38C2×#683—22no—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5C2311yescharacteristic
45#4015—42no—
46#4004—24no—
47#4004—22no—
48#4004D414yes—
49#4002—42no—
50#2868—51no—
51#1831—51no—
52#1767—51no—
53C2×#333—54no—
54C2×C5×Q8—24no—
55C2×C5×Q8—42no—
56C2×C5×Q8—42no—
57C22×C4×C5—22no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5C22⋊C411yescharacteristic
63C22×Dic5C22⋊C411yescharacteristic
64C22×Dic5C2×D411yescharacteristic
65C22×Dic5C2×D411yescharacteristic
66C2×Dic10—24no—
67C2×Dic10—42no—
68C2×Dic10—42no—
69C2×#170—24no—
70C2×#170—42no—
71C2×#170—42no—
72C2×#170—42no—
73C2×#170—42no—
74C2×#170—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C42×C5—22no—
78C4⋊Dic5—42no—
79C4⋊Dic5—42no—
80#683—44no—
81#683—44no—
82#683—44no—
83#683—42no—
84#683—42no—
85C4×Dic5—22no—
86C4×Dic5—22no—
87C4×Dic5—22no—
88C4×Dic5—22no—
89C4×Dic5SD1612yes—
90C4×Dic5Q1612yes—
91C4×Dic5C2×D412yes—
92C4×Dic5#4112yes—
93C2×C4⋊Q8—52no—
94C2×C4⋊Q8—52no—
95C2×C4⋊Q8—51no—
96C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
97C2×C4⋊C8—52no—
98C2×C4⋊C8—52no—
99C2×#97—101no—
100#384—101no—
101#384—101no—
102#384—101no—
103#384—101no—
104C43—51no—
105#336—101no—
106#336—101no—
107#336—101no—
108#333—108no—
109C23×C5C2×C22⋊C411yescharacteristic
110C5×Q8—84no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5#10012yes—
121C2×C4×C5#10312yes—
122C2×C4×C5C4×D412yes—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—21no—
126C2×Dic5—21no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130C2×Dic5#10012yes—
131C2×Dic5#10312yes—
132C2×Dic5#12112yes—
133C2×Dic5#12411yescharacteristic
134C2×Dic5#12711yescharacteristic
135C2×Dic5C2×SD1611yescharacteristic
136C2×Dic5C2×Q1611yescharacteristic
137C2×Dic5#13712yes—
138C2×Dic5#13712yes—
139C2×Dic5#13712yes—
140Dic10—84no—
141#170—44no—
142#170—82no—
143C22×Q8—52no—
144C22×Q8C2×AGL(1,𝔽5)12yes—
145C22×C8—102no—
146C22×C8—102no—
147C4⋊Q8—42no—
148C4⋊Q8—104no—
149C4⋊Q8—104no—
150C4⋊Q8—202no—
151C4⋊Q8—204no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—102no—
155C2×C4⋊C4—102no—
156C2×C4⋊C4—102no—
157C2×C4⋊C4—102no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4—101no—
160C2×C42—51no—
161C2×C42—51no—
162C2×C42—51no—
163C2×C42—51no—
164C2×C42—51no—
165C2×C42—51no—
166C2×C42C2×AGL(1,𝔽5)11yescharacteristic
167C4⋊C8—54no—
168C4⋊C8—102no—
169C4⋊C8—104no—
170#97—202no—
171C22×C5#39011yescharacteristic
172C22×C5C2×#10011yescharacteristic
173C22×C5C2×#10011yescharacteristic
174C22×C5C2×#10311yescharacteristic
175C22×C5#41911yescharacteristic
176C22×C5#41911yescharacteristic
177C22×C5#41911yescharacteristic
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—22no—
181C4×C5—82no—
182Dic5—22no—
183Dic5—22no—
184Dic5—82no—
185Dic5#46112yes—
186Dic5#46212yes—
187Dic5#49112yes—
188Dic5#49712yes—
189C2×Q8—24no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—104no—
193C2×Q8—202no—
194C2×Q8—202no—
195C22×C4—22no—
196C22×C4—51no—
197C22×C4—51no—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—102no—
201C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
202C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
203C22×C4C22×AGL(1,𝔽5)11yescharacteristic
204C2×C8—104no—
205C2×C8—202no—
206C2×C8—202no—
207C2×C8—202no—
208C2×C8—202no—
209C2×C8—202no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—202no—
213C4⋊C4—204no—
214C4⋊C4—202no—
215C4⋊C4—202no—
216C4⋊C4—204no—
217C4⋊C4—204no—
218C4⋊C4—202no—
219C42—22no—
220C42—52no—
221C42—52no—
222C42—52no—
223C42—52no—
224C42—102no—
225C42—102no—
226C42—102no—
227C42—102no—
228C2×C5#154811yescharacteristic
229C2×C5#154811yescharacteristic
230C2×C5#155811yescharacteristic
231C2×C5#155811yescharacteristic
232C2×C5#196011yescharacteristic
233C2×C5#196511yescharacteristic
234C2×C5#198111yescharacteristic
235C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
236Q8—84no—
237Q8—404no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—52no—
248C2×C4—51no—
249C2×C4—51no—
250C2×C4—51no—
251C2×C4—51no—
252C2×C4—52no—
253C2×C4—52no—
254C2×C4—52no—
255C2×C4—52no—
256C2×C4—52no—
257C2×C4—101no—
258C2×C4—101no—
259C2×C4—101no—
260C2×C4—101no—
261C2×C4—202no—
262C2×C4—202no—
263C2×C4—202no—
264C2×C4#400912yes—
265C2×C4#401312yes—
266C2×C4D4×AGL(1,𝔽5)12yes—
267C8—204no—
268C8—402no—
269C5#970211yescharacteristic, complemented, Sylow
270C22D5⋊#10011yescharacteristic
271C22#6578011yescharacteristic
272C22C2×#400911yescharacteristic
273C22#6578211yescharacteristic
274C22#6578211yescharacteristic
275C22#6578211yescharacteristic
276C22C2×#401311yescharacteristic
277C4—22no—
278C4—22no—
279C4—22no—
280C4—52no—
281C4—52no—
282C4—52no—
283C4—52no—
284C4—82no—
285C4—102no—
286C4—102no—
287C4—402no—
288C2#1060465911yescharacteristic
289C2#1060466211yescharacteristic
290C2#1060466711yescharacteristic
291C2#1060467311yescharacteristic
292C2#1060495311yescharacteristic
293C2#1060497111yescharacteristic
294C2#1060497211yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#9702
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
269. C5#9702semidirect

Maximal subgroups

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

subgroupindex
#106149842
C2×#649312
#106041862
#106041802
#97025