Finite Group Databasebeta

← #13021086

Subgroups — #13021086

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#10606087C211yesmaximal, characteristic
2C2×#64873C214yesmaximal
3#10604186C211yesmaximal, characteristic
4#10604180C211yesmaximal, characteristic
5C2×#4034—21no—
6C2×#4034—21no—
7C2×#4034C2212yes—
8C2×#4004C2212yes—
9C2×#4004C2212yes—
10C2×#4002—21no—
11C5×#384C411yescharacteristic
12#65265—21no—
13#65265—21no—
14#65265C412yes—
15#65224C411yescharacteristic
16C42×Dic5C2211yescharacteristic
17#64918—21no—
18#64918—21no—
19#64918—21no—
20#64873—28no—
21#9705—51nomaximal, Sylow
22C22×Dic10—22no—
23C22×#170—22no—
24C22×#170—22no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C42×C5C2×C411yescharacteristic
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5C2×C412yes—
32C2×#683—22no—
33C2×#683—22no—
34C2×#683—22no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5C2311yescharacteristic
41#4034—24no—
42#4034—24no—
43#4034—44no—
44#4034—42no—
45#4034—42no—
46#4004—24no—
47#4004—22no—
48#4004D414yes—
49#4002—42no—
50#2868—51no—
51#1831—51no—
52#1767—51no—
53C2×#332—54no—
54C22×C4×C5—22no—
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22×C411yescharacteristic
58C22×Dic5—22no—
59C22×Dic5C22⋊C411yescharacteristic
60C22×Dic5C22⋊C411yescharacteristic
61C22×Dic5C2×D411yescharacteristic
62C22×Dic5C2×D411yescharacteristic
63C2×Dic10—44no—
64C2×Dic10—42no—
65C2×Dic10—42no—
66C2×Dic10—44no—
67C2×#170—24no—
68C2×#170—42no—
69C2×#170—42no—
70C2×#170—42no—
71C2×#170—42no—
72C2×#170—42no—
73C5×C4⋊C4—24no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C42×C5—22no—
77C4⋊Dic5—24no—
78C4⋊Dic5—42no—
79C4⋊Dic5—42no—
80#683—44no—
81#683—44no—
82#683—42no—
83#683—42no—
84C4×Dic5—22no—
85C4×Dic5—22no—
86C4×Dic5—22no—
87C4×Dic5—22no—
88C4×Dic5D812yes—
89C4×Dic5SD1612yes—
90C4×Dic5C2×D412yes—
91C4×Dic5#4112yes—
92C2×C4⋊Q8—52no—
93C2×C4⋊Q8—101no—
94C2×C4⋊Q8—101no—
95C2×C4⋊C8—52no—
96C2×C4⋊C8—52no—
97C2×#97—101no—
98#384—52no—
99#384—51no—
100#384—101no—
101#384—101no—
102#384AGL(1,𝔽5)11yescharacteristic
103C43—51no—
104#336—101no—
105#336—101no—
106#336—101no—
107#332—108no—
108C23×C5C2×C22⋊C411yescharacteristic
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5#10112yes—
119C2×C4×C5#10212yes—
120C2×C4×C5C4×D412yes—
121C2×Dic5—21no—
122C2×Dic5—21no—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5#10112yes—
129C2×Dic5#10212yes—
130C2×Dic5#12112yes—
131C2×Dic5#12411yescharacteristic
132C2×Dic5#12711yescharacteristic
133C2×Dic5C2×D811yescharacteristic
134C2×Dic5C2×SD1611yescharacteristic
135C2×Dic5AGL(1,ℤ/8)12yes—
136C2×Dic5#13712yes—
137C2×Dic5#13712yes—
138Dic10—84no—
139Dic10—84no—
140#170—44no—
141#170—82no—
142C22×Q8—102no—
143C22×C8—102no—
144C22×C8—102no—
145C4⋊Q8—104no—
146C4⋊Q8—104no—
147C4⋊Q8—202no—
148C4⋊Q8—202no—
149C4⋊Q8—204no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—52no—
153C2×C4⋊C4—102no—
154C2×C4⋊C4—102no—
155C2×C4⋊C4—102no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4—101no—
158C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
159C2×C42—51no—
160C2×C42—51no—
161C2×C42—51no—
162C2×C42—51no—
163C2×C42—51no—
164C2×C42—51no—
165C2×C42C2×AGL(1,𝔽5)11yescharacteristic
166C4⋊C8—54no—
167C4⋊C8—102no—
168C4⋊C8—104no—
169#97—202no—
170C22×C5#39011yescharacteristic
171C22×C5C2×#10111yescharacteristic
172C22×C5C2×#10111yescharacteristic
173C22×C5C2×#10211yescharacteristic
174C22×C5#41811yescharacteristic
175C22×C5#41911yescharacteristic
176C22×C5#41911yescharacteristic
177C4×C5—22no—
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—82no—
181Dic5—22no—
182Dic5—22no—
183Dic5—82no—
184Dic5#45912yes—
185Dic5#46012yes—
186Dic5#49112yes—
187Dic5#49712yes—
188C2×Q8—204no—
189C2×Q8—202no—
190C2×Q8—202no—
191C2×Q8—204no—
192C22×C4—22no—
193C22×C4—51no—
194C22×C4—51no—
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—102no—
198C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
199C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
200C22×C4C22×AGL(1,𝔽5)11yescharacteristic
201C2×C8—104no—
202C2×C8—202no—
203C2×C8—202no—
204C2×C8—202no—
205C2×C8—202no—
206C2×C8—202no—
207C4⋊C4—24no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—104no—
211C4⋊C4—202no—
212C4⋊C4—202no—
213C4⋊C4—202no—
214C4⋊C4—204no—
215C4⋊C4—204no—
216C4⋊C4—202no—
217C42—22no—
218C42—52no—
219C42—52no—
220C42—52no—
221C42—52no—
222C42—102no—
223C42—102no—
224C42—102no—
225C42—102no—
226C2×C5#154611yescharacteristic
227C2×C5#154611yescharacteristic
228C2×C5#155611yescharacteristic
229C2×C5#155611yescharacteristic
230C2×C5#196011yescharacteristic
231C2×C5#196611yescharacteristic
232C2×C5#198211yescharacteristic
233C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
234Q8—404no—
235Q8—404no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—51no—
246C2×C4—51no—
247C2×C4—52no—
248C2×C4—51no—
249C2×C4—51no—
250C2×C4—52no—
251C2×C4—52no—
252C2×C4—52no—
253C2×C4—52no—
254C2×C4—52no—
255C2×C4—101no—
256C2×C4—101no—
257C2×C4—101no—
258C2×C4—101no—
259C2×C4—202no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4#400512yes—
263C2×C4#400712yes—
264C2×C4D4×AGL(1,𝔽5)12yes—
265C8—204no—
266C8—402no—
267C5#970511yescharacteristic, complemented, Sylow
268C22C2×#400511yescharacteristic
269C22C2×#400711yescharacteristic
270C22#6576711yescharacteristic
271C22#6578011yescharacteristic
272C22#6578211yescharacteristic
273C22#6578211yescharacteristic
274C22D5⋊#10111yescharacteristic
275C4—22no—
276C4—22no—
277C4—22no—
278C4—52no—
279C4—52no—
280C4—52no—
281C4—52no—
282C4—82no—
283C4—102no—
284C4—102no—
285C4—402no—
286C2#1060427711yescharacteristic
287C2#1060427911yescharacteristic
288C2#1060433911yescharacteristic
289C2#1060461311yescharacteristic
290C2#1060465811yescharacteristic
291C2#1060466111yescharacteristic
292C2#1060467311yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#384C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#384AGL(1,𝔽5)
hypocenterC5#9705
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
267. C5#9705semidirect

Maximal subgroups

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

subgroupindex
#106060872
C2×#648732
#106041862
#106041802
#97055