Finite Group Databasebeta

← #11996982

Subgroups — #11996982

Order 1280.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#10614206C211yesmaximal, characteristic
2#10614167C211yesmaximal, characteristic
3C5×#1467C211yesmaximal, characteristic
4#10601617C212yesmaximal
5#10598240C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090C412yes—
8C2×#4015C2211yescharacteristic
9C5×#432C2212yes—
10#65313—24no—
11#65272—21no—
12#65272—21no—
13#65263C412yes—
14C4×C4⋊Dic5C2211yescharacteristic
15#65217—21no—
16#65217—21no—
17#65215—21no—
18#65215C2212yes—
19#65214—21no—
20C5×#324—21no—
21C5×#324—21no—
22#64701—24no—
23#9452—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×Dic10C2×C412yes—
26C4×C5×Q8—22no—
27C4×C5×Q8—22no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34#4090—44no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×#683—22no—
39C2×#683—22no—
40C2×C4×Dic5C2×C412yes—
41#4015—22no—
42#4015—22no—
43C5×C4⋊C8—22no—
44C5×C22⋊C8—22no—
45C5×#97—22no—
46#3963—22no—
47#3963—22no—
48#3963—21no—
49C22⋊#168—22no—
50C4⋊#168—22no—
51C4⋊#168—22no—
52C4⋊#168D414yes—
53#3935—22no—
54#3935—22no—
55C4×#168—22no—
56#2983—51no—
57#2546—51no—
58#1558—52no—
59#1467D511yescharacteristic
60#1285—52no—
61C2×C5×Q8—22no—
62C2×C5×Q8—22no—
63C2×C5×Q8—41no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×Dic5—22no—
72C22×Dic5—22no—
73C2×Dic10—24no—
74C2×Dic10—42no—
75C2×Dic10—42no—
76C2×C5×C8—42no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5C2×D412yes—
85C42×C5#4112yes—
86C4⋊Dic5—24no—
87C4⋊Dic5—41no—
88C4⋊Dic5—42no—
89C4⋊Dic5—41no—
90#683—44no—
91#683—44no—
92C4×Dic5—42no—
93C2×#168—24no—
94C2×C4⋊Q8—52no—
95C2×C4⋊Q8—51no—
96C2×C4×Q8C2×D511yescharacteristic
97#446—104no—
98#432—52no—
99#432—101no—
100#432C2×D512yes—
101#431—101no—
102#398—101no—
103#398—101no—
104#391—52no—
105#389—101no—
106#389—101no—
107C4×C4⋊C4—51no—
108#333—104no—
109#324—21no—
110#324—21no—
111C23×C5C2×C22⋊C411yescharacteristic
112C5×Q8—44no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—22no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5#10012yes—
127C2×C4×C5C4×D412yes—
128C2×C4×C5#12011yescharacteristic
129C2×C4×C5#12112yes—
130C2×C4×C5#12311yescharacteristic
131C2×Dic5—24no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137Dic10—84no—
138C5×C8—82no—
139#168—44no—
140C22×Q8—52no—
141C22×Q8C4×D511yescharacteristic
142C4⋊Q8—102no—
143C4⋊Q8—102no—
144C4⋊Q8—204no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—101no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4—102no—
150C2×C4⋊C4—101no—
151C2×C4⋊C4—101no—
152C2×C4⋊C4C4×D511yescharacteristic
153C2×C4⋊C4C22⋊D511yescharacteristic
154C2×C4⋊C4C22⋊D511yescharacteristic
155C2×C42—52no—
156C2×C42D2011yescharacteristic
157C2×C42D2011yescharacteristic
158C2×C42C22×D511yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—54no—
161C4⋊C8—102no—
162C4⋊C8—102no—
163C22⋊C8—22no—
164C22⋊C8—102no—
165#97—22no—
166#97—102no—
167#97—102no—
168C4×C8—102no—
169#95—102no—
170#95—102no—
171#95—101no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5#38611yescharacteristic
175C22×C5C2×#10011yescharacteristic
176C22×C5#41311yescharacteristic
177C4×C5—21no—
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—22no—
181C4×C5—41no—
182C4×C5—41no—
183C4×C5—41no—
184C4×C5#45612yes—
185Dic5—44no—
186Dic5—82no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—104no—
191C2×Q8—202no—
192C2×Q8—202no—
193C22×C4—102no—
194C22×C4—102no—
195C22×C4#68511yescharacteristic
196C22×C4#68511yescharacteristic
197C22×C4#68511yescharacteristic
198C22×C4#68511yescharacteristic
199C22×C4C2×C4×D511yescharacteristic
200C22×C4C2×D2011yescharacteristic
201C22×C4C2×C22⋊D511yescharacteristic
202C2×C8—42no—
203C2×C8—104no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—104no—
208C4⋊C4—204no—
209C4⋊C4—204no—
210C4⋊C4—201no—
211C4⋊C4—201no—
212C4⋊C4—202no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—202no—
218C42D4×D512yes—
219C42#71112yes—
220C2×C5—21no—
221C2×C5—21no—
222C2×C5#188611yescharacteristic
223C2×C5#190011yescharacteristic
224C2×C5#190911yescharacteristic
225C23C2×#68511yescharacteristic
226Q8—44no—
227Q8—404no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—104no—
242C2×C4—202no—
243C2×C4—202no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—202no—
247C2×C4#395512yes—
248C2×C4#402712yes—
249C2×C4#402811yescharacteristic
250C2×C4#403211yescharacteristic
251C2×C4#408512yes—
252C8—82no—
253C8—204no—
254C5#945211yescharacteristic, complemented, Sylow
255C22—21no—
256C22—21no—
257C22#6524711yescharacteristic
258C22C2×#395511yescharacteristic
259C22#6542111yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—204no—
268C4—402no—
269C4#6504112yes—
270C2—21no—
271C2—21no—
272C2#1060077811yescharacteristic
273C2#1060083911yescharacteristic
274C2#1060089611yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1467C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1467D5
hypocenterC5#9452
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
254. C5#9452semidirect

Maximal subgroups

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

subgroupindex
#106142062
#106141672
C5×#14672
#106016172
#105982402
#94525