Finite Group Databasebeta

← #11997142

Subgroups — #11997142

Order 1280.

474 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 127 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#10614212C211yesmaximal, characteristic
2#10614166C211yesmaximal, characteristic
3C5×#1801C211yesmaximal, characteristic
4#10601293C212yesmaximal
5#10598204C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C5×#423C2212yes—
9C2×C5×#101—21no—
10#65519—21no—
11Q8×#168—24no—
12#65275C412yes—
13#65268C412yes—
14#65262—21no—
15#65225C2211yescharacteristic
16#65222—22no—
17#65214—22no—
18#65214C2212yes—
19C5×#343—21no—
20#64704—24no—
21#9484—51nomaximal, Sylow
22C22×C5×Q8D411yescharacteristic
23C22×Dic10C2×C411yescharacteristic
24C2×C5×M16—22no—
25C4×C5×Q8—22no—
26C4×C5×Q8—22no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C42×C5D412yes—
30C2×C42×C5C2311yescharacteristic
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—22no—
34C2×#683—21no—
35C2×C4×Dic5—21no—
36C4×Dic10—22no—
37C4×Dic10—22no—
38C5×C4⋊C8—22no—
39C5×C4⋊C8—22no—
40C5×#101—42no—
41#3963—22no—
42#3963—22no—
43#3963—22no—
44#3963—21no—
45#3963C2×C412yes—
46C22⋊#168—22no—
47C4⋊#168—24no—
48C4⋊#168—22no—
49C4×#168—24no—
50C4×#168D414yes—
51#2982—51no—
52#2581—51no—
53#1801D511yescharacteristic
54#1487—52no—
55#1286—52no—
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C2×C5×Q8SD1612yes—
59C2×C5×Q8Q1612yes—
60C22×C4×C5C22⋊C412yes—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22×C411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×Dic5—21no—
66C22×Dic5—22no—
67C22×Dic5—21no—
68C2×Dic10—22no—
69C2×Dic10—42no—
70C5×M16—42no—
71C5×M16—42no—
72C2×C5×C8—42no—
73C5×C4⋊C4—24no—
74C5×C4⋊C4—22no—
75C42×C5—22no—
76C42×C5—22no—
77C42×C5C2×D412yes—
78C42×C5#4112yes—
79C4⋊Dic5—22no—
80C4⋊Dic5—42no—
81#683—44no—
82#683—41no—
83#683—41no—
84C4×Dic5—42no—
85C2×#168—24no—
86C2×C4×Q8—51no—
87C2×C4×Q8C2×D511yescharacteristic
88C8×Q8—104no—
89#431—52no—
90#431—102no—
91#423C2×D512yes—
92C2×#101—21no—
93#400—52no—
94#395—52no—
95#391—101no—
96#389—101no—
97#387—102no—
98#382—51no—
99#343—21no—
100Q8⋊C8—104no—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×Q8—24no—
103C5×Q8—24no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—42no—
110C2×C4×C5#10314yes—
111C2×C4×C5C4×D412yes—
112C2×C4×C5#12011yescharacteristic
113C2×C4×C5#12112yes—
114C2×C4×C5#12311yescharacteristic
115C2×C4×C5C2×SD1611yescharacteristic
116C2×C4×C5C2×Q1611yescharacteristic
117C2×C4×C5#13512yes—
118C2×Dic5—22no—
119C2×Dic5—41no—
120C2×Dic5—41no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—41no—
125C2×Dic5—42no—
126Dic10—24no—
127Dic10—42no—
128C5×C8—82no—
129#168—44no—
130C22×Q8—51no—
131C22×Q8C22⋊D511yescharacteristic
132C2×M16—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—102no—
136C4×Q8—102no—
137C2×C4⋊C4—51no—
138C2×C4⋊C4—102no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4C4×D512yes—
142C2×C4⋊C4C22⋊D511yescharacteristic
143C2×C42—101no—
144C2×C42D2012yes—
145C2×C42C22×D511yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—104no—
149C4⋊C8—102no—
150#101—42no—
151C22⋊C8—102no—
152C4×C8—54no—
153C4×C8—104no—
154#95—52no—
155#95—102no—
156#95—102no—
157#95—102no—
158#95—101no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5#38611yescharacteristic
162C22×C5C2×#10311yescharacteristic
163C22×C5#41611yescharacteristic
164C4×C5—22no—
165C4×C5—24no—
166C4×C5—21no—
167C4×C5—21no—
168C4×C5—42no—
169C4×C5#46512yes—
170C4×C5#46712yes—
171Dic5—42no—
172Dic5—82no—
173Dic5—81no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—102no—
177C2×Q8—202no—
178C2×Q8#68712yes—
179C2×Q8#68912yes—
180C22×C4—101no—
181C22×C4—102no—
182C22×C4—101no—
183C22×C4#68512yes—
184C22×C4#68512yes—
185C22×C4C2×C4×D511yescharacteristic
186C22×C4C2×D2011yescharacteristic
187C22×C4C2×C22⋊D511yescharacteristic
188M16—42no—
189M16—42no—
190C2×C8—42no—
191C2×C8—104no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—102no—
195C4⋊C4—204no—
196C4⋊C4—202no—
197C4⋊C4—201no—
198C4⋊C4—201no—
199C42—22no—
200C42—22no—
201C42—202no—
202C42D4×D512yes—
203C42#71112yes—
204C2×C5—21no—
205C2×C5—21no—
206C2×C5#189111yescharacteristic
207C2×C5#189211yescharacteristic
208C2×C5#191211yescharacteristic
209C23C2×#68511yescharacteristic
210Q8—24no—
211Q8—24no—
212Q8—104no—
213Q8—202no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—102no—
221C2×C4—201no—
222C2×C4—201no—
223C2×C4—202no—
224C2×C4—202no—
225C2×C4—202no—
226C2×C4—202no—
227C2×C4—201no—
228C2×C4#394214yes—
229C2×C4#402712yes—
230C2×C4#402811yescharacteristic
231C2×C4#403211yescharacteristic
232C2×C4C2×#68711yescharacteristic
233C2×C4#408512yes—
234C2×C4C2×#68911yescharacteristic
235C2×C4#409612yes—
236C8—82no—
237C8—204no—
238C5#948411yescharacteristic, complemented, Sylow
239C22—21no—
240C22—21no—
241C22#6524711yescharacteristic
242C22C2×#394211yescharacteristic
243C22#6529111yescharacteristic
244C4—24no—
245C4—21no—
246C4—21no—
247C4—22no—
248C4—42no—
249C4—202no—
250C4—402no—
251C4—401no—
252C4#6533012yes—
253C4#6534012yes—
254C2—21no—
255C2—21no—
256C2#1060030711yescharacteristic
257C2#1060089811yescharacteristic
258C2#1060092911yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1801C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1801D5
hypocenterC5#9484
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
238. C5#9484semidirect

Maximal subgroups

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

subgroupindex
#106142122
#106141662
C5×#18012
#106012932
#105982042
#94845