Finite Group Databasebeta

← #11991803

Subgroups — #11991803

Order 1280.

818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#65869C211yesmaximal, characteristic
2C5×#1822C211yesmaximal, characteristic, complemented
3#10602387C211yesmaximal, characteristic, complemented
4#10600771C214yesmaximal, complemented
5C2×C5×#117C2211yescharacteristic
6C2×#4076C2212yes—
7#65869—28no—
8C2×#4040—22no—
9C2×#4030—22no—
10C2×#4020C411yescharacteristic, complemented
11C2×C4×D20C412yescomplemented
12C2×#4016C411yescharacteristic, complemented
13C5×#407C2212yes—
14#65500C2212yes—
15C5×#343—22no—
16#64746—22no—
17#64690—28no—
18#8518—51nomaximal, Sylow
19C23×C4×C5C2311yescharacteristic
20C22×C22⋊D5—22no—
21C22×D20—22no—
22C22×D20C2×C412yes—
23C22×C4×D5—22no—
24C2×C5×M16—22no—
25C5×#117—24no—
26C2×C5×C4⋊C4D412yes—
27C2×C5×C22⋊C4D412yes—
28C2×C42×C5C2×C411yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C22⋊Dic5—22no—
31#4076—24no—
32#4076D418yes—
33C2×#685—22no—
34C2×#685—22no—
35C2×C4⋊Dic5C2×C412yes—
36C2×#683—22no—
37#4040—216no—
38#4030—216no—
39#4020—24no—
40C4×D20—24no—
41C4×D20—24no—
42#4016—24no—
43C5×C22⋊C8—24no—
44#3963—24no—
45C2×#540—51no—
46#1822D511yescharacteristic, complemented
47#1820—51no—
48#1510—54no—
49C24×C5C2×D411yescharacteristic
50C23×D5—22no—
51C22×C4×C5—42no—
52C22×C4×C5C22⋊C412yes—
53C22×C4×C5C22⋊C412yes—
54C22×C4×C5C22×C411yescharacteristic
55C22×C4×C5C2×D414yes—
56C22×C4×C5C2×D411yescharacteristic
57C2×C22⋊D5—28no—
58C2×C22⋊D5—84no—
59C22×Dic5—22no—
60C22×Dic5—42no—
61C2×D20—22no—
62C2×D20—28no—
63C2×D20—44no—
64C2×D20—84no—
65C2×D20C22⋊C414yes—
66C2×C4×D5—28no—
67C2×C4×D5—84no—
68C5×M16—44no—
69C2×C5×C8—42no—
70C5×C4⋊C4—24no—
71C5×C22⋊C4—24no—
72C42×C5—22no—
73C42×C5—22no—
74C22⋊Dic5—44no—
75#685—28no—
76#685—28no—
77C4⋊Dic5—22no—
78C4⋊Dic5C22⋊C414yes—
79#683—28no—
80#540—108no—
81C2×#127—51no—
82C2×#125—51no—
83C2×#123—102no—
84C2×#121—52no—
85C2×#121—102no—
86C2×C4×D4—52no—
87C2×#117C2×D511yescharacteristic
88#407C2×D512yes—
89#381—52no—
90#343—22no—
91#342—102no—
92#327—108no—
93C23×C5—22no—
94C23×C5—42no—
95C23×C5C2×C22⋊C411yescharacteristic
96C23×C5#12012yes—
97C22×D5—24no—
98C22×D5—44no—
99C22×D5—44no—
100C22×D5—44no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—44no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5C2×C22⋊C412yes—
109C2×C4×C5#12012yes—
110C22⋊D5—88no—
111C2×Dic5—24no—
112C2×Dic5—44no—
113C2×Dic5—82no—
114C2×Dic5—84no—
115D20—44no—
116D20—44no—
117D20—88no—
118C4×D5—88no—
119C5×C8—82no—
120C22×D4—52no—
121C22×D4—102no—
122C22×D4—102no—
123C23×C4—102no—
124C23×C4C22×D511yescharacteristic
125C2×M16—22no—
126#127—104no—
127#125—104no—
128#123—1016no—
129#121—58no—
130#121—1016no—
131#121—104no—
132C4×D4—104no—
133C4×D4—104no—
134#117—24no—
135C2×C4⋊C4—52no—
136C2×C4⋊C4—102no—
137C2×C4⋊C4C22⋊D512yes—
138C2×C22⋊C4—102no—
139C2×C22⋊C4—102no—
140C2×C22⋊C4—102no—
141C2×C22⋊C4D2012yes—
142C2×C42C4×D511yescharacteristic
143C2×C42C4×D511yescharacteristic
144C22⋊C8—24no—
145#95—104no—
146C22×C5—22no—
147C22×C5—24no—
148C22×C5—22no—
149C22×C5—82no—
150C22×C5#37911yescharacteristic
151C22×C5#41012yes—
152C2×D5—44no—
153C2×D5—44no—
154C2×D5—44no—
155C2×D5—88no—
156C4×C5—22no—
157C4×C5—22no—
158C4×C5—42no—
159C4×C5—42no—
160Dic5—44no—
161Dic5—162no—
162C24—102no—
163C24C2×D2011yescharacteristic
164C2×D4—54no—
165C2×D4—108no—
166C2×D4—108no—
167C2×D4—102no—
168C2×D4—204no—
169C2×D4—404no—
170C2×D4—404no—
171C22×C4—42no—
172C22×C4—108no—
173C22×C4—102no—
174C22×C4—202no—
175C22×C4—404no—
176C22×C4#68512yes—
177C22×C4#68512yes—
178C22×C4C2×C4×D511yescharacteristic
179C22×C4D4×D514yes—
180C22×C4C2×C22⋊D511yescharacteristic
181M16—44no—
182C2×C8—42no—
183C4⋊C4—24no—
184C4⋊C4—54no—
185C4⋊C4—108no—
186C4⋊C4—102no—
187C22⋊C4—24no—
188C22⋊C4—108no—
189C22⋊C4—108no—
190C22⋊C4—204no—
191C42—22no—
192C42—22no—
193C2×C5—22no—
194C2×C5—42no—
195C2×C5#178211yescharacteristic
196C2×C5#179512yes—
197D5—84no—
198C23—22no—
199C23—42no—
200C23—104no—
201C23—204no—
202C23—204no—
203C23—204no—
204C23#402812yes—
205C23C2×#68511yescharacteristic
206D4—204no—
207D4—204no—
208D4—408no—
209D4—408no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—104no—
218C2×C4—204no—
219C2×C4—408no—
220C2×C4—402no—
221C2×C4—404no—
222C2×C4D5×C22⋊C412yes—
223C2×C4#408312yes—
224C8—82no—
225C5#851811yescharacteristic, complemented, Sylow
226C22—22no—
227C22—22no—
228C22—24no—
229C22—82no—
230C22—204no—
231C22—204no—
232C22—204no—
233C22—408no—
234C22#6524411yescharacteristic
235C22#6529512yes—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—204no—
241C4—802no—
242C2—22no—
243C2—42no—
244C2—404no—
245C2#1060033011yescharacteristic
246C2#1060093212yes—
subgroupG/H
centerC22#65244
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#1822C2
socleC22×C5#379
prime radicalC2×#65869C2
cosocleC23×C4×C5C23
hypercenter#1822D5
hypocenterC5#8518
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. C5×#1822C2semidirect
3. #10602387C2semidirect
4. #10600771C2semidirect
10. C2×#4020C4semidirect
11. C2×C4×D20C4semidirect
12. C2×#4016C4semidirect
46. #1822D5semidirect
225. C5#8518semidirect

Maximal subgroups

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

subgroupindex
C2×#658692
C5×#18222
#106023872
#106007712
#85185