Finite Group Databasebeta

← #12003798

Subgroups — #12003798

Order 1280.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#10605949C211yesmaximal, characteristic
2#10600609C212yesmaximal
3#10600343C211yesmaximal, characteristic
4C5×#1295C211yesmaximal, characteristic
5#10598150C212yesmaximal
6C2×C5×#97C2212yes—
7C5×#382C2211yescharacteristic
8C2×#3950—22no—
9C2×#3949—22no—
10#65275—21no—
11#65268—21no—
12C2×#3940—21no—
13C2×#3939—21no—
14#65225C2212yes—
15#65224C2211yescharacteristic
16C2×#3935C2211yescharacteristic
17#64949—22no—
18#64945—22no—
19#10583—51nomaximal, Sylow
20C22×Dic10—21no—
21C22×C5×C8—22no—
22C2×C5×C4⋊C4D411yescharacteristic
23C2×C5×C4⋊C4D411yescharacteristic
24C2×C42×C5C2311yescharacteristic
25C2×C4⋊Dic5—22no—
26C2×C4⋊Dic5—21no—
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5D412yes—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C22×#168—21no—
32C5×#97—22no—
33C5×#97Q814yescomplemented
34C5×#95—22no—
35#3963—22no—
36#3963—21no—
37#3963—21no—
38#3963—22no—
39#3963—22no—
40#3950—44no—
41#3949—44no—
42#3940—42no—
43#3939—42no—
44#3935—21no—
45#3935Q812yescomplemented
46#2844—51no—
47#1847—52no—
48#1847—51no—
49#1295—52no—
50#1295D511yescharacteristic
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5C2×D412yes—
55C22×Dic5—22no—
56C22×Dic5—22no—
57C22×Dic5—41no—
58C2×Dic10—82no—
59C2×Dic10—81no—
60C2×C5×C8—24no—
61C2×C5×C8—24no—
62C2×C5×C8—24no—
63C5×C4⋊C4—41no—
64C5×C4⋊C4—41no—
65C42×C5C2×Q812yes—
66C42×C5C2×Q811yescharacteristic
67C42×C5#4111yescharacteristic
68C4⋊Dic5—42no—
69C4⋊Dic5—42no—
70C4⋊Dic5—41no—
71C4⋊Dic5—41no—
72C4⋊Dic5—42no—
73C4⋊Dic5—42no—
74C4⋊Dic5—81no—
75#683—82no—
76C2×#168—22no—
77C2×#168—22no—
78C2×#168—22no—
79C2×#107—102no—
80C2×#107—101no—
81C2×#106—102no—
82C2×#106—101no—
83C2×#97—51no—
84C2×#97C2×D512yes—
85#400—102no—
86#400—101no—
87#395—102no—
88#395—101no—
89#384—51no—
90#382—52no—
91#382C2×D511yescharacteristic
92C23×C5#12011yescharacteristic
93C2×C4×C5—21no—
94C2×C4×C5—22no—
95C2×C4×C5—21no—
96C2×C4×C5—22no—
97C2×C4×C5—42no—
98C2×C4×C5—41no—
99C2×C4×C5—41no—
100C2×C4×C5—42no—
101C2×C4×C5C22⋊Q812yes—
102C2×C4×C5C22⋊Q811yescharacteristic
103C2×C4×C5C4⋊Q811yescharacteristic
104C2×C4×C5C4⋊Q812yes—
105C2×Dic5—42no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5—42no—
111C2×Dic5—81no—
112C2×Dic5—82no—
113Dic10—84no—
114C5×C8—28no—
115#168—24no—
116C22×Q8—101no—
117C22×C8—22no—
118C22×C8—101no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—101no—
122C2×C4⋊C4—102no—
123C2×C4⋊C4—102no—
124C2×C4⋊C4—101no—
125C2×C4⋊C4D2011yescharacteristic
126C2×C4⋊C4D2011yescharacteristic
127C2×C42C22×D511yescharacteristic
128#107—202no—
129#107—204no—
130#106—202no—
131#106—204no—
132#97—22no—
133#97—52no—
134#97—101no—
135#97Dic1014yescomplemented
136#95—22no—
137#95—102no—
138#95—101no—
139#95—101no—
140#95—102no—
141#95—102no—
142C22×C5#39511yescharacteristic
143C22×C5#45311yescharacteristic
144C22×C5#45312yes—
145C22×C5#45611yescharacteristic
146C22×C5#45612yes—
147C4×C5—21no—
148C4×C5—22no—
149C4×C5—21no—
150C4×C5—22no—
151C4×C5—81no—
152C4×C5—81no—
153Dic5—82no—
154Dic5—82no—
155Dic5—161no—
156C2×Q8—401no—
157C2×Q8—402no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—102no—
161C22×C4—102no—
162C22×C4—201no—
163C22×C4C2×D2011yescharacteristic
164C22×C4D4×D512yes—
165C2×C8—24no—
166C2×C8—24no—
167C2×C8—24no—
168C2×C8—102no—
169C2×C8—102no—
170C2×C8—102no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—202no—
174C4⋊C4—202no—
175C4⋊C4—201no—
176C4⋊C4—202no—
177C4⋊C4—201no—
178C4⋊C4—202no—
179C4⋊C4—402no—
180C4⋊C4—401no—
181C42C2×Dic1012yes—
182C42#71111yescharacteristic
183C42Q8×D511yescharacteristic
184C2×C5#165511yescharacteristic
185C2×C5#166011yescharacteristic
186C2×C5#166012yes—
187C2×C5#206011yescharacteristic
188C2×C5#206012yes—
189C23#402811yescharacteristic
190Q8—404no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—202no—
200C2×C4—202no—
201C2×C4—202no—
202C2×C4—202no—
203C2×C4—202no—
204C2×C4—202no—
205C2×C4—401no—
206C2×C4—402no—
207C2×C4#401511yescharacteristic
208C2×C4#402412yes—
209C2×C4#403412yes—
210C2×C4#404311yescharacteristic
211C8—28no—
212C8—104no—
213C5#1058311yescharacteristic, complemented, Sylow
214C22#6494511yescharacteristic
215C22#6503611yescharacteristic
216C22#6504111yescharacteristic
217C22#6511112yes—
218C22#6511512yes—
219C4—21no—
220C4—21no—
221C4—22no—
222C4—22no—
223C4—81no—
224C4—81no—
225C4—402no—
226C4—402no—
227C4—801no—
228C2#1059914311yescharacteristic
229C2#1059914811yescharacteristic
230C2#1059916512yes—
231C2#1059952812yes—
232C2#1059977111yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1295C2
socle, prime radicalC23×C5#120
hypercenter#1295D5
hypocenterC5#10583
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
33. C5×#97Q8semidirect
45. #3935Q8semidirect
135. #97Dic10semidirect
213. C5#10583semidirect

Maximal subgroups

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

subgroupindex
#106059492
#106006092
#106003432
C5×#12952
#105981502
#105835