Finite Group Databasebeta

← #12001546

Subgroups — #12001546

Order 1280.

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

normal subgroups only

This group has 542 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#10614900C212yesmaximal
2#10610210C211yesmaximal, characteristic, complemented
3C5×#1961C211yesmaximal, characteristic
4#10600339C212yesmaximal, complemented
5#10598152C211yesmaximal, characteristic, complemented
6C2×C5×#127C2211yescharacteristic
7#65804C2212yes—
8C2×C5×#102—22no—
9C2×C5×#97C2211yescharacteristic
10C5×#382C2211yescharacteristic
11#65507—24no—
12#65395—22no—
13#65365—22no—
14#65364—24no—
15#65359—22no—
16#65214C2212yes—
17#64991—22no—
18#64991—22no—
19#64672—24no—
20#10220—51nomaximal, Sylow
21C22×C5×D4—21no—
22C22×C5×D4—22no—
23C22×C5×C8D412yes—
24C5×#127—22no—
25C5×#127—21no—
26C5×#127D412yes—
27C2×C5×C4⋊C4—21no—
28C2×C42×C5C2311yescharacteristic
29C2×#687—28no—
30#4072—22no—
31#4070—22no—
32#4070—22no—
33#4016—22no—
34#4015D412yes—
35#4015D412yes—
36C4×Dic10—22no—
37C4×Dic10—22no—
38C5×#102—44no—
39C5×#97—22no—
40C5×#95—22no—
41#3964—28no—
42C22⋊#168D414yes—
43#3950—24no—
44#3949—22no—
45#3949—22no—
46C4⋊#168—22no—
47C4×#168—22no—
48#3208—52no—
49#3162—51no—
50#1961D511yescharacteristic
51#1518—52no—
52#1281—51no—
53C24×C5—41no—
54C2×C5×D4—24no—
55C2×C5×D4—22no—
56C2×C5×D4—41no—
57C2×C5×D4—42no—
58C2×C5×D4—42no—
59C2×C5×D4—42no—
60C2×C5×D4—84no—
61C22×C4×C5—41no—
62C22×C4×C5C2×D412yes—
63C22×C4×C5C2×D411yescharacteristic
64C2×Dic10—22no—
65C2×Dic10—22no—
66C2×C5×C8—22no—
67C2×C5×C8—22no—
68C2×C5×C8SD1614yescomplemented
69C5×C4⋊C4—42no—
70C42×C5C2×D411yescharacteristic
71C42×C5C2×D412yes—
72C42×C5#4111yescharacteristic
73C22⋊Dic5—42no—
74#687—88no—
75C4⋊Dic5—22no—
76C4⋊Dic5—22no—
77C4⋊Dic5—22no—
78C4⋊Dic5—22no—
79#683—42no—
80#683—42no—
81C4×Dic5—42no—
82C2×#168—24no—
83#533—52no—
84C2×#127C2×D511yescharacteristic
85#501—102no—
86#501—102no—
87#492—102no—
88#486—102no—
89#460—104no—
90#450—104no—
91#431—52no—
92#427—102no—
93C2×#102—22no—
94C2×#97C2×D511yescharacteristic
95#382C2×D511yescharacteristic
96#328—104no—
97C23×C5—42no—
98C23×C5—84no—
99C23×C5—81no—
100C23×C5—81no—
101C23×C5#12711yescharacteristic
102C5×D4—48no—
103C5×D4—44no—
104C5×D4—84no—
105C5×D4—82no—
106C2×C4×C5—42no—
107C2×C4×C5—82no—
108C2×C4×C5—81no—
109C2×C4×C5#12012yes—
110C2×C4×C5#12011yescharacteristic
111C2×C4×C5#12112yes—
112C2×C4×C5#12111yescharacteristic
113C2×C4×C5C2×SD1612yes—
114C2×C4×C5#13712yes—
115C2×Dic5—42no—
116C2×Dic5—42no—
117Dic10—44no—
118Dic10—82no—
119C5×C8—24no—
120#168—44no—
121C22×D4—22no—
122C22×D4—21no—
123C2×SD16—108no—
124C22×C8C22⋊D512yes—
125C4⋊Q8—52no—
126C4⋊Q8—52no—
127#127—21no—
128#127—22no—
129#127D2012yes—
130#125—102no—
131C22⋊Q8—102no—
132C22⋊Q8—102no—
133C4×Q8—102no—
134C4×Q8—102no—
135#117—102no—
136C2×C4⋊C4—21no—
137C2×C42C22×D511yescharacteristic
138#107—104no—
139#106—102no—
140#106—102no—
141C4⋊C8—102no—
142#102—44no—
143#102—108no—
144C22⋊C8—54no—
145#97—22no—
146C4×C8—102no—
147#95—22no—
148C22×C5—22no—
149C22×C5—84no—
150C22×C5—82no—
151C22×C5—162no—
152C22×C5—162no—
153C22×C5#39211yescharacteristic
154C22×C5#49211yescharacteristic
155C22×C5#49711yescharacteristic
156C4×C5—22no—
157C4×C5—22no—
158C4×C5—161no—
159C4×C5#44812yes—
160C4×C5#46112yes—
161Dic5—82no—
162Dic5—82no—
163C24—41no—
164C2×Q8—102no—
165C2×Q8—102no—
166C2×D4—24no—
167C2×D4—22no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—41no—
172C2×D4—84no—
173C22×C4—41no—
174C22×C4D4×D512yes—
175C22×C4C2×C22⋊D511yescharacteristic
176SD16—408no—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—104no—
180C2×C8#68714yescomplemented
181C4⋊C4—42no—
182C4⋊C4—102no—
183C4⋊C4—102no—
184C4⋊C4—102no—
185C4⋊C4—102no—
186C4⋊C4—202no—
187C4⋊C4—202no—
188C22⋊C4—202no—
189C42—202no—
190C42C2×D2011yescharacteristic
191C42#70911yescharacteristic
192C42D4×D512yes—
193C2×C5—21no—
194C2×C5—21no—
195C2×C5—162no—
196C2×C5#200812yes—
197C2×C5#201311yescharacteristic
198C23—42no—
199C23—84no—
200C23—81no—
201C23—81no—
202C23#408611yescharacteristic
203Q8—204no—
204Q8—402no—
205D4—48no—
206D4—44no—
207D4—84no—
208D4—82no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—202no—
213C2×C4—202no—
214C2×C4#402812yes—
215C2×C4#403012yes—
216C2×C4#407611yescharacteristic
217C2×C4C2×#68712yes—
218C2×C4#408311yescharacteristic
219C2×C4#409712yes—
220C8—24no—
221C8—204no—
222C5#1022011yescharacteristic, complemented, Sylow
223C22—22no—
224C22—82no—
225C22—84no—
226C22—162no—
227C22—162no—
228C22#6524911yescharacteristic
229C22#6534911yescharacteristic
230C22#6536511yescharacteristic
231C4—22no—
232C4—22no—
233C4—161no—
234C4—402no—
235C4—402no—
236C4#6530812yes—
237C4#6532912yes—
238C2—21no—
239C2—21no—
240C2—162no—
241C2#1060045411yescharacteristic
242C2#1060112412yes—
subgroupG/H
centerC22#65249
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1961C2
socleC22×C5#392
prime radicalC2×C5×#127C22
hypercenter#1961D5
hypocenterC5#10220
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #10610210C2semidirect
4. #10600339C2semidirect
5. #10598152C2semidirect
68. C2×C5×C8SD16semidirect
180. C2×C8#687semidirect
222. C5#10220semidirect

Maximal subgroups

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

subgroupindex
#106149002
#106102102
C5×#19612
#106003392
#105981522
#102205