Finite Group Databasebeta

← #11996720

Subgroups — #11996720

Order 1280.

450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C5×#2983C211yesmaximal, characteristic
2#10614210C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4#10601573C212yesmaximal
5#10598237C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4015C2211yescharacteristic
8C5×#446—24no—
9C5×#432—22no—
10C5×#431C2212yes—
11#65519—21no—
12C2×#3968—21no—
13#65275C414yes—
14#65266—21no—
15C4×C4⋊Dic5C2211yescharacteristic
16#65218—22no—
17#65213C2212yes—
18#64750—21no—
19#64702—24no—
20#9404—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C4×C5×Q8—22no—
24C4×C5×Q8—22no—
25C2×C5×C4⋊C4C2×C412yes—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C42×C5D412yes—
28C2×C42×C5C2311yescharacteristic
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5C2×C412yes—
32C2×C4×Dic5—21no—
33C2×#681—22no—
34#4015—22no—
35#4015—22no—
36C5×C4⋊C8—24no—
37C5×C4⋊C8D414yes—
38C5×C22⋊C8—22no—
39C5×#97—24no—
40C4×C5×C8—22no—
41#3968—42no—
42#3963—24no—
43#3963—24no—
44#3963C2×C412yes—
45C4⋊#168—22no—
46C4⋊#168—22no—
47#2983D511yescharacteristic
48#2568—51no—
49#1801—51no—
50#1549—52no—
51#1303—52no—
52C2×C5×Q8—22no—
53C2×C5×Q8—21no—
54C2×C5×Q8—21no—
55C2×C5×Q8—22no—
56C22×C4×C5C22⋊C412yes—
57C22×C4×C5C22⋊C412yes—
58C22×C4×C5C22×C411yescharacteristic
59C22×C4×C5C2×D411yescharacteristic
60C22×C4×C5C2×D411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5—22no—
63C2×Dic10—44no—
64C2×Dic10—41no—
65C2×Dic10—41no—
66C2×C5×C8—24no—
67C5×C4⋊C4—24no—
68C5×C4⋊C4—22no—
69C42×C5—22no—
70C42×C5—22no—
71C42×C5C2×D412yes—
72C42×C5#4112yes—
73C4⋊Dic5—24no—
74C4⋊Dic5—42no—
75C4⋊Dic5—42no—
76C4×Dic5—41no—
77C4×Dic5—41no—
78#681—42no—
79#681—42no—
80C2×#168—42no—
81C2×C4⋊Q8—51no—
82C2×C4×Q8C2×D511yescharacteristic
83#446—24no—
84#432—22no—
85#431C2×D512yes—
86#423—52no—
87C2×#101—101no—
88#400—54no—
89#391—101no—
90#391—102no—
91#382—101no—
92C4×C4⋊C4—51no—
93#343—101no—
94#332—104no—
95C23×C5C2×C22⋊C411yescharacteristic
96C5×Q8—42no—
97C5×Q8—42no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—41no—
104C2×C4×C5—42no—
105C2×C4×C5C4×D412yes—
106C2×C4×C5#12011yescharacteristic
107C2×C4×C5#12112yes—
108C2×C4×C5#12311yescharacteristic
109C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C5#13712yes—
111C2×C4×C5#13711yescharacteristic
112C2×Dic5—42no—
113C2×Dic5—44no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5—42no—
117Dic10—82no—
118Dic10—82no—
119C5×C8—44no—
120#168—82no—
121C22×Q8—101no—
122C22×Q8D2011yescharacteristic
123C2×M16—102no—
124C4⋊Q8—102no—
125C4⋊Q8—102no—
126C4×Q8—22no—
127C4×Q8—22no—
128C2×C4⋊C4—52no—
129C2×C4⋊C4—101no—
130C2×C4⋊C4—101no—
131C2×C4⋊C4C4×D512yes—
132C2×C4⋊C4D2011yescharacteristic
133C2×C42—101no—
134C2×C42C22⋊D512yes—
135C2×C42C22×D511yescharacteristic
136C4⋊C8—24no—
137C4⋊C8—102no—
138C4⋊C8—102no—
139C4⋊C8C22⋊D514yes—
140#101—202no—
141C22⋊C8—22no—
142#97—24no—
143C4×C8—22no—
144#95—52no—
145#95—104no—
146#95—104no—
147C22×C5—21no—
148C22×C5—21no—
149C22×C5#38611yescharacteristic
150C22×C5#41711yescharacteristic
151C22×C5#41911yescharacteristic
152C4×C5—21no—
153C4×C5—22no—
154C4×C5—42no—
155C4×C5—42no—
156C4×C5#45412yes—
157C4×C5#46812yes—
158C4×C5#47012yes—
159Dic5—82no—
160Dic5—82no—
161C2×Q8—21no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—22no—
165C2×Q8—204no—
166C2×Q8—201no—
167C2×Q8—201no—
168C22×C4—102no—
169C22×C4—102no—
170C22×C4#68512yes—
171C22×C4#68512yes—
172C22×C4C2×C4×D511yescharacteristic
173C22×C4C2×D2011yescharacteristic
174C22×C4C2×C22⋊D511yescharacteristic
175M16—202no—
176M16—202no—
177C2×C8—24no—
178C2×C8—202no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4—104no—
182C4⋊C4—202no—
183C4⋊C4—202no—
184C42—22no—
185C42—22no—
186C42—201no—
187C42—201no—
188C42#70912yes—
189C42C2×C22⋊D512yes—
190C2×C5—21no—
191C2×C5—21no—
192C2×C5#188811yescharacteristic
193C2×C5#189411yescharacteristic
194C2×C5#191511yescharacteristic
195C23C2×#68511yescharacteristic
196Q8—42no—
197Q8—42no—
198Q8—402no—
199Q8—402no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—202no—
208C2×C4—204no—
209C2×C4—202no—
210C2×C4—202no—
211C2×C4—202no—
212C2×C4#405411yescharacteristic
213C2×C4#405512yes—
214C2×C4#405511yescharacteristic
215C2×C4C4×C22⋊D512yes—
216C2×C4#407511yescharacteristic
217C2×C4#407612yes—
218C2×C4#409911yescharacteristic
219C8—44no—
220C8—402no—
221C5#940411yescharacteristic, complemented, Sylow
222C22—21no—
223C22—21no—
224C22#6540911yescharacteristic
225C22#6542211yescharacteristic
226C22#6550211yescharacteristic
227C4—22no—
228C4—21no—
229C4—42no—
230C4—42no—
231C4—402no—
232C4—402no—
233C4#6542312yes—
234C4#6542612yes—
235C4#6553412yes—
236C2—21no—
237C2—21no—
238C2#1060245411yescharacteristic
239C2#1060278211yescharacteristic
240C2#1060282411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2983C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2983D5
hypocenterC5#9404
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
221. C5#9404semidirect

Maximal subgroups

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

subgroupindex
C5×#29832
#106142102
#106024302
#106015732
#105982372
#94045