Finite Group Databasebeta

← #12018987

Subgroups — #12018987

Order 1280.

384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 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×#2809C211yesmaximal, characteristic
2#10600465C212yesmaximal
3#10600465C211yesmaximal, characteristic
4#10598135C212yesmaximal
5#10598135C211yesmaximal, characteristic
6#66146C2211yescharacteristic
7C5×#400—21no—
8C5×#398—22no—
9C5×#391C2212yes—
10C5×#391C2211yescharacteristic
11C5×#389—21no—
12C5×#387—22no—
13C2×#3968C2212yes—
14C2×#3968C2211yescharacteristic
15#65253—22no—
16#65253—21no—
17#64743—22no—
18#64743—21no—
19#13465—51nomaximal, Sylow
20C22×C5×Q8C2311yescharacteristic
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4D412yes—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C42×C5D412yes—
28C2×C42×C5D411yescharacteristic
29Q8×Dic5—41no—
30Q8×Dic5—41no—
31#4072—22no—
32#4072—21no—
33C2×#681—22no—
34C2×#681—21no—
35C5×#95—21no—
36C5×#95—22no—
37C5×#95—22no—
38C5×#95—22no—
39C5×#95—22no—
40#3968—22no—
41#3968—21no—
42#3968Q814yes—
43#3968Q812yes—
44#3940—42no—
45#3940—41no—
46#3939—42no—
47#3939—41no—
48#2809D511yescharacteristic
49#1857—52no—
50#1857—51no—
51#1394—51no—
52#1394—52no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8C2×Q812yes—
56C2×C5×Q8C2×Q811yescharacteristic
57C2×C5×Q8#4111yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—21no—
62C22×C4×C5C2×D412yes—
63C22×C4×C5C2×D411yescharacteristic
64C5×C4⋊C4—42no—
65C5×C4⋊C4—41no—
66C5×C4⋊C4—44no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—81no—
69C5×C4⋊C4—81no—
70C42×C5—41no—
71C42×C5—42no—
72C22⋊Dic5—41no—
73C4⋊Dic5—21no—
74C4⋊Dic5—22no—
75C4⋊Dic5—22no—
76C4⋊Dic5—21no—
77C4×Dic5—42no—
78C4×Dic5—41no—
79#681—24no—
80#681—22no—
81#681—41no—
82#681—42no—
83C2×#168—42no—
84C2×#168—41no—
85#519—51no—
86#428—102no—
87#428—101no—
88C2×#101—52no—
89C2×#101—51no—
90#400—21no—
91#398—22no—
92#391C2×D511yescharacteristic
93#391C2×D512yes—
94#389—21no—
95#387—22no—
96#339—102no—
97#339—101no—
98C23×C5#12011yescharacteristic
99C5×Q8—42no—
100C5×Q8—41no—
101C5×Q8—41no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—42no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5—41no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5C22⋊Q812yes—
118C2×C4×C5C22⋊Q811yescharacteristic
119C2×C4×C5C4⋊Q812yes—
120C2×C4×C5C4⋊Q811yescharacteristic
121C2×Dic5—41no—
122C2×Dic5—41no—
123#168—44no—
124#168—42no—
125C22×Q8C22×D511yescharacteristic
126C2×M16—102no—
127C2×M16—101no—
128C4×Q8—201no—
129C4×Q8—201no—
130#117—102no—
131#117—101no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C22⋊D512yes—
137C2×C4⋊C4C22⋊D511yescharacteristic
138C2×C42C22⋊D512yes—
139C2×C42C22⋊D511yescharacteristic
140#107—202no—
141#107—201no—
142#106—202no—
143#106—201no—
144#101—54no—
145#101—52no—
146#101—102no—
147#101—101no—
148#95—21no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—22no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5#39511yescharacteristic
156C22×C5B(4,𝔽2)11yescharacteristic
157C22×C5#45811yescharacteristic
158C4×C5—22no—
159C4×C5—21no—
160C4×C5—22no—
161C4×C5—21no—
162C4×C5—42no—
163C4×C5—82no—
164C4×C5—81no—
165C4×C5—82no—
166Dic5—81no—
167Dic5—81no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8Q8×D511yescharacteristic
171C2×Q8Q8×D512yes—
172C2×Q8#71311yescharacteristic
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4C2×C22⋊D512yes—
178C22×C4C2×C22⋊D511yescharacteristic
179M16—104no—
180M16—102no—
181M16—201no—
182M16—202no—
183C2×C8—202no—
184C2×C8—201no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C4⋊C4—81no—
190C4⋊C4—81no—
191C4⋊C4—102no—
192C4⋊C4—101no—
193C4⋊C4—101no—
194C4⋊C4—102no—
195C22⋊C4—201no—
196C42—41no—
197C42—42no—
198C42—202no—
199C42—201no—
200C2×C5—21no—
201C2×C5—21no—
202C2×C5#206211yescharacteristic
203C2×C5#220311yescharacteristic
204C2×C5#220411yescharacteristic
205C23#409911yescharacteristic
206Q8—41no—
207Q8—42no—
208Q8—41no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—201no—
225C2×C4—201no—
226C2×C4#409012yes—
227C2×C4#409011yescharacteristic
228C2×C4#409212yes—
229C2×C4#409211yescharacteristic
230C8—202no—
231C8—204no—
232C5#1346511yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22#6551811yescharacteristic
236C22#6553211yescharacteristic
237C22#6553311yescharacteristic
238C4—21no—
239C4—22no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—82no—
246C4—401no—
247C4—401no—
248C2—21no—
249C2—21no—
250C2#1060268811yescharacteristic
251C2#1060272311yescharacteristic
252C2#1060275211yescharacteristic
subgroupG/H
centerC22#65533
commutator, cosocleC22×C5×Q8C23
FrattiniC22×Q8C22×D5
FittingC5×#2809C2
socleC22×C5B(4,𝔽2)
prime radicalC23×C5#120
hypercenter#2809D5
hypocenterC5#13465
LCSG ▷ C22×C5×Q8 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
232. C5#13465semidirect

Maximal subgroups

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

subgroupindex
C5×#28092
#106004652
#105981352
#134655