Finite Group Databasebeta

← #13017522

Subgroups — #13017522

Order 1280.

826 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 120 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×D5×#125C211yesmaximal, characteristic
2C2×#64870C214yesmaximal, complemented
3#10604177C212yesmaximal
4C2×C5×#125C411yescharacteristic
5D5×#125—28no—
6C2×D5×C4⋊C4—22no—
7C2×D5×C4⋊C4C412yes—
8C2×#4036C2212yes—
9C2×#4035—22no—
10C2×C42×D5C2211yescharacteristic
11C2×#4016C411yescharacteristic
12C2×#4003—22no—
13C2×#4002C2214yes—
14#64918—22no—
15#64870—28no—
16#8335—51nomaximal, Sylow
17C22×C4×D5—22no—
18C22×C4×D5C2×C411yescharacteristic
19C22×C4×D5D412yes—
20C22×#170—24no—
21C5×#125—24no—
22C2×C5×C4⋊C4—22no—
23C2×C5×C4⋊C4C2×C412yes—
24C2×C42×C5C2×C411yescharacteristic
25C2×C4⋊Dic5—22no—
26C2×C4⋊Dic5C2×C412yes—
27C2×#683—22no—
28C2×#683—22no—
29C2×#683—22no—
30C2×C4×Dic5D412yes—
31C2×C4×Dic5C2311yescharacteristic
32D5×C4⋊C4—216no—
33D5×C4⋊C4—24no—
34D5×C4⋊C4—24no—
35#4036—24no—
36#4036D418yes—
37#4035—216no—
38C42×D5—24no—
39#4016—24no—
40#4003—28no—
41#4002—28no—
42C22×#125—51no—
43#1749—52no—
44C2×#330—54no—
45C23×D5C22⋊C411yescharacteristic
46C22×C4×C5—22no—
47C22×C4×C5C22⋊C412yes—
48C22×C4×C5C22×C411yescharacteristic
49C22×Dic5—22no—
50C22×Dic5C22⋊C411yescharacteristic
51C22×Dic5C2×D412yes—
52C2×C4×D5—22no—
53C2×C4×D5—22no—
54C2×C4×D5—22no—
55C2×C4×D5—28no—
56C2×C4×D5—24no—
57C2×C4×D5—24no—
58C2×C4×D5—42no—
59C2×C4×D5—44no—
60C2×C4×D5—44no—
61C2×#170—28no—
62C2×#170—44no—
63C2×#170—44no—
64C5×C4⋊C4—28no—
65C5×C4⋊C4—22no—
66C5×C4⋊C4C22⋊C414yes—
67C42×C5—22no—
68C4⋊Dic5—22no—
69C4⋊Dic5—28no—
70C4⋊Dic5C22⋊C414yes—
71#683—28no—
72#683—28no—
73#683—28no—
74C4×Dic5—24no—
75C4×Dic5C2×D414yes—
76C2×#125—52no—
77C2×#125—51no—
78C2×#125—102no—
79C2×#125—108no—
80C2×#125AGL(1,𝔽5)11yescharacteristic
81C22×C4⋊C4—52no—
82C22×C4⋊C4—102no—
83C22×C42—51no—
84C2×C22⋊C8—102no—
85C2×#97—54no—
86#336—102no—
87#330—108no—
88C23×C5C2×C22⋊C411yescharacteristic
89C22×D5—21no—
90C22×D5—21no—
91C22×D5—22no—
92C22×D5#10112yes—
93C22×D5#10414yes—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—22no—
97C2×C4×C5—24no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—42no—
101C2×C4×C5—42no—
102C2×C4×C5C2×C22⋊C412yes—
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—22no—
106C2×Dic5—22no—
107C2×Dic5—24no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5#10112yes—
111C2×Dic5#12014yes—
112C4×D5—28no—
113C4×D5—48no—
114C4×D5—416no—
115#170—48no—
116C23×C4—51no—
117C23×C4—52no—
118C23×C4—102no—
119C22×C8—104no—
120#125—24no—
121#125—58no—
122#125—104no—
123#125—104no—
124#125—1016no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—52no—
127C2×C4⋊C4—104no—
128C2×C4⋊C4—1016no—
129C2×C4⋊C4—102no—
130C2×C4⋊C4—102no—
131C2×C4⋊C4—102no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—104no—
134C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
135C2×C42—51no—
136C2×C42—52no—
137C2×C42—104no—
138C2×C42C2×AGL(1,𝔽5)11yescharacteristic
139C22⋊C8—108no—
140#97—108no—
141C22×C5#37911yescharacteristic
142C22×C5C2×#10111yescharacteristic
143C22×C5C2×#10111yescharacteristic
144C22×C5C2×#10412yes—
145C22×C5#42112yes—
146C2×D5—24no—
147C2×D5—22no—
148C2×D5—24no—
149C2×D5—22no—
150C2×D5#33014yescomplemented
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—44no—
154Dic5—22no—
155Dic5—24no—
156Dic5—44no—
157C24—51no—
158C22×C4—22no—
159C22×C4—52no—
160C22×C4—51no—
161C22×C4—102no—
162C22×C4—104no—
163C22×C4—102no—
164C22×C4—104no—
165C22×C4—108no—
166C22×C4—102no—
167C22×C4—102no—
168C22×C4—202no—
169C22×C4—204no—
170C22×C4—204no—
171C22×C4C22⋊AGL(1,𝔽5)12yes—
172C22×C4C22×AGL(1,𝔽5)11yescharacteristic
173C2×C8—108no—
174C2×C8—204no—
175C2×C8—204no—
176C4⋊C4—28no—
177C4⋊C4—22no—
178C4⋊C4—54no—
179C4⋊C4—108no—
180C4⋊C4—108no—
181C4⋊C4—108no—
182C4⋊C4—108no—
183C4⋊C4—102no—
184C4⋊C4C22⋊AGL(1,𝔽5)14yes—
185C42—22no—
186C42—54no—
187C42—104no—
188C2×C5C2×#33011yescharacteristic
189C2×C5#152812yes—
190C2×C5#153411yescharacteristic
191C2×C5#178411yescharacteristic
192C2×C5#178912yes—
193D5—24no—
194C23—54no—
195C23—52no—
196C23—102no—
197C23—101no—
198C23—101no—
199C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—24no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—54no—
209C2×C4—52no—
210C2×C4—108no—
211C2×C4—102no—
212C2×C4—102no—
213C2×C4—101no—
214C2×C4—101no—
215C2×C4—104no—
216C2×C4—208no—
217C2×C4—2016no—
218C2×C4—202no—
219C2×C4—202no—
220C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
221C8—208no—
222C5#833511yescharacteristic, complemented, Sylow
223C22—54no—
224C22—104no—
225C22—102no—
226C22—102no—
227C22—104no—
228C22D5⋊#10111yescharacteristic
229C22D5⋊#10111yescharacteristic
230C22D5⋊#10412yes—
231C22#6579512yes—
232C22#6580011yescharacteristic
233C4—22no—
234C4—42no—
235C4—44no—
236C4—102no—
237C4—104no—
238C4—204no—
239C2—104no—
240C2D5⋊#33011yescharacteristic
241C2#1060457812yes—
242C2#1060457911yescharacteristic
243C2#1060498611yescharacteristic
244C2#1060501412yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#125C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#8335
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. C2×#64870C2semidirect
150. C2×D5#330semidirect
222. C5#8335semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1252
C2×#648702
#106041772
#83355