Finite Group Databasebeta

← #11987589

Subgroups — #11987589

Order 1280.

646 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 163 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×C5×#391C211yesmaximal, characteristic
2#10602323C212yesmaximal
3#10598133C214yesmaximal, complemented
4C23×C5×Q8C411yescharacteristic
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C42×C5C2211yescharacteristic
7C5×#391—22no—
8C5×#391C412yes—
9C5×#391C2212yes—
10C2×C5×#95—22no—
11C2×C22⋊#168—22no—
12C2×C4⋊#168—22no—
13#64744C2214yes—
14#7643—51nomaximal, Sylow
15C22×C5×Q8—24no—
16C22×C5×Q8—21no—
17C22×C5×Q8—42no—
18C22×C5×Q8—42no—
19C22×C5×Q8C2×C412yes—
20C23×C4×C5—21no—
21C23×C4×C5—21no—
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D412yes—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—42no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C42×C5—42no—
28C2×C42×C5C2×C411yescharacteristic
29C2×C42×C5D412yes—
30C2×C42×C5C2311yescharacteristic
31C22×#168—24no—
32C5×#95—24no—
33C5×#95—24no—
34C22⋊#168—44no—
35C4⋊#168—44no—
36C2×#391D511yescharacteristic
37#1797—52no—
38#1272—54no—
39C24×C5C22⋊C411yescharacteristic
40C2×C5×Q8—24no—
41C2×C5×Q8—22no—
42C2×C5×Q8—416no—
43C2×C5×Q8—42no—
44C2×C5×Q8—42no—
45C2×C5×Q8—42no—
46C2×C5×Q8—42no—
47C2×C5×Q8M1614yes—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—24no—
52C22×C4×C5—22no—
53C22×C4×C5—22no—
54C22×C4×C5—42no—
55C22×C4×C5—42no—
56C22×C4×C5—42no—
57C22×C4×C5—42no—
58C22×C4×C5—44no—
59C22×C4×C5—42no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5SD1614yes—
63C22×C4×C5Q1614yes—
64C22×C4×C5C22×C411yescharacteristic
65C22×C4×C5C2×D412yes—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—42no—
68C42×C5—24no—
69C42×C5—41no—
70C42×C5—41no—
71C2×#168—44no—
72C2×#168—44no—
73C2×#168—44no—
74C23×Q8Dic511yescharacteristic
75C22×C4⋊C4Dic511yescharacteristic
76C22×C42C2×D511yescharacteristic
77C2×C4⋊C8—102no—
78C2×C22⋊C8—102no—
79#391—22no—
80#391Dic512yes—
81#391C2×D512yes—
82C2×#95—22no—
83#336—54no—
84C23×C5—21no—
85C23×C5—21no—
86C23×C5—22no—
87C23×C5#10012yes—
88C23×C5#10314yes—
89C23×C5C2×C22⋊C411yescharacteristic
90C5×Q8—44no—
91C5×Q8—48no—
92C5×Q8—44no—
93C2×C4×C5—28no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—24no—
103C2×C4×C5—44no—
104C2×C4×C5—44no—
105C2×C4×C5—48no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—44no—
110C2×C4×C5—84no—
111C2×C4×C5#9912yes—
112C2×C4×C5#10314yes—
113C2×C4×C5C2×M1612yes—
114C2×C4×C5C2×SD1612yes—
115C2×C4×C5C2×Q1612yes—
116#168—84no—
117C22×Q8—24no—
118C22×Q8—21no—
119C22×Q8—42no—
120C22×Q8—42no—
121C22×Q8C2×Dic512yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C2×Dic511yescharacteristic
125C23×C4C22⋊D512yes—
126C22×C8—104no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4C2×Dic512yes—
130C2×C42—42no—
131C2×C42C2×Dic511yescharacteristic
132C2×C42C22⋊D512yes—
133C2×C42C22×D511yescharacteristic
134C4⋊C8—204no—
135C22⋊C8—204no—
136#95—24no—
137#95—24no—
138C22×C5—22no—
139C22×C5—24no—
140C22×C5—24no—
141C22×C5—22no—
142C22×C5#33314yes—
143C22×C5#40711yescharacteristic
144C22×C5C2×#9911yescharacteristic
145C22×C5C2×#10011yescharacteristic
146C22×C5C2×#10312yes—
147C22×C5#42112yes—
148C4×C5—22no—
149C4×C5—22no—
150C4×C5—22no—
151C4×C5—24no—
152C4×C5—22no—
153C4×C5—44no—
154C4×C5—82no—
155C24C22⋊Dic511yescharacteristic
156C2×Q8—24no—
157C2×Q8—22no—
158C2×Q8—416no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8#68114yes—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—44no—
175C22×C4—42no—
176C22×C4#68814yes—
177C22×C4#68914yes—
178C22×C4C22⋊Dic511yescharacteristic
179C22×C4C22⋊Dic512yes—
180C22×C4C22×Dic511yescharacteristic
181C22×C4C2×C22⋊D512yes—
182C2×C8—204no—
183C2×C8—204no—
184C2×C8—204no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C42—24no—
188C42—41no—
189C42—41no—
190C2×C5—24no—
191C2×C5#146211yescharacteristic
192C2×C5#148712yes—
193C2×C5#152012yes—
194C2×C5#153311yescharacteristic
195C2×C5C2×#33311yescharacteristic
196C23—21no—
197C23—21no—
198C23—22no—
199C23#396512yes—
200C23#396714yes—
201C23C2×C22⋊Dic511yescharacteristic
202Q8—44no—
203Q8—48no—
204Q8—44no—
205C2×C4—28no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—44no—
216C2×C4—44no—
217C2×C4—48no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—84no—
223C2×C4#396612yes—
224C2×C4#396714yes—
225C2×C4C2×#68112yes—
226C2×C4C2×#68812yes—
227C2×C4C2×#68912yes—
228C8—404no—
229C5#764311yescharacteristic, complemented, Sylow
230C22—22no—
231C22—22no—
232C22—24no—
233C22—24no—
234C22#6476614yes—
235C22#6549611yescharacteristic
236C22C2×#396511yescharacteristic
237C22C2×#396611yescharacteristic
238C22C2×#396712yes—
239C22#6552512yes—
240C4—22no—
241C4—22no—
242C4—22no—
243C4—24no—
244C4—22no—
245C4—44no—
246C4—82no—
247C2—24no—
248C2#1060233211yescharacteristic
249C2#1060241512yes—
250C2#1060248312yes—
251C2#1060251211yescharacteristic
252C2C2×#6476611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#391C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenterC2×#391D5
hypocenterC5#7643
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #10598133C2semidirect
229. C5#7643semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3912
#106023232
#105981332
#76435