Finite Group Databasebeta

← #12015575

Subgroups — #12015575

Order 1280.

614 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2311C211yesmaximal, characteristic
2#10602930C212yesmaximal
3#10598135C214yesmaximal, complemented
4C22×C5×#41C2211yescharacteristic
5C2×C5×#117C411yescharacteristic
6C22×C5×C4⋊C4C411yescharacteristic
7C5×#391C2212yes—
8C5×#390C412yes—
9C5×#386—22no—
10C5×#380—22no—
11C2×#3968C2214yes—
12C2×#3965—22no—
13#65496—22no—
14#12863—51nomaximal, Sylow
15C2×C5×#41—24no—
16C2×C5×#41—42no—
17C2×C5×#41—42no—
18C22×C5×Q8C2311yescharacteristic
19C22×C5×D4C2×C411yescharacteristic
20C22×C5×D4D412yes—
21C23×C4×C5—21no—
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D412yes—
24C5×#117—42no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—42no—
28C2×C5×C4⋊C4C2×C412yes—
29C2×C5×C22⋊C4—21no—
30C2×C5×C22⋊C4—24no—
31C2×C42×C5C2×C412yes—
32C2×#681—24no—
33C5×#95—24no—
34#3968—28no—
35#3965—44no—
36C22⋊#168—44no—
37#2311D511yescharacteristic
38#1785—52no—
39#1394—54no—
40C24×C5C22⋊C412yes—
41C24×C5C22⋊C411yescharacteristic
42C5×#41—416no—
43C2×C5×Q8—41no—
44C2×C5×Q8—41no—
45C2×C5×Q8#4114yes—
46C2×C5×D4—24no—
47C2×C5×D4—22no—
48C2×C5×D4—24no—
49C2×C5×D4—41no—
50C2×C5×D4—41no—
51C2×C5×D4—42no—
52C22×C4×C5—22no—
53C22×C4×C5—22no—
54C22×C4×C5—22no—
55C22×C4×C5—24no—
56C22×C4×C5—24no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—42no—
60C22×C4×C5—42no—
61C22×C4×C5—82no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D412yes—
65C5×C4⋊C4—42no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—42no—
68C5×C22⋊C4—42no—
69C5×C22⋊C4—84no—
70C42×C5—42no—
71#681—44no—
72#681—44no—
73C2×#168—44no—
74C22×#41C2×D511yescharacteristic
75C2×#117Dic511yescharacteristic
76C22×C4⋊C4Dic511yescharacteristic
77C2×#101—54no—
78C2×#100—102no—
79#407—102no—
80#391C2×D512yes—
81#390Dic512yes—
82#386—22no—
83#380—22no—
84C23×C5—21no—
85C23×C5—21no—
86C23×C5—22no—
87C23×C5—22no—
88C23×C5—22no—
89C23×C5—41no—
90C23×C5—41no—
91C23×C5—42no—
92C23×C5—42no—
93C23×C5#9912yes—
94C23×C5C2×C22⋊C411yescharacteristic
95C5×Q8—44no—
96C5×D4—48no—
97C5×D4—44no—
98C2×C4×C5—28no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—48no—
106C2×C4×C5—42no—
107C2×C4×C5—44no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—84no—
112C2×C4×C5#9912yes—
113C2×C4×C5#11712yes—
114C2×C4×C5#12314yes—
115#168—84no—
116C2×#41—24no—
117C2×#41—42no—
118C2×#41—42no—
119C22×Q8C22×D511yescharacteristic
120C22×D4C2×Dic511yescharacteristic
121C22×D4C22⋊D512yes—
122C23×C4—21no—
123C23×C4C2×Dic511yescharacteristic
124C23×C4C22⋊D512yes—
125C2×M16—104no—
126#117—42no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4C2×Dic512yes—
131C2×C22⋊C4—21no—
132C2×C22⋊C4—24no—
133C2×C42C2×Dic512yes—
134#101—108no—
135#100—204no—
136C22⋊C8—204no—
137#95—24no—
138C22×C5—21no—
139C22×C5—21no—
140C22×C5—22no—
141C22×C5—42no—
142C22×C5—42no—
143C22×C5—44no—
144C22×C5—41no—
145C22×C5—41no—
146C22×C5—42no—
147C22×C5—42no—
148C22×C5—42no—
149C22×C5—82no—
150C22×C5#38111yescharacteristic
151C22×C5C2×#9911yescharacteristic
152C22×C5C2×#9911yescharacteristic
153C4×C5—24no—
154C4×C5—22no—
155C4×C5—22no—
156C4×C5—82no—
157C4×C5—82no—
158C24C22⋊Dic512yes—
159C24C22⋊Dic511yescharacteristic
160#41—416no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8#70914yes—
164C2×D4—24no—
165C2×D4—22no—
166C2×D4—24no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—42no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—82no—
180C22×C4C22⋊Dic511yescharacteristic
181C22×C4C22×Dic511yescharacteristic
182C22×C4C2×C22⋊D512yes—
183M16—204no—
184M16—204no—
185C2×C8—204no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—84no—
191C42—42no—
192C2×C5—21no—
193C2×C5—21no—
194C2×C5—42no—
195C2×C5—82no—
196C2×C5#181911yescharacteristic
197C2×C5#213411yescharacteristic
198C2×C5#213511yescharacteristic
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—41no—
205C23—41no—
206C23—42no—
207C23—42no—
208C23#396612yes—
209C23C2×C22⋊Dic511yescharacteristic
210Q8—44no—
211D4—48no—
212D4—44no—
213C2×C4—28no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—48no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—84no—
227C2×C4#396612yes—
228C2×C4#407212yes—
229C2×C4#407514yes—
230C8—404no—
231C5#1286311yescharacteristic, complemented, Sylow
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—44no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22#6550011yescharacteristic
245C22C2×#396611yescharacteristic
246C22C2×#396611yescharacteristic
247C4—24no—
248C4—22no—
249C4—22no—
250C4—82no—
251C4—82no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—82no—
256C2#1060233511yescharacteristic
257C2#1060265511yescharacteristic
258C2#1060266611yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC5×#2311C2
socleC22×C5C2×#99
prime radicalC22×C5×#41C22
cosocleC22×C5×Q8C23
hypercenter#2311D5
hypocenterC5#12863
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #10598135C2semidirect
231. C5#12863semidirect

Maximal subgroups

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

subgroupindex
C5×#23112
#106029302
#105981352
#128635