Finite Group Databasebeta

← #13017421

Subgroups — #13017421

Order 1280.

1050 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×#4033C211yesmaximal, characteristic
2#10604901C212yesmaximal
3C2×#64914C214yesmaximal
4C23×Dic10C411yescharacteristic
5C22×C5×C4⋊C4C411yescharacteristic
6C22×#683C2212yes—
7C22×C4×Dic5C412yes—
8C22×C4×Dic5C2211yescharacteristic
9C2×#4033—28no—
10C2×#4033—24no—
11C2×C22⋊#170C2214yes—
12#64918—24no—
13#64914—28no—
14#8303—51nomaximal, Sylow
15C23×C4×C5C2×C412yes—
16C23×C4×C5C2×C411yescharacteristic
17C23×Dic5C2×C411yescharacteristic
18C23×Dic5C2×C412yes—
19C23×Dic5C2311yescharacteristic
20C22×Dic10—22no—
21C22×Dic10—22no—
22C22×Dic10—24no—
23C22×Dic10—24no—
24C22×Dic10C814yescomplemented
25C22×#170—24no—
26C2×C5×C4⋊C4—24no—
27C2×C5×C4⋊C4—22no—
28C2×#683—24no—
29C2×#683—24no—
30C2×#683D418yes—
31C2×C4×Dic5—24no—
32C2×C4×Dic5—24no—
33C2×C4×Dic5—24no—
34C2×C4×Dic5—24no—
35C2×C4×Dic5D414yes—
36#4033—232no—
37C22⋊#170—28no—
38C22×C4×Q8—51no—
39#1817—52no—
40C2×#324—54no—
41C24×C5C22×C411yescharacteristic
42C22×C4×C5—22no—
43C22×C4×C5—22no—
44C22×C4×C5—22no—
45C22×C4×C5—22no—
46C22×C4×C5—44no—
47C22×C4×C5C22⋊C412yes—
48C22×C4×C5C22⋊C414yes—
49C22×C4×C5C2×C812yes—
50C22×C4×C5M1612yes—
51C22×Dic5—22no—
52C22×Dic5—22no—
53C22×Dic5—22no—
54C22×Dic5—22no—
55C22×Dic5—22no—
56C22×Dic5—24no—
57C22×Dic5—42no—
58C22×Dic5C22⋊C414yes—
59C22×Dic5C22⋊C412yes—
60C22×Dic5C2×C814yes—
61C22×Dic5M1614yes—
62C22×Dic5C2×D412yes—
63C22×Dic5C2×D414yes—
64C2×Dic10—216no—
65C2×Dic10—28no—
66C2×Dic10—28no—
67C2×Dic10—28no—
68C2×Dic10—216no—
69C2×#170—48no—
70C2×#170—44no—
71C5×C4⋊C4—28no—
72#683—216no—
73C4×Dic5—216no—
74C4×Dic5—28no—
75C23×Q8—51no—
76C2×C4×Q8—104no—
77C2×C4×Q8—108no—
78C22×C4⋊C4—52no—
79C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
80C22×C42—51no—
81C22×C42—52no—
82C2×C22⋊C8—54no—
83#336—104no—
84#324—108no—
85C23×C5—22no—
86C23×C5—22no—
87C23×C5C2×C22⋊C412yes—
88C23×C5C2×C22⋊C411yescharacteristic
89C23×C5C22×C811yescharacteristic
90C23×C5C2×M1611yescharacteristic
91C23×C5C2×M1612yes—
92C2×C4×C5—22no—
93C2×C4×C5—24no—
94C2×C4×C5—22no—
95C2×C4×C5—24no—
96C2×C4×C5—24no—
97C2×C4×C5—44no—
98C2×C4×C5—44no—
99C2×C4×C5—44no—
100C2×C4×C5C22⋊C814yes—
101C2×Dic5—28no—
102C2×Dic5—22no—
103C2×Dic5—24no—
104C2×Dic5—24no—
105C2×Dic5—24no—
106C2×Dic5—24no—
107C2×Dic5—24no—
108C2×Dic5—24no—
109C2×Dic5—24no—
110C2×Dic5—22no—
111C2×Dic5—44no—
112C2×Dic5C22⋊C818yes—
113C2×Dic5#10114yes—
114C2×Dic5#12014yes—
115Dic10—232no—
116#170—84no—
117C22×Q8—54no—
118C22×Q8—104no—
119C22×Q8—104no—
120C22×Q8—102no—
121C22×Q8—102no—
122C23×C4—52no—
123C23×C4—51no—
124C23×C4—51no—
125C23×C4C2×AGL(1,𝔽5)12yes—
126C23×C4C2×AGL(1,𝔽5)11yescharacteristic
127C22×C8—104no—
128C4×Q8—1032no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—58no—
132C2×C4⋊C4—104no—
133C2×C4⋊C4—104no—
134C2×C42—54no—
135C2×C42—104no—
136C2×C42—104no—
137C2×C42—104no—
138C2×C42—104no—
139C22⋊C8—108no—
140C22×C5—22no—
141C22×C5—22no—
142C22×C5—24no—
143C22×C5—22no—
144C22×C5—22no—
145C22×C5#37911yescharacteristic
146C22×C5C2×C22⋊C811yescharacteristic
147C22×C5C2×C22⋊C812yes—
148C22×C5#40711yescharacteristic
149C22×C5#40712yes—
150C22×C5#41012yes—
151C22×C5C2×#10112yes—
152C4×C5—24no—
153C4×C5—44no—
154Dic5—28no—
155Dic5—24no—
156Dic5—24no—
157C24C22×AGL(1,𝔽5)11yescharacteristic
158C2×Q8—1016no—
159C2×Q8—108no—
160C2×Q8—108no—
161C2×Q8—1016no—
162C2×Q8—108no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—44no—
168C22×C4—54no—
169C22×C4—54no—
170C22×C4—54no—
171C22×C4—52no—
172C22×C4—52no—
173C22×C4—54no—
174C22×C4—104no—
175C22×C4—102no—
176C22×C4—102no—
177C22×C4—102no—
178C22×C4—102no—
179C22×C4—102no—
180C22×C4—202no—
181C22×C4D5⋊C812yes—
182C22×C4#70012yes—
183C22×C4C22⋊AGL(1,𝔽5)12yes—
184C22×C4C22⋊AGL(1,𝔽5)14yes—
185C2×C8—204no—
186C2×C8—208no—
187C4⋊C4—28no—
188C4⋊C4—1016no—
189C42—108no—
190C42—1016no—
191C2×C5—22no—
192C2×C5—22no—
193C2×C5#146112yes—
194C2×C5#146712yes—
195C2×C5#177911yescharacteristic
196C2×C5#178211yescharacteristic
197C2×C5#178411yescharacteristic
198C23—22no—
199C23—22no—
200C23C2×D5⋊C811yescharacteristic
201C23C2×#70011yescharacteristic
202C23D5⋊M1612yes—
203C23C2×C22⋊AGL(1,𝔽5)12yes—
204C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
205Q8—1032no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—24no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—44no—
214C2×C4—54no—
215C2×C4—58no—
216C2×C4—54no—
217C2×C4—108no—
218C2×C4—102no—
219C2×C4—104no—
220C2×C4—104no—
221C2×C4—104no—
222C2×C4—104no—
223C2×C4—104no—
224C2×C4—104no—
225C2×C4—104no—
226C2×C4—102no—
227C2×C4—204no—
228C2×C4#400314yes—
229C8—404no—
230C5#830311yescharacteristic, complemented, Sylow
231C22—22no—
232C22—22no—
233C22—24no—
234C22—22no—
235C22—22no—
236C22C2×#400311yescharacteristic
237C22D5⋊(C22⋊C8)12yes—
238C22#6575511yescharacteristic
239C22#6575612yes—
240C22#6577112yes—
241C22D5⋊#10112yes—
242C22#6580011yescharacteristic
243C4—24no—
244C4—44no—
245C4—108no—
246C4—104no—
247C4—104no—
248C2—22no—
249C2—22no—
250C2#1060429112yes—
251C2#1060429512yes—
252C2#1060489811yescharacteristic
253C2#1060494211yescharacteristic
254C2#1060498611yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8303
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
24. C22×Dic10C8semidirect
230. C5#8303semidirect

Maximal subgroups

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

subgroupindex
C22×#40332
#106049012
C2×#649142
#83035