Finite Group Databasebeta

← #11997260

Subgroups — #11997260

Order 1280.

544 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2486C211yesmaximal, characteristic
2#10614033C211yesmaximal, characteristic
3#10602395C211yesmaximal, characteristic
4#10602355C212yesmaximal, complemented
5#10598117C212yesmaximal, complemented
6C2×C5×#123C412yes—
7C2×C4×C5×D4C2211yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C5×#398—21no—
10C5×#397—21no—
11C5×#389—21no—
12C5×#381C412yes—
13C5×#380—21no—
14C5×#380C2211yescharacteristic
15#65496C2212yes—
16#65496C2212yes—
17C2×C22⋊#168—21no—
18#65300—24no—
19#65215—21no—
20#64750—24no—
21#64748—21no—
22#64745—21no—
23#9507—51nomaximal, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5C2×C412yes—
26C23×C4×C5D411yescharacteristic
27C23×C4×C5C2311yescharacteristic
28C5×#123—44no—
29C4×C5×D4—22no—
30C4×C5×D4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C5×C22⋊C4—22no—
39C2×C5×C22⋊C4C2×C411yescharacteristic
40C2×C5×C22⋊C4C2×C412yes—
41C2×C5×C22⋊C4D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×#681—22no—
44C2×#681D414yes—
45C22×#168—22no—
46C5×#95—22no—
47C5×#95—22no—
48C5×#95—21no—
49C22⋊#168—22no—
50C22⋊#168—22no—
51C22⋊#168—22no—
52C22⋊#168—22no—
53C22⋊#168—22no—
54C4⋊#168—22no—
55#3935—22no—
56#2973—51no—
57#2486D511yescharacteristic
58#1821—52no—
59#1465—51no—
60#1305—52no—
61C24×C5C22⋊C411yescharacteristic
62C24×C5C22×C411yescharacteristic
63C2×C5×D4—22no—
64C2×C5×D4—22no—
65C2×C5×D4—41no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—24no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C2×D412yes—
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5#4112yes—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—42no—
84C5×C4⋊C4—44no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—41no—
88C5×C22⋊C4—22no—
89C5×C22⋊C4—22no—
90C5×C22⋊C4—44no—
91C5×C22⋊C4—42no—
92C42×C5—21no—
93C42×C5—21no—
94#681—44no—
95#681—44no—
96C2×#168—24no—
97C2×#168—42no—
98C2×#168—82no—
99C2×#123Dic512yes—
100C2×C4×D4C2×D511yescharacteristic
101C22×C4⋊C4C2×D511yescharacteristic
102#435—104no—
103#432—101no—
104#407—52no—
105#407—52no—
106C2×C22⋊C8—101no—
107#398—21no—
108#397—21no—
109#389—21no—
110#381Dic512yes—
111#380—21no—
112#380C2×D511yescharacteristic
113#343—104no—
114#324—101no—
115#323—101no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5#10012yes—
125C23×C5C2×C22⋊C411yescharacteristic
126C23×C5C4×D412yes—
127C5×D4—44no—
128C2×C4×C5—24no—
129C2×C4×C5—22no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—41no—
136C2×C4×C5—42no—
137C2×C4×C5—42no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—81no—
147C2×C4×C5—84no—
148C2×C4×C5#12011yescharacteristic
149C2×C4×C5#12112yes—
150C2×C4×C5#12311yescharacteristic
151#168—44no—
152#168—82no—
153C22×D4C2×Dic511yescharacteristic
154C23×C4C2×Dic512yes—
155C23×C4C22⋊D511yescharacteristic
156C23×C4C22×D511yescharacteristic
157C2×M16—54no—
158C2×M16—102no—
159C22×C8—102no—
160#123—44no—
161C4×D4—22no—
162C4×D4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C22⋊D511yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4C2×Dic511yescharacteristic
172C2×C22⋊C4C2×Dic512yes—
173C2×C22⋊C4C22⋊D511yescharacteristic
174C2×C42C22⋊D511yescharacteristic
175C4⋊C8—102no—
176C22⋊C8—102no—
177C22⋊C8—102no—
178C22⋊C8—102no—
179C22⋊C8—102no—
180C22⋊C8—102no—
181#97—102no—
182#95—22no—
183#95—22no—
184#95—21no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5—42no—
192C22×C5—42no—
193C22×C5—42no—
194C22×C5—41no—
195C22×C5—41no—
196C22×C5—81no—
197C22×C5#38611yescharacteristic
198C22×C5C2×#10011yescharacteristic
199C22×C5#41311yescharacteristic
200C4×C5—22no—
201C4×C5—21no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—82no—
206C4×C5—82no—
207C4×C5#45812yes—
208C24C22⋊Dic511yescharacteristic
209C24C22×Dic511yescharacteristic
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊Dic511yescharacteristic
223C22×C4C22⋊Dic511yescharacteristic
224C22×C4C22⋊Dic511yescharacteristic
225C22×C4D4×D512yes—
226C22×C4#71112yes—
227C22×C4C2×C22⋊D511yescharacteristic
228C22×C4C2×C22⋊D511yescharacteristic
229M16—204no—
230M16—204no—
231C2×C8—104no—
232C2×C8—202no—
233C2×C8—402no—
234C4⋊C4—22no—
235C4⋊C4—44no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C42—21no—
245C42—21no—
246C2×C5—21no—
247C2×C5—21no—
248C2×C5—42no—
249C2×C5—42no—
250C2×C5#189011yescharacteristic
251C2×C5#190011yescharacteristic
252C2×C5#191511yescharacteristic
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#396512yes—
262C23D4×Dic512yes—
263C23C2×C22⋊Dic511yescharacteristic
264D4—44no—
265C2×C4—22no—
266C2×C4—24no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—84no—
285C2×C4#408111yescharacteristic
286C2×C4#408311yescharacteristic
287C2×C4#408512yes—
288C8—204no—
289C8—402no—
290C5#950711yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#396511yescharacteristic
304C22#6550911yescharacteristic
305C22#6552611yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4#6534212yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1060247611yescharacteristic
319C2#1060249711yescharacteristic
320C2#1060265911yescharacteristic
subgroupG/H
centerC22#65509
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2486C2
socleC22×C5#386
prime radicalC22×C5×D4C2×C4
cosocleC23×C4×C5C23
hypercenter#2486D5
hypocenterC5#9507
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
4. #10602355C2semidirect
5. #10598117C2semidirect
290. C5#9507semidirect

Maximal subgroups

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

subgroupindex
C5×#24862
#106140332
#106023952
#106023552
#105981172
#95075