Finite Group Databasebeta

← #11997034

Subgroups — #11997034

Order 1280.

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

normal subgroups only

This group has 700 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×#2310C211yesmaximal, characteristic
2#10615796C211yesmaximal, characteristic
3#10602926C211yesmaximal, characteristic
4#10600326C212yesmaximal
5#10598119C212yesmaximal
6C23×C5×Q8C2211yescharacteristic
7C2×C5×#117—21no—
8C2×#4090C412yescomplemented
9C2×#4070C2211yescharacteristic
10C5×#391—24no—
11C5×#381—21no—
12C5×#381C2212yes—
13#65519C412yescomplemented
14#65518—22no—
15C2×#3968—22no—
16#65499—21no—
17#65499—21no—
18C4×C22⋊Dic5C2211yescharacteristic
19#65496C2212yes—
20#64672—24no—
21#9462—51nomaximal, Sylow
22C22×C5×Q8—22no—
23C22×C5×Q8—22no—
24C22×C5×Q8—44no—
25C22×C5×Q8C2×C412yes—
26C22×C5×Q8D412yes—
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5C2311yescharacteristic
30C22×Dic10C2×C411yescharacteristic
31C5×#117—44no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C22⋊C4—22no—
34C2×C42×C5—22no—
35C2×C22⋊Dic5—21no—
36C2×C22⋊Dic5—21no—
37#4090—44no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39#4070—22no—
40#4070—22no—
41C2×#683—22no—
42C2×#683—22no—
43C2×#683—21no—
44C2×C4×Dic5C2×C412yes—
45C2×#681—22no—
46C5×#95—24no—
47C5×#95—22no—
48C5×#95D414yes—
49#3968—44no—
50#3963—22no—
51#3963—22no—
52#3963—21no—
53C22⋊#168—22no—
54C22⋊#168—22no—
55#2434—51no—
56#2310D511yescharacteristic
57#1784—51no—
58#1511—52no—
59#1284—52no—
60C24×C5C2×D411yescharacteristic
61C2×C5×Q8—24no—
62C2×C5×Q8—24no—
63C2×C5×Q8—24no—
64C2×C5×Q8—24no—
65C2×C5×Q8—42no—
66C2×C5×Q8—42no—
67C2×C5×Q8—44no—
68C2×C5×Q8—44no—
69C2×C5×Q8—48no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—24no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—24no—
76C22×C4×C5—42no—
77C22×C4×C5—42no—
78C22×C4×C5C22⋊C412yes—
79C22×C4×C5C22⋊C412yes—
80C22×C4×C5C22×C411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5C2×D412yes—
83C22×C4×C5#4112yes—
84C22×Dic5—22no—
85C22×Dic5—21no—
86C22×Dic5—21no—
87C2×Dic10—22no—
88C2×Dic10—42no—
89C5×C4⋊C4—44no—
90C5×C22⋊C4—44no—
91C42×C5—44no—
92C22⋊Dic5—24no—
93C22⋊Dic5—41no—
94C22⋊Dic5—41no—
95C4⋊Dic5—22no—
96#683—44no—
97#683—44no—
98#683—42no—
99C4×Dic5—42no—
100#681—44no—
101C2×#168—42no—
102C23×Q8C2×D511yescharacteristic
103C2×C4⋊Q8—52no—
104C2×C22⋊Q8—51no—
105C2×#117—21no—
106C2×#101—102no—
107#407—52no—
108#395—102no—
109#391—24no—
110#391—52no—
111#385—101no—
112#385—101no—
113#381—21no—
114#381C2×D512yes—
115C4×C22⋊C4—51no—
116#328—104no—
117C23×C5—22no—
118C23×C5—22no—
119C23×C5—41no—
120C23×C5C2×C22⋊C411yescharacteristic
121C23×C5#12011yescharacteristic
122C23×C5#12311yescharacteristic
123C5×Q8—48no—
124C5×Q8—48no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—24no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—44no—
140C2×C4×C5—44no—
141C2×C4×C5—44no—
142C2×C4×C5#9914yes—
143C2×C4×C5C4×D412yes—
144C2×C4×C5#12112yes—
145C2×Dic5—24no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C2×Dic5—42no—
152Dic10—82no—
153#168—82no—
154C22×Q8—22no—
155C22×Q8—22no—
156C22×Q8—44no—
157C22×Q8—51no—
158C22×Q8C4×D512yes—
159C22×Q8D2012yes—
160C23×C4C22⋊D511yescharacteristic
161C23×C4C22⋊D511yescharacteristic
162C23×C4C22×D511yescharacteristic
163C2×M16—102no—
164C4⋊Q8—204no—
165C22⋊Q8—102no—
166C22⋊Q8—102no—
167#117—44no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—102no—
171C2×C4⋊C4—102no—
172C2×C4⋊C4—101no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—101no—
175C2×C22⋊C4—101no—
176C2×C42—22no—
177C2×C42—52no—
178#101—204no—
179C22⋊C8—102no—
180C22⋊C8—102no—
181#95—24no—
182#95—22no—
183#95—102no—
184#95—102no—
185#95—101no—
186#95C22⋊D514yes—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—44no—
195C22×C5#38611yescharacteristic
196C22×C5C2×#9912yes—
197C22×C5#45612yes—
198C4×C5—22no—
199C4×C5—22no—
200C4×C5—24no—
201C4×C5—42no—
202C4×C5—84no—
203Dic5—44no—
204Dic5—81no—
205Dic5—81no—
206C24C2×C22⋊D511yescharacteristic
207C2×Q8—24no—
208C2×Q8—24no—
209C2×Q8—24no—
210C2×Q8—24no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×Q8—44no—
214C2×Q8—44no—
215C2×Q8—48no—
216C2×Q8—102no—
217C2×Q8—202no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—24no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—102no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4#68512yes—
230C22×C4#68512yes—
231C22×C4C2×C4×D511yescharacteristic
232C22×C4C2×D2011yescharacteristic
233C22×C4#70912yes—
234C22×C4C2×C22⋊D512yes—
235M16—204no—
236C2×C8—202no—
237C4⋊C4—44no—
238C4⋊C4—102no—
239C4⋊C4—204no—
240C4⋊C4—204no—
241C4⋊C4—202no—
242C22⋊C4—44no—
243C22⋊C4—104no—
244C22⋊C4—201no—
245C22⋊C4—201no—
246C42—44no—
247C42—202no—
248C2×C5—22no—
249C2×C5—22no—
250C2×C5—41no—
251C2×C5#188611yescharacteristic
252C2×C5#189811yescharacteristic
253C2×C5#191211yescharacteristic
254C23—22no—
255C23—22no—
256C23—41no—
257C23C2×#68511yescharacteristic
258C23#407511yescharacteristic
259C23#409911yescharacteristic
260Q8—48no—
261Q8—48no—
262Q8—402no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—104no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4—202no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4#393814yes—
288C2×C4C4×C22⋊D512yes—
289C2×C4#407612yes—
290C8—402no—
291C5#946211yescharacteristic, complemented, Sylow
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22C2×#393812yes—
301C22#6550211yescharacteristic
302C22#6553512yes—
303C4—22no—
304C4—24no—
305C4—22no—
306C4—42no—
307C4—84no—
308C4—204no—
309C4—401no—
310C4—401no—
311C2—22no—
312C2—22no—
313C2—41no—
314C2#1060233611yescharacteristic
315C2#1060245311yescharacteristic
316C2#1060245611yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2310C2
socleC22×C5#386
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#2310D5
hypocenterC5#9462
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2310

Complements

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

NH ≅ G/Ntype
8. C2×#4090C4semidirect
13. #65519C4semidirect
291. C5#9462semidirect

Maximal subgroups

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

subgroupindex
C5×#23102
#106157962
#106029262
#106003262
#105981192
#94625