Finite Group Databasebeta

← #11995348

Subgroups — #11995348

Order 1280.

560 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2316C211yesmaximal, characteristic
2#10613914C211yesmaximal, characteristic
3C2×#64748C211yesmaximal, characteristic
4#10600303C212yesmaximal
5#10598116C212yesmaximal
6C2×C5×#117—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C2×#4070C2211yescharacteristic
9C5×#389—24no—
10C5×#380—21no—
11C5×#380C2212yes—
12#65501C2211yescharacteristic
13#65500—21no—
14#65499—21no—
15C2×C22⋊#168C2212yes—
16#65275C412yescomplemented
17#65273—22no—
18#65268C412yescomplemented
19#64748—22no—
20#64672—24no—
21#9200—51nomaximal, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C22×Dic10C2×C411yescharacteristic
26C5×#117—42no—
27C5×#117—42no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4C2×C412yes—
34C2×C5×C4⋊C4D412yes—
35C2×C5×C22⋊C4—22no—
36C2×C42×C5—22no—
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5—21no—
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5C2×C411yescharacteristic
41#4070—22no—
42#4070—22no—
43C2×#683—21no—
44C2×#683—22no—
45C22×#168—22no—
46C5×#95—22no—
47C5×#95D414yes—
48#3963—22no—
49#3963—22no—
50#3963—22no—
51#3963C2×C412yes—
52C22⋊#168—22no—
53C22⋊#168—22no—
54#2627—51no—
55#2316D511yescharacteristic
56#1520—52no—
57C2×#324—51no—
58#1289—52no—
59C24×C5C2×D411yescharacteristic
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—24no—
67C22×C4×C5—81no—
68C22×C4×C5—81no—
69C22×C4×C5C22⋊C412yes—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5SD1612yes—
72C22×C4×C5Q1612yes—
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D412yes—
76C22×C4×C5#4112yes—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C22×Dic5—22no—
80C2×Dic10—22no—
81C2×Dic10—81no—
82C5×C4⋊C4—24no—
83C5×C4⋊C4—24no—
84C5×C4⋊C4—44no—
85C5×C4⋊C4—82no—
86C5×C4⋊C4—82no—
87C5×C22⋊C4—42no—
88C5×C22⋊C4—42no—
89C42×C5—44no—
90C22⋊Dic5—41no—
91C22⋊Dic5—41no—
92C22⋊Dic5—41no—
93C22⋊Dic5—41no—
94C4⋊Dic5—22no—
95C4⋊Dic5—81no—
96#683—42no—
97#683—82no—
98C2×#168—42no—
99C2×#168—82no—
100C2×C22⋊Q8—51no—
101C2×#117—21no—
102C22×C4⋊C4C2×D511yescharacteristic
103C2×C22⋊C8—52no—
104#400—52no—
105#398—102no—
106#395—52no—
107#389—24no—
108#385—101no—
109#381—101no—
110#380—21no—
111#380—51no—
112#380C2×D512yes—
113#328—104no—
114#324—102no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5C2×C22⋊C411yescharacteristic
118C23×C5#12011yescharacteristic
119C23×C5#12311yescharacteristic
120C23×C5C2×SD1611yescharacteristic
121C23×C5C2×Q1611yescharacteristic
122C23×C5AGL(1,ℤ/8)11yescharacteristic
123C23×C5#13711yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—42no—
132C2×C4×C5—41no—
133C2×C4×C5—42no—
134C2×C4×C5—41no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—44no—
138C2×C4×C5—44no—
139C2×C4×C5—44no—
140C2×C4×C5—81no—
141C2×C4×C5#10314yes—
142C2×C4×C5C4×D412yes—
143C2×C4×C5#12112yes—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—42no—
151Dic10—82no—
152#168—82no—
153C22×Q8—51no—
154C23×C4C22⋊D511yescharacteristic
155C23×C4C22⋊D511yescharacteristic
156C23×C4C22×D511yescharacteristic
157C22×C8—102no—
158C22⋊Q8—102no—
159C22⋊Q8—102no—
160#117—42no—
161#117—42no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—51no—
168C2×C4⋊C4—101no—
169C2×C4⋊C4—102no—
170C2×C4⋊C4—101no—
171C2×C4⋊C4C4×D512yes—
172C2×C4⋊C4D2012yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—101no—
175C2×C22⋊C4—101no—
176C2×C42—22no—
177C22⋊C8—102no—
178C22⋊C8—102no—
179#95—22no—
180#95—52no—
181#95—102no—
182#95—102no—
183#95—102no—
184#95C22⋊D514yes—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5—41no—
192C22×C5—41no—
193C22×C5—41no—
194C22×C5—41no—
195C22×C5#38611yescharacteristic
196C22×C5C2×#10311yescharacteristic
197C22×C5#41711yescharacteristic
198C22×C5#45011yescharacteristic
199C22×C5#45111yescharacteristic
200C22×C5#48311yescharacteristic
201C22×C5#48411yescharacteristic
202C4×C5—24no—
203C4×C5—22no—
204C4×C5—22no—
205C4×C5—42no—
206C4×C5—84no—
207Dic5—82no—
208Dic5—81no—
209Dic5—81no—
210C24C2×C22⋊D511yescharacteristic
211C2×Q8—102no—
212C2×Q8—401no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—81no—
221C22×C4—81no—
222C22×C4—102no—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4#68512yes—
226C22×C4#68512yes—
227C22×C4#68712yes—
228C22×C4#68912yes—
229C22×C4C2×C4×D511yescharacteristic
230C22×C4C2×D2011yescharacteristic
231C22×C4#70912yes—
232C22×C4C2×C22⋊D512yes—
233C2×C8—202no—
234C2×C8—402no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—44no—
238C4⋊C4—82no—
239C4⋊C4—82no—
240C4⋊C4—102no—
241C4⋊C4—202no—
242C4⋊C4—402no—
243C4⋊C4—401no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—201no—
247C22⋊C4—201no—
248C22⋊C4—201no—
249C22⋊C4—201no—
250C42—44no—
251C2×C5—21no—
252C2×C5—21no—
253C2×C5—21no—
254C2×C5—21no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5#187211yescharacteristic
258C2×C5#191211yescharacteristic
259C2×C5#191311yescharacteristic
260C23—41no—
261C23—41no—
262C23C2×#68511yescharacteristic
263C23#407511yescharacteristic
264C23#407811yescharacteristic
265C23C2×#68711yescharacteristic
266C23#408811yescharacteristic
267C23C2×#68911yescharacteristic
268C23#409911yescharacteristic
269Q8—402no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—81no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4—202no—
294C2×C4#394214yes—
295C2×C4C4×C22⋊D512yes—
296C2×C4#407612yes—
297C8—402no—
298C5#920011yescharacteristic, complemented, Sylow
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#6525511yescharacteristic
310C22C2×#394211yescharacteristic
311C22#6525911yescharacteristic
312C22#6526011yescharacteristic
313C22#6550211yescharacteristic
314C22#6550711yescharacteristic
315C22#6551711yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—402no—
322C4—401no—
323C4—401no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1060235211yescharacteristic
331C2#1060244911yescharacteristic
332C2#1060245611yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2316C2
socleC22×C5#386
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#2316D5
hypocenterC5#9200
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
16. #65275C4semidirect
18. #65268C4semidirect
298. C5#9200semidirect

Maximal subgroups

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

subgroupindex
C5×#23162
#106139142
C2×#647482
#106003032
#105981162
#92005