Finite Group Databasebeta

← #11992809

Subgroups — #11992809

Order 1280.

538 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#10613824C211yesmaximal, characteristic
2C5×#1819C211yesmaximal, characteristic
3#10602335C211yesmaximal, characteristic
4#10598114C212yesmaximal
5#10598114C212yesmaximal
6C22×C5×C22⋊C4C2211yescharacteristic
7C5×#379C2212yes—
8#65536C2212yes—
9#65536C2211yescharacteristic
10#65536C2211yescharacteristic
11#65501C412yescomplemented
12C4×C22⋊Dic5C412yescomplemented
13#65240—22no—
14#65240—22no—
15C5×#342—22no—
16#64746—22no—
17#8750—51nomaximal, Sylow
18C25×C5C2311yescharacteristic
19C23×C4×C5C2×C411yescharacteristic
20C23×C4×C5C2×C411yescharacteristic
21C2×C5×C22⋊C4—22no—
22C2×C5×C22⋊C4—22no—
23C2×C5×C22⋊C4—22no—
24C2×C5×C22⋊C4—22no—
25C2×C5×C22⋊C4—22no—
26C2×C5×C22⋊C4D412yes—
27C2×C5×C22⋊C4D412yes—
28C2×C22⋊Dic5—22no—
29C2×C22⋊Dic5—21no—
30C2×C22⋊Dic5—21no—
31C2×C22⋊Dic5—21no—
32C2×C22⋊Dic5—21no—
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5C2×C412yes—
36C2×C22⋊Dic5C2×C412yes—
37C2×C4⋊Dic5—22no—
38C2×C4×Dic5—22no—
39#3963—22no—
40#3963—22no—
41#2312—51no—
42#1819—51no—
43#1819D511yescharacteristic
44#1304—52no—
45#1304—52no—
46C24×C5—42no—
47C24×C5—81no—
48C24×C5—81no—
49C24×C5C22×C411yescharacteristic
50C24×C5C2×D411yescharacteristic
51C24×C5C2×D411yescharacteristic
52C24×C5#4112yes—
53C24×C5#4112yes—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—42no—
59C22×C4×C5—81no—
60C22×C4×C5—81no—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22⋊C412yes—
63C22×Dic5—22no—
64C22×Dic5—22no—
65C22×Dic5—42no—
66C5×C22⋊C4—24no—
67C5×C22⋊C4—24no—
68C5×C22⋊C4—44no—
69C5×C22⋊C4—82no—
70C5×C22⋊C4—82no—
71C22⋊Dic5—42no—
72C22⋊Dic5—42no—
73C22⋊Dic5—44no—
74C22⋊Dic5—81no—
75C22⋊Dic5—81no—
76C22⋊Dic5—81no—
77C22⋊Dic5—81no—
78C22⋊Dic5—82no—
79C22⋊Dic5—82no—
80C4⋊Dic5—82no—
81C4×Dic5—82no—
82C22×C22⋊C4C2×D511yescharacteristic
83#388—102no—
84#388—102no—
85#380—52no—
86#379—51no—
87#379—51no—
88#379—52no—
89#379C2×D512yes—
90C4×C22⋊C4—52no—
91#342—22no—
92#342—102no—
93C23×C5—22no—
94C23×C5—22no—
95C23×C5—22no—
96C23×C5—41no—
97C23×C5—41no—
98C23×C5—41no—
99C23×C5—41no—
100C23×C5—41no—
101C23×C5—41no—
102C23×C5—42no—
103C23×C5—42no—
104C23×C5—42no—
105C23×C5—42no—
106C23×C5—42no—
107C23×C5—42no—
108C23×C5—88no—
109C23×C5C2×C22⋊C411yescharacteristic
110C23×C5#11711yescharacteristic
111C23×C5#11711yescharacteristic
112C23×C5#12312yes—
113C23×C5#12312yes—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—81no—
119C2×C4×C5—81no—
120C2×C4×C5—81no—
121C2×C4×C5—81no—
122C2×C4×C5—82no—
123C2×C4×C5—82no—
124C2×C4×C5—82no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130C2×Dic5—42no—
131C2×Dic5—82no—
132C2×Dic5—82no—
133C2×Dic5—82no—
134C25C22×D511yescharacteristic
135C23×C4C4×D511yescharacteristic
136C23×C4C4×D511yescharacteristic
137C2×C4⋊C4—102no—
138C2×C22⋊C4—22no—
139C2×C22⋊C4—22no—
140C2×C22⋊C4—22no—
141C2×C22⋊C4—22no—
142C2×C22⋊C4—22no—
143C2×C22⋊C4—52no—
144C2×C22⋊C4—52no—
145C2×C22⋊C4—102no—
146C2×C22⋊C4—101no—
147C2×C22⋊C4—101no—
148C2×C22⋊C4—101no—
149C2×C22⋊C4—101no—
150C2×C22⋊C4—102no—
151C2×C22⋊C4—102no—
152C2×C22⋊C4D2012yes—
153C2×C22⋊C4C22⋊D512yes—
154C2×C42—102no—
155#95—102no—
156#95—102no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5—22no—
160C22×C5—22no—
161C22×C5—21no—
162C22×C5—21no—
163C22×C5—22no—
164C22×C5—22no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—22no—
170C22×C5—22no—
171C22×C5—44no—
172C22×C5—82no—
173C22×C5—82no—
174C22×C5—84no—
175C22×C5—84no—
176C22×C5#38111yescharacteristic
177C22×C5#41012yes—
178C4×C5—42no—
179C4×C5—42no—
180C4×C5—162no—
181Dic5—82no—
182Dic5—82no—
183Dic5—162no—
184C24—42no—
185C24—81no—
186C24—81no—
187C24C2×C4×D511yescharacteristic
188C24C2×D2011yescharacteristic
189C24#71112yes—
190C24#71112yes—
191C24C2×C22⋊D511yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—42no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—102no—
200C22×C4—102no—
201C22×C4—202no—
202C22×C4#68512yes—
203C22×C4#68512yes—
204C4⋊C4—402no—
205C22⋊C4—24no—
206C22⋊C4—24no—
207C22⋊C4—44no—
208C22⋊C4—82no—
209C22⋊C4—82no—
210C22⋊C4—202no—
211C22⋊C4—202no—
212C22⋊C4—204no—
213C22⋊C4—401no—
214C22⋊C4—401no—
215C22⋊C4—401no—
216C22⋊C4—401no—
217C22⋊C4—402no—
218C22⋊C4—402no—
219C42—402no—
220C2×C5—22no—
221C2×C5—42no—
222C2×C5—42no—
223C2×C5—41no—
224C2×C5—41no—
225C2×C5#182011yescharacteristic
226C2×C5#182811yescharacteristic
227C2×C5#182811yescharacteristic
228C23—22no—
229C23—22no—
230C23—22no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—42no—
235C23—41no—
236C23—41no—
237C23—42no—
238C23—42no—
239C23—41no—
240C23—41no—
241C23—42no—
242C23—42no—
243C23—88no—
244C23#402311yescharacteristic
245C23#402311yescharacteristic
246C23#403212yes—
247C23C2×#68511yescharacteristic
248C23#408112yes—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4—202no—
263C2×C4—202no—
264C2×C4—202no—
265C2×C4—202no—
266C2×C4—402no—
267C2×C4—402no—
268C2×C4—402no—
269C5#875011yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22—44no—
285C22—82no—
286C22—82no—
287C22—84no—
288C22—84no—
289C22#6523211yescharacteristic
290C22#6529512yes—
291C4—42no—
292C4—42no—
293C4—162no—
294C4—402no—
295C4—402no—
296C4—802no—
297C2—22no—
298C2—42no—
299C2—42no—
300C2—41no—
301C2—41no—
302C2#1060032711yescharacteristic
303C2#1060081311yescharacteristic
304C2#1060081311yescharacteristic
subgroupG/H
centerC22#65232
commutatorC24×C5C22×C4
FrattiniC25C22×D5
FittingC5×#1819C2
socleC22×C5#381
prime radical, cosocleC25×C5C23
hypercenter#1819D5
hypocenterC5#8750
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
11. #65501C4semidirect
12. C4×C22⋊Dic5C4semidirect
269. C5#8750semidirect

Maximal subgroups

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

subgroupindex
#106138242
C5×#18192
#106023352
#105981142
#87505