Finite Group Databasebeta

← #13014960

Subgroups — #13014960

Order 1280.

370 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 90 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#10607924C211yesmaximal, characteristic
2#10604189C211yesmaximal, characteristic
3#10604173C211yesmaximal, characteristic
4#10598714C212yesmaximal
5#10598713C212yesmaximal
6C2×C4×#170—21no—
7C5×#389C411yescharacteristic
8#65274C2211yescharacteristic
9#65270—21no—
10#65267—21no—
11#65266C411yescharacteristic
12#65266C411yescharacteristic
13#65262C2211yescharacteristic
14C42×Dic5C2211yescharacteristic
15#65217C411yescharacteristic
16#64942—21no—
17#64941—21no—
18#64918—21no—
19#64918—21no—
20#64918—21no—
21#64918C2212yes—
22#64918C2212yes—
23#7657—51nomaximal, Sylow
24C22×#170—22no—
25C22×#170—22no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5C2×C411yescharacteristic
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×#683—21no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5C2311yescharacteristic
41C4×#170—24no—
42C5×#95—21no—
43#3963—21no—
44#3963—21no—
45#3963—21no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#2864—51no—
51#1839—51no—
52#1744—51no—
53#1271—52no—
54#1271—52no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C22×Dic5—21no—
61C22×Dic5—21no—
62C22×Dic5C22⋊C411yescharacteristic
63C22×Dic5C22⋊C411yescharacteristic
64C22×Dic5C2×D411yescharacteristic
65C22×Dic5C2×D411yescharacteristic
66C2×#170—24no—
67C2×#170—42no—
68C2×#170—42no—
69C2×#170—42no—
70C2×#170—42no—
71C2×#170—42no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C42×C5—22no—
76C4⋊Dic5—22no—
77C4⋊Dic5—42no—
78C4⋊Dic5—41no—
79#683—42no—
80#683—42no—
81C4×Dic5—22no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5—22no—
85C4×Dic5—41no—
86C4×Dic5—41no—
87C2×C4×C8—101no—
88#389—51no—
89#389—51no—
90#389—51no—
91#389AGL(1,𝔽5)11yescharacteristic
92#387—101no—
93#387—101no—
94#387—101no—
95#387—101no—
96#382—51no—
97#382—51no—
98C43—51no—
99#336—52no—
100#336—52no—
101#336—101no—
102#336—101no—
103#336—101no—
104C23×C5C2×C22⋊C411yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5#10412yes—
119C2×C4×C5#13112yes—
120C2×Dic5—21no—
121C2×Dic5—21no—
122C2×Dic5—21no—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—21no—
126C2×Dic5—21no—
127C2×Dic5—21no—
128C2×Dic5—21no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5—41no—
132C2×Dic5—41no—
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5#10112yes—
136C2×Dic5#13512yes—
137C2×Dic5#13512yes—
138#170—44no—
139#170—82no—
140C22×C8—102no—
141C22×C8—102no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—51no—
144C2×C4⋊C4—51no—
145C2×C4⋊C4—101no—
146C2×C4⋊C4—101no—
147C2×C4⋊C4—101no—
148C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
149C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
150C2×C42—51no—
151C2×C42—51no—
152C2×C42—51no—
153C2×C42—51no—
154C2×C42—51no—
155C2×C42—51no—
156C2×C42C2×AGL(1,𝔽5)11yescharacteristic
157C4×C8—104no—
158#95—21no—
159#95—101no—
160#95—101no—
161#95—101no—
162#95—101no—
163#95—101no—
164#95—101no—
165#95—101no—
166C22×C5#40811yescharacteristic
167C22×C5#41011yescharacteristic
168C22×C5C2×#10111yescharacteristic
169C22×C5#41611yescharacteristic
170C22×C5#41611yescharacteristic
171C22×C5C2×#10411yescharacteristic
172C22×C5#42111yescharacteristic
173C4×C5—22no—
174C4×C5—22no—
175C4×C5—41no—
176C4×C5—81no—
177C4×C5—81no—
178Dic5—22no—
179Dic5—22no—
180Dic5—22no—
181Dic5—41no—
182Dic5—81no—
183Dic5—81no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—51no—
187C22×C4—51no—
188C22×C4—51no—
189C22×C4—51no—
190C22×C4—101no—
191C22×C4—101no—
192C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
193C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
194C22×C4C22×AGL(1,𝔽5)11yescharacteristic
195C2×C8—104no—
196C2×C8—202no—
197C2×C8—202no—
198C2×C8—202no—
199C2×C8—202no—
200C2×C8—202no—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—102no—
205C4⋊C4—201no—
206C4⋊C4—202no—
207C4⋊C4—202no—
208C4⋊C4—202no—
209C42—22no—
210C42—102no—
211C42—102no—
212C42—102no—
213C42—102no—
214C42—201no—
215C42—201no—
216C2×C5#147011yescharacteristic
217C2×C5#148211yescharacteristic
218C2×C5#149411yescharacteristic
219C2×C5#150011yescharacteristic
220C2×C5#152111yescharacteristic
221C2×C5#153111yescharacteristic
222C2×C5#154411yescharacteristic
223C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—52no—
238C2×C4—52no—
239C2×C4—52no—
240C2×C4—101no—
241C2×C4—101no—
242C2×C4—101no—
243C2×C4—101no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—101no—
247C2×C4—101no—
248C2×C4—101no—
249C2×C4—201no—
250C2×C4—201no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4—201no—
254C2×C4—201no—
255C2×C4#400812yes—
256C2×C4#413112yes—
257C8—204no—
258C8—402no—
259C5#765711yescharacteristic, complemented, Sylow
260C22#6574511yescharacteristic
261C22C2×#400811yescharacteristic
262C22#6577511yescharacteristic
263C22#6578411yescharacteristic
264C22D5⋊#10111yescharacteristic
265C22#6579411yescharacteristic
266C22#6579411yescharacteristic
267C4—22no—
268C4—22no—
269C4—41no—
270C4—81no—
271C4—81no—
272C4—102no—
273C4—102no—
274C4—102no—
275C4—201no—
276C4—401no—
277C4—401no—
278C2#1060429711yescharacteristic
279C2#1060438811yescharacteristic
280C2#1060443011yescharacteristic
281C2#1060448211yescharacteristic
282C2#1060451011yescharacteristic
283C2#1060458411yescharacteristic
284C2#1060463611yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#389C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#389AGL(1,𝔽5)
hypocenterC5#7657
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
259. C5#7657semidirect

Maximal subgroups

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

subgroupindex
#106079242
#106041892
#106041732
#105987142
#105987132
#76575