Finite Group Databasebeta

← #13014693

Subgroups — #13014693

Order 1280.

424 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 106 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#10607693C211yesmaximal, characteristic
2#10604189C211yesmaximal, characteristic
3#10604174C211yesmaximal, characteristic
4#10598715C212yesmaximal
5#10598713C212yesmaximal
6C2×#4033C411yescharacteristic
7C2×C4×#170—21no—
8C5×#389C411yescharacteristic
9#65274C2211yescharacteristic
10#65267—21no—
11C4⋊C4×Dic5—21no—
12C4⋊C4×Dic5C411yescharacteristic
13#65263C2211yescharacteristic
14C42×Dic5C2211yescharacteristic
15#65218C411yescharacteristic
16#64944—21no—
17#64937—21no—
18#64918—21no—
19#64918—21no—
20#64918—21no—
21#64918C2212yes—
22#64918C2212yes—
23#7581—51nomaximal, Sylow
24C22×Dic10C2×C411yescharacteristic
25C22×#170—22no—
26C22×#170—22no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5—21no—
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5C2311yescharacteristic
42#4033—22no—
43#4033C814yescomplemented
44C4×#170—24no—
45C5×#95—21no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#2295—51no—
53#1839—51no—
54#1744—51no—
55#1272—52no—
56#1271—52no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22×C411yescharacteristic
62C22×Dic5—21no—
63C22×Dic5—21no—
64C22×Dic5C22⋊C411yescharacteristic
65C22×Dic5C22⋊C411yescharacteristic
66C22×Dic5C2×D411yescharacteristic
67C22×Dic5C2×D411yescharacteristic
68C2×Dic10—21no—
69C2×Dic10—41no—
70C2×Dic10—41no—
71C2×Dic10C2×C812yes—
72C2×#170—24no—
73C2×#170—42no—
74C2×#170—42no—
75C2×#170—42no—
76C2×#170—42no—
77C2×#170—42no—
78C5×C4⋊C4—21no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—42no—
81C5×C4⋊C4C2×C812yes—
82C42×C5—41no—
83C4⋊Dic5—42no—
84C4⋊Dic5—41no—
85#683—24no—
86C4×Dic5—22no—
87C4×Dic5—24no—
88C4×Dic5—22no—
89C4×Dic5—22no—
90C4×Dic5—41no—
91C4×Dic5—41no—
92C4×Dic5—42no—
93C4×Dic5C2×C812yes—
94C4×Dic5M1612yes—
95C2×C4×Q8—51no—
96C2×C4×C8—101no—
97#391—51no—
98#391—51no—
99#389—51no—
100#389AGL(1,𝔽5)11yescharacteristic
101#387—101no—
102#387—101no—
103C4×C4⋊C4—51no—
104C4×C4⋊C4—101no—
105#376—101no—
106C43—51no—
107#336—52no—
108#336—52no—
109#336—101no—
110#336—101no—
111#336—101no—
112C23×C5C2×C22⋊C411yescharacteristic
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—22no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5#10412yes—
127C2×C4×C5C22×C811yescharacteristic
128C2×C4×C5C2×M1611yescharacteristic
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—22no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5C22⋊C812yes—
144C2×Dic5C22⋊C812yes—
145C2×Dic5#13512yes—
146C2×Dic5#13712yes—
147Dic10—42no—
148Dic10—42no—
149#170—44no—
150#170—82no—
151C22×Q8—51no—
152C22×C8—102no—
153C22×C8—102no—
154C4×Q8—54no—
155C4×Q8—102no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4—101no—
160C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
161C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
162C2×C42—51no—
163C2×C42—51no—
164C2×C42—51no—
165C2×C42—51no—
166C2×C42—51no—
167C2×C42—51no—
168C2×C42—101no—
169C2×C42—101no—
170C2×C42C2×AGL(1,𝔽5)11yescharacteristic
171C4×C8—104no—
172#95—21no—
173#95—101no—
174#95—101no—
175#95—101no—
176#95—101no—
177#95—101no—
178#95—101no—
179C22×C5C2×C22⋊C811yescharacteristic
180C22×C5#41011yescharacteristic
181C22×C5#41311yescharacteristic
182C22×C5#41611yescharacteristic
183C22×C5#41911yescharacteristic
184C22×C5C2×#10411yescharacteristic
185C22×C5#42111yescharacteristic
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—22no—
189C4×C5—41no—
190C4×C5—42no—
191C4×C5—81no—
192Dic5—22no—
193Dic5—22no—
194Dic5—22no—
195Dic5—22no—
196Dic5—42no—
197Dic5—81no—
198C2×Q8—52no—
199C2×Q8—101no—
200C2×Q8—201no—
201C2×Q8—201no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—51no—
205C22×C4—51no—
206C22×C4—51no—
207C22×C4—51no—
208C22×C4—101no—
209C22×C4—101no—
210C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
211C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
212C22×C4C22×AGL(1,𝔽5)11yescharacteristic
213C2×C8—104no—
214C2×C8—202no—
215C2×C8—202no—
216C2×C8—202no—
217C2×C8—202no—
218C2×C8—202no—
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—104no—
223C4⋊C4—201no—
224C4⋊C4—202no—
225C4⋊C4D5⋊C812yes—
226C42—41no—
227C42—52no—
228C42—52no—
229C42—102no—
230C42—102no—
231C42—104no—
232C42—102no—
233C42—201no—
234C42—201no—
235C42—202no—
236C2×C5#145811yescharacteristic
237C2×C5#147611yescharacteristic
238C2×C5#147911yescharacteristic
239C2×C5#150611yescharacteristic
240C2×C5#152111yescharacteristic
241C2×C5#153211yescharacteristic
242C2×C5#155411yescharacteristic
243C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
244Q8—202no—
245Q8—202no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—52no—
260C2×C4—52no—
261C2×C4—52no—
262C2×C4—52no—
263C2×C4—101no—
264C2×C4—101no—
265C2×C4—101no—
266C2×C4—101no—
267C2×C4—101no—
268C2×C4—101no—
269C2×C4—101no—
270C2×C4—101no—
271C2×C4—102no—
272C2×C4—201no—
273C2×C4—201no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—201no—
277C2×C4#400812yes—
278C2×C4C2×D5⋊C811yescharacteristic
279C2×C4D5⋊M1611yescharacteristic
280C8—204no—
281C8—402no—
282C5#758111yescharacteristic, complemented, Sylow
283C22D5⋊(C22⋊C8)11yescharacteristic
284C22C2×#400811yescharacteristic
285C22#6577711yescharacteristic
286C22#6578211yescharacteristic
287C22#6578511yescharacteristic
288C22#6579411yescharacteristic
289C22#6579511yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—41no—
295C4—81no—
296C4—102no—
297C4—102no—
298C4—102no—
299C4—102no—
300C4—202no—
301C4—401no—
302C2#1060428911yescharacteristic
303C2#1060440111yescharacteristic
304C2#1060443811yescharacteristic
305C2#1060447511yescharacteristic
306C2#1060451911yescharacteristic
307C2#1060457611yescharacteristic
308C2#1060462511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#389C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#389AGL(1,𝔽5)
hypocenterC5#7581
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
43. #4033C8semidirect
282. C5#7581semidirect

Maximal subgroups

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

subgroupindex
#106076932
#106041892
#106041742
#105987152
#105987132
#75815