Finite Group Databasebeta

← #13026406

Subgroups — #13026406

Order 1280.

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

normal subgroups only

This group has 468 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
1C4×#4090C211yesmaximal, characteristic
2C2×#64929C212yesmaximal
3#10604194C212yesmaximal
4#10598724C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C2×#4005C2214yes—
9#65758—22no—
10#65519C411yescharacteristic
11#65265C411yescharacteristic
12#65263C2211yescharacteristic
13#65261—22no—
14C4×#683—22no—
15C42×Dic5C411yescharacteristic
16#64929—24no—
17#64919—22no—
18#12802—51nomaximal, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×Dic10C2311yescharacteristic
21C2×#704—24no—
22C4×C5×Q8—41no—
23C4×C5×Q8—41no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C42×C5—21no—
27C2×C42×C5C2×C411yescharacteristic
28#4090—22no—
29#4090D412yes—
30#4090Q812yes—
31C2×C4⋊Dic5C2×C411yescharacteristic
32C2×#683—22no—
33C2×#683—22no—
34C2×#683D412yes—
35C2×C4×Dic5—21no—
36C2×C4×Dic5—21no—
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5C2×C411yescharacteristic
39C2×C4×Dic5D412yes—
40C4×Dic10—41no—
41C4×Dic10—41no—
42#4005—24no—
43#4005—24no—
44#4004—42no—
45C4⋊#170—42no—
46#3963—22no—
47#3963—22no—
48C4×C4⋊Q8—51no—
49C2×#356—52no—
50#1801—52no—
51#1394—52no—
52C2×C5×Q8—21no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8C4⋊C412yes—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×Dic5—21no—
62C22×Dic5—21no—
63C22×Dic5C22⋊C412yes—
64C22×Dic5C2×D412yes—
65C2×Dic10—41no—
66C2×Dic10—41no—
67C2×Dic10C2×D411yescharacteristic
68C2×Dic10C2×Q811yescharacteristic
69C2×Dic10#4112yes—
70#704—44no—
71#704—44no—
72C2×#170—44no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—41no—
78C42×C5—41no—
79C4⋊Dic5—41no—
80#683—24no—
81#683—24no—
82#683—42no—
83#683—44no—
84C4×Dic5—24no—
85C4×Dic5—22no—
86C4×Dic5—22no—
87C4×Dic5—21no—
88C4×Dic5—42no—
89C4×Dic5—41no—
90C4×Dic5C4⋊C412yes—
91C2×C4⋊Q8—51no—
92C2×C4×Q8—51no—
93C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
94#423—102no—
95C2×#101—54no—
96#391—51no—
97#391—51no—
98#389—102no—
99#384—51no—
100C4×C4⋊C4—102no—
101C43—51no—
102#356—104no—
103#343—102no—
104C23×C5C2×C22⋊C411yescharacteristic
105C5×Q8—42no—
106C5×Q8—42no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—22no—
111C2×C4×C5—21no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—42no—
116C2×C4×C5—41no—
117C2×C4×C5#9911yescharacteristic
118C2×C4×C5#9911yescharacteristic
119C2×C4×C5C2×C4⋊C411yescharacteristic
120C2×C4×C5#11711yescharacteristic
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—22no—
124C2×Dic5—22no—
125C2×Dic5—22no—
126C2×Dic5—22no—
127C2×Dic5—22no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5#12112yes—
132C2×Dic5C22⋊Q812yes—
133Dic10—41no—
134Dic10—41no—
135Dic10—42no—
136#170—84no—
137C22×Q8—51no—
138C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
139C2×M16—104no—
140C4⋊Q8—52no—
141C4⋊Q8—52no—
142C4⋊Q8—102no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—201no—
146C4×Q8—201no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—52no—
149C2×C4⋊C4—51no—
150C2×C4⋊C4—102no—
151C2×C4⋊C4—102no—
152C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
153C2×C42—21no—
154C2×C42—51no—
155C2×C42—52no—
156C2×C42—51no—
157C2×C42—101no—
158C2×C42—101no—
159C2×C42C2×AGL(1,𝔽5)11yescharacteristic
160C4⋊C8—202no—
161C4⋊C8—202no—
162#101—104no—
163#101—104no—
164#95—102no—
165#95—102no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5#38011yescharacteristic
169C22×C5C2×#9911yescharacteristic
170C22×C5#41011yescharacteristic
171C4×C5—21no—
172C4×C5—21no—
173C4×C5—21no—
174C4×C5—42no—
175C4×C5—41no—
176C4×C5—81no—
177C4×C5#35612yescomplemented
178Dic5—24no—
179Dic5—22no—
180Dic5—22no—
181Dic5—42no—
182Dic5—42no—
183C2×Q8—21no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—51no—
187C2×Q8—51no—
188C2×Q8—52no—
189C2×Q8—201no—
190C2×Q8—201no—
191C2×Q8C4⋊AGL(1,𝔽5)12yes—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—52no—
195C22×C4—52no—
196C22×C4—101no—
197C22×C4—101no—
198C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
199C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
200C22×C4C22×AGL(1,𝔽5)11yescharacteristic
201M16—204no—
202M16—204no—
203C2×C8—204no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—104no—
207C4⋊C4—104no—
208C4⋊C4—202no—
209C4⋊C4—201no—
210C4⋊C4—204no—
211C42—21no—
212C42—21no—
213C42—41no—
214C42—41no—
215C42—52no—
216C42—104no—
217C42—101no—
218C42—102no—
219C42—102no—
220C42—201no—
221C42—202no—
222C2×C5—21no—
223C2×C5—21no—
224C2×C5#179911yescharacteristic
225C2×C5C2×#35611yescharacteristic
226C2×C5#213211yescharacteristic
227C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—201no—
231Q8—201no—
232Q8—202no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—52no—
244C2×C4—52no—
245C2×C4—102no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—102no—
251C2×C4—102no—
252C2×C4—201no—
253C2×C4—201no—
254C2×C4—202no—
255C2×C4#401111yescharacteristic
256C2×C4#401111yescharacteristic
257C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
258C2×C4#413011yescharacteristic
259C8—404no—
260C5#1280211yescharacteristic, complemented, Sylow
261C22—21no—
262C22—21no—
263C22#6574511yescharacteristic
264C22#6576511yescharacteristic
265C22C2×#401111yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—41no—
271C4—81no—
272C4—104no—
273C4—102no—
274C4—102no—
275C4—202no—
276C4—202no—
277C4#6492912yescomplemented
278C2—21no—
279C2—21no—
280C2#1060489211yescharacteristic
281C2C2×#6492911yescharacteristic
282C2#1060499811yescharacteristic
subgroupG/H
centerC22C2×#4011
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×Dic10C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#12802
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
177. C4×C5#356semidirect
260. C5#12802semidirect
277. C4#64929semidirect

Maximal subgroups

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

subgroupindex
C4×#40902
C2×#649292
#106041942
#105987242
#128025