Finite Group Databasebeta

← #13018290

Subgroups — #13018290

Order 1280.

486 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C2×C8×C22⋊D5C211yesmaximal, characteristic
2#10604884C212yesmaximal
3#10604731C212yesmaximal, complemented
4#10598767C212yesmaximal, complemented
5C23×C5×C8C411yescharacteristic
6C2×C4×C22⋊D5C2211yescharacteristic
7C22×C8×D5C2211yescharacteristic
8#65756C2214yes—
9C2×#3995—22no—
10C2×C22⋊#168C411yescharacteristic
11C8×C22⋊D5—22no—
12C8×C22⋊D5—22no—
13C2×#3952C2211yescharacteristic
14C2×#3946C411yescharacteristic
15C2×C8×Dic5C411yescharacteristic
16#64933—22no—
17#64914—22no—
18#64896—22no—
19#8611—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C22×C22⋊D5Q811yescharacteristic
22C22×C4×D5C2311yescharacteristic
23C2×#700—24no—
24C22×C5×C8—21no—
25C22×C5×C8—21no—
26C22×C5×C8—42no—
27C22×C5×C8C2×C411yescharacteristic
28C22×C5×C8C2×C411yescharacteristic
29C2×C22⋊Dic5D411yescharacteristic
30C4×C22⋊D5—22no—
31C4×C22⋊D5—22no—
32C2×#685Q811yescharacteristic
33C2×#683D411yescharacteristic
34C2×C4×Dic5C2×C411yescharacteristic
35C22×#168C2×C411yescharacteristic
36C22×#168C2×C411yescharacteristic
37C2×C8×D5—42no—
38C2×C8×D5D412yes—
39C2×C8×D5D412yes—
40C22⋊#170—24no—
41#4003—24no—
42#3995—44no—
43C22⋊#168—22no—
44#3952—22no—
45#3946—22no—
46C8×Dic5—21no—
47C8×Dic5—21no—
48C2×C8×D4—51no—
49#1810—52no—
50#1465—52no—
51#1293—52no—
52C24×C5C4⋊C411yescharacteristic
53C23×D5C2×Q811yescharacteristic
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—41no—
57C22×C4×C5—41no—
58C22×C4×C5C4⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C2×C22⋊D5—22no—
61C2×C22⋊D5—22no—
62C2×C22⋊D5—22no—
63C22×Dic5C4⋊C411yescharacteristic
64C22×Dic5C4⋊C411yescharacteristic
65C22×Dic5C2×D411yescharacteristic
66C2×C4×D5—41no—
67C2×C4×D5—41no—
68C2×C4×D5C2×D412yes—
69C2×C4×D5#4112yes—
70C2×#170—44no—
71#700—44no—
72#700—44no—
73C2×C5×C8—22no—
74C2×C5×C8—21no—
75C2×C5×C8—42no—
76C2×C5×C8—42no—
77C2×C5×C8—41no—
78C2×C5×C8C22⋊C411yescharacteristic
79C2×C5×C8C22⋊C411yescharacteristic
80C22⋊Dic5—22no—
81#685—22no—
82#683—22no—
83C4×Dic5—21no—
84C4×Dic5—21no—
85C2×#168—21no—
86C2×#168—41no—
87C2×#168—41no—
88C2×#168C22⋊C412yes—
89C8×D5—24no—
90C8×D5—42no—
91C23×C8—51no—
92C23×C8AGL(1,𝔽5)11yescharacteristic
93C2×C4×D4—51no—
94C8×D4—102no—
95C8×D4—102no—
96C2×#108—102no—
97C2×C4⋊C8—51no—
98#407—54no—
99C2×C22⋊C8—51no—
100C2×C22⋊C8—51no—
101C2×C4×C8—51no—
102#341—102no—
103#324—102no—
104#323—102no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—41no—
108C23×C5—41no—
109C23×C5#10812yescomplemented
110C23×C5C2×C4⋊C411yescharacteristic
111C22×D5—21no—
112C22×D5—21no—
113C22×D5—41no—
114C22×D5—41no—
115C22×D5C22⋊Q812yes—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—42no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5C2×C22⋊C411yescharacteristic
124C2×C4×C5#11711yescharacteristic
125C22⋊D5—28no—
126C2×Dic5—21no—
127C2×Dic5—21no—
128C2×Dic5—21no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5#10812yescomplemented
132C2×Dic5#12112yes—
133C4×D5—22no—
134C4×D5—22no—
135C4×D5—42no—
136#170—84no—
137C5×C8—21no—
138C5×C8—41no—
139C5×C8#9912yes—
140#168—22no—
141#168—41no—
142C22×D4—51no—
143C23×C4—51no—
144C23×C4C2×AGL(1,𝔽5)11yescharacteristic
145C2×M16—104no—
146C22×C8—21no—
147C22×C8—21no—
148C22×C8—42no—
149C22×C8—51no—
150C22×C8—52no—
151C22×C8—52no—
152C22×C8—51no—
153C22×C8—202no—
154C22×C8C2×AGL(1,𝔽5)11yescharacteristic
155C22×C8C2×AGL(1,𝔽5)11yescharacteristic
156C4×D4—102no—
157C4×D4—102no—
158C2×C4⋊C4—51no—
159C2×C22⋊C4—51no—
160C2×C22⋊C4—51no—
161C2×C42—51no—
162#108—204no—
163C4⋊C8—102no—
164C22⋊C8—102no—
165C22⋊C8—102no—
166C22⋊C8—104no—
167C22⋊C8—104no—
168C4×C8—101no—
169C4×C8—101no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—22no—
173C22×C5—42no—
174C22×C5—42no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5#38011yescharacteristic
178C22×C5C2×#10811yescharacteristic
179C22×C5C2×#10811yescharacteristic
180C2×D5—22no—
181C2×D5—22no—
182C2×D5—22no—
183C2×D5—42no—
184C2×D5—42no—
185C4×C5—21no—
186C4×C5—41no—
187C4×C5C2×#9911yescharacteristic
188C4×C5#41011yescharacteristic
189Dic5—22no—
190Dic5—22no—
191Dic5—41no—
192C24—51no—
193C24C4⋊AGL(1,𝔽5)11yescharacteristic
194C2×D4—102no—
195C2×D4—102no—
196C2×D4—102no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—51no—
202C22×C4—51no—
203C22×C4—52no—
204C22×C4—52no—
205C22×C4—51no—
206C22×C4—201no—
207C22×C4—201no—
208C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
209C22×C4C22×AGL(1,𝔽5)11yescharacteristic
210M16—204no—
211M16—204no—
212C2×C8—22no—
213C2×C8—21no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—41no—
217C2×C8—52no—
218C2×C8—104no—
219C2×C8—101no—
220C2×C8—202no—
221C2×C8—201no—
222C2×C8—201no—
223C2×C8—204no—
224C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
225C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
226C4⋊C4—102no—
227C22⋊C4—102no—
228C22⋊C4—102no—
229C42—101no—
230C42—101no—
231C2×C5—21no—
232C2×C5—21no—
233C2×C5—42no—
234C2×C5#179911yescharacteristic
235C2×C5#181011yescharacteristic
236C2×C5#181311yescharacteristic
237D5—42no—
238C23—21no—
239C23—21no—
240C23—41no—
241C23—41no—
242C23—52no—
243C23—101no—
244C23—101no—
245C23—201no—
246C23—201no—
247C23#399512yescomplemented
248C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
249D4—108no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—52no—
258C2×C4—52no—
259C2×C4—101no—
260C2×C4—101no—
261C2×C4—102no—
262C2×C4—102no—
263C2×C4—101no—
264C2×C4—202no—
265C2×C4—201no—
266C2×C4—201no—
267C2×C4#413011yescharacteristic
268C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
269C8—21no—
270C8—41no—
271C8—102no—
272C8—201no—
273C8—404no—
274C8#401112yes—
275C5#861111yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—102no—
284C22—102no—
285C22—102no—
286C22—202no—
287C22—202no—
288C22C2×#399511yescharacteristic
289C22D5⋊#10811yescharacteristic
290C22#6576511yescharacteristic
291C4—21no—
292C4—41no—
293C4—102no—
294C4—102no—
295C4—201no—
296C4#6574511yescharacteristic
297C4C2×#401111yescharacteristic
298C2—21no—
299C2—21no—
300C2—42no—
301C2—202no—
302C2#1060473111yescharacteristic
303C2#1060473311yescharacteristic
304C2#1060489211yescharacteristic
subgroupG/H
centerC22#65765
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC22×C5#380
prime radicalC22×C22⋊D5Q8
cosocleC22×C4×D5C23
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5#8611
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. #10604731C2semidirect
4. #10598767C2semidirect
109. C23×C5#108semidirect
131. C2×Dic5#108semidirect
247. C23#3995semidirect
275. C5#8611semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D52
#106048842
#106047312
#105987672
#86115