Finite Group Databasebeta

← D5⋊#1324 #13023168

Subgroups — D5⋊#1324 #13023168

Order 1280.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D5×#382C211yesmaximal, characteristic
2D5⋊#324C212yesmaximal
3#10598710C212yesmaximal, complemented
4#10598688C212yesmaximal, complemented
5C2×D5×C4⋊C4C411yescharacteristic
6C2×D5×C4⋊C4C2211yescharacteristic
7C2×C42×D5C411yescharacteristic
8D5⋊(C22⋊C8)—22no—
9C5×#382C411yescharacteristic
10#65266C411yescharacteristic
11#65266C2211yescharacteristic
12#65225C2211yescharacteristic
13D5×#95—22no—
14#64939—22no—
15#64914—22no—
16#64913C2214yes—
17C2×#1324—51nomaximal, Sylow
18C22×C4×D5—21no—
19C22×C4×D5—21no—
20C22×C4×D5C2×C411yescharacteristic
21C22×C4×D5D412yes—
22C2×D5⋊C8—42no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C42×C5C2×C411yescharacteristic
26C2×C4⋊Dic5C2×C411yescharacteristic
27C2×C4⋊Dic5C2311yescharacteristic
28C2×#683—21no—
29C2×#683D412yes—
30C2×C4×Dic5—21no—
31C2×C4×Dic5C2×C411yescharacteristic
32D5×C4⋊C4—41no—
33D5×C4⋊C4—41no—
34D5×C4⋊C4—41no—
35D5×C4⋊C4—41no—
36C42×D5—22no—
37C42×D5C814yescomplemented
38C22⋊#170—24no—
39#4003—42no—
40C5×#95—22no—
41#3963—22no—
42#3963—22no—
43#3963—22no—
44C2×#382—51no—
45C2×#324—52no—
46#1324—52no—
47#1324—52no—
48C23×D5C22⋊C411yescharacteristic
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5C22⋊C412yes—
52C22×C4×C5C22×C411yescharacteristic
53C22×Dic5—21no—
54C22×Dic5—21no—
55C22×Dic5C22⋊C411yescharacteristic
56C22×Dic5C2×D412yes—
57C2×C4×D5—21no—
58C2×C4×D5—21no—
59C2×C4×D5—22no—
60C2×C4×D5—24no—
61C2×C4×D5—22no—
62C2×C4×D5—22no—
63C2×C4×D5—42no—
64C2×C4×D5—42no—
65C2×C4×D5—44no—
66C2×C4×D5—44no—
67C2×C4×D5—41no—
68C2×C4×D5—41no—
69C2×C4×D5C2×C812yes—
70C2×C4×D5M1612yes—
71C2×#170—44no—
72D5⋊C8—84no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C42×C5—21no—
76C42×C5C2×C812yescomplemented
77C4⋊Dic5—41no—
78C4⋊Dic5—41no—
79#683—42no—
80#683—42no—
81C4×Dic5—21no—
82C4×Dic5—24no—
83C4×Dic5C2×C812yescomplemented
84C22×C4⋊C4—51no—
85C22×C4⋊C4—51no—
86C22×C42—51no—
87C2×C22⋊C8—102no—
88#382—51no—
89#382—51no—
90#382—51no—
91#382—102no—
92#382AGL(1,𝔽5)11yescharacteristic
93C2×#95—102no—
94#324—54no—
95#324—102no—
96C23×C5C2×C22⋊C411yescharacteristic
97C22×D5—22no—
98C22×D5—22no—
99C22×D5C22⋊C812yes—
100C22×D5#9911yescharacteristic
101C22×D5#9911yescharacteristic
102C22×D5#10112yes—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—41no—
112C2×C4×C5C22×C811yescharacteristic
113C2×C4×C5C2×M1611yescharacteristic
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—22no—
117C2×Dic5—22no—
118C2×Dic5—41no—
119C2×Dic5—41no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122C2×Dic5—41no—
123C2×Dic5C22⋊C812yes—
124C4×D5—22no—
125C4×D5—22no—
126C4×D5—22no—
127C4×D5—22no—
128C4×D5—48no—
129C4×D5—44no—
130C4×D5—82no—
131C4×D5—82no—
132C4×D5—82no—
133#170—84no—
134C23×C4—51no—
135C23×C4—52no—
136C23×C4—101no—
137C23×C4—101no—
138C22×C8—202no—
139C2×C4⋊C4—52no—
140C2×C4⋊C4—51no—
141C2×C4⋊C4—51no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4—201no—
144C2×C4⋊C4—201no—
145C2×C4⋊C4—201no—
146C2×C4⋊C4—201no—
147C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
148C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
149C2×C42—51no—
150C2×C42—54no—
151C2×C42—102no—
152C2×C42—101no—
153C2×C42C2×AGL(1,𝔽5)11yescharacteristic
154C22⋊C8—104no—
155C22⋊C8—202no—
156#95—22no—
157#95—102no—
158#95—102no—
159#95—102no—
160C22×C5—21no—
161C22×C5—21no—
162C22×C5C2×C22⋊C811yescharacteristic
163C22×C5C2×#9911yescharacteristic
164C22×C5C2×#10111yescharacteristic
165C2×D5—21no—
166C2×D5—21no—
167C2×D5—24no—
168C2×D5—24no—
169C2×D5#32412yes—
170C2×D5#32412yes—
171C2×D5#35412yes—
172C2×D5#35512yes—
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—42no—
176C4×C5—42no—
177C4×C5—81no—
178Dic5—22no—
179Dic5—42no—
180Dic5—42no—
181Dic5—81no—
182C24—51no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—51no—
186C22×C4—52no—
187C22×C4—52no—
188C22×C4—52no—
189C22×C4—101no—
190C22×C4—101no—
191C22×C4—102no—
192C22×C4—104no—
193C22×C4—102no—
194C22×C4—102no—
195C22×C4—101no—
196C22×C4—101no—
197C22×C4—202no—
198C22×C4—202no—
199C22×C4—204no—
200C22×C4—201no—
201C22×C4—201no—
202C22×C4—204no—
203C22×C4C22⋊AGL(1,𝔽5)12yes—
204C22×C4C22×AGL(1,𝔽5)11yescharacteristic
205C2×C8—204no—
206C2×C8—404no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—202no—
210C4⋊C4—201no—
211C4⋊C4—201no—
212C4⋊C4—202no—
213C42—21no—
214C42—52no—
215C42—104no—
216C42—101no—
217C42D5⋊C812yescomplemented
218C2×C5—21no—
219C2×C5—21no—
220C2×C5C2×#32411yescharacteristic
221C2×C5C2×#35411yescharacteristic
222C2×C5C2×#35511yescharacteristic
223D5—22no—
224D5#132414yescomplemented
225C23—51no—
226C23—52no—
227C23—51no—
228C23—52no—
229C23—102no—
230C23—102no—
231C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—52no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—102no—
245C2×C4—102no—
246C2×C4—101no—
247C2×C4—101no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—204no—
251C2×C4—208no—
252C2×C4—201no—
253C2×C4—201no—
254C2×C4—202no—
255C2×C4—202no—
256C2×C4—201no—
257C2×C4—402no—
258C2×C4—402no—
259C2×C4—402no—
260C2×C4C2×D5⋊C811yescharacteristic
261C2×C4D5⋊M1611yescharacteristic
262C8—404no—
263C5C2×#132411yescharacteristic, complemented, Sylow
264C22—21no—
265C22—21no—
266C22—52no—
267C22—52no—
268C22—52no—
269C22—52no—
270C22—104no—
271C22—104no—
272C22—101no—
273C22—101no—
274C22D5⋊(C22⋊C8)11yescharacteristic
275C22D5⋊#9911yescharacteristic
276C22D5⋊#10111yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—102no—
283C4—202no—
284C4—202no—
285C4—401no—
286C2—21no—
287C2—21no—
288C2—54no—
289C2—102no—
290C2D5⋊#32411yescharacteristic
291C2D5⋊#35411yescharacteristic
292C2D5⋊#35511yescharacteristic
subgroupG/H
centerC22D5⋊#99
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#382C4
socleC22×C5C2×#99
prime radicalC23×D5C22⋊C4
cosocleC2×C4⋊Dic5C23
hypercenter#382AGL(1,𝔽5)
hypocenterC5C2×#1324
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #10598710C2semidirect
4. #10598688C2semidirect
37. C42×D5C8semidirect
76. C42×C5C2×C8semidirect
83. C4×Dic5C2×C8semidirect
217. C42D5⋊C8semidirect
224. D5#1324semidirect
263. C5C2×#1324semidirect

Maximal subgroups

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

subgroupindex
D5×#3822
D5⋊#3242
#105987102
#105986882
C2×#13245