Finite Group Databasebeta

← #13025513

Subgroups — #13025513

Order 1280.

630 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3993C211yesmaximal, characteristic
2C2×D5⋊M32C211yesmaximal, characteristic
3D5×#427C211yesmaximal, characteristic
4#10598621C214yesmaximal, complemented
5C22×C4⋊AGL(1,𝔽5)—21no—
6C22×C8×D5C2211yescharacteristic
7D5×#117—21no—
8C2×#3998—21no—
9C2×#3993—22no—
10C2×#3993—21no—
11C2×#3993C414yescomplemented
12C2×#3993C2212yes—
13D5⋊M32—22no—
14D5⋊M32C414yescomplemented
15C2×#3990C2212yes—
16C2×D5⋊C16—21no—
17C5×#427C411yescharacteristic, complemented
18#65395C411yescharacteristic, complemented
19#65287—21no—
20#65169C2212yes—
21D5×#107C412yescomplemented
22#65149—21no—
23D5×#106—21no—
24C2×#1386—51nomaximal, Sylow
25C23×AGL(1,𝔽5)—41no—
26C22×C4×D5D411yescharacteristic
27C2×C4⋊AGL(1,𝔽5)—24no—
28C2×C4⋊AGL(1,𝔽5)—22no—
29C2×C4⋊AGL(1,𝔽5)—41no—
30C2×C4⋊AGL(1,𝔽5)—42no—
31C22×C5×C8C2×C411yescharacteristic
32C5×#117—21no—
33#4072—21no—
34C22×#168D411yescharacteristic
35C2×C8×D5C2×C411yescharacteristic
36C2×C8×D5C2×C412yes—
37C2×C8×D5C2×C412yes—
38C2×C8×D5D411yescharacteristic
39C2×C8×D5D411yescharacteristic
40C2×C8×D5D412yes—
41C2×C8×D5Q812yes—
42C2×C8×D5C2311yescharacteristic
43#4038—22no—
44D5×C4⋊C4—22no—
45D5×C22⋊C4—41no—
46#4023—41no—
47#4018—41no—
48C42×D5—41no—
49#3998—24no—
50C2×#674—22no—
51#3993—24no—
52#3993—22no—
53#3993C2×C414yescomplemented
54#3990—22no—
55#3990C2×C414yescomplemented
56D5⋊C16—24no—
57C5×#107C2×C412yescomplemented
58C5×#106—21no—
59#3950C2×C412yescomplemented
60#3949—21no—
61#3940—22no—
62#3939—22no—
63C22×M32—51no—
64C2×#427—51no—
65C22×#106—51no—
66#1386—54no—
67C23×D5D811yescharacteristic
68C22×AGL(1,𝔽5)—44no—
69C22×AGL(1,𝔽5)—42no—
70C22×AGL(1,𝔽5)—84no—
71C22×C4×C5C22⋊C411yescharacteristic
72C22×Dic5SD1611yescharacteristic
73C2×C4×D5—42no—
74C2×C4×D5C22⋊C411yescharacteristic
75C2×C4×D5C22⋊C412yes—
76C2×C4×D5C4⋊C412yes—
77C2×C4×D5D811yescharacteristic
78C2×C4×D5SD1612yes—
79C2×C4×D5SD1611yescharacteristic
80C2×C4×D5Q1612yes—
81C2×C4×D5C2×D411yescharacteristic
82C4⋊AGL(1,𝔽5)—24no—
83C4⋊AGL(1,𝔽5)—44no—
84C4⋊AGL(1,𝔽5)—42no—
85C2×C5×C8C4212yes—
86C2×C5×C8C22⋊C411yescharacteristic
87C2×C5×C8C4⋊C412yes—
88C2×C5×C8C22×C411yescharacteristic
89C5×C4⋊C4—22no—
90C5×C22⋊C4—41no—
91C42×C5—41no—
92C22⋊Dic5—41no—
93#685—42no—
94C4⋊Dic5—22no—
95#683—42no—
96C4×Dic5—41no—
97C4×Dic5—42no—
98C2×#168C22⋊C411yescharacteristic
99C2×#168C22⋊C412yes—
100C2×#168C4⋊C412yes—
101C2×#168C2×D411yescharacteristic
102C8×D5C4212yes—
103C8×D5C22⋊C412yes—
104C8×D5C22⋊C412yes—
105C8×D5C4⋊C412yes—
106C8×D5C4⋊C412yes—
107C8×D5C4⋊C412yes—
108C8×D5C22×C411yescharacteristic
109C8×D5C22×C411yescharacteristic
110C8×D5C2×D411yescharacteristic
111C8×D5C2×Q811yescharacteristic
112#674—24no—
113C23×C8—51no—
114C2×#117—101no—
115C22×C4⋊C4—101no—
116C2×M32—52no—
117C2×M32—54no—
118C2×M32—102no—
119C2×M32—101no—
120C22×C16—101no—
121#427—51no—
122#427—52no—
123#427—101no—
124#427—101no—
125#427AGL(1,𝔽5)11yescharacteristic, complemented
126C2×#107—52no—
127C2×#106—52no—
128C2×#106—54no—
129C2×#106—101no—
130C2×#106—102no—
131C2×#106—101no—
132C23×C5#10211yescharacteristic
133C22×D5—24no—
134C22×D5#10212yes—
135C22×D5#10211yescharacteristic
136C22×D5#10712yes—
137C22×D5C2×D811yescharacteristic
138C2×AGL(1,𝔽5)—44no—
139C2×AGL(1,𝔽5)—84no—
140C2×AGL(1,𝔽5)—88no—
141C2×C4×C5—42no—
142C2×C4×C5#9512yes—
143C2×C4×C5#10211yescharacteristic
144C2×C4×C5#10312yes—
145C2×C4×C5C2×C22⋊C411yescharacteristic
146C2×Dic5—42no—
147C2×Dic5#10211yescharacteristic
148C2×Dic5#10312yes—
149C2×Dic5#10612yes—
150C2×Dic5C2×SD1611yescharacteristic
151C4×D5—84no—
152C4×D5#9512yes—
153C4×D5#10212yes—
154C4×D5#10312yes—
155C4×D5#10312yes—
156C4×D5#10612yes—
157C4×D5#10712yes—
158C4×D5C2×C22⋊C411yescharacteristic
159C4×D5C2×C4⋊C411yescharacteristic
160C4×D5C2×SD1611yescharacteristic
161C4×D5C2×Q1611yescharacteristic
162C5×C8#9512yes—
163C5×C8C2×C4211yescharacteristic
164C5×C8C2×C4⋊C411yescharacteristic
165#168#9512yes—
166#168C2×C22⋊C411yescharacteristic
167#168C2×C4⋊C411yescharacteristic
168C23×C4—51no—
169C23×C4—201no—
170C22×C8—51no—
171C22×C8—52no—
172C22×C8—52no—
173C22×C8—52no—
174C22×C8—52no—
175C22×C8—51no—
176C22×C8—51no—
177C22×C8—51no—
178C22×C8—51no—
179C22×C8C2×AGL(1,𝔽5)11yescharacteristic
180#117—21no—
181#117—102no—
182#117—101no—
183#117—201no—
184#117—201no—
185C2×C4⋊C4—102no—
186C2×C4⋊C4—102no—
187C2×C4⋊C4—104no—
188C2×C4⋊C4—201no—
189C2×C4⋊C4—202no—
190C2×C22⋊C4—201no—
191C2×C42—201no—
192M32—54no—
193M32—102no—
194M32—104no—
195C2×C16—104no—
196C2×C16—102no—
197#107—52no—
198#107—102no—
199#107C2×AGL(1,𝔽5)12yescomplemented
200#106—21no—
201#106—54no—
202#106—102no—
203#106—102no—
204#106—104no—
205#106—101no—
206C22×C5—22no—
207C22×C5#34012yes—
208C22×C5C2×#10211yescharacteristic
209C2×D5—22no—
210C2×D5—24no—
211C2×D5—24no—
212C2×D5#34012yes—
213C2×D5#36014yes—
214C2×D5C2×#10211yescharacteristic
215C2×D5C2×#10711yescharacteristic
216AGL(1,𝔽5)—84no—
217C4×C5—82no—
218C4×C5#34012yes—
219C4×C5C2×#9511yescharacteristic
220C4×C5C2×#10311yescharacteristic
221Dic5—82no—
222Dic5#34012yes—
223Dic5C2×#10311yescharacteristic
224Dic5C2×#10611yescharacteristic
225C24—51no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—52no—
230C22×C4—52no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—52no—
234C22×C4—52no—
235C22×C4—202no—
236C22×C4—204no—
237C22×C4—202no—
238C22×C4—404no—
239C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
240C2×C8—51no—
241C2×C8—51no—
242C2×C8—52no—
243C2×C8—52no—
244C2×C8—51no—
245C2×C8—51no—
246C2×C8—52no—
247C2×C8—51no—
248C2×C8—52no—
249C2×C8—51no—
250C2×C8—52no—
251C2×C8—52no—
252C2×C8—52no—
253C2×C8—52no—
254C2×C8C4×AGL(1,𝔽5)12yes—
255C2×C8C4⋊AGL(1,𝔽5)12yes—
256C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
257C2×C8C22×AGL(1,𝔽5)11yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—104no—
260C4⋊C4—102no—
261C4⋊C4—202no—
262C4⋊C4—204no—
263C4⋊C4—202no—
264C22⋊C4—41no—
265C22⋊C4—202no—
266C22⋊C4—201no—
267C42—41no—
268C42—202no—
269C42—201no—
270C16—104no—
271C2×C5—22no—
272C2×C5C2×#34011yescharacteristic
273C2×C5C2×#36012yes—
274D5—21no—
275D5—21no—
276D5#138614yescomplemented
277C23—51no—
278C23—52no—
279C23—52no—
280C23—51no—
281C23—104no—
282C23#400711yescharacteristic
283C2×C4—42no—
284C2×C4—52no—
285C2×C4—52no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—52no—
289C2×C4—52no—
290C2×C4—52no—
291C2×C4—52no—
292C2×C4—51no—
293C2×C4—52no—
294C2×C4—51no—
295C2×C4—51no—
296C2×C4—52no—
297C2×C4—51no—
298C2×C4—204no—
299C2×C4—202no—
300C2×C4—404no—
301C2×C4—408no—
302C2×C4—404no—
303C2×C4(C2×AGL(1,𝔽5))⋊C412yes—
304C2×C4#400711yescharacteristic
305C2×C4#400912yes—
306C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C8—51no—
308C8—52no—
309C8—51no—
310C8(C2×AGL(1,𝔽5))⋊C412yes—
311C8C2×C4×AGL(1,𝔽5)11yescharacteristic
312C8C2×C4⋊AGL(1,𝔽5)11yescharacteristic
313C5C2×#138611yescharacteristic, complemented, Sylow
314C22—22no—
315C22—54no—
316C22—52no—
317C22—51no—
318C22—51no—
319C22—104no—
320C22—104no—
321C22—102no—
322C22#6487412yes—
323C22C2×#400711yescharacteristic
324C4—52no—
325C4—51no—
326C4—51no—
327C4—82no—
328C4—404no—
329C4—402no—
330C4#6487412yes—
331C4C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
332C4C2×#400911yescharacteristic
333C2—22no—
334C2—54no—
335C2—101no—
336C2—101no—
337C2C2×#6487411yescharacteristic
338C2D5⋊#36012yes—
subgroupG/H
centerC22C2×#4007
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#427C4
socleC22×C5C2×#102
prime radicalC23×D5D8
cosocleC2×C8×D5C23
hypercenter#427AGL(1,𝔽5)
hypocenterC5C2×#1386
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
4. #10598621C2semidirect
11. C2×#3993C4semidirect
14. D5⋊M32C4semidirect
17. C5×#427C4semidirect
18. #65395C4semidirect
21. D5×#107C4semidirect
53. #3993C2×C4semidirect
55. #3990C2×C4semidirect
57. C5×#107C2×C4semidirect
59. #3950C2×C4semidirect
125. #427AGL(1,𝔽5)semidirect
199. #107C2×AGL(1,𝔽5)semidirect
276. D5#1386semidirect
313. C5C2×#1386semidirect

Maximal subgroups

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

subgroupindex
C22×#39932
C2×D5⋊M322
D5×#4272
#105986212
C2×#13865