Finite Group Databasebeta

← #11998553

Subgroups — #11998553

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#486C211yesmaximal, characteristic
2#10602572C211yesmaximal, characteristic, complemented
3C2×#64766C211yesmaximal, characteristic, complemented
4#10602554C211yesmaximal, characteristic
5C2×#64764C211yesmaximal, characteristic
6C8×C4⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#64677C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C5×#127C2211yescharacteristic
10C5×#486—22no—
11C5×#486C414yescomplemented
12C2×C5×#102—21no—
13C2×C5×#102—21no—
14C2×C4×C5×C8C2211yescharacteristic
15C2×#3964—22no—
16C2×C8×Dic5—21no—
17C4×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21#64770—21no—
22#64766—22no—
23#64764—22no—
24#64749—22no—
25#64677—22no—
26#9735—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C22×C5×C8D411yescharacteristic
32C22×C5×C8D411yescharacteristic
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8C2×C412yes—
37C5×#127—21no—
38C5×#127—21no—
39C5×#127—21no—
40C5×#127C2×C412yes—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C42×C5C2311yescharacteristic
44C2×C4⋊Dic5D412yes—
45C2×C4×Dic5—21no—
46C22×#168—21no—
47C22×#168—21no—
48C22×#168—21no—
49C5×#102—24no—
50C5×#102—24no—
51C4×C5×C8C2×C412yes—
52C4×C5×C8D412yes—
53#3964—44no—
54#3963—21no—
55C8×Dic5—42no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58C4⋊#168—21no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168D412yes—
62C2×#486D511yescharacteristic
63#1987—51no—
64#1982—51no—
65C8×C4⋊C4—51no—
66C2×#334—51no—
67C2×#333—51no—
68C2×#331—51no—
69C24×C5—41no—
70C2×C5×Q8—22no—
71C2×C5×Q8—41no—
72C2×C5×Q8—82no—
73C2×C5×D4—22no—
74C2×C5×D4—22no—
75C2×C5×D4—22no—
76C2×C5×D4—41no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—42no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—42no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C2×C5×D4—82no—
86C22×C4×C5—41no—
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5#4111yescharacteristic
90C22×Dic5—22no—
91C2×C5×C8—21no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8C22⋊C412yes—
96C2×C5×C8C22⋊C412yes—
97C5×C4⋊C4—22no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C42×C5C22×C411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5C2×D411yescharacteristic
104C42×C5#4111yescharacteristic
105C4⋊Dic5—22no—
106C4⋊Dic5SD1614yes—
107C4×Dic5—41no—
108C4×Dic5—41no—
109C2×#168—22no—
110C2×#168—41no—
111C2×#168—41no—
112C2×#168—41no—
113C2×#168—41no—
114C2×#168—42no—
115C2×#168—42no—
116C2×C4⋊Q8C2×D511yescharacteristic
117C2×#127C2×D511yescharacteristic
118#486—22no—
119#486Dic514yescomplemented
120C2×C4⋊C8—51no—
121C2×C4⋊C8—51no—
122C2×C4⋊C8—51no—
123C2×#102—21no—
124C2×#102—21no—
125C2×#102—102no—
126C2×C4×C8—101no—
127C2×C4×C8C2×D511yescharacteristic
128C4×C4⋊C4—51no—
129#340—102no—
130#336—101no—
131#334—102no—
132#333—102no—
133#331—102no—
134C23×C5—42no—
135C23×C5—81no—
136C23×C5—81no—
137C23×C5—82no—
138C23×C5—82no—
139C23×C5#12111yescharacteristic
140C5×Q8—82no—
141C5×Q8—82no—
142C5×D4—42no—
143C5×D4—42no—
144C5×D4—44no—
145C5×D4—82no—
146C5×D4—82no—
147C5×D4—81no—
148C5×D4—81no—
149C5×D4—81no—
150C5×D4—81no—
151C2×C4×C5—22no—
152C2×C4×C5—42no—
153C2×C4×C5—82no—
154C2×C4×C5C2×C22⋊C411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5C4×D411yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5#12411yescharacteristic
159C2×C4×C5#12711yescharacteristic
160C2×C4×C5C2×SD1612yes—
161C2×C4×C5#13511yescharacteristic
162C2×C4×C5#13511yescharacteristic
163C2×C4×C5#13512yes—
164C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C5#13711yescharacteristic
166C2×Dic5—24no—
167C2×Dic5—42no—
168C2×Dic5—42no—
169C5×C8—22no—
170C5×C8—22no—
171#168—42no—
172#168—81no—
173#168—81no—
174C22×Q8—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×C8—101no—
179C22×C8—101no—
180C22×C8—101no—
181C22×C8C22⋊D511yescharacteristic
182C22×C8C22⋊D511yescharacteristic
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8C2×Dic512yes—
187#127—21no—
188#127—21no—
189#127—21no—
190#127C2×Dic512yes—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—52no—
194C2×C42—101no—
195C2×C42C22×D511yescharacteristic
196C4⋊C8—52no—
197C4⋊C8—101no—
198C4⋊C8—101no—
199C4⋊C8—101no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202#102—24no—
203#102—24no—
204#102—204no—
205C4×C8—202no—
206C4×C8C2×Dic512yes—
207C4×C8C22⋊D512yes—
208#95—101no—
209C22×C5—82no—
210C22×C5—82no—
211C22×C5—82no—
212C22×C5—162no—
213C22×C5—162no—
214C22×C5#39011yescharacteristic
215C22×C5#46311yescharacteristic
216C22×C5#46411yescharacteristic
217C22×C5#46512yes—
218C22×C5#47212yes—
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—82no—
222C4×C5#41611yescharacteristic
223C4×C5#41711yescharacteristic
224C4×C5C4×SD1612yes—
225C4×C5#46311yescharacteristic
226C4×C5#46411yescharacteristic
227C4×C5#49211yescharacteristic
228C4×C5#49511yescharacteristic
229Dic5—44no—
230C24—41no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—82no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—82no—
247C22×C4—41no—
248C22×C4—102no—
249C22×C4D4×D511yescharacteristic
250C22×C4#71111yescharacteristic
251C22×C4C2×C22⋊D511yescharacteristic
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—102no—
257C2×C8—201no—
258C2×C8—201no—
259C2×C8—202no—
260C2×C8—202no—
261C2×C8—201no—
262C2×C8—201no—
263C2×C8C22⋊Dic512yes—
264C2×C8C22⋊Dic512yes—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—54no—
270C4⋊C4—102no—
271C42—201no—
272C42—201no—
273C42D4×D511yescharacteristic
274C42#71111yescharacteristic
275C42C22×Dic511yescharacteristic
276C42C2×C22⋊D511yescharacteristic
277C2×C5—162no—
278C2×C5#167712yes—
279C2×C5#167812yes—
280C2×C5#196811yescharacteristic
281C2×C5#197811yescharacteristic
282C2×C5#198311yescharacteristic
283C23—42no—
284C23—81no—
285C23—81no—
286C23—82no—
287C23—82no—
288C23#408411yescharacteristic
289Q8—82no—
290Q8—82no—
291D4—44no—
292D4—42no—
293D4—42no—
294D4—82no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—81no—
299D4—81no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—104no—
304C2×C4—202no—
305C2×C4—202no—
306C2×C4D5×SD1612yes—
307C2×C4#406212yes—
308C2×C4D4×Dic511yescharacteristic
309C2×C4D4×Dic511yescharacteristic
310C2×C4#408211yescharacteristic
311C2×C4#408411yescharacteristic
312C2×C4#408611yescharacteristic
313C2×C4#409511yescharacteristic
314C2×C4#409611yescharacteristic
315C2×C4#409611yescharacteristic
316C2×C4#409711yescharacteristic
317C2×C4C2×C22⋊Dic511yescharacteristic
318C8—22no—
319C8—22no—
320C8—202no—
321C8—401no—
322C8—401no—
323C5#973511yescharacteristic, complemented, Sylow
324C22—82no—
325C22—82no—
326C22—82no—
327C22—162no—
328C22—162no—
329C22#6534311yescharacteristic
330C22#6534611yescharacteristic
331C22#6544912yes—
332C22#6546012yes—
333C22#6551011yescharacteristic
334C4—21no—
335C4—21no—
336C4—82no—
337C4—204no—
338C4#6534311yescharacteristic
339C4#6534611yescharacteristic
340C4SD16×Dic512yes—
341C4#6545711yescharacteristic
342C4#6546411yescharacteristic
343C4#6552111yescharacteristic
344C4#6552211yescharacteristic
345C2—162no—
346C2#1060199312yes—
347C2#1060200112yes—
348C2#1060251411yescharacteristic
349C2#1060283411yescharacteristic
350C2#1060284211yescharacteristic
subgroupG/H
centerC23#4084
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#486C2
socleC23×C5#121
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenterC2×#486D5
hypocenterC5#9735
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. #10602572C2semidirect
3. C2×#64766C2semidirect
6. C8×C4⋊Dic5C2semidirect
7. C2×#64677C2semidirect
11. C5×#486C4semidirect
119. #486Dic5semidirect
323. C5#9735semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4862
#106025722
C2×#647662
#106025542
C2×#647642
C8×C4⋊Dic52
C2×#646772
#97355