Finite Group Databasebeta

← #11995945

Subgroups — #11995945

Order 1280.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3227C211yesmaximal, characteristic
2#10615007C211yesmaximal, characteristic
3#10602607C211yesmaximal, characteristic
4#10602581C211yesmaximal, characteristic, complemented
5#10602567C211yesmaximal, characteristic, complemented
6#10598231C211yesmaximal, characteristic, complemented
7#10598229C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×#4094—21no—
11C5×#498C412yescomplemented
12C5×#486C412yescomplemented
13C5×#481—22no—
14C5×#476—22no—
15C5×#431C2211yescharacteristic
16#65523—21no—
17#65300—22no—
18#65300—22no—
19#65225C2211yescharacteristic
20#65214C2211yescharacteristic
21#65213C2211yescharacteristic
22C2×#3935C2211yescharacteristic
23#64766—22no—
24#64757—22no—
25#64749—21no—
26#64749—21no—
27#9287—51nomaximal, Sylow
28C2×C5×#41—21no—
29C22×C5×Q8—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8C2×C412yes—
34C5×C4⋊Q8C2×C411yescharacteristic
35C5×#127C2×C411yescharacteristic
36C5×#124—21no—
37C5×#121—21no—
38C5×#121D412yes—
39C4×C5×D4—21no—
40C4×C5×D4D412yes—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C42×C5C2311yescharacteristic
44#4094—42no—
45#4094—42no—
46C2×C4⋊Dic5—21no—
47C2×#681—22no—
48C2×#681—21no—
49C22×#168—22no—
50C22×#168D411yescharacteristic
51C22×#168D411yescharacteristic
52C5×#106—24no—
53C5×C4⋊C8—21no—
54C5×#102—24no—
55C5×C22⋊C8—21no—
56C4×C5×C8C2×C412yes—
57#3963—21no—
58#3963—21no—
59C22⋊#168—24no—
60C22⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168D412yes—
64#3935—21no—
65#3935—21no—
66C4×#168—21no—
67#3227D511yescharacteristic
68#2932—51no—
69#1993—51no—
70#1548—51no—
71#1517—51no—
72#1286—51no—
73#1275—51no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×Q8—22no—
80C2×C5×Q8—41no—
81C2×C5×Q8—82no—
82C2×C5×D4—22no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4C22⋊C412yes—
86C22×C4×C5—22no—
87C22×C4×C5—41no—
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5#4111yescharacteristic
91C22×Dic5—41no—
92C2×C5×C8—22no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—22no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4C22⋊C412yes—
99C5×C22⋊C4—22no—
100C5×C22⋊C4—22no—
101C42×C5C22×C411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5C2×D411yescharacteristic
104C42×C5#4111yescharacteristic
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107#681—44no—
108#681—41no—
109#681—41no—
110C2×#168—21no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—22no—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168—44no—
117C2×#168—41no—
118C2×#168SD1612yes—
119C2×#131—101no—
120#532C2×D511yescharacteristic
121C2×C4⋊Q8C2×D511yescharacteristic
122#498Dic512yescomplemented
123#486Dic512yescomplemented
124#481—22no—
125#476—22no—
126#435—102no—
127#435—102no—
128#431—51no—
129#431C2×D511yescharacteristic
130#423—51no—
131#408—101no—
132C2×#97—51no—
133#382—51no—
134#340—101no—
135#340—101no—
136#333—102no—
137#327—102no—
138C23×C5—22no—
139C23×C5#12111yescharacteristic
140C5×Q8—41no—
141C5×Q8—41no—
142C5×Q8—82no—
143C5×Q8—82no—
144C5×D4—42no—
145C5×D4—42no—
146C5×D4—42no—
147C5×D4—41no—
148C5×D4—41no—
149C5×D4—81no—
150C2×C4×C5—22no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—82no—
157C2×C4×C5C2×C22⋊C411yescharacteristic
158C2×C4×C5C4×D411yescharacteristic
159C2×C4×C5C4×D411yescharacteristic
160C2×C4×C5#12011yescharacteristic
161C2×C4×C5#12111yescharacteristic
162C2×C4×C5#12311yescharacteristic
163C2×C4×C5C2×SD1611yescharacteristic
164C2×C4×C5#13511yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C5#13711yescharacteristic
167C2×Dic5—81no—
168C2×Dic5—81no—
169C2×Dic5—81no—
170C5×C8—42no—
171#168—22no—
172#168—42no—
173#168—41no—
174#168—81no—
175C2×#41—21no—
176C22×Q8—21no—
177#131—202no—
178#131—202no—
179C2×M16—102no—
180C2×M16—101no—
181C22×C8—51no—
182C22×C8—51no—
183C22×C8—102no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8C2×Dic512yes—
188C4⋊Q8C2×Dic511yescharacteristic
189#127C2×Dic511yescharacteristic
190#124—21no—
191#121—21no—
192#121C22⋊D512yes—
193C4×D4—21no—
194C4×D4C22⋊D512yes—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—101no—
198C2×C42C22×D511yescharacteristic
199#106—24no—
200C4⋊C8—21no—
201C4⋊C8—52no—
202C4⋊C8—101no—
203C4⋊C8—101no—
204#102—24no—
205C22⋊C8—21no—
206C22⋊C8—104no—
207C22⋊C8—101no—
208#97—101no—
209#97—101no—
210C4×C8—101no—
211C4×C8C2×Dic512yes—
212#95—101no—
213#95—101no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—42no—
219C22×C5#38611yescharacteristic
220C22×C5#46111yescharacteristic
221C22×C5#46311yescharacteristic
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—42no—
227C4×C5—82no—
228C4×C5C4×SD1611yescharacteristic
229C4×C5#44011yescharacteristic
230C4×C5#45011yescharacteristic
231C4×C5#45211yescharacteristic
232Dic5—161no—
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—82no—
241C2×D4—22no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4C22⋊Dic512yes—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—201no—
248C22×C4D4×D511yescharacteristic
249C22×C4#71111yescharacteristic
250C22×C4C2×C22⋊D511yescharacteristic
251M16—204no—
252M16—201no—
253M16—201no—
254C2×C8—22no—
255C2×C8—52no—
256C2×C8—101no—
257C2×C8—101no—
258C2×C8—101no—
259C2×C8—101no—
260C2×C8—101no—
261C2×C8—102no—
262C2×C8—204no—
263C2×C8—201no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C4⋊C4C22⋊Dic512yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42D4×D511yescharacteristic
275C42#71111yescharacteristic
276C42C22×Dic511yescharacteristic
277C42C2×C22⋊D511yescharacteristic
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—82no—
281C2×C5#187711yescharacteristic
282C2×C5#190311yescharacteristic
283C2×C5#190911yescharacteristic
284C23—22no—
285C23#408511yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—82no—
289Q8—82no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—81no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—401no—
304C2×C4—401no—
305C2×C4—401no—
306C2×C4D5×SD1611yescharacteristic
307C2×C4#406011yescharacteristic
308C2×C4#406111yescharacteristic
309C2×C4#406211yescharacteristic
310C2×C4D4×Dic511yescharacteristic
311C2×C4D4×Dic511yescharacteristic
312C2×C4#408111yescharacteristic
313C2×C4#408311yescharacteristic
314C2×C4#408511yescharacteristic
315C2×C4C2×C22⋊Dic511yescharacteristic
316C8—42no—
317C8—102no—
318C8—202no—
319C8—201no—
320C8—401no—
321C5#928711yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#6545111yescharacteristic
328C22#6545411yescharacteristic
329C22#6550911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—82no—
336C4—801no—
337C4SD16×Dic511yescharacteristic
338C4#6545311yescharacteristic
339C4#6545811yescharacteristic
340C4#6546211yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1060265811yescharacteristic
345C2#1060284011yescharacteristic
346C2#1060288311yescharacteristic
subgroupG/H
centerC22#65509
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3227C2
socleC22×C5#386
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#3227D5
hypocenterC5#9287
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
4. #10602581C2semidirect
5. #10602567C2semidirect
6. #10598231C2semidirect
7. #10598229C2semidirect
11. C5×#498C4semidirect
12. C5×#486C4semidirect
122. #498Dic5semidirect
123. #486Dic5semidirect
321. C5#9287semidirect

Maximal subgroups

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

subgroupindex
C5×#32272
#106150072
#106026072
#106025812
#106025672
#105982312
#105982292
#92875