Finite Group Databasebeta

← #11996008

Subgroups — #11996008

Order 1280.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3229C211yesmaximal, characteristic
2#10614958C211yesmaximal, characteristic
3#10602633C211yesmaximal, characteristic
4#10602631C211yesmaximal, characteristic
5#10602566C211yesmaximal, characteristic
6#10598229C211yesmaximal, characteristic
7#10598228C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×Q8×Dic5—21no—
11C5×#498C412yescomplemented
12C5×#487C412yescomplemented
13C5×#483—22no—
14C5×#475—22no—
15C5×#431C2211yescharacteristic
16#65519—21no—
17#65270—22no—
18#65270—22no—
19#65225C2211yescharacteristic
20#65221C2211yescharacteristic
21#65214C2211yescharacteristic
22#65213C2211yescharacteristic
23#64767—22no—
24#64758—22no—
25#64752—21no—
26#64752—21no—
27#9296—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C5×C4⋊Q8—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8C2×C411yescharacteristic
32C5×C4⋊Q8C2×C411yescharacteristic
33C5×C4⋊Q8C2×C412yes—
34C5×C4⋊Q8D412yes—
35C5×#125—21no—
36C5×C22⋊Q8—21no—
37C5×C22⋊Q8—21no—
38C4×C5×Q8—21no—
39C4×C5×Q8—21no—
40C5×#117—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4D412yes—
43C2×C42×C5C2311yescharacteristic
44Q8×Dic5—42no—
45Q8×Dic5—42no—
46C2×C4⋊Dic5—22no—
47C2×C4⋊Dic5—21no—
48C2×C4×Dic5—22no—
49C2×C4×Dic5D411yescharacteristic
50C2×C4×Dic5D411yescharacteristic
51C2×#681—21no—
52C5×#106—24no—
53C5×C4⋊C8—21no—
54C5×#103—24no—
55C5×C22⋊C8—21no—
56C4×C5×C8C2×C412yes—
57#3963—24no—
58#3963—21no—
59#3963—21no—
60#3963—21no—
61#3963D412yes—
62C22⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4×#168—21no—
67#3229D511yescharacteristic
68#2327—51no—
69#1995—51no—
70#1546—51no—
71#1518—51no—
72#1286—51no—
73#1274—51no—
74C2×C5×Q8—22no—
75C2×C5×Q8—22no—
76C2×C5×Q8—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C22×C4×C5—22no—
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×Dic5—21no—
87C22×Dic5—21no—
88C22×Dic5—22no—
89C2×C5×C8—22no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—22no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4C22⋊C414yes—
100C5×C22⋊C4—41no—
101C42×C5—41no—
102C42×C5C22×C411yescharacteristic
103C42×C5C2×D411yescharacteristic
104C42×C5#4111yescharacteristic
105C42×C5#4111yescharacteristic
106C4⋊Dic5—44no—
107C4⋊Dic5—41no—
108C4⋊Dic5—41no—
109C4×Dic5—21no—
110C4×Dic5—21no—
111C4×Dic5—21no—
112C4×Dic5—44no—
113C4×Dic5SD1612yes—
114#681—41no—
115#681—41no—
116C2×#168—41no—
117C2×#168—41no—
118#533C2×D511yescharacteristic
119C2×C4⋊Q8C2×D511yescharacteristic
120C2×C4×Q8—101no—
121#498Dic512yescomplemented
122#487Dic512yescomplemented
123#483—22no—
124#475—22no—
125#431—51no—
126#431C2×D511yescharacteristic
127#423—51no—
128#391—101no—
129#387—102no—
130#387—102no—
131#382—51no—
132#376—51no—
133#339—101no—
134#339—101no—
135#332—102no—
136#328—102no—
137C23×C5#12011yescharacteristic
138C5×Q8—42no—
139C5×Q8—42no—
140C5×Q8—42no—
141C5×Q8—42no—
142C5×Q8—42no—
143C5×Q8—81no—
144C2×C4×C5—24no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5C2×C22⋊C411yescharacteristic
152C2×C4×C5C4×D411yescharacteristic
153C2×C4×C5C4×D411yescharacteristic
154C2×C4×C5#12111yescharacteristic
155C2×C4×C5#12111yescharacteristic
156C2×C4×C5#12311yescharacteristic
157C2×C4×C5C2×SD1611yescharacteristic
158C2×C4×C5#13511yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5#13711yescharacteristic
161C2×Dic5—22no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—42no—
166C2×Dic5—41no—
167C2×Dic5—42no—
168C2×Dic5—42no—
169C2×Dic5—41no—
170C5×C8—42no—
171#168—81no—
172#168—81no—
173C22×Q8—21no—
174C2×M16—101no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8C2×Dic511yescharacteristic
178C4⋊Q8C2×Dic511yescharacteristic
179C4⋊Q8C2×Dic512yes—
180C4⋊Q8C22⋊D512yes—
181#125—21no—
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184C4×Q8—21no—
185C4×Q8—21no—
186C4×Q8—202no—
187C4×Q8—202no—
188#117—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—102no—
191C2×C4⋊C4—101no—
192C2×C4⋊C4C22⋊D512yes—
193C2×C42—51no—
194C2×C42—51no—
195C2×C42—102no—
196C2×C42C22×D511yescharacteristic
197#106—24no—
198C4⋊C8—21no—
199C4⋊C8—101no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202#103—24no—
203C22⋊C8—21no—
204C22⋊C8—101no—
205C4×C8—101no—
206C4×C8C2×Dic512yes—
207#95—52no—
208#95—104no—
209#95—101no—
210#95—101no—
211#95—101no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5#38611yescharacteristic
215C22×C5#45011yescharacteristic
216C22×C5#45211yescharacteristic
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—44no—
222C4×C5—81no—
223C4×C5—81no—
224C4×C5C4×SD1611yescharacteristic
225C4×C5#44011yescharacteristic
226C4×C5#46111yescharacteristic
227C4×C5#46311yescharacteristic
228Dic5—42no—
229Dic5—82no—
230Dic5—81no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C22×C4—22no—
240C22×C4—101no—
241C22×C4—102no—
242C22×C4—101no—
243C22×C4D4×D511yescharacteristic
244C22×C4D4×D511yescharacteristic
245C22×C4C2×C22⋊D511yescharacteristic
246M16—201no—
247M16—201no—
248C2×C8—22no—
249C2×C8—201no—
250C2×C8—201no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—204no—
261C4⋊C4—201no—
262C4⋊C4—201no—
263C4⋊C4C22⋊Dic514yes—
264C22⋊C4—41no—
265C42—41no—
266C42—52no—
267C42—101no—
268C42—101no—
269C42—101no—
270C42—204no—
271C42#71111yescharacteristic
272C42#71111yescharacteristic
273C42C22×Dic511yescharacteristic
274C42C2×C22⋊D511yescharacteristic
275C2×C5—21no—
276C2×C5—21no—
277C2×C5#187711yescharacteristic
278C2×C5#190511yescharacteristic
279C2×C5#191211yescharacteristic
280C23#408311yescharacteristic
281Q8—42no—
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—81no—
287C2×C4—24no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—102no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—202no—
298C2×C4—201no—
299C2×C4—202no—
300C2×C4—201no—
301C2×C4—202no—
302C2×C4—201no—
303C2×C4D5×SD1611yescharacteristic
304C2×C4#406011yescharacteristic
305C2×C4#406111yescharacteristic
306C2×C4#406211yescharacteristic
307C2×C4D4×Dic511yescharacteristic
308C2×C4D4×Dic511yescharacteristic
309C2×C4#408111yescharacteristic
310C2×C4#408511yescharacteristic
311C2×C4#408511yescharacteristic
312C2×C4C2×C22⋊Dic511yescharacteristic
313C8—42no—
314C8—401no—
315C8—401no—
316C5#929611yescharacteristic, complemented, Sylow
317C22—21no—
318C22—21no—
319C22#6545811yescharacteristic
320C22#6546211yescharacteristic
321C22#6550911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—44no—
327C4—81no—
328C4—81no—
329C4—202no—
330C4—402no—
331C4—401no—
332C4SD16×Dic511yescharacteristic
333C4#6545111yescharacteristic
334C4#6545311yescharacteristic
335C4#6545411yescharacteristic
336C2—21no—
337C2—21no—
338C2#1060265711yescharacteristic
339C2#1060284011yescharacteristic
340C2#1060289411yescharacteristic
subgroupG/H
centerC22#65509
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3229C2
socleC22×C5#386
prime radicalC23×C5#120
cosocleC2×C42×C5C23
hypercenter#3229D5
hypocenterC5#9296
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
11. C5×#498C4semidirect
12. C5×#487C4semidirect
121. #498Dic5semidirect
122. #487Dic5semidirect
316. C5#9296semidirect

Maximal subgroups

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

subgroupindex
C5×#32292
#106149582
#106026332
#106026312
#106025662
#105982292
#105982282
#92965