Finite Group Databasebeta

← #11995994

Subgroups — #11995994

Order 1280.

490 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3208C211yesmaximal, characteristic
2#10615060C211yesmaximal, characteristic, complemented
3#10602631C211yesmaximal, characteristic, complemented
4#10602558C211yesmaximal, characteristic
5#10602552C211yesmaximal, characteristic
6#10598231C211yesmaximal, characteristic, complemented
7#10598229C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C5×#127C2211yescharacteristic
10C5×#492C412yescomplemented
11C5×#486C412yescomplemented
12C5×#460—22no—
13C5×#450—22no—
14C5×#431C2211yescharacteristic
15C2×#3964—21no—
16C2×#3964—21no—
17#65313—22no—
18#65313—22no—
19#65288—21no—
20#65286—21no—
21#65225C2211yescharacteristic
22#65214C2211yescharacteristic
23#65213C2211yescharacteristic
24C2×#3935C2211yescharacteristic
25#64764—22no—
26#64758—22no—
27#9294—51nomaximal, Sylow
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C2×C5×SD16—24no—
32C5×C4⋊Q8C2×C411yescharacteristic
33C5×C4⋊Q8C2×C411yescharacteristic
34C5×#127—21no—
35C5×#127—21no—
36C5×#127—21no—
37C5×#127C2×C412yes—
38C5×#125—21no—
39C5×C22⋊Q8—21no—
40C5×C22⋊Q8D412yes—
41C4×C5×Q8—21no—
42C4×C5×Q8D412yes—
43C5×#117—21no—
44C2×C42×C5C2311yescharacteristic
45C2×C4⋊Dic5—21no—
46C2×#681—21no—
47C22×#168D411yescharacteristic
48C22×#168D411yescharacteristic
49C5×C4⋊C8—21no—
50C5×#102—24no—
51C5×C22⋊C8—21no—
52C4×C5×C8C2×C412yes—
53#3964—42no—
54#3964—42no—
55#3963—21no—
56#3963—21no—
57C22⋊#168—21no—
58C4⋊#168—24no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168D412yes—
62#3935—22no—
63#3935—21no—
64#3935—21no—
65C4×#168—22no—
66C4×#168—21no—
67#3208D511yescharacteristic
68#2961—51no—
69#1961—51no—
70#1545—51no—
71#1518—51no—
72#1286—51no—
73#1275—51no—
74C24×C5—41no—
75C2×C5×Q8—21no—
76C2×C5×Q8C22⋊C412yes—
77C2×C5×D4—22no—
78C2×C5×D4—22no—
79C2×C5×D4—22no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—41no—
87C2×C5×D4—82no—
88C2×C5×D4—82no—
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5#4111yescharacteristic
92C22×Dic5—41no—
93C5×SD16—84no—
94C2×C5×C8—22no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—21no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4C22⋊C412yes—
101C5×C22⋊C4—22no—
102C42×C5—22no—
103C42×C5C22×C411yescharacteristic
104C42×C5C2×D411yescharacteristic
105C42×C5C2×D411yescharacteristic
106C42×C5#4111yescharacteristic
107C4⋊Dic5—41no—
108C4⋊Dic5—41no—
109#681—41no—
110#681—41no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—22no—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—41no—
118C2×#168SD1612yescomplemented
119#533C2×D511yescharacteristic
120C2×#127C2×D511yescharacteristic
121#492Dic512yescomplemented
122#486Dic512yescomplemented
123#460—22no—
124#450—22no—
125#446—102no—
126#446—102no—
127#431—51no—
128#431C2×D511yescharacteristic
129#424—101no—
130#423—51no—
131C2×#102—101no—
132C2×#102—101no—
133#405—101no—
134C2×#97—51no—
135#382—51no—
136#331—102no—
137#328—102no—
138C23×C5—42no—
139C23×C5—82no—
140C23×C5—82no—
141C23×C5—81no—
142C23×C5—81no—
143C23×C5#12111yescharacteristic
144C5×Q8—42no—
145C5×Q8—81no—
146C5×D4—44no—
147C5×D4—42no—
148C5×D4—42no—
149C5×D4—82no—
150C5×D4—82no—
151C5×D4—82no—
152C5×D4—81no—
153C5×D4—81no—
154C2×C4×C5—22no—
155C2×C4×C5—22no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5C2×C22⋊C411yescharacteristic
159C2×C4×C5C4×D411yescharacteristic
160C2×C4×C5C4×D411yescharacteristic
161C2×C4×C5#12011yescharacteristic
162C2×C4×C5#12111yescharacteristic
163C2×C4×C5#12311yescharacteristic
164C2×C4×C5C2×SD1611yescharacteristic
165C2×C4×C5#13511yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5#13711yescharacteristic
168C2×Dic5—81no—
169C2×Dic5—81no—
170C2×Dic5—81no—
171C5×C8—42no—
172#168—22no—
173#168—41no—
174#168—42no—
175#168—81no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C2×SD16—24no—
180C2×M16—101no—
181C22×C8—51no—
182C22×C8—51no—
183C4⋊Q8C2×Dic511yescharacteristic
184C4⋊Q8C2×Dic511yescharacteristic
185#127—21no—
186#127—21no—
187#127—21no—
188#127C2×Dic512yes—
189#125—21no—
190C22⋊Q8—21no—
191C22⋊Q8C22⋊D512yes—
192C4×Q8—21no—
193C4×Q8C22⋊D512yes—
194#117—21no—
195C2×C4⋊C4—101no—
196C2×C42C22×D511yescharacteristic
197C4⋊C8—21no—
198C4⋊C8—52no—
199C4⋊C8—104no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202#102—24no—
203#102—202no—
204#102—202no—
205C22⋊C8—21no—
206C22⋊C8—101no—
207#97—102no—
208#97—101no—
209#97—101no—
210C4×C8—102no—
211C4×C8—101no—
212C4×C8C2×Dic512yes—
213#95—101no—
214#95—101no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—82no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5—162no—
221C22×C5—162no—
222C22×C5#38611yescharacteristic
223C22×C5#46011yescharacteristic
224C22×C5#46411yescharacteristic
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—42no—
230C4×C5—42no—
231C4×C5C4×SD1611yescharacteristic
232C4×C5#44011yescharacteristic
233C4×C5#44811yescharacteristic
234C4×C5#44911yescharacteristic
235Dic5—161no—
236C24—41no—
237C2×Q8—21no—
238C2×Q8C22⋊Dic512yes—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—82no—
250C2×D4—82no—
251C22×C4—201no—
252C22×C4D4×D511yescharacteristic
253C22×C4#71111yescharacteristic
254C22×C4C2×C22⋊D511yescharacteristic
255SD16—84no—
256M16—201no—
257M16—201no—
258C2×C8—22no—
259C2×C8—52no—
260C2×C8—101no—
261C2×C8—101no—
262C2×C8—101no—
263C2×C8—101no—
264C2×C8—102no—
265C2×C8—101no—
266C2×C8—201no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—201no—
273C4⋊C4—201no—
274C4⋊C4C22⋊Dic512yes—
275C22⋊C4—22no—
276C42—22no—
277C42D4×D511yescharacteristic
278C42#71111yescharacteristic
279C42C22×Dic511yescharacteristic
280C42C2×C22⋊D511yescharacteristic
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—162no—
284C2×C5#188011yescharacteristic
285C2×C5#190311yescharacteristic
286C2×C5#191011yescharacteristic
287C23—42no—
288C23—82no—
289C23—82no—
290C23—81no—
291C23—81no—
292C23#408511yescharacteristic
293Q8—42no—
294Q8—81no—
295D4—44no—
296D4—42no—
297D4—42no—
298D4—82no—
299D4—82no—
300D4—82no—
301D4—81no—
302D4—81no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—401no—
308C2×C4—401no—
309C2×C4—401no—
310C2×C4D5×SD1611yescharacteristic
311C2×C4#406011yescharacteristic
312C2×C4#406111yescharacteristic
313C2×C4#406211yescharacteristic
314C2×C4D4×Dic511yescharacteristic
315C2×C4D4×Dic511yescharacteristic
316C2×C4#408111yescharacteristic
317C2×C4#408311yescharacteristic
318C2×C4#408511yescharacteristic
319C2×C4C2×C22⋊Dic511yescharacteristic
320C8—42no—
321C8—102no—
322C8—201no—
323C8—202no—
324C8—401no—
325C5#929411yescharacteristic, complemented, Sylow
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—162no—
332C22—162no—
333C22#6545211yescharacteristic
334C22#6545511yescharacteristic
335C22#6550911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—801no—
343C4SD16×Dic511yescharacteristic
344C4#6545311yescharacteristic
345C4#6545911yescharacteristic
346C4#6546111yescharacteristic
347C2—21no—
348C2—21no—
349C2—162no—
350C2#1060264711yescharacteristic
351C2#1060284111yescharacteristic
352C2#1060288311yescharacteristic
subgroupG/H
centerC22#65509
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3208C2
socleC22×C5#386
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenter#3208D5
hypocenterC5#9294
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
2. #10615060C2semidirect
3. #10602631C2semidirect
6. #10598231C2semidirect
7. #10598229C2semidirect
10. C5×#492C4semidirect
11. C5×#486C4semidirect
118. C2×#168SD16semidirect
121. #492Dic5semidirect
122. #486Dic5semidirect
325. C5#9294semidirect

Maximal subgroups

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

subgroupindex
C5×#32082
#106150602
#106026312
#106025582
#106025522
#105982312
#105982292
#92945