Finite Group Databasebeta

← #12003779

Subgroups — #12003779

Order 1280.

442 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
1#10605448C211yesmaximal, characteristic
2#10601247C211yesmaximal, characteristic
3#10600557C211yesmaximal, characteristic
4#10600259C211yesmaximal, characteristic
5C5×#1279C211yesmaximal, characteristic
6#10598193C211yesmaximal, characteristic
7#10598146C211yesmaximal, characteristic
8C2×#4036—21no—
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12C2×#3949—21no—
13C2×#3949—22no—
14#65274—21no—
15C2×#3939—21no—
16#65224—21no—
17#65224C2211yescharacteristic
18#65224C2211yescharacteristic
19C4×C4⋊Dic5C2211yescharacteristic
20#65217—21no—
21C2×C4⋊#168C2211yescharacteristic
22#64950—22no—
23#64771—21no—
24#64749—21no—
25#10580—51nomaximal, Sylow
26C22×C5×C8—21no—
27C22×C5×C8—21no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C42×C5—21no—
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—22no—
39C2×C4⋊Dic5D411yescharacteristic
40C2×C4⋊Dic5D411yescharacteristic
41C2×C4⋊Dic5D412yes—
42C2×#683—22no—
43C2×C4×Dic5—21no—
44C22×#168—21no—
45#4036—42no—
46#4036—42no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8Q812yes—
49C4×C5×C8—21no—
50C4×C5×C8Q812yes—
51C5×#95—21no—
52#3963—22no—
53#3963—21no—
54#3949—42no—
55#3949—44no—
56#3939—42no—
57C4⋊#168—21no—
58C4⋊#168Q812yes—
59#2552—51no—
60#1948—51no—
61#1947—51no—
62#1844—51no—
63#1296—51no—
64#1279—51no—
65#1279D511yescharacteristic
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×Dic5—21no—
72C22×Dic5—21no—
73C22×Dic5—22no—
74C22×Dic5—41no—
75C2×C5×C8—22no—
76C2×C5×C8—22no—
77C2×C5×C8—22no—
78C2×C5×C8—22no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C5×C4⋊C4—21no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4SD1612yes—
84C5×C4⋊C4SD1612yes—
85C42×C5—41no—
86C42×C5—41no—
87C42×C5C2×Q811yescharacteristic
88C42×C5C2×Q811yescharacteristic
89C42×C5C2×Q811yescharacteristic
90C42×C5#4111yescharacteristic
91C4⋊Dic5—21no—
92C4⋊Dic5—21no—
93C4⋊Dic5—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5—44no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100C4⋊Dic5—42no—
101C4⋊Dic5—42no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104C4⋊Dic5—41no—
105C4⋊Dic5—41no—
106C4⋊Dic5—82no—
107#683—44no—
108C4×Dic5—41no—
109C4×Dic5—41no—
110C2×#168—22no—
111C2×#168—41no—
112C2×#168—41no—
113C2×#125—101no—
114C2×#107—101no—
115C2×#106—102no—
116C2×#106—101no—
117C2×C4⋊C8—51no—
118C2×C4⋊C8C2×D511yescharacteristic
119C2×C4×C8C2×D511yescharacteristic
120#398—102no—
121#389—101no—
122#389—101no—
123#384—51no—
124#384—51no—
125#384—101no—
126C4×C4⋊C4—51no—
127C4×C4⋊C4C2×D511yescharacteristic
128#340—101no—
129#340—101no—
130C23×C5#12011yescharacteristic
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5C22⋊Q811yescharacteristic
140C2×C4×C5C22⋊Q811yescharacteristic
141C2×C4×C5C22⋊Q811yescharacteristic
142C2×C4×C5C4⋊Q811yescharacteristic
143C2×C4×C5C4⋊Q811yescharacteristic
144C2×C4×C5C4⋊Q811yescharacteristic
145C2×C4×C5C2×SD1611yescharacteristic
146C2×C4×C5C2×SD1611yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5#13511yescharacteristic
149C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C5#13711yescharacteristic
152C2×C4×C5#13711yescharacteristic
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—42no—
157C2×Dic5—41no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—81no—
163C2×Dic5—81no—
164C2×Dic5—81no—
165C5×C8—24no—
166C5×C8—42no—
167#168—42no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—101no—
171#125—202no—
172#125—202no—
173C2×C4⋊C4—51no—
174C2×C4⋊C4—51no—
175C2×C4⋊C4—52no—
176C2×C4⋊C4—102no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4—101no—
183C2×C4⋊C4—102no—
184C2×C4⋊C4D2011yescharacteristic
185C2×C4⋊C4D2011yescharacteristic
186C2×C42—21no—
187C2×C42—101no—
188C2×C42C22×D511yescharacteristic
189#107—202no—
190#106—202no—
191#106—204no—
192C4⋊C8—21no—
193C4⋊C8—52no—
194C4⋊C8—101no—
195C4⋊C8Dic1012yes—
196C4×C8—21no—
197C4×C8Dic1012yes—
198#95—21no—
199#95—102no—
200#95—101no—
201C22×C5#39511yescharacteristic
202C22×C5#44811yescharacteristic
203C22×C5#44911yescharacteristic
204C22×C5#45011yescharacteristic
205C22×C5#45211yescharacteristic
206C22×C5#45311yescharacteristic
207C22×C5#45611yescharacteristic
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—42no—
211C4×C5—42no—
212C4×C5#47511yescharacteristic
213C4×C5#47611yescharacteristic
214C4×C5#47811yescharacteristic
215C4×C5#47911yescharacteristic
216C4×C5#49811yescharacteristic
217C4×C5#49911yescharacteristic
218C4×C5#50111yescharacteristic
219C4×C5#50111yescharacteristic
220Dic5—81no—
221Dic5—82no—
222Dic5—81no—
223Dic5—161no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—101no—
227C22×C4—101no—
228C22×C4—102no—
229C22×C4—201no—
230C22×C4C2×D2011yescharacteristic
231C22×C4D4×D511yescharacteristic
232C22×C4D4×D511yescharacteristic
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—102no—
240C2×C8—201no—
241C2×C8—201no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—202no—
249C4⋊C4—204no—
250C4⋊C4—204no—
251C4⋊C4—202no—
252C4⋊C4—201no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C4⋊C4—402no—
261C4⋊C4#67712yes—
262C4⋊C4#67712yes—
263C42—41no—
264C42—41no—
265C42—201no—
266C42—201no—
267C42C2×Dic1011yescharacteristic
268C42C2×Dic1011yescharacteristic
269C42#71111yescharacteristic
270C42Q8×D511yescharacteristic
271C2×C5#162211yescharacteristic
272C2×C5#163111yescharacteristic
273C2×C5#165311yescharacteristic
274C2×C5#165411yescharacteristic
275C2×C5#205811yescharacteristic
276C2×C5#205911yescharacteristic
277C2×C5#206011yescharacteristic
278C23#402811yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—201no—
288C2×C4—201no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4—201no—
294C2×C4—201no—
295C2×C4—202no—
296C2×C4—401no—
297C2×C4—401no—
298C2×C4—401no—
299C2×C4#401511yescharacteristic
300C2×C4#402411yescharacteristic
301C2×C4#402411yescharacteristic
302C2×C4#403411yescharacteristic
303C2×C4#403411yescharacteristic
304C2×C4#404311yescharacteristic
305C2×C4C2×#67711yescharacteristic
306C2×C4C2×#67711yescharacteristic
307C2×C4#405411yescharacteristic
308C2×C4#405511yescharacteristic
309C2×C4#405711yescharacteristic
310C2×C4#406211yescharacteristic
311C2×C4#406211yescharacteristic
312C2×C4#406411yescharacteristic
313C8—24no—
314C8—42no—
315C8—202no—
316C5#1058011yescharacteristic, complemented, Sylow
317C22#6494511yescharacteristic
318C22#6502011yescharacteristic
319C22#6502711yescharacteristic
320C22#6507011yescharacteristic
321C22#6509911yescharacteristic
322C22#6511111yescharacteristic
323C22#6511511yescharacteristic
324C4—21no—
325C4—21no—
326C4—42no—
327C4—42no—
328C4—401no—
329C4—401no—
330C4—402no—
331C4—801no—
332C4#6496911yescharacteristic
333C4#6499111yescharacteristic
334C4#6505211yescharacteristic
335C4#6508811yescharacteristic
336C4#6513111yescharacteristic
337C4#6514011yescharacteristic
338C4#6514711yescharacteristic
339C4#6516511yescharacteristic
340C2#1059897811yescharacteristic
341C2#1059899111yescharacteristic
342C2#1059905411yescharacteristic
343C2#1059906811yescharacteristic
344C2#1059942611yescharacteristic
345C2#1059952811yescharacteristic
346C2#1059962111yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1279C2
socle, prime radicalC23×C5#120
hypercenter#1279D5
hypocenterC5#10580
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
316. C5#10580semidirect

Maximal subgroups

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

subgroupindex
#106054482
#106012472
#106005572
#106002592
C5×#12792
#105981932
#105981462
#105805