Finite Group Databasebeta

← #12003764

Subgroups — #12003764

Order 1280.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10605456C211yesmaximal, characteristic
2C5×#1947C211yesmaximal, characteristic
3#10600367C211yesmaximal, characteristic
4#10600361C211yesmaximal, characteristic
5#10598195C211yesmaximal, characteristic
6#10598193C211yesmaximal, characteristic
7#10598110C211yesmaximal, characteristic
8C2×C5×#107—21no—
9C2×C5×C4⋊C8C2211yescharacteristic
10C5×#384C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12#65266—21no—
13#65262—21no—
14C2×#3940—21no—
15#65225—21no—
16#65224C2211yescharacteristic
17C4×C4⋊Dic5C2211yescharacteristic
18#65217—21no—
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21#64949—22no—
22C5×#340—21no—
23#64749—21no—
24#64749—22no—
25#10578—51nomaximal, Sylow
26C22×C5×C8—21no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C42×C5—21no—
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5D411yescharacteristic
37C2×C4⋊Dic5D411yescharacteristic
38C2×C4⋊Dic5D412yes—
39C2×#683—22no—
40C2×C4×Dic5—21no—
41C22×#168—21no—
42C22×#168—21no—
43C5×#107—42no—
44C5×C4⋊C8—21no—
45C5×C4⋊C8Q812yes—
46C5×#95—21no—
47#3963—22no—
48#3963—22no—
49#3963—22no—
50#3963—21no—
51#3940—42no—
52C4⋊#168—21no—
53C4⋊#168Q812yes—
54C4×#168—21no—
55C4×#168Q812yes—
56#2571—51no—
57#1948—51no—
58#1947D511yescharacteristic
59#1834—51no—
60#1296—51no—
61#1279—51no—
62#1279—51no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—41no—
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—22no—
72C2×C5×C8—22no—
73C2×C5×C8—41no—
74C2×C5×C8—41no—
75C5×C4⋊C4—21no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4—21no—
78C5×C4⋊C4—21no—
79C5×C4⋊C4—42no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C42×C5—41no—
85C42×C5—41no—
86C42×C5C2×Q811yescharacteristic
87C42×C5C2×Q811yescharacteristic
88C42×C5C2×Q811yescharacteristic
89C42×C5#4111yescharacteristic
90C4⋊Dic5—21no—
91C4⋊Dic5—21no—
92C4⋊Dic5—21no—
93C4⋊Dic5—21no—
94C4⋊Dic5—41no—
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98C4⋊Dic5—42no—
99#683—82no—
100C4×Dic5—41no—
101C4×Dic5—41no—
102C2×#168—22no—
103C2×#168—22no—
104C2×#168—41no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#107—21no—
109C2×#106—101no—
110C2×C4⋊C8—51no—
111C2×C4⋊C8C2×D511yescharacteristic
112C2×C4×C8—51no—
113#400—102no—
114#389—101no—
115#389—101no—
116#384—51no—
117#384C2×D511yescharacteristic
118#382—101no—
119#382—101no—
120C4×C4⋊C4—51no—
121C4×C4⋊C4C2×D511yescharacteristic
122#340—21no—
123#340—102no—
124#340—101no—
125C23×C5#12011yescharacteristic
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—81no—
135C2×C4×C5—81no—
136C2×C4×C5—81no—
137C2×C4×C5C22⋊Q811yescharacteristic
138C2×C4×C5C22⋊Q811yescharacteristic
139C2×C4×C5C22⋊Q811yescharacteristic
140C2×C4×C5C4⋊Q811yescharacteristic
141C2×C4×C5C4⋊Q811yescharacteristic
142C2×C4×C5C4⋊Q811yescharacteristic
143C2×C4×C5#13511yescharacteristic
144C2×C4×C5#13511yescharacteristic
145C2×C4×C5#13511yescharacteristic
146C2×C4×C5#13511yescharacteristic
147C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C5#13711yescharacteristic
150C2×C4×C5#13711yescharacteristic
151C2×Dic5—41no—
152C2×Dic5—42no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—42no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—42no—
160C5×C8—42no—
161#168—42no—
162#168—42no—
163C22×C8—21no—
164C22×C8—101no—
165C22×C8—101no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—52no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4—101no—
174C2×C4⋊C4—102no—
175C2×C4⋊C4C22⋊D511yescharacteristic
176C2×C4⋊C4C22⋊D511yescharacteristic
177C2×C42—21no—
178C2×C42—101no—
179C2×C42C22×D511yescharacteristic
180#107—42no—
181#106—202no—
182C4⋊C8—21no—
183C4⋊C8—52no—
184C4⋊C8—101no—
185C4⋊C8Dic1012yes—
186C4×C8—52no—
187C4×C8—101no—
188#95—21no—
189#95—102no—
190#95—102no—
191#95—102no—
192#95—101no—
193C22×C5#39511yescharacteristic
194C22×C5#44911yescharacteristic
195C22×C5#44911yescharacteristic
196C22×C5#45211yescharacteristic
197C22×C5#45211yescharacteristic
198C22×C5#45411yescharacteristic
199C22×C5#45511yescharacteristic
200C4×C5—21no—
201C4×C5—21no—
202C4×C5—81no—
203C4×C5—81no—
204C4×C5—161no—
205C4×C5#47811yescharacteristic
206C4×C5#47811yescharacteristic
207C4×C5#47911yescharacteristic
208C4×C5#47911yescharacteristic
209C4×C5#49911yescharacteristic
210C4×C5#49911yescharacteristic
211C4×C5#50111yescharacteristic
212C4×C5#50111yescharacteristic
213Dic5—81no—
214Dic5—82no—
215Dic5—81no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—41no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4—102no—
222C22×C4D4×D511yescharacteristic
223C22×C4D4×D511yescharacteristic
224C22×C4C2×C22⋊D511yescharacteristic
225C2×C8—22no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—102no—
229C2×C8—102no—
230C2×C8—201no—
231C2×C8—201no—
232C2×C8—201no—
233C2×C8—201no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—202no—
248C4⋊C4—201no—
249C4⋊C4—201no—
250C4⋊C4—201no—
251C4⋊C4—201no—
252C4⋊C4—402no—
253C42—41no—
254C42—41no—
255C42—201no—
256C42—201no—
257C42C2×Dic1011yescharacteristic
258C42#70911yescharacteristic
259C42Q8×D511yescharacteristic
260C42Q8×D511yescharacteristic
261C2×C5#162811yescharacteristic
262C2×C5#163811yescharacteristic
263C2×C5#164011yescharacteristic
264C2×C5#164611yescharacteristic
265C2×C5#205911yescharacteristic
266C2×C5#205911yescharacteristic
267C2×C5#206111yescharacteristic
268C23#408311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—202no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4—202no—
286C2×C4—201no—
287C2×C4—202no—
288C2×C4—201no—
289C2×C4#403411yescharacteristic
290C2×C4#403411yescharacteristic
291C2×C4#404211yescharacteristic
292C2×C4#404211yescharacteristic
293C2×C4#405711yescharacteristic
294C2×C4#405811yescharacteristic
295C2×C4#406411yescharacteristic
296C2×C4#406511yescharacteristic
297C2×C4#407011yescharacteristic
298C2×C4#407811yescharacteristic
299C2×C4#408811yescharacteristic
300C2×C4#409011yescharacteristic
301C2×C4#409611yescharacteristic
302C2×C4#409611yescharacteristic
303C8—42no—
304C8—202no—
305C8—202no—
306C5#1057811yescharacteristic, complemented, Sylow
307C22#6526811yescharacteristic
308C22#6532611yescharacteristic
309C22#6533611yescharacteristic
310C22#6544711yescharacteristic
311C22#6547611yescharacteristic
312C22#6549011yescharacteristic
313C22#6549111yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—161no—
319C4—402no—
320C4—401no—
321C4—401no—
322C4#6516511yescharacteristic
323C4#6516611yescharacteristic
324C4#6516711yescharacteristic
325C4#6518011yescharacteristic
326C4#6529811yescharacteristic
327C4#6531111yescharacteristic
328C4#6535311yescharacteristic
329C4#6536911yescharacteristic
330C2#1060039911yescharacteristic
331C2#1060141111yescharacteristic
332C2#1060146011yescharacteristic
333C2#1060181211yescharacteristic
334C2#1060185311yescharacteristic
335C2#1060190211yescharacteristic
336C2#1060195011yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1947C2
socle, prime radicalC23×C5#120
hypercenter#1947D5
hypocenterC5#10578
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
306. C5#10578semidirect

Maximal subgroups

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

subgroupindex
#106054562
C5×#19472
#106003672
#106003612
#105981952
#105981932
#105981102
#105785