Finite Group Databasebeta

← #12003763

Subgroups — #12003763

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#10606073C211yesmaximal, characteristic
2#10601247C211yesmaximal, characteristic
3#10601246C211yesmaximal, characteristic
4#10600367C211yesmaximal, characteristic
5C5×#1296C211yesmaximal, characteristic
6#10598195C211yesmaximal, characteristic
7#10598195C211yesmaximal, characteristic
8C2×C5×C4⋊C8C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C5×#384C2211yescharacteristic
11C2×#3950—21no—
12C2×#3949—21no—
13#65275—22no—
14#65274—21no—
15#65274—21no—
16#65266—21no—
17#65266—21no—
18#65224C2211yescharacteristic
19C4×C4⋊Dic5C2211yescharacteristic
20C4×C4⋊Dic5C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22#64771—21no—
23#64771—21no—
24#64749—22no—
25#10578—51nomaximal, Sylow
26C22×C5×C8—21no—
27C22×C5×C8—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4D412yes—
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5D411yescharacteristic
37C2×C4⋊Dic5D411yescharacteristic
38C2×C4⋊Dic5D411yescharacteristic
39C2×C4⋊Dic5D411yescharacteristic
40C2×C4×Dic5—21no—
41C2×C4×Dic5—21no—
42C22×#168—21no—
43C5×C4⋊C8—21no—
44C5×C4⋊C8—21no—
45C5×C4⋊C8Q812yes—
46C5×C4⋊C8Q812yes—
47#3963—22no—
48#3963—22no—
49#3963—22no—
50#3963—21no—
51#3963—21no—
52#3950—42no—
53#3949—42no—
54C4×#168—21no—
55C4×#168Q812yes—
56#2571—51no—
57#1948—51no—
58#1947—51no—
59#1834—51no—
60#1296D511yescharacteristic
61#1279—51no—
62#1279—51no—
63C22×C4×C5—22no—
64C22×C4×C5C2×D411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×Dic5—21no—
68C22×Dic5—21no—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—41no—
72C2×C5×C8—22no—
73C2×C5×C8—22no—
74C2×C5×C8—41no—
75C2×C5×C8—41no—
76C2×C5×C8—41no—
77C2×C5×C8—41no—
78C5×C4⋊C4—42no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C42×C5C2×Q811yescharacteristic
84C42×C5C2×Q811yescharacteristic
85C42×C5C2×Q811yescharacteristic
86C42×C5#4111yescharacteristic
87C4⋊Dic5—21no—
88C4⋊Dic5—21no—
89C4⋊Dic5—21no—
90C4⋊Dic5—21no—
91C4⋊Dic5—21no—
92C4⋊Dic5—21no—
93C4⋊Dic5—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5—42no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5—41no—
100C4⋊Dic5—82no—
101C4×Dic5—41no—
102C4×Dic5—41no—
103C4×Dic5—41no—
104C4×Dic5—41no—
105C2×#168—22no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#107—101no—
109C2×#106—101no—
110C2×C4⋊C8C2×D511yescharacteristic
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⋊C4—51no—
122#340—101no—
123#340—101no—
124#340—102no—
125C23×C5#12011yescharacteristic
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—42no—
129C2×C4×C5—42no—
130C2×C4×C5—42no—
131C2×C4×C5C22⋊Q811yescharacteristic
132C2×C4×C5C22⋊Q811yescharacteristic
133C2×C4×C5C22⋊Q811yescharacteristic
134C2×C4×C5C4⋊Q811yescharacteristic
135C2×C4×C5C4⋊Q811yescharacteristic
136C2×C4×C5C4⋊Q811yescharacteristic
137C2×C4×C5#13511yescharacteristic
138C2×C4×C5#13511yescharacteristic
139C2×C4×C5#13511yescharacteristic
140C2×C4×C5#13511yescharacteristic
141C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×C4×C5#13711yescharacteristic
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—81no—
158C2×Dic5—81no—
159C2×Dic5—81no—
160C5×C8—42no—
161C5×C8—42no—
162#168—42no—
163C22×C8—21no—
164C22×C8—21no—
165C22×C8—101no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—51no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4—101no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4—102no—
176C2×C4⋊C4D2012yes—
177C2×C42—101no—
178C2×C42—101no—
179C2×C42C22×D511yescharacteristic
180#107—202no—
181#106—202no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8Dic1012yes—
185C4⋊C8Dic1012yes—
186C4×C8—52no—
187C4×C8—101no—
188#95—102no—
189#95—102no—
190#95—102no—
191#95—101no—
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—82no—
203C4×C5#47811yescharacteristic
204C4×C5#47811yescharacteristic
205C4×C5#47911yescharacteristic
206C4×C5#47911yescharacteristic
207C4×C5#49911yescharacteristic
208C4×C5#49911yescharacteristic
209C4×C5#50111yescharacteristic
210C4×C5#50111yescharacteristic
211Dic5—81no—
212Dic5—81no—
213Dic5—81no—
214Dic5—81no—
215Dic5—161no—
216C22×C4—22no—
217C22×C4—101no—
218C22×C4—101no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4—201no—
222C22×C4C2×D2011yescharacteristic
223C22×C4D4×D511yescharacteristic
224C22×C4D4×D511yescharacteristic
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—102no—
232C2×C8—201no—
233C2×C8—201no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—101no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4—101no—
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—201no—
254C42—201no—
255C42—201no—
256C42—201no—
257C42C2×Dic1011yescharacteristic
258C42C2×Dic1011yescharacteristic
259C42#71111yescharacteristic
260C42Q8×D511yescharacteristic
261C2×C5#162811yescharacteristic
262C2×C5#163811yescharacteristic
263C2×C5#164011yescharacteristic
264C2×C5#164611yescharacteristic
265C2×C5#205911yescharacteristic
266C2×C5#205911yescharacteristic
267C2×C5#206111yescharacteristic
268C23#402811yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—201no—
277C2×C4—201no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—201no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4—201no—
286C2×C4—401no—
287C2×C4—401no—
288C2×C4—401no—
289C2×C4#401511yescharacteristic
290C2×C4#402411yescharacteristic
291C2×C4#402411yescharacteristic
292C2×C4#403411yescharacteristic
293C2×C4#403411yescharacteristic
294C2×C4#404311yescharacteristic
295C2×C4#405711yescharacteristic
296C2×C4#405811yescharacteristic
297C2×C4#406011yescharacteristic
298C2×C4#406111yescharacteristic
299C2×C4#406211yescharacteristic
300C2×C4#406211yescharacteristic
301C2×C4#406411yescharacteristic
302C2×C4#406511yescharacteristic
303C8—42no—
304C8—42no—
305C8—202no—
306C5#1057811yescharacteristic, complemented, Sylow
307C22#6494511yescharacteristic
308C22#6503511yescharacteristic
309C22#6504211yescharacteristic
310C22#6507011yescharacteristic
311C22#6507211yescharacteristic
312C22#6509911yescharacteristic
313C22#6510011yescharacteristic
314C4—21no—
315C4—21no—
316C4—82no—
317C4—401no—
318C4—401no—
319C4—401no—
320C4—401no—
321C4—801no—
322C4#6505211yescharacteristic
323C4#6505511yescharacteristic
324C4#6508511yescharacteristic
325C4#6508811yescharacteristic
326C4#6514511yescharacteristic
327C4#6514711yescharacteristic
328C4#6516511yescharacteristic
329C4#6516711yescharacteristic
330C2#1059919911yescharacteristic
331C2#1059922611yescharacteristic
332C2#1059922811yescharacteristic
333C2#1059928811yescharacteristic
334C2#1059962111yescharacteristic
335C2#1059962211yescharacteristic
336C2#1059977211yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1296C2
socle, prime radicalC23×C5#120
hypercenter#1296D5
hypocenterC5#10578
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

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
#106060732
#106012472
#106012462
#106003672
C5×#12962
#105981952
#105785