Finite Group Databasebeta

← #12003789

Subgroups — #12003789

Order 1280.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2552C211yesmaximal, characteristic
2#10600367C211yesmaximal, characteristic
3#10600260C211yesmaximal, characteristic
4#10600260C211yesmaximal, characteristic
5#10598125C211yesmaximal, characteristic
6#10598110C211yesmaximal, characteristic
7#10598110C211yesmaximal, characteristic
8C2×C5×#125—21no—
9C5×#398—22no—
10C5×#389—21no—
11C5×#389—21no—
12C5×#384—21no—
13C5×#384C2211yescharacteristic
14C4×C5×C4⋊C4C2211yescharacteristic
15C4×C5×C4⋊C4C2211yescharacteristic
16C2×#3940—21no—
17C2×#3940—21no—
18#65224C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22#64749—21no—
23#64749—21no—
24#64749—22no—
25#10582—51nomaximal, Sylow
26C5×#125—42no—
27C5×#125—42no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C4⋊C4D411yescharacteristic
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C4⋊C4D412yes—
38C2×C42×C5—21no—
39C2×C42×C5—21no—
40C2×C42×C5C2311yescharacteristic
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C2×C4⋊Dic5—21no—
44C22×#168—21no—
45C22×#168—21no—
46C22×#168—21no—
47C5×#95—22no—
48C5×#95—21no—
49C5×#95—21no—
50#3940—42no—
51#3940—42no—
52C4⋊#168—21no—
53C4⋊#168—21no—
54C4⋊#168Q812yes—
55C4⋊#168Q812yes—
56C4×#168—21no—
57C4×#168Q812yes—
58#2552D511yescharacteristic
59#1948—51no—
60#1948—51no—
61#1834—51no—
62#1296—51no—
63#1279—51no—
64#1279—51no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—22no—
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×Dic5—41no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4—21no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4—21no—
78C5×C4⋊C4—21no—
79C5×C4⋊C4—21no—
80C5×C4⋊C4—42no—
81C5×C4⋊C4—44no—
82C5×C4⋊C4—44no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—82no—
88C5×C4⋊C4SD1612yes—
89C5×C4⋊C4SD1612yes—
90C42×C5—41no—
91C42×C5—41no—
92C42×C5—41no—
93C42×C5—41no—
94C42×C5C2×Q811yescharacteristic
95C42×C5C2×Q811yescharacteristic
96C42×C5C2×Q811yescharacteristic
97C42×C5#4111yescharacteristic
98C4⋊Dic5—42no—
99C4⋊Dic5—41no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C2×#168—22no—
104C2×#168—22no—
105C2×#168—22no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×#168—41no—
112C2×#125—21no—
113C2×#106—101no—
114C2×#106—101no—
115C2×C4⋊C8—51no—
116C2×C4⋊C8—51no—
117C2×C4×C8—51no—
118#398—22no—
119#389—21no—
120#389—21no—
121#384—21no—
122#384—51no—
123#384C2×D511yescharacteristic
124C4×C4⋊C4C2×D511yescharacteristic
125C4×C4⋊C4C2×D511yescharacteristic
126#340—102no—
127#340—101no—
128#340—101no—
129C23×C5#12011yescharacteristic
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—42no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—42no—
146C2×C4×C5—41no—
147C2×C4×C5C22⋊Q811yescharacteristic
148C2×C4×C5C22⋊Q811yescharacteristic
149C2×C4×C5C22⋊Q811yescharacteristic
150C2×C4×C5C4⋊Q811yescharacteristic
151C2×C4×C5C4⋊Q811yescharacteristic
152C2×C4×C5C4⋊Q811yescharacteristic
153C2×C4×C5C2×SD1611yescharacteristic
154C2×C4×C5C2×SD1611yescharacteristic
155C2×C4×C5#13511yescharacteristic
156C2×C4×C5#13511yescharacteristic
157C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C5#13711yescharacteristic
160C2×C4×C5#13711yescharacteristic
161C2×Dic5—81no—
162C2×Dic5—81no—
163C2×Dic5—81no—
164#168—42no—
165#168—42no—
166#168—42no—
167C22×C8—101no—
168C22×C8—101no—
169C22×C8—101no—
170#125—42no—
171#125—42no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4C22⋊D511yescharacteristic
181C2×C4⋊C4C22⋊D511yescharacteristic
182C2×C4⋊C4C22⋊D511yescharacteristic
183C2×C4⋊C4C22⋊D511yescharacteristic
184C2×C4⋊C4C22⋊D512yes—
185C2×C42—21no—
186C2×C42—21no—
187C2×C42C22×D511yescharacteristic
188#106—202no—
189#106—202no—
190C4⋊C8—52no—
191C4⋊C8—52no—
192C4⋊C8—101no—
193C4⋊C8—101no—
194C4×C8—52no—
195C4×C8—101no—
196#95—22no—
197#95—21no—
198#95—21no—
199C22×C5#39511yescharacteristic
200C22×C5#44811yescharacteristic
201C22×C5#44911yescharacteristic
202C22×C5#45011yescharacteristic
203C22×C5#45211yescharacteristic
204C22×C5#45411yescharacteristic
205C22×C5#45511yescharacteristic
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—42no—
209C4×C5—42no—
210C4×C5—81no—
211C4×C5—81no—
212C4×C5—82no—
213C4×C5#47511yescharacteristic
214C4×C5#47611yescharacteristic
215C4×C5#47811yescharacteristic
216C4×C5#47911yescharacteristic
217C4×C5#49811yescharacteristic
218C4×C5#49911yescharacteristic
219C4×C5#50111yescharacteristic
220C4×C5#50111yescharacteristic
221Dic5—161no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—201no—
228C22×C4C2×C22⋊D511yescharacteristic
229C22×C4C2×C22⋊D511yescharacteristic
230C22×C4C2×C22⋊D511yescharacteristic
231C2×C8—102no—
232C2×C8—102no—
233C2×C8—102no—
234C2×C8—201no—
235C2×C8—201no—
236C2×C8—201no—
237C2×C8—201no—
238C2×C8—201no—
239C2×C8—201no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—44no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—82no—
254C4⋊C4—202no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4#68712yes—
260C4⋊C4#68812yes—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42Q8×D511yescharacteristic
266C42Q8×D511yescharacteristic
267C42Q8×D511yescharacteristic
268C42#71311yescharacteristic
269C2×C5#162611yescharacteristic
270C2×C5#163511yescharacteristic
271C2×C5#164211yescharacteristic
272C2×C5#164311yescharacteristic
273C2×C5#205811yescharacteristic
274C2×C5#205911yescharacteristic
275C2×C5#206111yescharacteristic
276C23#409911yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—401no—
295C2×C4—401no—
296C2×C4—401no—
297C2×C4#407811yescharacteristic
298C2×C4C2×#68711yescharacteristic
299C2×C4C2×#68811yescharacteristic
300C2×C4#408811yescharacteristic
301C2×C4#409011yescharacteristic
302C2×C4#409011yescharacteristic
303C2×C4#409011yescharacteristic
304C2×C4#409211yescharacteristic
305C2×C4#409211yescharacteristic
306C2×C4#409211yescharacteristic
307C2×C4#409511yescharacteristic
308C2×C4#409611yescharacteristic
309C2×C4#409611yescharacteristic
310C2×C4#409711yescharacteristic
311C8—202no—
312C8—202no—
313C8—202no—
314C5#1058211yescharacteristic, complemented, Sylow
315C22#6550711yescharacteristic
316C22#6551611yescharacteristic
317C22#6551811yescharacteristic
318C22#6552711yescharacteristic
319C22#6552811yescharacteristic
320C22#6553111yescharacteristic
321C22#6553411yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4—82no—
329C4—801no—
330C4#6535211yescharacteristic
331C4#6535311yescharacteristic
332C4#6535411yescharacteristic
333C4#6535511yescharacteristic
334C4#6536811yescharacteristic
335C4#6536911yescharacteristic
336C4#6537311yescharacteristic
337C4#6538311yescharacteristic
338C2#1060253211yescharacteristic
339C2#1060257611yescharacteristic
340C2#1060269411yescharacteristic
341C2#1060270411yescharacteristic
342C2#1060271411yescharacteristic
343C2#1060271811yescharacteristic
344C2#1060272811yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2552C2
socle, prime radicalC23×C5#120
hypercenter#2552D5
hypocenterC5#10582
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2552

Complements

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

NH ≅ G/Ntype
314. C5#10582semidirect

Maximal subgroups

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

subgroupindex
C5×#25522
#106003672
#106002602
#105981252
#105981102
#105825