Finite Group Databasebeta

← #11994360

Subgroups — #11994360

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2#10613887C211yesmaximal, characteristic
3#10602346C212yesmaximal
4C2×#64748C211yesmaximal, characteristic
5#10598103C212yesmaximal
6C22×C5×C4⋊C4—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C2×#4072—21no—
10C5×#398—22no—
11C5×#398C414yescomplemented
12C2×C5×#95—21no—
13C2×C5×#95C2211yescharacteristic
14#65501—21no—
15#65501C2212yes—
16C2×C22⋊#168C2212yes—
17#65274—24no—
18#64749—24no—
19#64748—22no—
20#9027—51nomaximal, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—24no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—42no—
33C2×C5×C4⋊C4—42no—
34C2×C5×C4⋊C4C2×C412yes—
35C2×C5×C4⋊C4C2×C412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C22⋊Dic5—22no—
38#4072—42no—
39#4072—42no—
40C2×C4⋊Dic5—22no—
41C2×C4⋊Dic5—22no—
42C2×C4⋊Dic5D414yes—
43C2×C4×Dic5—22no—
44C22×#168—22no—
45C5×#95—24no—
46C5×#95—21no—
47C5×#95C2×C412yes—
48#3963—22no—
49#3963—22no—
50C22⋊#168—22no—
51C22⋊#168—22no—
52C2×#398D511yescharacteristic
53#2316—51no—
54#1823—52no—
55C2×#324—51no—
56#1294—52no—
57C24×C5C2×D411yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—24no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—22no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—42no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5C22⋊C412yes—
79C22×C4×C5C22⋊C412yes—
80C22×C4×C5D812yes—
81C22×C4×C5SD1612yes—
82C22×C4×C5C22×C411yescharacteristic
83C22×C4×C5C2×D412yes—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5#4112yes—
86C22×Dic5—24no—
87C5×C4⋊C4—24no—
88C5×C4⋊C4—24no—
89C5×C4⋊C4—24no—
90C5×C4⋊C4—48no—
91C5×C4⋊C4—42no—
92C22⋊Dic5—42no—
93C22⋊Dic5—42no—
94C4⋊Dic5—44no—
95C4⋊Dic5—44no—
96C4⋊Dic5—82no—
97C4×Dic5—44no—
98C2×#168—44no—
99C2×#168—42no—
100C2×#117—101no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4C2×D511yescharacteristic
103C22×C4⋊C4C2×D511yescharacteristic
104C2×C22⋊C8—52no—
105#398—22no—
106#398Dic514yescomplemented
107#389—104no—
108#380—52no—
109#380—101no—
110C2×#95—21no—
111C2×#95C2×D511yescharacteristic
112#340—104no—
113#324—102no—
114C23×C5—22no—
115C23×C5—22no—
116C23×C5C2×C22⋊C411yescharacteristic
117C23×C5#12011yescharacteristic
118C23×C5#12311yescharacteristic
119C23×C5C2×D811yescharacteristic
120C23×C5C2×SD1611yescharacteristic
121C23×C5AGL(1,ℤ/8)11yescharacteristic
122C23×C5#13711yescharacteristic
123C2×C4×C5—22no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—24no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—24no—
131C2×C4×C5—22no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—42no—
135C2×C4×C5—44no—
136C2×C4×C5—44no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—81no—
145C2×C4×C5—81no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5#10214yes—
150C2×C4×C5C4×D412yes—
151C2×C4×C5#12112yes—
152C2×Dic5—44no—
153C2×Dic5—44no—
154C2×Dic5—44no—
155#168—82no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4C22⋊D511yescharacteristic
159C23×C4C22⋊D511yescharacteristic
160C23×C4C22×D511yescharacteristic
161C22×C8—102no—
162#117—202no—
163#117—202no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—54no—
173C2×C4⋊C4—102no—
174C2×C4⋊C4—102no—
175C2×C4⋊C4C2×Dic512yes—
176C2×C4⋊C4C2×Dic512yes—
177C2×C4⋊C4C22⋊D512yes—
178C2×C22⋊C4—102no—
179C2×C42—102no—
180C22⋊C8—102no—
181C22⋊C8—102no—
182#95—24no—
183#95—21no—
184#95—102no—
185#95—102no—
186#95C2×Dic512yes—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5#38611yescharacteristic
196C22×C5C2×#10211yescharacteristic
197C22×C5#41711yescharacteristic
198C22×C5#44711yescharacteristic
199C22×C5#44811yescharacteristic
200C22×C5#45612yes—
201C22×C5#45812yes—
202C22×C5#48011yescharacteristic
203C22×C5#48111yescharacteristic
204C4×C5—24no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—44no—
208C4×C5—42no—
209C4×C5—82no—
210Dic5—84no—
211C24C2×C22⋊D511yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—104no—
233C22×C4#68612yes—
234C22×C4#68712yes—
235C22×C4C22⋊Dic512yes—
236C22×C4C22⋊Dic512yes—
237C22×C4D4×D512yes—
238C22×C4#71112yes—
239C22×C4C22×Dic511yescharacteristic
240C22×C4C2×C22⋊D511yescharacteristic
241C2×C8—204no—
242C2×C8—202no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—48no—
247C4⋊C4—42no—
248C4⋊C4—204no—
249C4⋊C4—204no—
250C4⋊C4—402no—
251C22⋊C4—202no—
252C22⋊C4—202no—
253C42—204no—
254C2×C5—21no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#161012yes—
259C2×C5#161112yes—
260C2×C5#187411yescharacteristic
261C2×C5#188611yescharacteristic
262C2×C5#189011yescharacteristic
263C23—22no—
264C23—22no—
265C23C2×#68611yescharacteristic
266C23C2×#68711yescharacteristic
267C23#408111yescharacteristic
268C23#408311yescharacteristic
269C23#409511yescharacteristic
270C23#409711yescharacteristic
271C23C2×C22⋊Dic511yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—204no—
299C2×C4—204no—
300C2×C4—204no—
301C2×C4#396414yes—
302C2×C4D4×Dic512yes—
303C2×C4#408512yes—
304C8—402no—
305C5#902711yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—21no—
313C22—21no—
314C22#6532211yescharacteristic
315C22#6532311yescharacteristic
316C22#6532511yescharacteristic
317C22#6532911yescharacteristic
318C22#6534212yes—
319C22#6538412yes—
320C22C2×#396411yescharacteristic
321C22#6550911yescharacteristic
322C22#6552111yescharacteristic
323C4—22no—
324C4—22no—
325C4—24no—
326C4—44no—
327C4—42no—
328C4—82no—
329C4—404no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1060050512yes—
335C2#1060050612yes—
336C2#1060247011yescharacteristic
337C2#1060249711yescharacteristic
338C2#1060257711yescharacteristic
subgroupG/H
centerC23#4083
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#398C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#398D5
hypocenterC5#9027
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
11. C5×#398C4semidirect
106. #398Dic5semidirect
305. C5#9027semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3982
#106138872
#106023462
C2×#647482
#105981032
#90275