Finite Group Databasebeta

← #12009811

Subgroups — #12009811

Order 1280.

446 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2484C211yesmaximal, characteristic
2C2×#64750C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4#10598143C212yesmaximal, complemented
5#10598141C212yesmaximal, complemented
6C2×C5×#117C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×#681—21no—
9C5×#400C411yescharacteristic
10C5×#400C2211yescharacteristic
11C5×#398C411yescharacteristic
12C5×#398C2211yescharacteristic
13C5×#387—21no—
14C5×#387—21no—
15C5×#385—21no—
16C5×#381—21no—
17C5×#381C411yescharacteristic
18#65496—21no—
19#64750—21no—
20#64750C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11764—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C5×#117—41no—
28C5×#117—41no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—41no—
32C2×C5×C4⋊C4—41no—
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C5×C4⋊C4C2311yescharacteristic
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C42×C5—21no—
42C2×#681—24no—
43C2×#681—22no—
44C2×#681—41no—
45C2×#681—42no—
46C2×#681—41no—
47C22×#168—41no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95C2×C411yescharacteristic
56C5×#95C2×C411yescharacteristic
57C22⋊#168—22no—
58C22⋊#168—41no—
59#2484D511yescharacteristic
60C2×#343—51no—
61#1463—51no—
62#1353—52no—
63#1346—52no—
64C24×C5C22⋊C411yescharacteristic
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—42no—
79C22×C4×C5—42no—
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C22⋊C411yescharacteristic
83C22×C4×C5C22×C411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C5×C4⋊C4—41no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C5×C22⋊C4—42no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—41no—
98C42×C5—42no—
99#681—24no—
100#681—44no—
101#681—42no—
102#681—82no—
103C2×#168—44no—
104C2×#168—42no—
105C2×#168—42no—
106C22×M16—101no—
107C2×#117Dic511yescharacteristic
108C22×C4⋊C4C2×D511yescharacteristic
109#407—101no—
110#400Dic511yescharacteristic
111#400C2×D511yescharacteristic
112#398Dic511yescharacteristic
113#398C2×D511yescharacteristic
114#387—21no—
115#387—21no—
116#385—21no—
117#381—21no—
118#381Dic511yescharacteristic
119#343—52no—
120#343—101no—
121#324—52no—
122#324—101no—
123C23×C5—22no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—41no—
127C23×C5#9911yescharacteristic
128C23×C5#9911yescharacteristic
129C23×C5C2×C22⋊C411yescharacteristic
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—42no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—81no—
161C2×C4×C5#10412yes—
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5#13711yescharacteristic
164#168—44no—
165#168—82no—
166C23×C4C2×Dic511yescharacteristic
167C23×C4C22⋊D511yescharacteristic
168C23×C4C22⋊D511yescharacteristic
169C2×M16—104no—
170C2×M16—102no—
171C2×M16—201no—
172C2×M16—202no—
173C2×M16—201no—
174C22×C8—201no—
175#117—41no—
176#117—41no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×Dic511yescharacteristic
182C2×C4⋊C4C2×Dic511yescharacteristic
183C2×C4⋊C4C2×Dic511yescharacteristic
184C2×C4⋊C4C22⋊D511yescharacteristic
185C2×C4⋊C4C22⋊D511yescharacteristic
186C2×C4⋊C4C22×D511yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C42—21no—
190C22⋊C8—102no—
191C22⋊C8—201no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95C2×Dic511yescharacteristic
200#95C2×Dic511yescharacteristic
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—42no—
209C22×C5—42no—
210C22×C5#35212yes—
211C22×C5C2×#9911yescharacteristic
212C22×C5#41711yescharacteristic
213C22×C5C2×#10411yescharacteristic
214C4×C5—21no—
215C4×C5—22no—
216C4×C5—21no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—81no—
222C4×C5—81no—
223C4×C5—81no—
224C4×C5—81no—
225C24C22⋊Dic511yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊Dic511yescharacteristic
242C22×C4C22⋊Dic511yescharacteristic
243C22×C4C22⋊Dic511yescharacteristic
244C22×C4C22×Dic511yescharacteristic
245C22×C4C2×C22⋊D511yescharacteristic
246C22×C4C2×C22⋊D511yescharacteristic
247M16—104no—
248M16—204no—
249M16—202no—
250M16—402no—
251C2×C8—204no—
252C2×C8—202no—
253C2×C8—202no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—42no—
267C2×C5—21no—
268C2×C5—21no—
269C2×C5—22no—
270C2×C5—41no—
271C2×C5#150411yescharacteristic
272C2×C5C2×#35211yescharacteristic
273C2×C5#213311yescharacteristic
274C23—21no—
275C23—21no—
276C23—22no—
277C23—41no—
278C23#396611yescharacteristic
279C23#396611yescharacteristic
280C23C2×C22⋊Dic511yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4#396912yes—
313C2×C4#409511yescharacteristic
314C2×C4#409711yescharacteristic
315C8—204no—
316C8—402no—
317C5#1176411yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#6475912yes—
328C22C2×#396611yescharacteristic
329C22#6552111yescharacteristic
330C22C2×#396911yescharacteristic
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—81no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2C2×#6475911yescharacteristic
347C2#1060250111yescharacteristic
348C2#1060266511yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2484C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2484D5
hypocenterC5#11764
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
4. #10598143C2semidirect
5. #10598141C2semidirect
317. C5#11764semidirect

Maximal subgroups

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

subgroupindex
C5×#24842
C2×#647502
#106023452
#105981432
#105981412
#117645