Finite Group Databasebeta

← C5×#11764 #11934484

Subgroups — C5×#11764 #11934484

Order 1280.

446 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 106 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×C5×#343C211yesmaximal, characteristic
3C5×#1463C211yesmaximal, characteristic
4C5×#1353C212yesmaximal, complemented
5C5×#1346C212yesmaximal, complemented
6C22×C5×M16—21no—
7C2×C5×#117C411yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C5×#407—21no—
10C5×#400C411yescharacteristic
11C5×#400C2211yescharacteristic
12C5×#398C411yescharacteristic
13C5×#398C2211yescharacteristic
14C5×#387—21no—
15C5×#387—21no—
16C5×#385—21no—
17C5×#381—21no—
18C5×#381C411yescharacteristic
19C5×#343—21no—
20C5×#343C2212yes—
21C5×#324—21no—
22C5×#324C2212yes—
23#11764C511yesmaximal, characteristic, direct product factor, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C2×C5×M16—24no—
28C2×C5×M16—22no—
29C2×C5×M16—41no—
30C2×C5×M16—42no—
31C2×C5×M16—41no—
32C22×C5×C8—41no—
33C5×#117—41no—
34C5×#117—41no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—41no—
38C2×C5×C4⋊C4—41no—
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C4⋊C4C2×C411yescharacteristic
42C2×C5×C4⋊C4D411yescharacteristic
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C5×C4⋊C4C2311yescharacteristic
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C42×C5—21no—
48C5×C22⋊C8—22no—
49C5×C22⋊C8—41no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95C2×C411yescharacteristic
58C5×#95C2×C411yescharacteristic
59#2484C2×C511yescharacteristic
60C2×#343C2×C511yescharacteristic
61#1463C2×C511yescharacteristic
62#1353C2×C512yescomplemented
63#1346C2×C512yescomplemented
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×M16—24no—
87C5×M16—44no—
88C5×M16—42no—
89C5×M16—82no—
90C2×C5×C8—44no—
91C2×C5×C8—42no—
92C2×C5×C8—42no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—42no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C5×C22⋊C4—42no—
103C5×C22⋊C4—41no—
104C5×C22⋊C4—41no—
105C42×C5—42no—
106C22×M16—21no—
107C2×#117C4×C511yescharacteristic
108C22×C4⋊C4C22×C511yescharacteristic
109#407—21no—
110#400C4×C511yescharacteristic
111#400C22×C511yescharacteristic
112#398C4×C511yescharacteristic
113#398C22×C511yescharacteristic
114#387—21no—
115#387—21no—
116#385—21no—
117#381—21no—
118#381C4×C511yescharacteristic
119#343—21no—
120#343C22×C512yes—
121#324—21no—
122#324C22×C512yes—
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
164C5×C8—44no—
165C5×C8—82no—
166C23×C4C2×C4×C511yescharacteristic
167C23×C4C5×D411yescharacteristic
168C23×C4C5×D411yescharacteristic
169C2×M16—24no—
170C2×M16—22no—
171C2×M16—41no—
172C2×M16—42no—
173C2×M16—41no—
174C22×C8—41no—
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×C4×C511yescharacteristic
182C2×C4⋊C4C2×C4×C511yescharacteristic
183C2×C4⋊C4C2×C4×C511yescharacteristic
184C2×C4⋊C4C5×D411yescharacteristic
185C2×C4⋊C4C5×D411yescharacteristic
186C2×C4⋊C4C23×C511yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C42—21no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95C2×C4×C511yescharacteristic
200#95C2×C4×C511yescharacteristic
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—
225C24C5×C22⋊C411yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
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×C4C5×C22⋊C411yescharacteristic
242C22×C4C5×C22⋊C411yescharacteristic
243C22×C4C5×C22⋊C411yescharacteristic
244C22×C4C22×C4×C511yescharacteristic
245C22×C4C2×C5×D411yescharacteristic
246C22×C4C2×C5×D411yescharacteristic
247M16—24no—
248M16—44no—
249M16—42no—
250M16—82no—
251C2×C8—44no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
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—
278C23C5×#9911yescharacteristic
279C23C5×#9911yescharacteristic
280C23C2×C5×C22⋊C411yescharacteristic
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×C4C5×#10412yes—
313C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
314C2×C4C5×#13711yescharacteristic
315C8—44no—
316C8—82no—
317C5#1176411yescharacteristic, direct product factor, Sylow
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22C5×#35212yes—
328C22C2×C5×#9911yescharacteristic
329C22C5×#41711yescharacteristic
330C22C2×C5×#10411yescharacteristic
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—
346C2C5×#150411yescharacteristic
347C2C2×C5×#35211yescharacteristic
348C2C5×#213311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C4⋊C4C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1353C2semidirect
5. C5×#1346C2semidirect
23. #11764C5direct (N × H)
62. #1353C2×C5semidirect
63. #1346C2×C5semidirect
317. C5#11764direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24842
C2×C5×#3432
C5×#14632
C5×#13532
C5×#13462
#117645