Finite Group Databasebeta

← C5×#7608 #11930328

Subgroups — C5×#7608 #11930328

Order 1280.

484 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2293C211yesmaximal, characteristic
2C5×#1839C211yesmaximal, characteristic, complemented
3C5×#1745C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C4×C5×D4C411yescharacteristic
7C2×C5×#117—21no—
8C2×C5×#97—21no—
9C5×#390C411yescharacteristic
10C5×#390C2211yescharacteristic
11C5×#389C411yescharacteristic
12C5×#389C2211yescharacteristic
13C5×#388—21no—
14C5×#388—21no—
15C4×C5×C4⋊C4C411yescharacteristic
16C4×C5×C22⋊C4—21no—
17C43×C5C2211yescharacteristic
18C5×#336—21no—
19C5×#336—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7608C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5—21no—
26C22×C5×C8—22no—
27C22×C5×C8—22no—
28C4×C5×D4—22no—
29C4×C5×D4—22no—
30C5×#117—44no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C42×C5—21no—
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5C2×C411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5C2311yescharacteristic
49C5×#97—24no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53#2293C2×C511yescharacteristic
54#1839C2×C511yescharacteristic, complemented
55#1745C2×C511yescharacteristic, complemented
56#1271C2×C512yescomplemented
57#1270C2×C512yes—
58C24×C5—21no—
59C2×C5×D4—21no—
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C2×C5×D4M1612yes—
63C22×C4×C5—24no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C2×C5×C8—24no—
77C2×C5×C8—42no—
78C2×C5×C8—42no—
79C2×C5×C8—42no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—42no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4M1612yes—
88C5×C22⋊C4—24no—
89C5×C22⋊C4—42no—
90C5×C22⋊C4—42no—
91C5×C22⋊C4—42no—
92C5×C22⋊C4—42no—
93C42×C5—22no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—22no—
97C42×C5—22no—
98C42×C5—41no—
99C42×C5—41no—
100C42×C5—41no—
101C42×C5—42no—
102C2×C4×D4C4×C511yescharacteristic
103C2×#117—21no—
104C2×#97—21no—
105#390C4×C511yescharacteristic
106#390C22×C511yescharacteristic
107#389C4×C511yescharacteristic
108#389C22×C511yescharacteristic
109#388—21no—
110#388—21no—
111C4×C4⋊C4C4×C511yescharacteristic
112C4×C22⋊C4—21no—
113C43C22×C511yescharacteristic
114#336—21no—
115#336—21no—
116#336—21no—
117#336C22×C512yes—
118#336C22×C512yes—
119C23×C5—22no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5—41no—
126C23×C5C2×C22⋊C411yescharacteristic
127C5×D4—42no—
128C5×D4—42no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—22no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—48no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5#10412yes—
157C2×C4×C5C2×M1611yescharacteristic
158C2×C4×C5C2×M1611yescharacteristic
159C2×C4×C5#13512yes—
160C2×C4×C5AGL(1,ℤ/8)12yes—
161C5×C8—44no—
162C5×C8—82no—
163C22×D4C2×C4×C511yescharacteristic
164C23×C4—21no—
165C22×C8—22no—
166C22×C8—22no—
167C4×D4—22no—
168C4×D4—22no—
169#117—44no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C2×C4×C511yescharacteristic
173C2×C4⋊C4C2×C4×C511yescharacteristic
174C2×C4⋊C4C2×C4×C511yescharacteristic
175C2×C22⋊C4—21no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—21no—
180C2×C42—21no—
181C2×C42C2×C4×C511yescharacteristic
182C2×C42C2×C4×C511yescharacteristic
183C2×C42C5×D411yescharacteristic
184C2×C42C5×D411yescharacteristic
185C2×C42C5×D411yescharacteristic
186C2×C42C5×D411yescharacteristic
187C2×C42C23×C511yescharacteristic
188#97—24no—
189#95—21no—
190#95—21no—
191#95—21no—
192C22×C5—42no—
193C22×C5—42no—
194C22×C5—42no—
195C22×C5—81no—
196C22×C5—81no—
197C22×C5—81no—
198C22×C5—81no—
199C22×C5#40711yescharacteristic
200C22×C5#41011yescharacteristic
201C22×C5#41311yescharacteristic
202C22×C5#41611yescharacteristic
203C22×C5#41811yescharacteristic
204C22×C5C2×#10411yescharacteristic
205C22×C5#42111yescharacteristic
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—22no—
209C4×C5—22no—
210C4×C5—22no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—42no—
214C4×C5—41no—
215C4×C5—81no—
216C4×C5—81no—
217C24—21no—
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4C5×M1612yes—
222C22×C4—24no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4C5×C22⋊C411yescharacteristic
229C22×C4C5×C22⋊C411yescharacteristic
230C22×C4C5×C22⋊C411yescharacteristic
231C22×C4C5×C22⋊C411yescharacteristic
232C22×C4C22×C4×C511yescharacteristic
233C22×C4C2×C5×D411yescharacteristic
234C22×C4C2×C5×D411yescharacteristic
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4C5×M1612yes—
247C22⋊C4—24no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—21no—
253C42—21no—
254C42—22no—
255C42—22no—
256C42—22no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—42no—
261C2×C5—82no—
262C2×C5#146411yescharacteristic
263C2×C5#148811yescharacteristic
264C2×C5#149011yescharacteristic
265C2×C5#150011yescharacteristic
266C2×C5#151411yescharacteristic
267C2×C5#152911yescharacteristic
268C2×C5#155311yescharacteristic
269C23—22no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23C2×C5×C22⋊C411yescharacteristic
277D4—42no—
278D4—42no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—48no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4C5×#10412yes—
307C2×C4C2×C5×M1611yescharacteristic
308C2×C4C2×C5×M1611yescharacteristic
309C2×C4C5×#13512yes—
310C2×C4C5×AGL(1,ℤ/8)12yes—
311C8—44no—
312C8—82no—
313C5#760811yescharacteristic, direct product factor, Sylow
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C5×#40711yescharacteristic
322C22C5×#41011yescharacteristic
323C22C5×#41311yescharacteristic
324C22C5×#41611yescharacteristic
325C22C5×#41811yescharacteristic
326C22C2×C5×#10411yescharacteristic
327C22C5×#42111yescharacteristic
328C4—22no—
329C4—22no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—42no—
337C4—81no—
338C4—81no—
339C2—82no—
340C2C5×#146411yescharacteristic
341C2C5×#148811yescharacteristic
342C2C5×#149011yescharacteristic
343C2C5×#150011yescharacteristic
344C2C5×#151411yescharacteristic
345C2C5×#152911yescharacteristic
346C2C5×#155311yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1839C2semidirect
3. C5×#1745C2semidirect
4. C5×#1271C2semidirect
23. #7608C5direct (N × H)
54. #1839C2×C5semidirect
55. #1745C2×C5semidirect
56. #1271C2×C5semidirect
313. C5#7608direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22932
C5×#18392
C5×#17452
C5×#12712
C5×#12702
#76085