Finite Group Databasebeta

← C5×#7628 #11930348

Subgroups — C5×#7628 #11930348

Order 1280.

510 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2293C211yesmaximal, characteristic
2C5×#1767C211yesmaximal, characteristic, complemented
3C5×#1745C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C4×C5×D4C411yescharacteristic
7C2×C5×#117—21no—
8C2×C5×C4⋊C8—21no—
9C2×C5×#97—21no—
10C2×C5×#97—21no—
11C5×#390C411yescharacteristic
12C5×#390C2211yescharacteristic
13C5×#389C411yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#388—21no—
16C5×#388—21no—
17C4×C5×C4⋊C4C411yescharacteristic
18C4×C5×C22⋊C4—21no—
19C43×C5C2211yescharacteristic
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7628C511yesmaximal, 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×C4⋊C8—24no—
50C5×#97—24no—
51C5×#97—42no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55#2293C2×C511yescharacteristic
56#1767C2×C511yescharacteristic, complemented
57#1745C2×C511yescharacteristic, complemented
58#1271C2×C512yescomplemented
59#1270C2×C512yes—
60C24×C5—21no—
61C2×C5×D4—21no—
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C2×C5×D4M1612yes—
65C22×C4×C5—24no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—42no—
70C22×C4×C5—42no—
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C2×C5×C8—24no—
79C2×C5×C8—24no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C2×C5×C8—42no—
83C2×C5×C8—42no—
84C5×C4⋊C4—21no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4M1612yes—
90C5×C22⋊C4—24no—
91C5×C22⋊C4—42no—
92C5×C22⋊C4—42no—
93C5×C22⋊C4—41no—
94C5×C22⋊C4—42no—
95C5×C22⋊C4—41no—
96C42×C5—22no—
97C42×C5—22no—
98C42×C5—21no—
99C42×C5—21no—
100C42×C5—22no—
101C42×C5—21no—
102C42×C5—21no—
103C42×C5—41no—
104C42×C5—41no—
105C42×C5—42no—
106C2×C4×D4C4×C511yescharacteristic
107C2×#117—21no—
108C2×C4⋊C8—21no—
109C2×#97—21no—
110C2×#97—21no—
111#390C4×C511yescharacteristic
112#390C22×C511yescharacteristic
113#389C4×C511yescharacteristic
114#389C22×C511yescharacteristic
115#388—21no—
116#388—21no—
117C4×C4⋊C4C4×C511yescharacteristic
118C4×C22⋊C4—21no—
119C43C22×C511yescharacteristic
120#336—21no—
121#336C22×C512yes—
122#336C22×C512yes—
123C23×C5—22no—
124C23×C5—41no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5C2×C22⋊C411yescharacteristic
131C5×D4—42no—
132C5×D4—42no—
133C2×C4×C5—21no—
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—21no—
143C2×C4×C5—21no—
144C2×C4×C5—22no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—48no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5#10412yes—
160C2×C4×C5#10412yes—
161C2×C4×C5C2×M1611yescharacteristic
162C2×C4×C5C2×M1611yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5AGL(1,ℤ/8)12yes—
165C2×C4×C5#13711yescharacteristic
166C5×C8—44no—
167C5×C8—44no—
168C22×D4C2×C4×C511yescharacteristic
169C23×C4—21no—
170C22×C8—22no—
171C22×C8—22no—
172C4×D4—22no—
173C4×D4—22no—
174#117—44no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C2×C4×C511yescharacteristic
178C2×C4⋊C4C2×C4×C511yescharacteristic
179C2×C4⋊C4C2×C4×C511yescharacteristic
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C42—21no—
186C2×C42C2×C4×C511yescharacteristic
187C2×C42C2×C4×C511yescharacteristic
188C2×C42C5×D411yescharacteristic
189C2×C42C5×D411yescharacteristic
190C2×C42C5×D411yescharacteristic
191C2×C42C5×D411yescharacteristic
192C2×C42C23×C511yescharacteristic
193C4⋊C8—24no—
194#97—24no—
195#97—42no—
196#95—21no—
197#95—21no—
198#95—21no—
199C22×C5—42no—
200C22×C5—42no—
201C22×C5—42no—
202C22×C5—81no—
203C22×C5—81no—
204C22×C5—81no—
205C22×C5—81no—
206C22×C5#40711yescharacteristic
207C22×C5#41011yescharacteristic
208C22×C5#41311yescharacteristic
209C22×C5#41711yescharacteristic
210C22×C5#41811yescharacteristic
211C22×C5C2×#10411yescharacteristic
212C22×C5C2×#10411yescharacteristic
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—22no—
216C4×C5—22no—
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—22no—
220C4×C5—41no—
221C4×C5—41no—
222C4×C5—42no—
223C4×C5—81no—
224C4×C5—81no—
225C24—21no—
226C2×D4—21no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4C5×M1612yes—
230C22×C4—24no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C5×C22⋊C411yescharacteristic
237C22×C4C5×C22⋊C411yescharacteristic
238C22×C4C5×C22⋊C411yescharacteristic
239C22×C4C5×C22⋊C411yescharacteristic
240C22×C4C22×C4×C511yescharacteristic
241C22×C4C2×C5×D411yescharacteristic
242C22×C4C2×C5×D411yescharacteristic
243C2×C8—24no—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4C5×M1612yes—
255C22⋊C4—24no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—22no—
265C42—21no—
266C42—22no—
267C42—22no—
268C42—41no—
269C42—41no—
270C42—42no—
271C2×C5—82no—
272C2×C5#146411yescharacteristic
273C2×C5#148911yescharacteristic
274C2×C5#149011yescharacteristic
275C2×C5#150511yescharacteristic
276C2×C5#150911yescharacteristic
277C2×C5#152411yescharacteristic
278C2×C5#155711yescharacteristic
279C23—22no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C2×C5×C22⋊C411yescharacteristic
287D4—42no—
288D4—42no—
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—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—48no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4C5×#10412yes—
316C2×C4C5×#10412yes—
317C2×C4C2×C5×M1611yescharacteristic
318C2×C4C2×C5×M1611yescharacteristic
319C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
320C2×C4C5×AGL(1,ℤ/8)12yes—
321C2×C4C5×#13711yescharacteristic
322C8—44no—
323C8—44no—
324C5#762811yescharacteristic, direct product factor, Sylow
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22C5×#40711yescharacteristic
333C22C5×#41011yescharacteristic
334C22C5×#41311yescharacteristic
335C22C5×#41711yescharacteristic
336C22C5×#41811yescharacteristic
337C22C2×C5×#10411yescharacteristic
338C22C2×C5×#10411yescharacteristic
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—42no—
349C4—81no—
350C4—81no—
351C2—82no—
352C2C5×#146411yescharacteristic
353C2C5×#148911yescharacteristic
354C2C5×#149011yescharacteristic
355C2C5×#150511yescharacteristic
356C2C5×#150911yescharacteristic
357C2C5×#152411yescharacteristic
358C2C5×#155711yescharacteristic
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×#1767C2semidirect
3. C5×#1745C2semidirect
4. C5×#1271C2semidirect
23. #7628C5direct (N × H)
56. #1767C2×C5semidirect
57. #1745C2×C5semidirect
58. #1271C2×C5semidirect
324. C5#7628direct (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×#17672
C5×#17452
C5×#12712
C5×#12702
#76285