Finite Group Databasebeta

← C5×#7642 #11930362

Subgroups — C5×#7642 #11930362

Order 1280.

478 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×#1839C211yesmaximal, characteristic, complemented
3C5×#1831C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C4×C5×D4C411yescharacteristic
7C2×C5×#117—21no—
8C2×C5×C4⋊C8—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#7642C511yesmaximal, 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—42no—
31C5×#117—42no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C42×C5—21no—
43C2×C42×C5C2×C411yescharacteristic
44C2×C42×C5C2×C411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5D411yescharacteristic
49C2×C42×C5C2311yescharacteristic
50C5×C4⋊C8—42no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54#2293C2×C511yescharacteristic
55#1839C2×C511yescharacteristic, complemented
56#1831C2×C511yescharacteristic, complemented
57#1271C2×C512yescomplemented
58#1270C2×C512yes—
59C24×C5—21no—
60C2×C5×D4—21no—
61C2×C5×D4—41no—
62C2×C5×D4—41no—
63C2×C5×D4M1612yes—
64C22×C4×C5—24no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22×C411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C2×C5×C8—42no—
78C2×C5×C8—42no—
79C2×C5×C8—42no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C2×C5×C8—42no—
83C5×C4⋊C4—21no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4M1612yes—
90C5×C22⋊C4—24no—
91C5×C22⋊C4—42no—
92C5×C22⋊C4—42no—
93C5×C22⋊C4—41no—
94C5×C22⋊C4—41no—
95C5×C22⋊C4—42no—
96C42×C5—21no—
97C42×C5—21no—
98C42×C5—22no—
99C42×C5—41no—
100C42×C5—41no—
101C42×C5—41no—
102C42×C5—41no—
103C42×C5—42no—
104C42×C5D812yes—
105C42×C5SD1612yes—
106C2×C4×D4C4×C511yescharacteristic
107C2×#117—21no—
108C2×C4⋊C8—21no—
109#390C4×C511yescharacteristic
110#390C22×C511yescharacteristic
111#389C4×C511yescharacteristic
112#389C22×C511yescharacteristic
113#388—21no—
114#388—21no—
115C4×C4⋊C4C4×C511yescharacteristic
116C4×C22⋊C4—21no—
117C43C22×C511yescharacteristic
118#336—21no—
119#336—21no—
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#10212yes—
160C2×C4×C5#10212yes—
161C2×C4×C5C2×M1611yescharacteristic
162C2×C4×C5C2×M1611yescharacteristic
163C2×C4×C5C2×D811yescharacteristic
164C2×C4×C5C2×SD1611yescharacteristic
165C2×C4×C5#13512yes—
166C5×C8—82no—
167C5×C8—82no—
168C22×D4C2×C4×C511yescharacteristic
169C23×C4—21no—
170C22×C8—22no—
171C22×C8—22no—
172C4×D4—22no—
173C4×D4—22no—
174#117—42no—
175#117—42no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×C4×C511yescharacteristic
179C2×C4⋊C4C2×C4×C511yescharacteristic
180C2×C4⋊C4C2×C4×C511yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C42—21no—
187C2×C42C2×C4×C511yescharacteristic
188C2×C42C2×C4×C511yescharacteristic
189C2×C42C5×D411yescharacteristic
190C2×C42C5×D411yescharacteristic
191C2×C42C5×D411yescharacteristic
192C2×C42C5×D411yescharacteristic
193C2×C42C23×C511yescharacteristic
194C4⋊C8—42no—
195#95—21no—
196#95—21no—
197#95—21no—
198C22×C5—42no—
199C22×C5—42no—
200C22×C5—42no—
201C22×C5—81no—
202C22×C5—81no—
203C22×C5—81no—
204C22×C5—81no—
205C22×C5#40711yescharacteristic
206C22×C5#41011yescharacteristic
207C22×C5#41311yescharacteristic
208C22×C5C2×#10211yescharacteristic
209C22×C5#41611yescharacteristic
210C22×C5#42111yescharacteristic
211C22×C5#42111yescharacteristic
212C4×C5—22no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—22no—
216C4×C5—21no—
217C4×C5—21no—
218C4×C5—22no—
219C4×C5—42no—
220C4×C5—41no—
221C4×C5—41no—
222C4×C5—81no—
223C4×C5—81no—
224C24—21no—
225C2×D4—21no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4C5×M1612yes—
229C22×C4—24no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C5×C22⋊C411yescharacteristic
236C22×C4C5×C22⋊C411yescharacteristic
237C22×C4C5×C22⋊C411yescharacteristic
238C22×C4C5×C22⋊C411yescharacteristic
239C22×C4C22×C4×C511yescharacteristic
240C22×C4C2×C5×D411yescharacteristic
241C22×C4C2×C5×D411yescharacteristic
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4C5×M1612yes—
255C22⋊C4—24no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—21no—
262C42—21no—
263C42—22no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—42no—
269C42C5×D812yes—
270C42C5×SD1612yes—
271C2×C5—82no—
272C2×C5#146411yescharacteristic
273C2×C5#148611yescharacteristic
274C2×C5#148811yescharacteristic
275C2×C5#151711yescharacteristic
276C2×C5#152111yescharacteristic
277C2×C5#153511yescharacteristic
278C2×C5#154011yescharacteristic
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×#10212yes—
316C2×C4C5×#10212yes—
317C2×C4C2×C5×M1611yescharacteristic
318C2×C4C2×C5×M1611yescharacteristic
319C2×C4C2×C5×D811yescharacteristic
320C2×C4C2×C5×SD1611yescharacteristic
321C2×C4C5×#13512yes—
322C8—82no—
323C8—82no—
324C5#764211yescharacteristic, direct product factor, Sylow
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22C5×#40711yescharacteristic
333C22C5×#41011yescharacteristic
334C22C5×#41311yescharacteristic
335C22C2×C5×#10211yescharacteristic
336C22C5×#41611yescharacteristic
337C22C5×#42111yescharacteristic
338C22C5×#42111yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—81no—
351C2—82no—
352C2C5×#146411yescharacteristic
353C2C5×#148611yescharacteristic
354C2C5×#148811yescharacteristic
355C2C5×#151711yescharacteristic
356C2C5×#152111yescharacteristic
357C2C5×#153511yescharacteristic
358C2C5×#154011yescharacteristic
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×#1831C2semidirect
4. C5×#1271C2semidirect
23. #7642C5direct (N × H)
55. #1839C2×C5semidirect
56. #1831C2×C5semidirect
57. #1271C2×C5semidirect
324. C5#7642direct (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×#18312
C5×#12712
C5×#12702
#76425