Finite Group Databasebeta

← C5×#7716 #11930436

Subgroups — C5×#7716 #11930436

Order 1280.

414 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2861C211yesmaximal, characteristic
2C5×#1839C211yesmaximal, characteristic, complemented
3C5×#1831C211yesmaximal, characteristic, complemented
4C5×#1272C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C5×#125C411yescharacteristic
7C2×C5×#124C411yescharacteristic
8C2×C5×C4⋊C8—21no—
9C5×#391C411yescharacteristic
10C5×#391C2211yescharacteristic
11C5×#390C411yescharacteristic
12C5×#390C2211yescharacteristic
13C5×#388—21no—
14C5×#388—21no—
15C5×#388—21no—
16C5×#388—21no—
17C43×C5C2211yescharacteristic
18C5×#336—21no—
19C5×#336—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7716C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×C5×D4C2×C411yescharacteristic
26C22×C5×C8—22no—
27C22×C5×C8—22no—
28C5×#125—42no—
29C5×#124—42no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—21no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C42×C5C2×C411yescharacteristic
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5C2311yescharacteristic
47C5×C4⋊C8—42no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52#2861C2×C511yescharacteristic
53#1839C2×C511yescharacteristic, complemented
54#1831C2×C511yescharacteristic, complemented
55#1272C2×C512yescomplemented
56#1270C2×C512yes—
57C24×C5—21no—
58C2×C5×Q8—22no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×D4—22no—
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C2×C5×C8—42no—
75C2×C5×C8—42no—
76C2×C5×C8—42no—
77C2×C5×C8—42no—
78C2×C5×C8—42no—
79C2×C5×C8—42no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4—42no—
84C5×C22⋊C4—42no—
85C5×C22⋊C4—42no—
86C5×C22⋊C4—42no—
87C5×C22⋊C4—42no—
88C5×C22⋊C4—42no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—41no—
91C42×C5—22no—
92C42×C5—22no—
93C42×C5—22no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—41no—
97C42×C5—41no—
98C42×C5—41no—
99C2×#125C4×C511yescharacteristic
100C2×#124C4×C511yescharacteristic
101C2×C4⋊C8—21no—
102#391C4×C511yescharacteristic
103#391C22×C511yescharacteristic
104#390C4×C511yescharacteristic
105#390C22×C511yescharacteristic
106#388—21no—
107#388—21no—
108#388—21no—
109#388—21no—
110C43C22×C511yescharacteristic
111#336—21no—
112#336—21no—
113#336—21no—
114#336C22×C512yes—
115#336C22×C512yes—
116C23×C5—41no—
117C23×C5—41no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5C2×C22⋊C411yescharacteristic
124C5×Q8—82no—
125C5×D4—82no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
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—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
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#10012yes—
153C2×C4×C5#13112yes—
154C2×C4×C5#13512yes—
155C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C5#13711yescharacteristic
157C5×C8—82no—
158C5×C8—82no—
159C22×Q8C2×C4×C511yescharacteristic
160C22×D4C2×C4×C511yescharacteristic
161C22×C8—22no—
162C22×C8—22no—
163#125—42no—
164#124—42no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×C4×C511yescharacteristic
168C2×C4⋊C4C2×C4×C511yescharacteristic
169C2×C22⋊C4—21no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175C2×C42C2×C4×C511yescharacteristic
176C2×C42C2×C4×C511yescharacteristic
177C2×C42C5×D411yescharacteristic
178C2×C42C5×D411yescharacteristic
179C2×C42C5×D411yescharacteristic
180C2×C42C5×D411yescharacteristic
181C2×C42C23×C511yescharacteristic
182C4⋊C8—42no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187C22×C5—81no—
188C22×C5—81no—
189C22×C5—81no—
190C22×C5—81no—
191C22×C5—81no—
192C22×C5—81no—
193C22×C5—81no—
194C22×C5#40811yescharacteristic
195C22×C5#41011yescharacteristic
196C22×C5C2×#10011yescharacteristic
197C22×C5#41611yescharacteristic
198C22×C5#41711yescharacteristic
199C22×C5#42111yescharacteristic
200C22×C5#42111yescharacteristic
201C4×C5—22no—
202C4×C5—22no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—22no—
206C4×C5—41no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—81no—
210C4×C5—81no—
211C4×C5—81no—
212C24—21no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×D4—22no—
217C2×D4—41no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C5×C22⋊C411yescharacteristic
223C22×C4C5×C22⋊C411yescharacteristic
224C22×C4C5×C22⋊C411yescharacteristic
225C22×C4C5×C22⋊C411yescharacteristic
226C22×C4C22×C4×C511yescharacteristic
227C22×C4C2×C5×D411yescharacteristic
228C22×C4C2×C5×D411yescharacteristic
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—42no—
246C42—22no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—22no—
251C42—41no—
252C42—41no—
253C42—41no—
254C2×C5—161no—
255C2×C5#146911yescharacteristic
256C2×C5#148211yescharacteristic
257C2×C5#149511yescharacteristic
258C2×C5#151211yescharacteristic
259C2×C5#152111yescharacteristic
260C2×C5#153611yescharacteristic
261C2×C5#155111yescharacteristic
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23C2×C5×C22⋊C411yescharacteristic
270Q8—82no—
271D4—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C5×#10012yes—
299C2×C4C5×#13112yes—
300C2×C4C5×#13512yes—
301C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
302C2×C4C5×#13711yescharacteristic
303C8—82no—
304C8—82no—
305C5#771611yescharacteristic, direct product factor, Sylow
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C5×#40811yescharacteristic
314C22C5×#41011yescharacteristic
315C22C2×C5×#10011yescharacteristic
316C22C5×#41611yescharacteristic
317C22C5×#41711yescharacteristic
318C22C5×#42111yescharacteristic
319C22C5×#42111yescharacteristic
320C4—21no—
321C4—21no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2C5×#146911yescharacteristic
333C2C5×#148211yescharacteristic
334C2C5×#149511yescharacteristic
335C2C5×#151211yescharacteristic
336C2C5×#152111yescharacteristic
337C2C5×#153611yescharacteristic
338C2C5×#155111yescharacteristic
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×#1272C2semidirect
23. #7716C5direct (N × H)
53. #1839C2×C5semidirect
54. #1831C2×C5semidirect
55. #1272C2×C5semidirect
305. C5#7716direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28612
C5×#18392
C5×#18312
C5×#12722
C5×#12702
#77165