Finite Group Databasebeta

← C5×#9473 #11932193

Subgroups — C5×#9473 #11932193

Order 1280.

556 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2973C211yesmaximal, characteristic
2C5×#2487C211yesmaximal, characteristic
3C5×#1824C212yesmaximal, complemented
4C5×#1799C211yesmaximal, characteristic
5C5×#1289C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C5×#435—24no—
9C5×#432—21no—
10C2×C5×#99—21no—
11C5×#407—21no—
12C2×C5×C22⋊C8C2212yes—
13C5×#400C412yescomplemented
14C5×#399C412yescomplemented
15C5×#389—21no—
16C5×#386—21no—
17C5×#385—21no—
18C5×#380—21no—
19C5×#380C2212yes—
20C5×#380C2211yescharacteristic
21C5×#342—21no—
22C5×#340—24no—
23#9473C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5—21no—
26C23×C4×C5D411yescharacteristic
27C23×C4×C5C2311yescharacteristic
28C2×C5×M16—22no—
29C22×C5×C8D414yes—
30C4×C5×D4—22no—
31C4×C5×D4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—22no—
37C2×C5×C4⋊C4—22no—
38C2×C5×C4⋊C4C2×C412yes—
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—22no—
42C2×C5×C22⋊C4—22no—
43C2×C5×C22⋊C4C2×C411yescharacteristic
44C2×C5×C22⋊C4D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C5×C4⋊C8—22no—
47C5×#99—42no—
48C5×C22⋊C8—22no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8—22no—
51C5×#97—22no—
52C5×#95—22no—
53C5×#95—22no—
54C5×#95—22no—
55C5×#95C2×C412yes—
56#2973C2×C511yescharacteristic
57#2487C2×C511yescharacteristic
58#1824C2×C512yescomplemented
59#1799C2×C511yescharacteristic
60#1289C2×C512yescomplemented
61C24×C5C22⋊C411yescharacteristic
62C24×C5C2×D411yescharacteristic
63C2×C5×D4—22no—
64C2×C5×D4—21no—
65C2×C5×D4—21no—
66C2×C5×D4—22no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5—82no—
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D412yes—
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5#4112yes—
83C5×M16—82no—
84C2×C5×C8—24no—
85C2×C5×C8—44no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—24no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—44no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—82no—
93C5×C22⋊C4—22no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C5×C22⋊C4—82no—
100C42×C5—21no—
101C42×C5—21no—
102C2×C4×D4C22×C511yescharacteristic
103C22×C4⋊C4C22×C511yescharacteristic
104#435—24no—
105#432—21no—
106C2×#99—21no—
107#407—21no—
108C2×C22⋊C8C22×C512yes—
109#400C4×C512yescomplemented
110#399C4×C512yescomplemented
111#389—21no—
112#386—21no—
113#385—21no—
114#380—21no—
115#380C22×C512yes—
116#380C22×C511yescharacteristic
117#342—21no—
118#340—24no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5—41no—
126C23×C5C2×C22⋊C411yescharacteristic
127C23×C5#12112yes—
128C23×C5AGL(1,ℤ/8)11yescharacteristic
129C23×C5#13711yescharacteristic
130C23×C5#13712yes—
131C5×D4—42no—
132C5×D4—42no—
133C2×C4×C5—24no—
134C2×C4×C5—22no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—41no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—81no—
152C2×C4×C5—84no—
153C2×C4×C5—82no—
154C2×C4×C5—82no—
155C2×C4×C5—82no—
156C2×C4×C5C4×D412yes—
157C2×C4×C5#12011yescharacteristic
158C2×C4×C5#12311yescharacteristic
159C5×C8—44no—
160C22×D4C5×D411yescharacteristic
161C23×C4—21no—
162C23×C4C5×D411yescharacteristic
163C23×C4C23×C511yescharacteristic
164C2×M16—22no—
165C22×C8C5×D414yes—
166C4×D4—22no—
167C4×D4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4C2×C4×C512yes—
175C2×C4⋊C4C2×C4×C511yescharacteristic
176C2×C22⋊C4—21no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4C2×C4×C511yescharacteristic
180C2×C22⋊C4C5×D411yescharacteristic
181C2×C42C5×D411yescharacteristic
182C4⋊C8—22no—
183#99—42no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#97—22no—
188#95—22no—
189#95—22no—
190#95—22no—
191#95C2×C4×C512yes—
192C22×C5—21no—
193C22×C5—22no—
194C22×C5—21no—
195C22×C5—22no—
196C22×C5—41no—
197C22×C5—41no—
198C22×C5—42no—
199C22×C5—42no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5—81no—
204C22×C5#38611yescharacteristic
205C22×C5#41711yescharacteristic
206C22×C5#41911yescharacteristic
207C22×C5#46812yes—
208C22×C5#47012yes—
209C4×C5—21no—
210C4×C5—22no—
211C4×C5—41no—
212C4×C5—41no—
213C4×C5—41no—
214C4×C5—82no—
215C4×C5—82no—
216C4×C5—162no—
217C4×C5#45812yes—
218C24C5×C22⋊C411yescharacteristic
219C24C2×C5×D411yescharacteristic
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—82no—
233C22×C4C5×C22⋊C411yescharacteristic
234C22×C4C5×C22⋊C411yescharacteristic
235C22×C4C5×C22⋊C411yescharacteristic
236C22×C4C22×C4×C511yescharacteristic
237C22×C4C2×C5×D412yes—
238C22×C4C2×C5×D411yescharacteristic
239C22×C4C5×#4112yes—
240M16—82no—
241C2×C8—24no—
242C2×C8—44no—
243C4⋊C4—22no—
244C4⋊C4—24no—
245C4⋊C4—42no—
246C4⋊C4—44no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—82no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—82no—
257C42—21no—
258C42—21no—
259C2×C5—21no—
260C2×C5—22no—
261C2×C5—21no—
262C2×C5—22no—
263C2×C5—81no—
264C2×C5#189011yescharacteristic
265C2×C5#189411yescharacteristic
266C2×C5#191011yescharacteristic
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C5×C22⋊C411yescharacteristic
275C23C5×#12112yes—
276C23C5×AGL(1,ℤ/8)11yescharacteristic
277C23C5×#13711yescharacteristic
278C23C5×#13712yes—
279D4—42no—
280D4—42no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—84no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4C4×C5×D412yes—
305C2×C4C5×#12011yescharacteristic
306C2×C4C5×#12311yescharacteristic
307C8—44no—
308C5#947311yescharacteristic, direct product factor, Sylow
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C5×#38611yescharacteristic
322C22C5×#41711yescharacteristic
323C22C5×#41911yescharacteristic
324C22C5×#46812yes—
325C22C5×#47012yes—
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—82no—
332C4—82no—
333C4—162no—
334C4C5×#45812yes—
335C2—21no—
336C2—22no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2C5×#189011yescharacteristic
341C2C5×#189411yescharacteristic
342C2C5×#191011yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1824C2semidirect
5. C5×#1289C2semidirect
13. C5×#400C4semidirect
14. C5×#399C4semidirect
23. #9473C5direct (N × H)
58. #1824C2×C5semidirect
60. #1289C2×C5semidirect
109. #400C4×C5semidirect
110. #399C4×C5semidirect
308. C5#9473direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29732
C5×#24872
C5×#18242
C5×#17992
C5×#12892
#94735