Finite Group Databasebeta

← C5×#10570 #11933290

Subgroups — C5×#10570 #11933290

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2659C211yesmaximal, characteristic
2C5×#1853C212yesmaximal
3C5×#1444C211yesmaximal, characteristic
4C5×#1294C212yesmaximal
5C5×#1280C211yesmaximal, characteristic
6C2×C5×C22⋊Q8—21no—
7C22×C5×C4⋊C4—21no—
8C22×C5×C4⋊C4C2211yescharacteristic
9C2×C5×#106—22no—
10C2×C5×C22⋊C8C2212yes—
11C5×#398—22no—
12C5×#395—22no—
13C5×#380—21no—
14C5×#380C2212yes—
15C2×C5×#95—21no—
16C2×C5×#95C2211yescharacteristic
17C2×C5×#95C2211yescharacteristic
18C5×#340—22no—
19#10570C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×Q8—21no—
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×C5×C8—22no—
27C5×C22⋊Q8—42no—
28C5×C22⋊Q8—42no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—42no—
35C2×C5×C4⋊C4—42no—
36C2×C5×C4⋊C4—42no—
37C2×C5×C4⋊C4—42no—
38C2×C5×C4⋊C4D412yes—
39C2×C5×C4⋊C4D412yes—
40C2×C5×C22⋊C4—22no—
41C5×#106—44no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8Q814yescomplemented
44C5×#95—22no—
45C5×#95—22no—
46C5×#95—22no—
47C5×#95—21no—
48C5×#95—42no—
49C5×#95Q812yescomplemented
50#2659C2×C511yescharacteristic
51#1853C2×C512yes—
52#1444C2×C511yescharacteristic
53#1294C2×C512yes—
54#1280C2×C511yescharacteristic
55C24×C5C2×D411yescharacteristic
56C2×C5×Q8—42no—
57C2×C5×Q8—81no—
58C2×C5×Q8—81no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—22no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5SD1612yes—
86C22×C4×C5SD1612yes—
87C22×C4×C5C2×D412yes—
88C22×C4×C5C2×Q812yes—
89C22×C4×C5C2×Q811yescharacteristic
90C22×C4×C5#4111yescharacteristic
91C2×C5×C8—24no—
92C2×C5×C8—42no—
93C2×C5×C8—42no—
94C5×C4⋊C4—24no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—42no—
97C5×C4⋊C4—42no—
98C5×C4⋊C4—42no—
99C5×C4⋊C4—44no—
100C5×C4⋊C4—48no—
101C5×C4⋊C4—81no—
102C5×C4⋊C4—81no—
103C5×C22⋊C4—42no—
104C5×C22⋊C4—42no—
105C2×C22⋊Q8—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4C22×C511yescharacteristic
108C2×#106—22no—
109C2×C22⋊C8C22×C512yes—
110#398—22no—
111#395—22no—
112#380—21no—
113#380C22×C512yes—
114C2×#95—21no—
115C2×#95C22×C511yescharacteristic
116C2×#95C22×C511yescharacteristic
117#340—22no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5#12011yescharacteristic
123C23×C5C22⋊Q811yescharacteristic
124C23×C5C4⋊Q811yescharacteristic
125C23×C5C2×SD1611yescharacteristic
126C23×C5C2×SD1611yescharacteristic
127C23×C5AGL(1,ℤ/8)11yescharacteristic
128C23×C5#13711yescharacteristic
129C5×Q8—84no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—24no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—42no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—42no—
158C2×C4×C5—42no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5C22⋊Q812yes—
166C2×C4×C5C4⋊Q812yes—
167C5×C8—44no—
168C22×Q8—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4C5×D411yescharacteristic
172C23×C4C5×D411yescharacteristic
173C23×C4C23×C511yescharacteristic
174C22×C8—22no—
175C22⋊Q8—42no—
176C22⋊Q8—42no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4C5×D412yes—
187C2×C4⋊C4C5×D412yes—
188C2×C22⋊C4—22no—
189#106—44no—
190C22⋊C8—22no—
191C22⋊C8C5×Q814yescomplemented
192#95—22no—
193#95—22no—
194#95—22no—
195#95—21no—
196#95—42no—
197#95C5×Q812yescomplemented
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5#39511yescharacteristic
211C22×C5#44811yescharacteristic
212C22×C5#45011yescharacteristic
213C22×C5#45311yescharacteristic
214C22×C5#45611yescharacteristic
215C22×C5B(4,𝔽2)11yescharacteristic
216C22×C5#45811yescharacteristic
217C22×C5#47511yescharacteristic
218C22×C5#47611yescharacteristic
219C22×C5#49811yescharacteristic
220C22×C5#50111yescharacteristic
221C4×C5—22no—
222C4×C5—22no—
223C4×C5—44no—
224C4×C5—42no—
225C4×C5—42no—
226C4×C5—82no—
227C4×C5—82no—
228C4×C5—82no—
229C24C2×C5×D411yescharacteristic
230C2×Q8—42no—
231C2×Q8—81no—
232C2×Q8—81no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C5×SD1612yes—
260C22×C4C5×SD1612yes—
261C22×C4C2×C5×D412yes—
262C22×C4C2×C5×Q812yes—
263C22×C4C2×C5×Q811yescharacteristic
264C22×C4C5×#4111yescharacteristic
265C2×C8—24no—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—24no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—44no—
274C4⋊C4—48no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5#159611yescharacteristic
284C2×C5#160411yescharacteristic
285C2×C5#161111yescharacteristic
286C2×C5#161311yescharacteristic
287C2×C5#205811yescharacteristic
288C2×C5#206011yescharacteristic
289C2×C5#206211yescharacteristic
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C5×#12011yescharacteristic
295C23C5×C22⋊Q811yescharacteristic
296C23C5×C4⋊Q811yescharacteristic
297C23C2×C5×SD1611yescharacteristic
298C23C2×C5×SD1611yescharacteristic
299C23C5×AGL(1,ℤ/8)11yescharacteristic
300C23C5×#13711yescharacteristic
301Q8—84no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C5×C22⋊Q812yes—
338C2×C4C5×C4⋊Q812yes—
339C8—44no—
340C5#1057011yescharacteristic, direct product factor, Sylow
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22C5×#39511yescharacteristic
354C22C5×#44811yescharacteristic
355C22C5×#45011yescharacteristic
356C22C5×#45311yescharacteristic
357C22C5×#45611yescharacteristic
358C22C5×B(4,𝔽2)11yescharacteristic
359C22C5×#45811yescharacteristic
360C22C5×#47511yescharacteristic
361C22C5×#47611yescharacteristic
362C22C5×#49811yescharacteristic
363C22C5×#50111yescharacteristic
364C4—22no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—82no—
370C4—82no—
371C4—82no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C5×#159611yescharacteristic
377C2C5×#160411yescharacteristic
378C2C5×#161111yescharacteristic
379C2C5×#161311yescharacteristic
380C2C5×#205811yescharacteristic
381C2C5×#206011yescharacteristic
382C2C5×#206211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
19. #10570C5direct (N × H)
43. C5×C22⋊C8Q8semidirect
49. C5×#95Q8semidirect
191. C22⋊C8C5×Q8semidirect
197. #95C5×Q8semidirect
340. C5#10570direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26592
C5×#18532
C5×#14442
C5×#12942
C5×#12802
#105705