Finite Group Databasebeta

← C5×#10160 #11932880

Subgroups — C5×#10160 #11932880

Order 1280.

578 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3205C211yesmaximal, characteristic
2C5×#3141C211yesmaximal, characteristic, complemented
3C2×C5×#486C211yesmaximal, characteristic, complemented
4C5×#1965C211yesmaximal, characteristic, complemented
5C5×#1548C211yesmaximal, characteristic, complemented
6C5×#1492C211yesmaximal, characteristic, complemented
7C5×#1278C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×C5×#127C2211yescharacteristic
11C5×#493—21no—
12C5×#489—22no—
13C5×#487—21no—
14C5×#486—22no—
15C5×#486—22no—
16C5×#486—21no—
17C5×#486—21no—
18C5×#459—22no—
19C5×#447—22no—
20C5×#431C2211yescharacteristic
21C5×#423C2211yescharacteristic
22C5×#417—22no—
23C2×C5×#102—22no—
24C2×C5×#100—22no—
25C4×C5×M16C2211yescharacteristic
26C2×C4×C5×C8C2211yescharacteristic
27C5×#333—22no—
28C5×D4⋊C8—22no—
29#10160C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×Q8—21no—
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4D412yes—
35C2×C5×D8—24no—
36C2×C5×M16—21no—
37C2×C5×M16D412yes—
38C22×C5×C8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8D411yescharacteristic
43C5×C4⋊Q8D412yes—
44C5×#127—21no—
45C5×#127—21no—
46C5×#127—21no—
47C5×#127—21no—
48C5×#127D411yescharacteristic
49C5×#124—21no—
50C5×#121—21no—
51C5×#121—21no—
52C4×C5×D4—21no—
53C4×C5×D4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C42×C5C2311yescharacteristic
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8D412yes—
60C5×#103—24no—
61C5×#102—28no—
62C5×#102—24no—
63C5×#102—24no—
64C5×#100—44no—
65C5×C22⋊C8—21no—
66C5×#97—21no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69C4×C5×C8—21no—
70C4×C5×C8D412yes—
71#3205C2×C511yescharacteristic
72#3141C2×C511yescharacteristic, complemented
73C2×#486C2×C511yescharacteristic, complemented
74#1965C2×C511yescharacteristic, complemented
75#1548C2×C511yescharacteristic, complemented
76#1492C2×C511yescharacteristic, complemented
77#1278C2×C511yescharacteristic, complemented
78C24×C5—22no—
79C5×#41—42no—
80C5×#41—42no—
81C2×C5×Q8—21no—
82C2×C5×Q8—22no—
83C2×C5×Q8—41no—
84C2×C5×Q8—82no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—22no—
88C2×C5×D4—22no—
89C2×C5×D4—21no—
90C2×C5×D4—44no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—42no—
97C2×C5×D4—42no—
98C2×C5×D4—82no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5#4111yescharacteristic
104C5×D8—84no—
105C5×M16—22no—
106C5×M16—22no—
107C5×M16—42no—
108C2×C5×C8—22no—
109C2×C5×C8—22no—
110C2×C5×C8—22no—
111C2×C5×C8—42no—
112C2×C5×C8—41no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C22⋊C4—41no—
120C5×C22⋊C4—41no—
121C42×C5C2×D411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5C2×D411yescharacteristic
124C42×C5C2×D411yescharacteristic
125#532C22×C511yescharacteristic
126C2×C4⋊Q8C22×C511yescharacteristic
127C2×#127C22×C511yescharacteristic
128#493—21no—
129#489—22no—
130#487—21no—
131#486—22no—
132#486—21no—
133#486—21no—
134#486—22no—
135#459—22no—
136#447—22no—
137#431C22×C511yescharacteristic
138#423C22×C511yescharacteristic
139#417—22no—
140C2×#102—22no—
141C2×#100—22no—
142C4×M16C22×C511yescharacteristic
143C2×C4×C8C22×C511yescharacteristic
144#333—22no—
145D4⋊C8—22no—
146C23×C5—41no—
147C23×C5—42no—
148C23×C5—44no—
149C23×C5—82no—
150C23×C5—82no—
151C23×C5#12111yescharacteristic
152C5×Q8—42no—
153C5×Q8—82no—
154C5×Q8—82no—
155C5×D4—44no—
156C5×D4—42no—
157C5×D4—42no—
158C5×D4—44no—
159C5×D4—42no—
160C5×D4—82no—
161C5×D4—82no—
162C5×D4—82no—
163C5×D4—82no—
164C5×D4—81no—
165C5×D4—81no—
166C2×C4×C5—22no—
167C2×C4×C5—22no—
168C2×C4×C5—41no—
169C2×C4×C5—42no—
170C2×C4×C5—82no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5#12011yescharacteristic
174C2×C4×C5#12011yescharacteristic
175C2×C4×C5#12011yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12711yescharacteristic
179C2×C4×C5#13512yes—
180C2×C4×C5AGL(1,ℤ/8)12yes—
181C5×C8—42no—
182C5×C8—42no—
183C5×C8—42no—
184C5×C8—81no—
185C2×#41—21no—
186C22×Q8—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4C5×D412yes—
190C2×D8—24no—
191C2×M16—21no—
192C2×M16C5×D412yes—
193C22×C8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C5×D412yes—
198C4⋊Q8C5×D411yescharacteristic
199#127—21no—
200#127—21no—
201#127—21no—
202#127—21no—
203#127C5×D411yescharacteristic
204#124—21no—
205#121—21no—
206#121—21no—
207C4×D4—21no—
208C4×D4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C42C23×C511yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8C5×D412yes—
215#103—24no—
216#102—28no—
217#102—24no—
218#102—24no—
219#100—44no—
220C22⋊C8—21no—
221#97—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8C5×D412yes—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—82no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5—82no—
232C22×C5—81no—
233C22×C5—82no—
234C22×C5—164no—
235C22×C5#39211yescharacteristic
236C22×C5#46312yes—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—81no—
240C4×C5—82no—
241C4×C5#44912yes—
242C4×C5#45512yes—
243C4×C5#47212yes—
244C4×C5#49511yescharacteristic
245C4×C5#49611yescharacteristic
246C24—22no—
247#41—42no—
248#41—42no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×D4—21no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—44no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—82no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4C2×C5×D411yescharacteristic
270C22×C4C2×C5×D411yescharacteristic
271C22×C4C5×#4111yescharacteristic
272D8—84no—
273M16—22no—
274M16—22no—
275M16—42no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—42no—
280C2×C8—41no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42C2×C5×D411yescharacteristic
290C42C2×C5×D411yescharacteristic
291C42C2×C5×D411yescharacteristic
292C42C2×C5×D411yescharacteristic
293C2×C5—22no—
294C2×C5—161no—
295C2×C5—162no—
296C2×C5#200411yescharacteristic
297C2×C5#201211yescharacteristic
298C2×C5#201811yescharacteristic
299C23—41no—
300C23—42no—
301C23—44no—
302C23—82no—
303C23—82no—
304C23C5×#12111yescharacteristic
305Q8—42no—
306Q8—82no—
307Q8—82no—
308D4—44no—
309D4—42no—
310D4—42no—
311D4—44no—
312D4—42no—
313D4—82no—
314D4—82no—
315D4—82no—
316D4—82no—
317D4—81no—
318D4—81no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4C5×#12011yescharacteristic
327C2×C4C5×#12011yescharacteristic
328C2×C4C5×#12011yescharacteristic
329C2×C4C5×#12111yescharacteristic
330C2×C4C5×#12111yescharacteristic
331C2×C4C5×#12711yescharacteristic
332C2×C4C5×#13512yes—
333C2×C4C5×AGL(1,ℤ/8)12yes—
334C8—42no—
335C8—42no—
336C8—42no—
337C8—81no—
338C5#1016011yescharacteristic, direct product factor, Sylow
339C22—21no—
340C22—21no—
341C22—81no—
342C22—82no—
343C22—81no—
344C22—82no—
345C22—82no—
346C22—81no—
347C22—164no—
348C22C5×#39211yescharacteristic
349C22C5×#46312yes—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—82no—
354C4C5×#44912yes—
355C4C5×#45512yes—
356C4C5×#47212yes—
357C4C5×#49511yescharacteristic
358C4C5×#49611yescharacteristic
359C2—22no—
360C2—162no—
361C2—161no—
362C2C5×#200411yescharacteristic
363C2C5×#201211yescharacteristic
364C2C5×#201811yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3205C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3141C2semidirect
3. C2×C5×#486C2semidirect
4. C5×#1965C2semidirect
5. C5×#1548C2semidirect
6. C5×#1492C2semidirect
7. C5×#1278C2semidirect
29. #10160C5direct (N × H)
72. #3141C2×C5semidirect
73. C2×#486C2×C5semidirect
74. #1965C2×C5semidirect
75. #1548C2×C5semidirect
76. #1492C2×C5semidirect
77. #1278C2×C5semidirect
338. C5#10160direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32052
C5×#31412
C2×C5×#4862
C5×#19652
C5×#15482
C5×#14922
C5×#12782
#101605