Finite Group Databasebeta

← C5×#10206 #11932926

Subgroups — C5×#10206 #11932926

Order 1280.

560 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3246C211yesmaximal, characteristic
2C5×#3229C211yesmaximal, characteristic, complemented
3C5×#3152C211yesmaximal, characteristic
4C5×#1988C211yesmaximal, characteristic, complemented
5C5×#1986C211yesmaximal, characteristic, complemented
6C5×#1502C211yesmaximal, characteristic
7C5×#1283C211yesmaximal, characteristic, complemented
8C2×C5×#137—22no—
9C5×#533C2211yescharacteristic
10C5×#532C2211yescharacteristic
11C2×C5×C4⋊Q8C2211yescharacteristic
12C5×#498—21no—
13C5×#497—22no—
14C5×#494—21no—
15C5×#492—21no—
16C5×#487—21no—
17C5×#483—22no—
18C5×#476—21no—
19C5×#475—21no—
20C5×#475—22no—
21C5×#465—22no—
22C5×#461—21no—
23C5×#460—21no—
24C5×#431C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C4×C5×M16C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C5×#340—22no—
29C5×#339—22no—
30C5×#327—22no—
31#10206C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×Q8—21no—
34C5×#137—44no—
35C5×#137—44no—
36C2×C5×Q16—24no—
37C2×C5×SD16—24no—
38C2×C5×SD16—22no—
39C2×C5×M16D412yes—
40C22×C5×C8D412yes—
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8—21no—
43C5×C4⋊Q8—21no—
44C5×C4⋊Q8D411yescharacteristic
45C5×C4⋊Q8D411yescharacteristic
46C5×C4⋊Q8D412yes—
47C5×C4⋊Q8D411yescharacteristic
48C5×#127D411yescharacteristic
49C5×#125—21no—
50C5×#124—21no—
51C5×C22⋊Q8—21no—
52C5×C22⋊Q8—21no—
53C5×#121—21no—
54C5×#121—21no—
55C4×C5×Q8—21no—
56C4×C5×Q8—21no—
57C4×C5×D4—21no—
58C4×C5×D4—21no—
59C5×#117—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4—21no—
63C2×C42×C5—21no—
64C2×C42×C5C2311yescharacteristic
65C5×#106—22no—
66C5×#106—24no—
67C5×C4⋊C8—21no—
68C5×C4⋊C8—21no—
69C5×C4⋊C8—21no—
70C5×#103—22no—
71C5×#103—24no—
72C5×#102—22no—
73C5×C22⋊C8D412yes—
74C5×#97—21no—
75C4×C5×C8—21no—
76C4×C5×C8—21no—
77C5×#95—21no—
78#3246C2×C511yescharacteristic
79#3229C2×C511yescharacteristic, complemented
80#3152C2×C511yescharacteristic
81#1988C2×C511yescharacteristic, complemented
82#1986C2×C511yescharacteristic, complemented
83#1502C2×C511yescharacteristic
84#1283C2×C511yescharacteristic, complemented
85C5×#41—42no—
86C5×#41—42no—
87C2×C5×Q8—21no—
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8—22no—
91C2×C5×Q8—41no—
92C2×C5×Q8—42no—
93C2×C5×Q8—42no—
94C2×C5×D4—21no—
95C2×C5×D4—21no—
96C2×C5×D4—21no—
97C2×C5×D4—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C5×Q16—48no—
105C5×SD16—48no—
106C5×SD16—82no—
107C5×M16—22no—
108C5×M16SD1614yescomplemented
109C2×C5×C8—22no—
110C2×C5×C8—22no—
111C2×C5×C8—22no—
112C2×C5×C8—42no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4—41no—
126C5×C4⋊C4—41no—
127C5×C22⋊C4—41no—
128C5×C22⋊C4—41no—
129C5×C22⋊C4—41no—
130C42×C5—41no—
131C42×C5—42no—
132C42×C5C2×D411yescharacteristic
133C42×C5C2×D411yescharacteristic
134C42×C5C2×D411yescharacteristic
135C42×C5#4111yescharacteristic
136C2×#137—22no—
137#533C22×C511yescharacteristic
138#532C22×C511yescharacteristic
139C2×C4⋊Q8C22×C511yescharacteristic
140#498—21no—
141#497—22no—
142#494—21no—
143#492—21no—
144#487—21no—
145#483—22no—
146#476—21no—
147#475—22no—
148#475—21no—
149#465—22no—
150#461—21no—
151#460—21no—
152#431C22×C511yescharacteristic
153C2×C4⋊C8C22×C511yescharacteristic
154C4×M16C22×C511yescharacteristic
155C4×C4⋊C4C22×C511yescharacteristic
156#340—22no—
157#339—22no—
158#327—22no—
159C23×C5—41no—
160C23×C5#12711yescharacteristic
161C5×Q8—42no—
162C5×Q8—44no—
163C5×Q8—42no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×Q8—82no—
167C5×D4—42no—
168C5×D4—41no—
169C5×D4—41no—
170C5×D4—81no—
171C5×D4—81no—
172C5×D4—81no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—41no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—42no—
181C2×C4×C5—81no—
182C2×C4×C5—81no—
183C2×C4×C5—81no—
184C2×C4×C5—81no—
185C2×C4×C5—82no—
186C2×C4×C5#12011yescharacteristic
187C2×C4×C5#12011yescharacteristic
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12111yescharacteristic
190C2×C4×C5#12111yescharacteristic
191C2×C4×C5#12111yescharacteristic
192C2×C4×C5C2×SD1612yes—
193C2×C4×C5AGL(1,ℤ/8)12yes—
194C5×C8—24no—
195C5×C8—42no—
196C5×C8—42no—
197C2×#41—21no—
198C22×Q8—21no—
199#137—44no—
200#137—44no—
201C2×Q16—24no—
202C2×SD16—24no—
203C2×SD16—22no—
204C2×M16C5×D412yes—
205C22×C8C5×D412yes—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C5×D412yes—
210C4⋊Q8C5×D411yescharacteristic
211C4⋊Q8C5×D411yescharacteristic
212C4⋊Q8C5×D411yescharacteristic
213#127C5×D411yescharacteristic
214#125—21no—
215#124—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218#121—21no—
219#121—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×D4—21no—
223C4×D4—21no—
224#117—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C42—21no—
229C2×C42C23×C511yescharacteristic
230#106—22no—
231#106—24no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—22no—
236#103—24no—
237#102—22no—
238C22⋊C8C5×D412yes—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242#95—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—81no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5#39211yescharacteristic
249C22×C5#49211yescharacteristic
250C22×C5#49611yescharacteristic
251C4×C5—21no—
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—82no—
255C4×C5—81no—
256C4×C5—81no—
257C4×C5—81no—
258C4×C5—82no—
259C4×C5#45012yes—
260C4×C5#45511yescharacteristic
261C4×C5#45611yescharacteristic
262C4×C5#46012yes—
263#41—42no—
264#41—42no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C2×C5×D411yescharacteristic
280C22×C4C2×C5×D411yescharacteristic
281C22×C4C2×C5×D411yescharacteristic
282Q16—48no—
283SD16—48no—
284SD16—82no—
285M16—22no—
286M16C5×SD1614yescomplemented
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—42no—
310C42C2×C5×D411yescharacteristic
311C42C2×C5×D411yescharacteristic
312C42C2×C5×D411yescharacteristic
313C42C5×#4111yescharacteristic
314C2×C5—21no—
315C2×C5—21no—
316C2×C5—161no—
317C2×C5#200711yescharacteristic
318C2×C5#200911yescharacteristic
319C2×C5#201411yescharacteristic
320C23—41no—
321C23C5×#12711yescharacteristic
322Q8—42no—
323Q8—44no—
324Q8—42no—
325Q8—41no—
326Q8—41no—
327Q8—82no—
328D4—42no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4C5×#12011yescharacteristic
348C2×C4C5×#12011yescharacteristic
349C2×C4C5×#12011yescharacteristic
350C2×C4C5×#12111yescharacteristic
351C2×C4C5×#12111yescharacteristic
352C2×C4C5×#12111yescharacteristic
353C2×C4C2×C5×SD1612yes—
354C2×C4C5×AGL(1,ℤ/8)12yes—
355C8—24no—
356C8—42no—
357C8—42no—
358C5#1020611yescharacteristic, direct product factor, Sylow
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C5×#39211yescharacteristic
365C22C5×#49211yescharacteristic
366C22C5×#49611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—82no—
373C4—81no—
374C4—81no—
375C4C5×#45012yes—
376C4C5×#45511yescharacteristic
377C4C5×#45611yescharacteristic
378C4C5×#46012yes—
379C2—21no—
380C2—21no—
381C2—161no—
382C2C5×#200711yescharacteristic
383C2C5×#200911yescharacteristic
384C2C5×#201411yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
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×#3229C2semidirect
4. C5×#1988C2semidirect
5. C5×#1986C2semidirect
7. C5×#1283C2semidirect
31. #10206C5direct (N × H)
79. #3229C2×C5semidirect
81. #1988C2×C5semidirect
82. #1986C2×C5semidirect
84. #1283C2×C5semidirect
108. C5×M16SD16semidirect
286. M16C5×SD16semidirect
358. C5#10206direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32462
C5×#32292
C5×#31522
C5×#19882
C5×#19862
C5×#15022
C5×#12832
#102065