Finite Group Databasebeta

← C5×#10549 #11933269

Subgroups — C5×#10549 #11933269

Order 1280.

502 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3151C211yesmaximal, characteristic
2C5×#1950C211yesmaximal, characteristic, complemented
3C5×#1547C211yesmaximal, characteristic, complemented
4C5×#1545C211yesmaximal, characteristic, complemented
5C2×C5×#331C211yesmaximal, characteristic, complemented
6C5×#1480C211yesmaximal, characteristic, complemented
7C5×#1283C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C2×C5×AGL(1,ℤ/8)—21no—
10C5×#532C2211yescharacteristic
11C2×C5×#127C2211yescharacteristic
12C5×#496—22no—
13C5×#493—21no—
14C5×#492—21no—
15C5×#431C2211yescharacteristic
16C2×C5×#108—21no—
17C5×#423C2211yescharacteristic
18C2×C5×C4⋊C8C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20C4×C5×M16C2211yescharacteristic
21C5×#341—21no—
22C5×#332—21no—
23C5×#331—22no—
24C5×#331—22no—
25C5×#331—21no—
26C5×D4⋊C8—22no—
27#10549C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C22×C5×D4—21no—
32C5×AGL(1,ℤ/8)—42no—
33C5×AGL(1,ℤ/8)—42no—
34C5×AGL(1,ℤ/8)—42no—
35C5×AGL(1,ℤ/8)—42no—
36C2×C5×SD16—22no—
37C2×C5×SD16—22no—
38C2×C5×D8—22no—
39C2×C5×D8—22no—
40C2×C5×M16—21no—
41C2×C5×M16D411yescharacteristic
42C2×C5×M16D411yescharacteristic
43C22×C5×C8—21no—
44C22×C5×C8—21no—
45C5×C4⋊Q8D411yescharacteristic
46C5×#127—21no—
47C5×#127—21no—
48C5×#127—21no—
49C5×#127D411yescharacteristic
50C5×#127D412yes—
51C5×#124—21no—
52C5×#121—21no—
53C5×#121—21no—
54C4×C5×D4—21no—
55C4×C5×D4—21no—
56C2×C42×C5C2311yescharacteristic
57C5×#108—42no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8D412yes—
65C5×C22⋊C8—21no—
66C5×#97—21no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69#3151C2×C511yescharacteristic
70#1950C2×C511yescharacteristic, complemented
71#1547C2×C511yescharacteristic, complemented
72#1545C2×C511yescharacteristic, complemented
73C2×#331C2×C511yescharacteristic, complemented
74#1480C2×C511yescharacteristic, complemented
75#1283C2×C511yescharacteristic, complemented
76C24×C5—41no—
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C5×#41—41no—
81C2×C5×Q8—21no—
82C2×C5×D4—21no—
83C2×C5×D4—22no—
84C2×C5×D4—21no—
85C2×C5×D4—22no—
86C2×C5×D4—21no—
87C2×C5×D4—22no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—81no—
97C2×C5×D4—81no—
98C2×C5×D4—82no—
99C22×C4×C5—41no—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5#4111yescharacteristic
102C22×C4×C5#4111yescharacteristic
103C5×SD16—44no—
104C5×SD16—44no—
105C5×D8—44no—
106C5×D8—44no—
107C5×M16—21no—
108C5×M16—21no—
109C5×M16—41no—
110C5×M16—41no—
111C5×M16D812yes—
112C5×M16SD1612yes—
113C2×C5×C8—21no—
114C2×C5×C8—21no—
115C2×C5×C8—22no—
116C2×C5×C8—41no—
117C2×C5×C8—41no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8—41no—
121C2×C5×C8—81no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—41no—
126C42×C5C2×D411yescharacteristic
127C42×C5C2×D411yescharacteristic
128C42×C5C2×D411yescharacteristic
129C42×C5#4111yescharacteristic
130C2×AGL(1,ℤ/8)—21no—
131C2×AGL(1,ℤ/8)—21no—
132#532C22×C511yescharacteristic
133C2×#127C22×C511yescharacteristic
134#496—22no—
135#493—21no—
136#492—21no—
137#431C22×C511yescharacteristic
138C2×#108—21no—
139#423C22×C511yescharacteristic
140C2×C4⋊C8C22×C511yescharacteristic
141C2×C4⋊C8C22×C511yescharacteristic
142C4×M16C22×C511yescharacteristic
143#341—21no—
144#332—21no—
145#331—22no—
146#331—21no—
147#331—22no—
148D4⋊C8—22no—
149C23×C5—41no—
150C23×C5—42no—
151C23×C5—82no—
152C23×C5—82no—
153C23×C5—81no—
154C23×C5—81no—
155C23×C5#12411yescharacteristic
156C5×Q8—41no—
157C5×Q8—41no—
158C5×D4—41no—
159C5×D4—42no—
160C5×D4—41no—
161C5×D4—42no—
162C5×D4—41no—
163C5×D4—41no—
164C5×D4—81no—
165C5×D4—82no—
166C5×D4—82no—
167C5×D4—82no—
168C5×D4—81no—
169C5×D4—81no—
170C5×D4—81no—
171C5×D4—81no—
172C5×D4—81no—
173C5×D4—81no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5#12011yescharacteristic
181C2×C4×C5#12111yescharacteristic
182C2×C4×C5#12111yescharacteristic
183C2×C4×C5#12111yescharacteristic
184C2×C4×C5#12311yescharacteristic
185C2×C4×C5#12311yescharacteristic
186C2×C4×C5C2×D811yescharacteristic
187C2×C4×C5C2×SD1611yescharacteristic
188C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
190C5×C8—22no—
191C5×C8—22no—
192C5×C8—42no—
193C5×C8—81no—
194C5×C8—81no—
195C5×C8—81no—
196C2×#41—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200AGL(1,ℤ/8)—42no—
201AGL(1,ℤ/8)—42no—
202AGL(1,ℤ/8)—42no—
203AGL(1,ℤ/8)—42no—
204C2×SD16—22no—
205C2×SD16—22no—
206C2×D8—22no—
207C2×D8—22no—
208C2×M16—21no—
209C2×M16C5×D411yescharacteristic
210C2×M16C5×D411yescharacteristic
211C22×C8—21no—
212C22×C8—21no—
213C4⋊Q8C5×D411yescharacteristic
214#127—21no—
215#127—21no—
216#127—21no—
217#127C5×D412yes—
218#127C5×D411yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C42C23×C511yescharacteristic
225#108—42no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8C5×D412yes—
233C22⋊C8—21no—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—82no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5—82no—
243C22×C5—81no—
244C22×C5—82no—
245C22×C5—162no—
246C22×C5—162no—
247C22×C5#39411yescharacteristic
248C22×C5#48611yescharacteristic
249C22×C5#49011yescharacteristic
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—21no—
253C4×C5—81no—
254C4×C5#44711yescharacteristic
255C4×C5#45011yescharacteristic
256C4×C5#45911yescharacteristic
257C4×C5#46011yescharacteristic
258C4×C5#47111yescharacteristic
259C4×C5#47211yescharacteristic
260C24—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264#41—41no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—81no—
281C2×D4—81no—
282C2×D4—82no—
283C22×C4—41no—
284C22×C4C2×C5×D411yescharacteristic
285C22×C4C5×#4111yescharacteristic
286C22×C4C5×#4111yescharacteristic
287SD16—44no—
288SD16—44no—
289D8—44no—
290D8—44no—
291M16—21no—
292M16—21no—
293M16—41no—
294M16—41no—
295M16C5×D812yes—
296M16C5×SD1612yes—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—81no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42C2×C5×D411yescharacteristic
311C42C2×C5×D411yescharacteristic
312C42C2×C5×D411yescharacteristic
313C42C5×#4111yescharacteristic
314C2×C5—21no—
315C2×C5—21no—
316C2×C5—161no—
317C2×C5—162no—
318C2×C5#204111yescharacteristic
319C2×C5#204811yescharacteristic
320C2×C5#205111yescharacteristic
321C23—41no—
322C23—42no—
323C23—82no—
324C23—82no—
325C23—81no—
326C23—81no—
327C23C5×#12411yescharacteristic
328Q8—41no—
329Q8—41no—
330D4—41no—
331D4—42no—
332D4—41no—
333D4—42no—
334D4—41no—
335D4—41no—
336D4—82no—
337D4—82no—
338D4—81no—
339D4—82no—
340D4—81no—
341D4—81no—
342D4—81no—
343D4—81no—
344D4—81no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C5×#12011yescharacteristic
353C2×C4C5×#12111yescharacteristic
354C2×C4C5×#12111yescharacteristic
355C2×C4C5×#12111yescharacteristic
356C2×C4C5×#12311yescharacteristic
357C2×C4C5×#12311yescharacteristic
358C2×C4C2×C5×D811yescharacteristic
359C2×C4C2×C5×SD1611yescharacteristic
360C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
361C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
362C8—22no—
363C8—22no—
364C8—42no—
365C8—81no—
366C8—81no—
367C8—81no—
368C5#1054911yescharacteristic, direct product factor, Sylow
369C22—21no—
370C22—21no—
371C22—81no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—82no—
377C22—162no—
378C22—162no—
379C22C5×#39411yescharacteristic
380C22C5×#48611yescharacteristic
381C22C5×#49011yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—81no—
386C4C5×#44711yescharacteristic
387C4C5×#45011yescharacteristic
388C4C5×#45911yescharacteristic
389C4C5×#46011yescharacteristic
390C4C5×#47111yescharacteristic
391C4C5×#47211yescharacteristic
392C2—21no—
393C2—21no—
394C2—162no—
395C2—161no—
396C2C5×#204111yescharacteristic
397C2C5×#204811yescharacteristic
398C2C5×#205111yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3151C2
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×#1950C2semidirect
3. C5×#1547C2semidirect
4. C5×#1545C2semidirect
5. C2×C5×#331C2semidirect
6. C5×#1480C2semidirect
7. C5×#1283C2semidirect
27. #10549C5direct (N × H)
70. #1950C2×C5semidirect
71. #1547C2×C5semidirect
72. #1545C2×C5semidirect
73. C2×#331C2×C5semidirect
74. #1480C2×C5semidirect
75. #1283C2×C5semidirect
368. C5#10549direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31512
C5×#19502
C5×#15472
C5×#15452
C2×C5×#3312
C5×#14802
C5×#12832
#105495