Finite Group Databasebeta

← C5×#10547 #11933267

Subgroups — C5×#10547 #11933267

Order 1280.

386 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3135C211yesmaximal, characteristic
2C5×#1940C211yesmaximal, characteristic, complemented
3C5×#1542C211yesmaximal, characteristic, complemented
4C5×#1540C211yesmaximal, characteristic
5C5×#1503C211yesmaximal, characteristic, complemented
6C5×#1502C211yesmaximal, characteristic
7C5×#1275C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C5×#491—21no—
11C5×#490—21no—
12C5×#489—21no—
13C5×#489—21no—
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C2×C5×C4⋊C8—21no—
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#416—21no—
19C5×#416—21no—
20C2×C5×#97C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C5×#336—21no—
23C5×#333—21no—
24C5×#332—21no—
25C5×#332—21no—
26C5×#331—21no—
27C5×#328—21no—
28C5×#328—21no—
29C5×#327—21no—
30C5×#327—21no—
31#10547C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×C8—21no—
34C22×C5×C8D411yescharacteristic
35C22×C5×C8D411yescharacteristic
36C5×C4⋊Q8D411yescharacteristic
37C5×C4⋊Q8D411yescharacteristic
38C5×C4⋊Q8D411yescharacteristic
39C5×#127D411yescharacteristic
40C5×#125—21no—
41C5×#124—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×#121—21no—
45C5×#121—21no—
46C4×C5×Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C5×#117—21no—
51C2×C5×C4⋊C4—21no—
52C2×C42×C5—21no—
53C2×C42×C5C2311yescharacteristic
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—42no—
59C5×#103—21no—
60C5×#103—21no—
61C5×#103—21no—
62C5×#103—21no—
63C5×#102—21no—
64C5×#102—21no—
65C5×#102—21no—
66C5×#102—21no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×#97—21no—
70C5×#97—21no—
71C4×C5×C8—21no—
72C4×C5×C8—21no—
73C5×#95D411yescharacteristic
74C5×#95D411yescharacteristic
75#3135C2×C511yescharacteristic
76#1940C2×C511yescharacteristic, complemented
77#1542C2×C511yescharacteristic, complemented
78#1540C2×C511yescharacteristic
79#1503C2×C511yescharacteristic, complemented
80#1502C2×C511yescharacteristic
81#1275C2×C511yescharacteristic, complemented
82C5×#41—41no—
83C5×#41—41no—
84C5×#41—41no—
85C5×#41—41no—
86C2×C5×Q8—21no—
87C2×C5×Q8—21no—
88C2×C5×Q8—21no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—21no—
92C2×C5×D4—41no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—41no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5#4111yescharacteristic
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—42no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C22⋊C4—41no—
120C5×C22⋊C4—41no—
121C5×C22⋊C4—41no—
122C42×C5—41no—
123C42×C5—41no—
124C42×C5—41no—
125C42×C5C2×D411yescharacteristic
126C42×C5C2×D411yescharacteristic
127C42×C5#4111yescharacteristic
128C42×C5#4111yescharacteristic
129#533C22×C511yescharacteristic
130#532C22×C511yescharacteristic
131#491—21no—
132#490—21no—
133#489—21no—
134#489—21no—
135#431C22×C511yescharacteristic
136#431C22×C511yescharacteristic
137C2×C4⋊C8—21no—
138C2×C4⋊C8C22×C511yescharacteristic
139#416—21no—
140#416—21no—
141C2×#97C22×C511yescharacteristic
142C4×C4⋊C4C22×C511yescharacteristic
143#336—21no—
144#333—21no—
145#332—21no—
146#332—21no—
147#331—21no—
148#328—21no—
149#328—21no—
150#327—21no—
151#327—21no—
152C23×C5—41no—
153C23×C5#12111yescharacteristic
154C5×Q8—41no—
155C5×Q8—41no—
156C5×Q8—81no—
157C5×Q8—81no—
158C5×D4—41no—
159C5×D4—41no—
160C5×D4—81no—
161C5×D4—81no—
162C5×D4—81no—
163C5×D4—81no—
164C2×C4×C5—22no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—81no—
176C2×C4×C5—81no—
177C2×C4×C5#12011yescharacteristic
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12311yescharacteristic
181C2×C4×C5#12311yescharacteristic
182C2×C4×C5#12411yescharacteristic
183C2×C4×C5#13511yescharacteristic
184C2×C4×C5#13511yescharacteristic
185C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C5#13711yescharacteristic
187C5×C8—41no—
188C5×C8—41no—
189C5×C8—81no—
190C5×C8—81no—
191C5×C8—81no—
192C2×#41—21no—
193C22×C8—21no—
194C22×C8C5×D411yescharacteristic
195C22×C8C5×D411yescharacteristic
196C4⋊Q8C5×D411yescharacteristic
197C4⋊Q8C5×D411yescharacteristic
198C4⋊Q8C5×D411yescharacteristic
199#127C5×D411yescharacteristic
200#125—21no—
201#124—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204#121—21no—
205#121—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×D4—21no—
209C4×D4—21no—
210#117—21no—
211C2×C4⋊C4—21no—
212C2×C42—21no—
213C2×C42C23×C511yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—42no—
219#103—21no—
220#103—21no—
221#103—21no—
222#103—21no—
223#102—21no—
224#102—21no—
225#102—21no—
226#102—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229#97—21no—
230#97—21no—
231C4×C8—21no—
232C4×C8—21no—
233#95C5×D411yescharacteristic
234#95C5×D411yescharacteristic
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5#39411yescharacteristic
241C22×C5#46311yescharacteristic
242C22×C5#46411yescharacteristic
243C4×C5—21no—
244C4×C5—21no—
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—42no—
248C4×C5—81no—
249C4×C5—81no—
250C4×C5—81no—
251C4×C5—81no—
252C4×C5#44911yescharacteristic
253C4×C5#45211yescharacteristic
254C4×C5#48811yescharacteristic
255C4×C5#48911yescharacteristic
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C2×C5×D411yescharacteristic
271C22×C4C2×C5×D411yescharacteristic
272C22×C4C5×#4111yescharacteristic
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42C2×C5×D411yescharacteristic
300C42C2×C5×D411yescharacteristic
301C42C5×#4111yescharacteristic
302C42C5×#4111yescharacteristic
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—161no—
306C2×C5#204211yescharacteristic
307C2×C5#205011yescharacteristic
308C2×C5#205311yescharacteristic
309C23—41no—
310C23C5×#12111yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—81no—
314Q8—81no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—81no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C5×#12011yescharacteristic
335C2×C4C5×#12111yescharacteristic
336C2×C4C5×#12111yescharacteristic
337C2×C4C5×#12311yescharacteristic
338C2×C4C5×#12311yescharacteristic
339C2×C4C5×#12411yescharacteristic
340C2×C4C5×#13511yescharacteristic
341C2×C4C5×#13511yescharacteristic
342C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
343C2×C4C5×#13711yescharacteristic
344C8—41no—
345C8—41no—
346C8—81no—
347C8—81no—
348C8—81no—
349C5#1054711yescharacteristic, direct product factor, Sylow
350C22—21no—
351C22—21no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22C5×#39411yescharacteristic
356C22C5×#46311yescharacteristic
357C22C5×#46411yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4C5×#44911yescharacteristic
368C4C5×#45211yescharacteristic
369C4C5×#48811yescharacteristic
370C4C5×#48911yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2C5×#204211yescharacteristic
375C2C5×#205011yescharacteristic
376C2C5×#205311yescharacteristic
subgroupG/H
centerC2×C4×C5#124
commutator, Frattini, cosocleC2×C42C23×C5
socleC22×C5#394
prime radicalC5×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1940C2semidirect
3. C5×#1542C2semidirect
5. C5×#1503C2semidirect
7. C5×#1275C2semidirect
31. #10547C5direct (N × H)
76. #1940C2×C5semidirect
77. #1542C2×C5semidirect
79. #1503C2×C5semidirect
81. #1275C2×C5semidirect
349. C5#10547direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31352
C5×#19402
C5×#15422
C5×#15402
C5×#15032
C5×#15022
C5×#12752
#105475