Finite Group Databasebeta

← C5×#10466 #11933186

Subgroups — C5×#10466 #11933186

Order 1280.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3037C211yesmaximal, characteristic
2C5×#1805C211yesmaximal, characteristic, complemented
3C5×#1571C211yesmaximal, characteristic, complemented
4C5×#1540C211yesmaximal, characteristic
5C5×#1517C211yesmaximal, characteristic
6C5×#1461C211yesmaximal, characteristic, complemented
7C5×#1286C211yesmaximal, characteristic, complemented
8C2×C5×#137—21no—
9C5×#532C2211yescharacteristic
10C2×C4×C5×Q8C2211yescharacteristic
11C5×#464—22no—
12C5×#462—21no—
13C5×#460—21no—
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#417—21no—
19C2×C5×#103—21no—
20C5×#382C2211yescharacteristic
21C5×#340—21no—
22C5×#335—22no—
23C5×#332—21no—
24C5×#331—21no—
25C5×#327—22no—
26C5×#324—22no—
27#10466C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×Q8D411yescharacteristic
30C5×#137—42no—
31C5×#137—42no—
32C2×C5×Q16—22no—
33C2×C5×SD16—22no—
34C2×C5×M16—21no—
35C22×C5×C8—21no—
36C5×C4⋊Q8D411yescharacteristic
37C5×#127D411yescharacteristic
38C5×#124—21no—
39C5×#121—21no—
40C5×#121—21no—
41C4×C5×Q8—21no—
42C4×C5×Q8—21no—
43C4×C5×Q8—21no—
44C4×C5×Q8—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C42×C5—21no—
51C2×C42×C5C2311yescharacteristic
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8D412yes—
58C5×#103—22no—
59C5×#103—42no—
60C5×#102—22no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8D412yes—
63C4×C5×C8—21no—
64C4×C5×C8—21no—
65C5×#95—21no—
66C5×#95—21no—
67#3037C2×C511yescharacteristic
68#1805C2×C511yescharacteristic, complemented
69#1571C2×C511yescharacteristic, complemented
70#1540C2×C511yescharacteristic
71#1517C2×C511yescharacteristic
72#1461C2×C511yescharacteristic, complemented
73#1286C2×C511yescharacteristic, complemented
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8—21no—
83C2×C5×Q8—21no—
84C2×C5×Q8D812yes—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—41no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5#4111yescharacteristic
96C5×Q16—44no—
97C5×SD16—44no—
98C5×M16—41no—
99C5×M16—41no—
100C2×C5×C8—22no—
101C2×C5×C8—22no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—41no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C42×C5—41no—
117C42×C5—41no—
118C42×C5C2×D411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C42×C5#4111yescharacteristic
121C42×C5#4111yescharacteristic
122C2×#137—21no—
123#532C22×C511yescharacteristic
124C2×C4×Q8C22×C511yescharacteristic
125#464—22no—
126#462—21no—
127#460—21no—
128#431C22×C511yescharacteristic
129#431C22×C511yescharacteristic
130#423C22×C511yescharacteristic
131C2×C4⋊C8C22×C511yescharacteristic
132#417—21no—
133C2×#103—21no—
134#382C22×C511yescharacteristic
135#340—21no—
136#335—22no—
137#332—21no—
138#331—21no—
139#327—22no—
140#324—22no—
141C23×C5—41no—
142C23×C5#12111yescharacteristic
143C5×Q8—22no—
144C5×Q8—22no—
145C5×Q8—41no—
146C5×Q8—41no—
147C5×Q8—41no—
148C5×Q8—41no—
149C5×D4—41no—
150C5×D4—41no—
151C5×D4—81no—
152C5×D4—81no—
153C5×D4—81no—
154C5×D4—81no—
155C2×C4×C5—22no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5—81no—
167C2×C4×C5—81no—
168C2×C4×C5#12011yescharacteristic
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5#12111yescharacteristic
171C2×C4×C5#12311yescharacteristic
172C2×C4×C5#12311yescharacteristic
173C2×C4×C5#12411yescharacteristic
174C2×C4×C5C2×D811yescharacteristic
175C2×C4×C5#13511yescharacteristic
176C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C5#13711yescharacteristic
178C5×C8—42no—
179C5×C8—42no—
180C5×C8—81no—
181C5×C8—81no—
182C2×#41—21no—
183C22×Q8C5×D411yescharacteristic
184#137—42no—
185#137—42no—
186C2×Q16—22no—
187C2×SD16—22no—
188C2×M16—21no—
189C22×C8—21no—
190C4⋊Q8C5×D411yescharacteristic
191#127C5×D411yescharacteristic
192#124—21no—
193#121—21no—
194#121—21no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×D4—21no—
200C4×D4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C5×D411yescharacteristic
204C2×C42—21no—
205C2×C42C23×C511yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8C5×D412yes—
212#103—22no—
213#103—42no—
214#102—22no—
215C22⋊C8—21no—
216C22⋊C8C5×D412yes—
217C4×C8—21no—
218C4×C8—21no—
219#95—21no—
220#95—21no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5—81no—
224C22×C5—81no—
225C22×C5—81no—
226C22×C5#39411yescharacteristic
227C22×C5#46611yescharacteristic
228C22×C5#46811yescharacteristic
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—42no—
234C4×C5—81no—
235C4×C5—81no—
236C4×C5—161no—
237C4×C5#44711yescharacteristic
238C4×C5#45211yescharacteristic
239C4×C5#48011yescharacteristic
240C4×C5#48211yescharacteristic
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8C5×D812yes—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C2×C5×D411yescharacteristic
261C22×C4C2×C5×D411yescharacteristic
262C22×C4C5×#4111yescharacteristic
263Q16—44no—
264SD16—44no—
265M16—41no—
266M16—41no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42—41no—
285C42C2×C5×D411yescharacteristic
286C42C2×C5×D411yescharacteristic
287C42C5×#4111yescharacteristic
288C42C5×#4111yescharacteristic
289C2×C5—21no—
290C2×C5—21no—
291C2×C5—161no—
292C2×C5#203311yescharacteristic
293C2×C5#204911yescharacteristic
294C2×C5#205311yescharacteristic
295C23—41no—
296C23C5×#12111yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—41no—
302Q8—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C5×#12011yescharacteristic
323C2×C4C5×#12111yescharacteristic
324C2×C4C5×#12111yescharacteristic
325C2×C4C5×#12311yescharacteristic
326C2×C4C5×#12311yescharacteristic
327C2×C4C5×#12411yescharacteristic
328C2×C4C2×C5×D811yescharacteristic
329C2×C4C5×#13511yescharacteristic
330C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
331C2×C4C5×#13711yescharacteristic
332C8—42no—
333C8—42no—
334C8—81no—
335C8—81no—
336C5#1046611yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C5×#39411yescharacteristic
343C22C5×#46611yescharacteristic
344C22C5×#46811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—161no—
353C4C5×#44711yescharacteristic
354C4C5×#45211yescharacteristic
355C4C5×#48011yescharacteristic
356C4C5×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C5×#203311yescharacteristic
361C2C5×#204911yescharacteristic
362C2C5×#205311yescharacteristic
subgroupG/H
center, socleC22×C5#394
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×#1805C2semidirect
3. C5×#1571C2semidirect
6. C5×#1461C2semidirect
7. C5×#1286C2semidirect
27. #10466C5direct (N × H)
68. #1805C2×C5semidirect
69. #1571C2×C5semidirect
72. #1461C2×C5semidirect
73. #1286C2×C5semidirect
336. C5#10466direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30372
C5×#18052
C5×#15712
C5×#15402
C5×#15172
C5×#14612
C5×#12862
#104665