Finite Group Databasebeta

← C5×#10465 #11933185

Subgroups — C5×#10465 #11933185

Order 1280.

452 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3036C211yesmaximal, characteristic
2C5×#1804C211yesmaximal, characteristic, complemented
3C5×#1570C211yesmaximal, characteristic, complemented
4C5×#1540C211yesmaximal, characteristic, complemented
5C5×#1517C211yesmaximal, characteristic, complemented
6C5×#1460C211yesmaximal, characteristic, complemented
7C5×#1286C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C5×#532C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#463—22no—
12C5×#461—21no—
13C5×#459—21no—
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#417—21no—
19C2×C5×#102—21no—
20C5×#382C2211yescharacteristic
21C5×#340—21no—
22C5×#334—22no—
23C5×#332—21no—
24C5×#331—21no—
25C5×#327—22no—
26C5×#323—22no—
27#10465C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C5×AGL(1,ℤ/8)—42no—
32C5×AGL(1,ℤ/8)—42no—
33C2×C5×SD16—22no—
34C2×C5×D8—22no—
35C2×C5×M16—21no—
36C22×C5×C8—21no—
37C5×C4⋊Q8D411yescharacteristic
38C5×#127D411yescharacteristic
39C5×#124—21no—
40C5×#121—21no—
41C5×#121—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C22⋊C4—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×#102—22no—
60C5×#102—42no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8D412yes—
63C4×C5×C8—21no—
64C4×C5×C8—21no—
65C5×#95—21no—
66C5×#95—21no—
67#3036C2×C511yescharacteristic
68#1804C2×C511yescharacteristic, complemented
69#1570C2×C511yescharacteristic, complemented
70#1540C2×C511yescharacteristic, complemented
71#1517C2×C511yescharacteristic, complemented
72#1460C2×C511yescharacteristic, complemented
73#1286C2×C511yescharacteristic, complemented
74C24×C5—21no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C2×C5×Q8—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—41no—
89C2×C5×D4SD1612yes—
90C22×C4×C5—21no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—82no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5#4111yescharacteristic
99C5×SD16—44no—
100C5×D8—44no—
101C5×M16—41no—
102C5×M16—41no—
103C2×C5×C8—22no—
104C2×C5×C8—22no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—41no—
119C42×C5C2×D411yescharacteristic
120C42×C5C2×D411yescharacteristic
121C42×C5#4111yescharacteristic
122C42×C5#4111yescharacteristic
123C2×AGL(1,ℤ/8)—21no—
124#532C22×C511yescharacteristic
125C2×C4×D4C22×C511yescharacteristic
126#463—22no—
127#461—21no—
128#459—21no—
129#431C22×C511yescharacteristic
130#431C22×C511yescharacteristic
131#423C22×C511yescharacteristic
132C2×C4⋊C8C22×C511yescharacteristic
133#417—21no—
134C2×#102—21no—
135#382C22×C511yescharacteristic
136#340—21no—
137#334—22no—
138#332—21no—
139#331—21no—
140#327—22no—
141#323—22no—
142C23×C5—22no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—81no—
147C23×C5—81no—
148C23×C5#12111yescharacteristic
149C5×Q8—41no—
150C5×Q8—41no—
151C5×D4—22no—
152C5×D4—22no—
153C5×D4—41no—
154C5×D4—41no—
155C5×D4—41no—
156C5×D4—41no—
157C5×D4—81no—
158C5×D4—81no—
159C5×D4—81no—
160C5×D4—81no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—82no—
166C2×C4×C5—82no—
167C2×C4×C5—81no—
168C2×C4×C5—81no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5#12011yescharacteristic
174C2×C4×C5#12111yescharacteristic
175C2×C4×C5#12111yescharacteristic
176C2×C4×C5#12311yescharacteristic
177C2×C4×C5#12311yescharacteristic
178C2×C4×C5#12411yescharacteristic
179C2×C4×C5C2×SD1611yescharacteristic
180C2×C4×C5#13511yescharacteristic
181C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C5×C8—42no—
184C5×C8—42no—
185C5×C8—81no—
186C5×C8—81no—
187C2×#41—21no—
188C22×D4C5×D411yescharacteristic
189C23×C4—21no—
190AGL(1,ℤ/8)—42no—
191AGL(1,ℤ/8)—42no—
192C2×SD16—22no—
193C2×D8—22no—
194C2×M16—21no—
195C22×C8—21no—
196C4⋊Q8C5×D411yescharacteristic
197#127C5×D411yescharacteristic
198#124—21no—
199#121—21no—
200#121—21no—
201C4×D4—21no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C5×D411yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C23×C511yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8C5×D412yes—
217#103—22no—
218#102—22no—
219#102—42no—
220C22⋊C8—21no—
221C22⋊C8C5×D412yes—
222C4×C8—21no—
223C4×C8—21no—
224#95—21no—
225#95—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5—82no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5—81no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5#39411yescharacteristic
237C22×C5#46511yescharacteristic
238C22×C5#46911yescharacteristic
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—81no—
244C4×C5—81no—
245C4×C5—161no—
246C4×C5#44911yescharacteristic
247C4×C5#45011yescharacteristic
248C4×C5#48111yescharacteristic
249C4×C5#48211yescharacteristic
250C24—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255C2×Q8—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4C5×SD1612yes—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—82no—
272C22×C4C2×C5×D411yescharacteristic
273C22×C4C2×C5×D411yescharacteristic
274C22×C4C5×#4111yescharacteristic
275SD16—44no—
276D8—44no—
277M16—41no—
278M16—41no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42C2×C5×D411yescharacteristic
296C42C2×C5×D411yescharacteristic
297C42C5×#4111yescharacteristic
298C42C5×#4111yescharacteristic
299C2×C5—21no—
300C2×C5—21no—
301C2×C5—82no—
302C2×C5—161no—
303C2×C5#203411yescharacteristic
304C2×C5#204811yescharacteristic
305C2×C5#205311yescharacteristic
306C23—22no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—81no—
311C23—81no—
312C23C5×#12111yescharacteristic
313Q8—41no—
314Q8—41no—
315D4—22no—
316D4—22no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C5×#12011yescharacteristic
338C2×C4C5×#12111yescharacteristic
339C2×C4C5×#12111yescharacteristic
340C2×C4C5×#12311yescharacteristic
341C2×C4C5×#12311yescharacteristic
342C2×C4C5×#12411yescharacteristic
343C2×C4C2×C5×SD1611yescharacteristic
344C2×C4C5×#13511yescharacteristic
345C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
347C8—42no—
348C8—42no—
349C8—81no—
350C8—81no—
351C5#1046511yescharacteristic, direct product factor, Sylow
352C22—21no—
353C22—21no—
354C22—42no—
355C22—82no—
356C22—82no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22C5×#39411yescharacteristic
363C22C5×#46511yescharacteristic
364C22C5×#46911yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—81no—
371C4—161no—
372C4C5×#44911yescharacteristic
373C4C5×#45011yescharacteristic
374C4C5×#48111yescharacteristic
375C4C5×#48211yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2C5×#203411yescharacteristic
381C2C5×#204811yescharacteristic
382C2C5×#205311yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3036C2
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×#1804C2semidirect
3. C5×#1570C2semidirect
4. C5×#1540C2semidirect
5. C5×#1517C2semidirect
6. C5×#1460C2semidirect
7. C5×#1286C2semidirect
27. #10465C5direct (N × H)
68. #1804C2×C5semidirect
69. #1570C2×C5semidirect
70. #1540C2×C5semidirect
71. #1517C2×C5semidirect
72. #1460C2×C5semidirect
73. #1286C2×C5semidirect
351. C5#10465direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30362
C5×#18042
C5×#15702
C5×#15402
C5×#15172
C5×#14602
C5×#12862
#104655