Finite Group Databasebeta

← C5×#9571 #11932291

Subgroups — C5×#9571 #11932291

Order 1280.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1982C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic
3C5×#1947C211yesmaximal, characteristic, complemented
4C5×#1770C211yesmaximal, characteristic, complemented
5C2×C5×#331C211yesmaximal, characteristic
6C5×#1296C211yesmaximal, characteristic, complemented
7C5×#1277C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×C5×#107—21no—
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×#102—21no—
14C2×C5×#102—21no—
15C2×C5×#102—21no—
16C2×C5×#102—21no—
17C2×C5×#97—21no—
18C2×C4×C5×C8C2211yescharacteristic
19C5×#384C2211yescharacteristic
20C4×C5×C4⋊C4C2211yescharacteristic
21C5×#340—21no—
22C5×#336—21no—
23C5×#331C414yescomplemented
24#9571C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×D4—21no—
26C22×C5×D4—21no—
27C22×C5×D4—21no—
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C22×C5×C8D411yescharacteristic
32C22×C5×C8D411yescharacteristic
33C5×#127—21no—
34C5×#127—21no—
35C5×#127—21no—
36C5×#127C2×C412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C4⋊C4D411yescharacteristic
42C2×C42×C5—21no—
43C2×C42×C5C2311yescharacteristic
44C5×#107—42no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C5×C4⋊C8C2×C412yes—
50C5×C4⋊C8C2×C412yes—
51C5×#102—42no—
52C5×#102—42no—
53C5×#102—42no—
54C5×#102—42no—
55C5×#97—42no—
56C4×C5×C8—21no—
57C4×C5×C8—21no—
58C5×#95—21no—
59#1982C2×C511yescharacteristic
60#1957C2×C511yescharacteristic
61#1947C2×C511yescharacteristic, complemented
62#1770C2×C511yescharacteristic, complemented
63C2×#331C2×C511yescharacteristic
64#1296C2×C511yescharacteristic, complemented
65#1277C2×C511yescharacteristic, complemented
66C24×C5—41no—
67C2×C5×D4—22no—
68C2×C5×D4—22no—
69C2×C5×D4—22no—
70C2×C5×D4—41no—
71C2×C5×D4—41no—
72C2×C5×D4—41no—
73C2×C5×D4—41no—
74C2×C5×D4—41no—
75C2×C5×D4—41no—
76C2×C5×D4—41no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—81no—
82C2×C5×D4—81no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—22no—
92C2×C5×C8—22no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8D812yes—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—81no—
113C42×C5—41no—
114C42×C5—41no—
115C42×C5C22×C411yescharacteristic
116C42×C5#4111yescharacteristic
117C42×C5#4111yescharacteristic
118C42×C5#4111yescharacteristic
119C2×#127C22×C511yescharacteristic
120C2×#107—21no—
121C2×C4⋊C8C22×C511yescharacteristic
122C2×C4⋊C8C22×C511yescharacteristic
123C2×C4⋊C8C22×C511yescharacteristic
124C2×#102—21no—
125C2×#102—21no—
126C2×#102—21no—
127C2×#102—21no—
128C2×#97—21no—
129C2×C4×C8C22×C511yescharacteristic
130#384C22×C511yescharacteristic
131C4×C4⋊C4C22×C511yescharacteristic
132#340—21no—
133#336—21no—
134#331C4×C514yescomplemented
135C23×C5—42no—
136C23×C5—81no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5—81no—
140C23×C5—81no—
141C23×C5—81no—
142C23×C5#12111yescharacteristic
143C5×D4—42no—
144C5×D4—42no—
145C5×D4—42no—
146C5×D4—42no—
147C5×D4—82no—
148C5×D4—82no—
149C5×D4—81no—
150C5×D4—81no—
151C5×D4—81no—
152C5×D4—81no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5#11711yescharacteristic
165C2×C4×C5C4×D411yescharacteristic
166C2×C4×C5C4×D411yescharacteristic
167C2×C4×C5#12311yescharacteristic
168C2×C4×C5#12411yescharacteristic
169C2×C4×C5#12611yescharacteristic
170C2×C4×C5C2×D811yescharacteristic
171C2×C4×C5#13511yescharacteristic
172C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C5#13711yescharacteristic
177C2×C4×C5#13711yescharacteristic
178C5×C8—22no—
179C5×C8—42no—
180C5×C8—42no—
181C5×C8—41no—
182C5×C8—81no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8C5×D411yescharacteristic
190C22×C8C5×D411yescharacteristic
191#127—21no—
192#127—21no—
193#127—21no—
194#127C2×C4×C512yes—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C5×D411yescharacteristic
199C2×C4⋊C4C5×D411yescharacteristic
200C2×C42—21no—
201C2×C42C23×C511yescharacteristic
202#107—42no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8C2×C4×C512yes—
208C4⋊C8C2×C4×C512yes—
209#102—42no—
210#102—42no—
211#102—42no—
212#102—42no—
213#97—42no—
214C4×C8—21no—
215C4×C8—21no—
216#95—21no—
217C22×C5—82no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5—161no—
221C22×C5—161no—
222C22×C5—161no—
223C22×C5—161no—
224C22×C5#38811yescharacteristic
225C22×C5#45911yescharacteristic
226C22×C5#46411yescharacteristic
227C22×C5#46811yescharacteristic
228C22×C5#46911yescharacteristic
229C22×C5#47111yescharacteristic
230C22×C5#47211yescharacteristic
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—81no—
234C4×C5—81no—
235C4×C5—161no—
236C4×C5C4×D811yescharacteristic
237C4×C5#44011yescharacteristic
238C4×C5#44011yescharacteristic
239C4×C5#44211yescharacteristic
240C4×C5#48011yescharacteristic
241C4×C5#48211yescharacteristic
242C4×C5#48911yescharacteristic
243C4×C5#49011yescharacteristic
244C24—41no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—81no—
260C2×D4—81no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4C2×C5×D411yescharacteristic
265C22×C4C2×C5×D411yescharacteristic
266C22×C4C5×#4111yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C5×D812yes—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C42—41no—
292C42—41no—
293C42C22×C4×C511yescharacteristic
294C42C5×#4111yescharacteristic
295C42C5×#4111yescharacteristic
296C42C5×#4111yescharacteristic
297C2×C5—162no—
298C2×C5#168511yescharacteristic
299C2×C5#168711yescharacteristic
300C2×C5#169811yescharacteristic
301C2×C5#170211yescharacteristic
302C2×C5#192511yescharacteristic
303C2×C5#193111yescharacteristic
304C2×C5#193611yescharacteristic
305C23—42no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23C5×#12111yescharacteristic
313D4—42no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—82no—
318D4—82no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C5×#11711yescharacteristic
335C2×C4C4×C5×D411yescharacteristic
336C2×C4C4×C5×D411yescharacteristic
337C2×C4C5×#12311yescharacteristic
338C2×C4C5×#12411yescharacteristic
339C2×C4C5×#12611yescharacteristic
340C2×C4C2×C5×D811yescharacteristic
341C2×C4C5×#13511yescharacteristic
342C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
343C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
344C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
345C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C5×#13711yescharacteristic
347C2×C4C5×#13711yescharacteristic
348C8—22no—
349C8—42no—
350C8—42no—
351C8—41no—
352C8—81no—
353C5#957111yescharacteristic, direct product factor, Sylow
354C22—82no—
355C22—82no—
356C22—82no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—161no—
361C22C5×#38811yescharacteristic
362C22C5×#45911yescharacteristic
363C22C5×#46411yescharacteristic
364C22C5×#46811yescharacteristic
365C22C5×#46911yescharacteristic
366C22C5×#47111yescharacteristic
367C22C5×#47211yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4C4×C5×D811yescharacteristic
374C4C5×#44011yescharacteristic
375C4C5×#44011yescharacteristic
376C4C5×#44211yescharacteristic
377C4C5×#48011yescharacteristic
378C4C5×#48211yescharacteristic
379C4C5×#48911yescharacteristic
380C4C5×#49011yescharacteristic
381C2—162no—
382C2C5×#168511yescharacteristic
383C2C5×#168711yescharacteristic
384C2C5×#169811yescharacteristic
385C2C5×#170211yescharacteristic
386C2C5×#192511yescharacteristic
387C2C5×#193111yescharacteristic
388C2C5×#193611yescharacteristic
subgroupG/H
center, socleC23×C5#121
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1947C2semidirect
4. C5×#1770C2semidirect
6. C5×#1296C2semidirect
7. C5×#1277C2semidirect
23. C5×#331C4semidirect
24. #9571C5direct (N × H)
61. #1947C2×C5semidirect
62. #1770C2×C5semidirect
64. #1296C2×C5semidirect
65. #1277C2×C5semidirect
134. #331C4×C5semidirect
353. C5#9571direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#19822
C5×#19572
C5×#19472
C5×#17702
C2×C5×#3312
C5×#12962
C5×#12772
#95715