Finite Group Databasebeta

← C5×#10176 #11932896

Subgroups — C5×#10176 #11932896

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3205C211yesmaximal, characteristic, complemented
2C5×#3036C211yesmaximal, characteristic, complemented
3C2×C5×#459C211yesmaximal, characteristic, complemented
4C5×#1545C211yesmaximal, characteristic, complemented
5C5×#1480C211yesmaximal, characteristic, complemented
6C5×#1460C211yesmaximal, characteristic, complemented
7C5×#1301C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C22×C5×D8—21no—
10C5×#532C2211yescharacteristic
11C2×C5×#127C2211yescharacteristic
12C2×C4×C5×D4C2211yescharacteristic
13C5×#493—21no—
14C5×#486—21no—
15C5×#463—22no—
16C5×#461—21no—
17C5×#459—22no—
18C5×#459—22no—
19C5×#459—21no—
20C5×#459—22no—
21C5×#447—22no—
22C5×#431C2211yescharacteristic
23C5×#431C2211yescharacteristic
24C5×#423C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#417—21no—
27C2×C5×#102—21no—
28C5×#331—22no—
29C5×D4⋊C8—22no—
30C5×#323—22no—
31#10176C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4D411yescharacteristic
37C23×C4×C5—21no—
38C5×AGL(1,ℤ/8)—42no—
39C5×AGL(1,ℤ/8)—42no—
40C2×C5×SD16—22no—
41C2×C5×D8—24no—
42C2×C5×D8—22no—
43C2×C5×D8—24no—
44C2×C5×D8—42no—
45C2×C5×D8—42no—
46C2×C5×M16—21no—
47C22×C5×C8—21no—
48C5×C4⋊Q8D411yescharacteristic
49C5×#127—21no—
50C5×#127—21no—
51C5×#127—21no—
52C5×#127D412yes—
53C5×#127D411yescharacteristic
54C5×#124—21no—
55C5×#121—21no—
56C5×#121—21no—
57C4×C5×D4—21no—
58C4×C5×D4—21no—
59C4×C5×D4—21no—
60C4×C5×D4—21no—
61C4×C5×D4—21no—
62C4×C5×D4—21no—
63C2×C5×C4⋊C4D411yescharacteristic
64C2×C5×C22⋊C4—21no—
65C2×C42×C5C2311yescharacteristic
66C5×C4⋊C8—21no—
67C5×C4⋊C8—21no—
68C5×C4⋊C8—21no—
69C5×C4⋊C8—21no—
70C5×C4⋊C8D412yes—
71C5×C4⋊C8D412yes—
72C5×#103—22no—
73C5×#102—24no—
74C5×#102—22no—
75C5×#102—24no—
76C5×C22⋊C8—21no—
77C5×C22⋊C8D412yes—
78C4×C5×C8—21no—
79C4×C5×C8—21no—
80#3205C2×C511yescharacteristic, complemented
81#3036C2×C511yescharacteristic, complemented
82C2×#459C2×C511yescharacteristic, complemented
83#1545C2×C511yescharacteristic, complemented
84#1480C2×C511yescharacteristic, complemented
85#1460C2×C511yescharacteristic, complemented
86#1301C2×C511yescharacteristic, complemented
87C24×C5—21no—
88C24×C5—41no—
89C5×#41—41no—
90C5×#41—41no—
91C5×#41—41no—
92C5×#41—41no—
93C2×C5×Q8—21no—
94C2×C5×D4—21no—
95C2×C5×D4—21no—
96C2×C5×D4—21no—
97C2×C5×D4—21no—
98C2×C5×D4—22no—
99C2×C5×D4—22no—
100C2×C5×D4—21no—
101C2×C5×D4—22no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—82no—
114C2×C5×D4—82no—
115C2×C5×D4D812yescomplemented
116C22×C4×C5—21no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5—82no—
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D411yescharacteristic
123C22×C4×C5#4111yescharacteristic
124C5×SD16—44no—
125C5×D8—48no—
126C5×D8—44no—
127C5×D8—84no—
128C5×M16—41no—
129C5×M16—41no—
130C2×C5×C8—22no—
131C2×C5×C8—22no—
132C2×C5×C8—22no—
133C2×C5×C8—41no—
134C2×C5×C8—41no—
135C2×C5×C8—41no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C22⋊C4—41no—
141C5×C22⋊C4—41no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C42×C5C2×D411yescharacteristic
145C42×C5C2×D411yescharacteristic
146C42×C5C2×D411yescharacteristic
147C42×C5C2×D411yescharacteristic
148C2×AGL(1,ℤ/8)—21no—
149C22×D8—21no—
150#532C22×C511yescharacteristic
151C2×#127C22×C511yescharacteristic
152C2×C4×D4C22×C511yescharacteristic
153#493—21no—
154#486—21no—
155#463—22no—
156#461—21no—
157#459—22no—
158#459—22no—
159#459—21no—
160#459—22no—
161#447—22no—
162#431C22×C511yescharacteristic
163#431C22×C511yescharacteristic
164#423C22×C511yescharacteristic
165C2×C4⋊C8C22×C511yescharacteristic
166#417—21no—
167C2×#102—21no—
168#331—22no—
169D4⋊C8—22no—
170#323—22no—
171C23×C5—22no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—42no—
176C23×C5—81no—
177C23×C5—81no—
178C23×C5—82no—
179C23×C5—82no—
180C23×C5—81no—
181C23×C5—81no—
182C23×C5#12111yescharacteristic
183C5×Q8—41no—
184C5×Q8—41no—
185C5×D4—22no—
186C5×D4—22no—
187C5×D4—42no—
188C5×D4—44no—
189C5×D4—42no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—41no—
193C5×D4—42no—
194C5×D4—41no—
195C5×D4—42no—
196C5×D4—82no—
197C5×D4—82no—
198C5×D4—81no—
199C5×D4—81no—
200C5×D4—81no—
201C5×D4—81no—
202C5×D4—82no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—82no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5—82no—
211C2×C4×C5—81no—
212C2×C4×C5#12011yescharacteristic
213C2×C4×C5#12011yescharacteristic
214C2×C4×C5#12011yescharacteristic
215C2×C4×C5#12111yescharacteristic
216C2×C4×C5#12111yescharacteristic
217C2×C4×C5#12711yescharacteristic
218C2×C4×C5C2×D811yescharacteristic
219C2×C4×C5#13511yescharacteristic
220C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
222C5×C8—42no—
223C5×C8—42no—
224C5×C8—42no—
225C5×C8—81no—
226C2×#41—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4C5×D411yescharacteristic
231C23×C4—21no—
232AGL(1,ℤ/8)—42no—
233AGL(1,ℤ/8)—42no—
234C2×SD16—22no—
235C2×D8—24no—
236C2×D8—22no—
237C2×D8—24no—
238C2×D8—42no—
239C2×D8—42no—
240C2×M16—21no—
241C22×C8—21no—
242C4⋊Q8C5×D411yescharacteristic
243#127—21no—
244#127—21no—
245#127—21no—
246#127C5×D412yes—
247#127C5×D411yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C2×C4⋊C4C5×D411yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42C23×C511yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8C5×D412yes—
265C4⋊C8C5×D412yes—
266#103—22no—
267#102—24no—
268#102—22no—
269#102—24no—
270C22⋊C8—21no—
271C22⋊C8C5×D412yes—
272C4×C8—21no—
273C4×C8—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—42no—
277C22×C5—82no—
278C22×C5—82no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—82no—
283C22×C5—82no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5—82no—
287C22×C5—162no—
288C22×C5—162no—
289C22×C5#39211yescharacteristic
290C22×C5#46611yescharacteristic
291C22×C5#46911yescharacteristic
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—21no—
295C4×C5—81no—
296C4×C5—81no—
297C4×C5#44711yescharacteristic
298C4×C5#44711yescharacteristic
299C4×C5#44911yescharacteristic
300C4×C5#44911yescharacteristic
301C4×C5#47212yes—
302C24—21no—
303C24—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—82no—
329C2×D4—82no—
330C2×D4C5×D812yescomplemented
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—82no—
336C22×C4C2×C5×D411yescharacteristic
337C22×C4C2×C5×D411yescharacteristic
338C22×C4C5×#4111yescharacteristic
339SD16—44no—
340D8—48no—
341D8—44no—
342D8—84no—
343M16—41no—
344M16—41no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C42C2×C5×D411yescharacteristic
360C42C2×C5×D411yescharacteristic
361C42C2×C5×D411yescharacteristic
362C42C2×C5×D411yescharacteristic
363C2×C5—21no—
364C2×C5—21no—
365C2×C5—82no—
366C2×C5—161no—
367C2×C5—162no—
368C2×C5#199911yescharacteristic
369C2×C5#200811yescharacteristic
370C2×C5#201811yescharacteristic
371C23—22no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—81no—
377C23—81no—
378C23—82no—
379C23—82no—
380C23—81no—
381C23—81no—
382C23C5×#12111yescharacteristic
383Q8—41no—
384Q8—41no—
385D4—22no—
386D4—22no—
387D4—42no—
388D4—44no—
389D4—42no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—42no—
394D4—41no—
395D4—42no—
396D4—82no—
397D4—82no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—82no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4C5×#12011yescharacteristic
413C2×C4C5×#12011yescharacteristic
414C2×C4C5×#12011yescharacteristic
415C2×C4C5×#12111yescharacteristic
416C2×C4C5×#12111yescharacteristic
417C2×C4C5×#12711yescharacteristic
418C2×C4C2×C5×D811yescharacteristic
419C2×C4C5×#13511yescharacteristic
420C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
421C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
422C8—42no—
423C8—42no—
424C8—42no—
425C8—81no—
426C5#1017611yescharacteristic, direct product factor, Sylow
427C22—21no—
428C22—21no—
429C22—42no—
430C22—82no—
431C22—82no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—82no—
436C22—81no—
437C22—82no—
438C22—82no—
439C22—81no—
440C22—162no—
441C22—162no—
442C22C5×#39211yescharacteristic
443C22C5×#46611yescharacteristic
444C22C5×#46911yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4C5×#44711yescharacteristic
451C4C5×#44711yescharacteristic
452C4C5×#44911yescharacteristic
453C4C5×#44911yescharacteristic
454C4C5×#47212yes—
455C2—21no—
456C2—21no—
457C2—82no—
458C2—162no—
459C2—161no—
460C2C5×#199911yescharacteristic
461C2C5×#200811yescharacteristic
462C2C5×#201811yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
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
1. C5×#3205C2semidirect
2. C5×#3036C2semidirect
3. C2×C5×#459C2semidirect
4. C5×#1545C2semidirect
5. C5×#1480C2semidirect
6. C5×#1460C2semidirect
7. C5×#1301C2semidirect
31. #10176C5direct (N × H)
80. #3205C2×C5semidirect
81. #3036C2×C5semidirect
82. C2×#459C2×C5semidirect
83. #1545C2×C5semidirect
84. #1480C2×C5semidirect
85. #1460C2×C5semidirect
86. #1301C2×C5semidirect
115. C2×C5×D4D8semidirect
330. C2×D4C5×D8semidirect
426. C5#10176direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32052
C5×#30362
C2×C5×#4592
C5×#15452
C5×#14802
C5×#14602
C5×#13012
#101765