Finite Group Databasebeta

← C5×#10473 #11933193

Subgroups — C5×#10473 #11933193

Order 1280.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#459C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic, complemented
3C5×#1954C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic, complemented
5C2×C5×#334C211yesmaximal, characteristic, complemented
6C2×C5×#331C211yesmaximal, characteristic, complemented
7C5×#1296C211yesmaximal, characteristic, complemented
8C22×C5×D8—21no—
9C2×C5×#127C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#459—22no—
12C5×#459—22no—
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C5×#102—21no—
17C2×C5×#102—21no—
18C2×C5×#102—21no—
19C2×C5×#102—21no—
20C2×C5×C22⋊C8—21no—
21C2×C5×C22⋊C8—21no—
22C2×C4×C5×C8C2211yescharacteristic
23C5×#384C2211yescharacteristic
24C5×#340—21no—
25C5×#334—22no—
26C5×#331—22no—
27#10473C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C22×C5×D4D411yescharacteristic
32C23×C4×C5—21no—
33C2×C5×D8—24no—
34C2×C5×D8—42no—
35C2×C5×D8—42no—
36C22×C5×C8—21no—
37C22×C5×C8—21no—
38C22×C5×C8—21no—
39C22×C5×C8D411yescharacteristic
40C22×C5×C8D411yescharacteristic
41C5×#127—21no—
42C5×#127—21no—
43C5×#127—21no—
44C5×#127D412yes—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C4×C5×D4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C22⋊C4—21no—
54C2×C42×C5C2311yescharacteristic
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8D412yes—
61C5×#102—24no—
62C5×#102—42no—
63C5×#102—42no—
64C5×#102—42no—
65C5×C22⋊C8—42no—
66C5×C22⋊C8—42no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69C2×#459C2×C511yescharacteristic
70#1957C2×C511yescharacteristic, complemented
71#1954C2×C511yescharacteristic, complemented
72#1802C2×C511yescharacteristic, complemented
73C2×#334C2×C511yescharacteristic, complemented
74C2×#331C2×C511yescharacteristic, complemented
75#1296C2×C511yescharacteristic, complemented
76C24×C5—21no—
77C24×C5—41no—
78C2×C5×D4—21no—
79C2×C5×D4—22no—
80C2×C5×D4—22no—
81C2×C5×D4—21no—
82C2×C5×D4—22no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—41no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—81no—
98C2×C5×D4—81no—
99C2×C5×D4SD1612yes—
100C22×C4×C5—21no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5#4111yescharacteristic
111C5×D8—48no—
112C2×C5×C8—21no—
113C2×C5×C8—21no—
114C2×C5×C8—22no—
115C2×C5×C8—21no—
116C2×C5×C8—21no—
117C2×C5×C8—21no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8D812yescomplemented
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—41no—
131C5×C4⋊C4—41no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—81no—
134C5×C22⋊C4—41no—
135C5×C22⋊C4—41no—
136C42×C5C2×D411yescharacteristic
137C42×C5C2×D411yescharacteristic
138C42×C5#4111yescharacteristic
139C42×C5#4111yescharacteristic
140C22×D8—21no—
141C2×#127C22×C511yescharacteristic
142C2×C4×D4C22×C511yescharacteristic
143#459—22no—
144#459—22no—
145C2×C4⋊C8C22×C511yescharacteristic
146C2×C4⋊C8C22×C511yescharacteristic
147C2×C4⋊C8C22×C511yescharacteristic
148C2×#102—21no—
149C2×#102—21no—
150C2×#102—21no—
151C2×#102—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C4×C8C22×C511yescharacteristic
155#384C22×C511yescharacteristic
156#340—21no—
157#334—22no—
158#331—22no—
159C23×C5—22no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5—42no—
167C23×C5—81no—
168C23×C5—81no—
169C23×C5—81no—
170C23×C5—81no—
171C23×C5—81no—
172C23×C5—81no—
173C23×C5#12111yescharacteristic
174C5×D4—22no—
175C5×D4—22no—
176C5×D4—41no—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—42no—
180C5×D4—42no—
181C5×D4—41no—
182C5×D4—82no—
183C5×D4—82no—
184C5×D4—81no—
185C5×D4—81no—
186C5×D4—81no—
187C5×D4—81no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—81no—
194C2×C4×C5—81no—
195C2×C4×C5—81no—
196C2×C4×C5—81no—
197C2×C4×C5—81no—
198C2×C4×C5—81no—
199C2×C4×C5—81no—
200C2×C4×C5#12011yescharacteristic
201C2×C4×C5#12111yescharacteristic
202C2×C4×C5#12111yescharacteristic
203C2×C4×C5#12311yescharacteristic
204C2×C4×C5#12311yescharacteristic
205C2×C4×C5#12411yescharacteristic
206C2×C4×C5C2×D811yescharacteristic
207C2×C4×C5C2×SD1611yescharacteristic
208C2×C4×C5#13511yescharacteristic
209C2×C4×C5#13511yescharacteristic
210C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
214C5×C8—22no—
215C5×C8—42no—
216C5×C8—41no—
217C5×C8—81no—
218C5×C8—81no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C5×D411yescharacteristic
223C23×C4—21no—
224C2×D8—24no—
225C2×D8—42no—
226C2×D8—42no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8C5×D411yescharacteristic
231C22×C8C5×D411yescharacteristic
232#127—21no—
233#127—21no—
234#127—21no—
235#127C5×D412yes—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C5×D411yescharacteristic
244C2×C22⋊C4—21no—
245C2×C42C23×C511yescharacteristic
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8C5×D412yes—
252#102—24no—
253#102—42no—
254#102—42no—
255#102—42no—
256C22⋊C8—42no—
257C22⋊C8—42no—
258C4×C8—21no—
259C4×C8—21no—
260C22×C5—42no—
261C22×C5—42no—
262C22×C5—42no—
263C22×C5—81no—
264C22×C5—81no—
265C22×C5—81no—
266C22×C5—81no—
267C22×C5—82no—
268C22×C5—82no—
269C22×C5—82no—
270C22×C5—161no—
271C22×C5—161no—
272C22×C5—161no—
273C22×C5—161no—
274C22×C5#39411yescharacteristic
275C22×C5#45911yescharacteristic
276C22×C5#46311yescharacteristic
277C22×C5#46511yescharacteristic
278C22×C5#46911yescharacteristic
279C22×C5#47111yescharacteristic
280C22×C5#47211yescharacteristic
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—81no—
284C4×C5—161no—
285C4×C5#44911yescharacteristic
286C4×C5#45011yescharacteristic
287C4×C5#45911yescharacteristic
288C4×C5#46311yescharacteristic
289C4×C5#46611yescharacteristic
290C4×C5#46911yescharacteristic
291C4×C5#48111yescharacteristic
292C4×C5#48211yescharacteristic
293C24—21no—
294C24—41no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—81no—
315C2×D4—81no—
316C2×D4C5×SD1612yes—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C5×#4111yescharacteristic
328D8—48no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8C5×D812yescomplemented
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—81no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42C2×C5×D411yescharacteristic
354C42C2×C5×D411yescharacteristic
355C42C5×#4111yescharacteristic
356C42C5×#4111yescharacteristic
357C2×C5—82no—
358C2×C5—162no—
359C2×C5#166511yescharacteristic
360C2×C5#167711yescharacteristic
361C2×C5#168711yescharacteristic
362C2×C5#170111yescharacteristic
363C2×C5#203411yescharacteristic
364C2×C5#205111yescharacteristic
365C2×C5#205411yescharacteristic
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—42no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23C5×#12111yescharacteristic
381D4—22no—
382D4—22no—
383D4—41no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—41no—
389D4—82no—
390D4—82no—
391D4—81no—
392D4—81no—
393D4—81no—
394D4—81no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C5×#12011yescharacteristic
408C2×C4C5×#12111yescharacteristic
409C2×C4C5×#12111yescharacteristic
410C2×C4C5×#12311yescharacteristic
411C2×C4C5×#12311yescharacteristic
412C2×C4C5×#12411yescharacteristic
413C2×C4C2×C5×D811yescharacteristic
414C2×C4C2×C5×SD1611yescharacteristic
415C2×C4C5×#13511yescharacteristic
416C2×C4C5×#13511yescharacteristic
417C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
418C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
419C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
420C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
421C8—22no—
422C8—42no—
423C8—41no—
424C8—81no—
425C8—81no—
426C5#1047311yescharacteristic, direct product factor, Sylow
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22C5×#39411yescharacteristic
442C22C5×#45911yescharacteristic
443C22C5×#46311yescharacteristic
444C22C5×#46511yescharacteristic
445C22C5×#46911yescharacteristic
446C22C5×#47111yescharacteristic
447C22C5×#47211yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4C5×#44911yescharacteristic
453C4C5×#45011yescharacteristic
454C4C5×#45911yescharacteristic
455C4C5×#46311yescharacteristic
456C4C5×#46611yescharacteristic
457C4C5×#46911yescharacteristic
458C4C5×#48111yescharacteristic
459C4C5×#48211yescharacteristic
460C2—82no—
461C2—162no—
462C2C5×#166511yescharacteristic
463C2C5×#167711yescharacteristic
464C2C5×#168711yescharacteristic
465C2C5×#170111yescharacteristic
466C2C5×#203411yescharacteristic
467C2C5×#205111yescharacteristic
468C2C5×#205411yescharacteristic
subgroupG/H
center, socleC23×C5#121
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1957C2semidirect
3. C5×#1954C2semidirect
4. C5×#1802C2semidirect
5. C2×C5×#334C2semidirect
6. C2×C5×#331C2semidirect
7. C5×#1296C2semidirect
27. #10473C5direct (N × H)
70. #1957C2×C5semidirect
71. #1954C2×C5semidirect
72. #1802C2×C5semidirect
73. C2×#334C2×C5semidirect
74. C2×#331C2×C5semidirect
75. #1296C2×C5semidirect
126. C2×C5×C8D8semidirect
343. C2×C8C5×D8semidirect
426. C5#10473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4592
C5×#19572
C5×#19542
C5×#18022
C2×C5×#3342
C2×C5×#3312
C5×#12962
#104735