Subgroups — C₂⁴×C₄²×C₅ #11985358

Order 1280.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₅	C₂	1	3	yes	maximal
2	C₂³×C₄²×C₅	C₂	1	60	yes	maximal, direct product factor
3	C₂⁶×C₅	C₂²	1	1	yes	characteristic
4	C₂⁴×C₄×C₅	C₄	1	96	yes	direct product factor
5	C₂⁴×C₄×C₅	C₂²	1	90	yes	—
6	C₂²×C₄²×C₅	C₂²	1	560	yes	direct product factor
7	C₂⁴×C₄²	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂⁵×C₅	C₂×C₄	1	48	yes	—
9	C₂⁵×C₅	C₂³	1	15	yes	—
10	C₂³×C₄×C₅	C₂×C₄	1	1440	yes	direct product factor
11	C₂³×C₄×C₅	C₂³	1	420	yes	—
12	C₂×C₄²×C₅	C₂³	1	960	yes	direct product factor
13	C₂⁵×C₄	C₂×C₅	1	3	yes	—
14	C₂³×C₄²	C₂×C₅	1	60	yes	direct product factor
15	C₂⁴×C₅	C₄²	1	256	yes	direct product factor
16	C₂⁴×C₅	C₂²×C₄	1	360	yes	—
17	C₂⁴×C₅	C₂⁴	1	35	yes	—
18	C₂²×C₄×C₅	C₂²×C₄	1	3360	yes	direct product factor
19	C₂²×C₄×C₅	C₂⁴	1	360	yes	—
20	C₄²×C₅	C₂⁴	1	256	yes	direct product factor
21	C₂⁶	C₂²×C₅	1	1	yes	characteristic
22	C₂⁴×C₄	C₄×C₅	1	96	yes	direct product factor
23	C₂⁴×C₄	C₂²×C₅	1	90	yes	—
24	C₂²×C₄²	C₂²×C₅	1	560	yes	direct product factor
25	C₂³×C₅	C₂×C₄²	1	960	yes	direct product factor
26	C₂³×C₅	C₂³×C₄	1	420	yes	—
27	C₂³×C₅	C₂⁵	1	15	yes	—
28	C₂×C₄×C₅	C₂³×C₄	1	1440	yes	direct product factor
29	C₂×C₄×C₅	C₂⁵	1	48	yes	—
30	C₂⁵	C₂×C₄×C₅	1	48	yes	—
31	C₂⁵	C₂³×C₅	1	15	yes	—
32	C₂³×C₄	C₂×C₄×C₅	1	1440	yes	direct product factor
33	C₂³×C₄	C₂³×C₅	1	420	yes	—
34	C₂×C₄²	C₂³×C₅	1	960	yes	direct product factor
35	C₂²×C₅	C₂²×C₄²	1	560	yes	direct product factor
36	C₂²×C₅	C₂⁴×C₄	1	90	yes	—
37	C₂²×C₅	C₂⁶	1	1	yes	characteristic
38	C₄×C₅	C₂⁴×C₄	1	96	yes	direct product factor
39	C₂⁴	C₄²×C₅	1	256	yes	direct product factor
40	C₂⁴	C₂²×C₄×C₅	1	360	yes	—
41	C₂⁴	C₂⁴×C₅	1	35	yes	—
42	C₂²×C₄	C₂²×C₄×C₅	1	3360	yes	direct product factor
43	C₂²×C₄	C₂⁴×C₅	1	360	yes	—
44	C₄²	C₂⁴×C₅	1	256	yes	direct product factor
45	C₂×C₅	C₂³×C₄²	1	60	yes	direct product factor
46	C₂×C₅	C₂⁵×C₄	1	3	yes	—
47	C₂³	C₂×C₄²×C₅	1	960	yes	direct product factor
48	C₂³	C₂³×C₄×C₅	1	420	yes	—
49	C₂³	C₂⁵×C₅	1	15	yes	—
50	C₂×C₄	C₂³×C₄×C₅	1	1440	yes	direct product factor
51	C₂×C₄	C₂⁵×C₅	1	48	yes	—
52	C₅	C₂⁴×C₄²	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	C₂²×C₄²×C₅	1	560	yes	direct product factor
54	C₂²	C₂⁴×C₄×C₅	1	90	yes	—
55	C₂²	C₂⁶×C₅	1	1	yes	characteristic
56	C₄	C₂⁴×C₄×C₅	1	96	yes	direct product factor
57	C₂	C₂³×C₄²×C₅	1	60	yes	direct product factor
58	C₂	C₂⁵×C₄×C₅	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁶×C₅
socle, prime radical	C₂⁶×C₅	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₅	C₂	direct (N × H)
4. C₂⁴×C₄×C₅	C₄	direct (N × H)
6. C₂²×C₄²×C₅	C₂²	direct (N × H)
7. C₂⁴×C₄²	C₅	direct (N × H)
10. C₂³×C₄×C₅	C₂×C₄	direct (N × H)
12. C₂×C₄²×C₅	C₂³	direct (N × H)
14. C₂³×C₄²	C₂×C₅	direct (N × H)
15. C₂⁴×C₅	C₄²	direct (N × H)
18. C₂²×C₄×C₅	C₂²×C₄	direct (N × H)
20. C₄²×C₅	C₂⁴	direct (N × H)
22. C₂⁴×C₄	C₄×C₅	direct (N × H)
24. C₂²×C₄²	C₂²×C₅	direct (N × H)
25. C₂³×C₅	C₂×C₄²	direct (N × H)
28. C₂×C₄×C₅	C₂³×C₄	direct (N × H)
32. C₂³×C₄	C₂×C₄×C₅	direct (N × H)
34. C₂×C₄²	C₂³×C₅	direct (N × H)
35. C₂²×C₅	C₂²×C₄²	direct (N × H)
38. C₄×C₅	C₂⁴×C₄	direct (N × H)
39. C₂⁴	C₄²×C₅	direct (N × H)
42. C₂²×C₄	C₂²×C₄×C₅	direct (N × H)
44. C₄²	C₂⁴×C₅	direct (N × H)
45. C₂×C₅	C₂³×C₄²	direct (N × H)
47. C₂³	C₂×C₄²×C₅	direct (N × H)
50. C₂×C₄	C₂³×C₄×C₅	direct (N × H)
52. C₅	C₂⁴×C₄²	direct (N × H)
53. C₂²	C₂²×C₄²×C₅	direct (N × H)
56. C₄	C₂⁴×C₄×C₅	direct (N × H)
57. C₂	C₂³×C₄²×C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₅	2
C₂³×C₄²×C₅	2
C₂⁴×C₄²	5

Subgroups — C24×C42×C5 #11985358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄²×C₅ #11985358