Subgroups — C₂⁵×D₄×C₅₃ #27270607

Order 13568.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₅₃	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₄×C₅₃	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶×C₅₃	—	2	64	no	—
5	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
6	C₂⁶×C₅₃	C₂²	1	124	yes	complemented
7	C₂³×D₄×C₅₃	C₂²	1	2480	yes	direct product factor
8	C₂⁴×C₄×C₅₃	C₂²	1	62	yes	complemented
9	C₂⁵×C₅₃	—	2	1984	no	—
10	C₂⁵×C₅₃	D₄	1	32	yes	direct product factor
11	C₂⁵×C₅₃	C₂³	1	31	yes	—
12	C₂⁵×C₅₃	C₂³	1	1240	yes	complemented
13	C₂²×D₄×C₅₃	C₂³	1	9920	yes	direct product factor
14	C₂³×C₄×C₅₃	C₂³	1	620	yes	complemented
15	C₂⁴×C₅₃	—	2	9920	no	—
16	C₂⁴×C₅₃	C₂×D₄	1	496	yes	direct product factor
17	C₂⁴×C₅₃	C₂⁴	1	155	yes	—
18	C₂⁴×C₅₃	C₂⁴	1	2480	yes	complemented
19	C₂×D₄×C₅₃	C₂⁴	1	7936	yes	direct product factor
20	C₂²×C₄×C₅₃	C₂⁴	1	1240	yes	complemented
21	C₂³×C₅₃	—	2	9920	no	—
22	C₂³×C₅₃	C₂²×D₄	1	1240	yes	direct product factor
23	C₂³×C₅₃	C₂⁵	1	155	yes	—
24	C₂³×C₅₃	C₂⁵	1	992	yes	complemented
25	D₄×C₅₃	C₂⁵	1	1024	yes	direct product factor
26	C₂×C₄×C₅₃	C₂⁵	1	496	yes	complemented
27	C₂⁵×D₄	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₅₃	—	2	1984	no	—
29	C₂²×C₅₃	C₂³×D₄	1	620	yes	direct product factor
30	C₂²×C₅₃	C₂⁶	1	31	yes	—
31	C₂²×C₅₃	C₂⁶	1	64	yes	complemented
32	C₄×C₅₃	C₂⁶	1	32	yes	complemented
33	C₂⁷	C₂×C₅₃	1	2	yes	complemented
34	C₂⁴×D₄	C₂×C₅₃	1	124	yes	direct product factor
35	C₂⁵×C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
36	C₂×C₅₃	—	2	64	no	—
37	C₂×C₅₃	C₂⁴×D₄	1	62	yes	direct product factor
38	C₂×C₅₃	C₂⁷	1	1	yes	characteristic
39	C₂⁶	—	2	64	no	—
40	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
41	C₂⁶	C₂²×C₅₃	1	124	yes	complemented
42	C₂³×D₄	C₂²×C₅₃	1	2480	yes	direct product factor
43	C₂⁴×C₄	C₂²×C₅₃	1	62	yes	complemented
44	C₅₃	C₂⁵×D₄	1	1	yes	characteristic, direct product factor, Sylow
45	C₂⁵	—	2	1984	no	—
46	C₂⁵	D₄×C₅₃	1	32	yes	direct product factor
47	C₂⁵	C₂³×C₅₃	1	31	yes	—
48	C₂⁵	C₂³×C₅₃	1	1240	yes	complemented
49	C₂²×D₄	C₂³×C₅₃	1	9920	yes	direct product factor
50	C₂³×C₄	C₂³×C₅₃	1	620	yes	complemented
51	C₂⁴	—	2	9920	no	—
52	C₂⁴	C₂×D₄×C₅₃	1	496	yes	direct product factor
53	C₂⁴	C₂⁴×C₅₃	1	155	yes	—
54	C₂⁴	C₂⁴×C₅₃	1	2480	yes	complemented
55	C₂×D₄	C₂⁴×C₅₃	1	7936	yes	direct product factor
56	C₂²×C₄	C₂⁴×C₅₃	1	1240	yes	complemented
57	C₂³	—	2	9920	no	—
58	C₂³	C₂²×D₄×C₅₃	1	1240	yes	direct product factor
59	C₂³	C₂⁵×C₅₃	1	155	yes	—
60	C₂³	C₂⁵×C₅₃	1	992	yes	complemented
61	D₄	C₂⁵×C₅₃	1	1024	yes	direct product factor
62	C₂×C₄	C₂⁵×C₅₃	1	496	yes	complemented
63	C₂²	—	2	1984	no	—
64	C₂²	C₂³×D₄×C₅₃	1	620	yes	direct product factor
65	C₂²	C₂⁶×C₅₃	1	31	yes	—
66	C₂²	C₂⁶×C₅₃	1	64	yes	complemented
67	C₄	C₂⁶×C₅₃	1	32	yes	complemented
68	C₂	—	2	64	no	—
69	C₂	C₂⁴×D₄×C₅₃	1	62	yes	direct product factor
70	C₂	C₂⁷×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶×C₅₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁷×C₅₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁷×C₅₃	C₂	semidirect
2. C₂⁴×D₄×C₅₃	C₂	direct (N × H)
3. C₂⁵×C₄×C₅₃	C₂	semidirect
6. C₂⁶×C₅₃	C₂²	semidirect
7. C₂³×D₄×C₅₃	C₂²	direct (N × H)
8. C₂⁴×C₄×C₅₃	C₂²	semidirect
10. C₂⁵×C₅₃	D₄	direct (N × H)
12. C₂⁵×C₅₃	C₂³	semidirect
13. C₂²×D₄×C₅₃	C₂³	direct (N × H)
14. C₂³×C₄×C₅₃	C₂³	semidirect
16. C₂⁴×C₅₃	C₂×D₄	direct (N × H)
18. C₂⁴×C₅₃	C₂⁴	semidirect
19. C₂×D₄×C₅₃	C₂⁴	direct (N × H)
20. C₂²×C₄×C₅₃	C₂⁴	semidirect
22. C₂³×C₅₃	C₂²×D₄	direct (N × H)
24. C₂³×C₅₃	C₂⁵	semidirect
25. D₄×C₅₃	C₂⁵	direct (N × H)
26. C₂×C₄×C₅₃	C₂⁵	semidirect
27. C₂⁵×D₄	C₅₃	direct (N × H)
29. C₂²×C₅₃	C₂³×D₄	direct (N × H)
31. C₂²×C₅₃	C₂⁶	semidirect
32. C₄×C₅₃	C₂⁶	semidirect
33. C₂⁷	C₂×C₅₃	semidirect
34. C₂⁴×D₄	C₂×C₅₃	direct (N × H)
35. C₂⁵×C₄	C₂×C₅₃	semidirect
37. C₂×C₅₃	C₂⁴×D₄	direct (N × H)
41. C₂⁶	C₂²×C₅₃	semidirect
42. C₂³×D₄	C₂²×C₅₃	direct (N × H)
43. C₂⁴×C₄	C₂²×C₅₃	semidirect
44. C₅₃	C₂⁵×D₄	direct (N × H)
46. C₂⁵	D₄×C₅₃	direct (N × H)
48. C₂⁵	C₂³×C₅₃	semidirect
49. C₂²×D₄	C₂³×C₅₃	direct (N × H)
50. C₂³×C₄	C₂³×C₅₃	semidirect
52. C₂⁴	C₂×D₄×C₅₃	direct (N × H)
54. C₂⁴	C₂⁴×C₅₃	semidirect
55. C₂×D₄	C₂⁴×C₅₃	direct (N × H)
56. C₂²×C₄	C₂⁴×C₅₃	semidirect
58. C₂³	C₂²×D₄×C₅₃	direct (N × H)
60. C₂³	C₂⁵×C₅₃	semidirect
61. D₄	C₂⁵×C₅₃	direct (N × H)
62. C₂×C₄	C₂⁵×C₅₃	semidirect
64. C₂²	C₂³×D₄×C₅₃	direct (N × H)
66. C₂²	C₂⁶×C₅₃	semidirect
67. C₄	C₂⁶×C₅₃	semidirect
69. C₂	C₂⁴×D₄×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷×C₅₃	2
C₂⁴×D₄×C₅₃	2
C₂⁵×C₄×C₅₃	2
C₂⁵×D₄	53

Subgroups — C25×D4×C53 #27270607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₄×C₅₃ #27270607