Subgroups — C₂⁵×C₄×D₆₁ #30593887

Order 15616.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×C₄×D₆₁	C₂	1	124	yes	maximal, direct product factor
4	C₂⁵×C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×D₆₁	C₄	1	64	yes	direct product factor
6	C₂⁵×D₆₁	C₂²	1	62	yes	—
7	C₂⁴×Dic₆₁	C₂²	1	62	yes	complemented
8	C₂³×C₄×D₆₁	C₂²	1	2480	yes	direct product factor
9	C₂⁶×C₆₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₆₁	C₂²	1	62	yes	complemented
11	C₂⁴×D₆₁	C₂×C₄	1	1984	yes	direct product factor
12	C₂⁴×D₆₁	C₂³	1	620	yes	—
13	C₂³×Dic₆₁	C₂³	1	620	yes	complemented
14	C₂²×C₄×D₆₁	C₂³	1	9920	yes	direct product factor
15	C₂⁵×C₆₁	C₂×C₄	1	32	yes	complemented
16	C₂⁵×C₆₁	C₂³	1	31	yes	—
17	C₂³×C₄×C₆₁	C₂³	1	620	yes	complemented
18	C₂⁴×C₆₁	C₂²×C₄	1	496	yes	complemented
19	C₂⁴×C₆₁	C₂⁴	1	155	yes	—
20	C₂³×D₆₁	C₂²×C₄	1	9920	yes	direct product factor
21	C₂³×D₆₁	C₂⁴	1	1240	yes	—
22	C₂²×C₄×C₆₁	C₂⁴	1	1240	yes	complemented
23	C₂²×Dic₆₁	C₂⁴	1	1240	yes	complemented
24	C₂×C₄×D₆₁	C₂⁴	1	7936	yes	direct product factor
25	C₂³×C₆₁	C₂³×C₄	1	1240	yes	complemented
26	C₂³×C₆₁	C₂⁵	1	155	yes	—
27	C₂²×D₆₁	C₂³×C₄	1	9920	yes	direct product factor
28	C₂²×D₆₁	C₂⁵	1	496	yes	—
29	C₂×C₄×C₆₁	C₂⁵	1	496	yes	complemented
30	C₂×Dic₆₁	C₂⁵	1	496	yes	complemented
31	C₄×D₆₁	C₂⁵	1	1024	yes	direct product factor
32	C₂⁶×C₄	—	61	1	no	maximal, Sylow
33	C₂²×C₆₁	C₂⁴×C₄	1	620	yes	complemented
34	C₂²×C₆₁	C₂⁶	1	31	yes	—
35	C₂×D₆₁	C₂⁴×C₄	1	1984	yes	direct product factor
36	C₂×D₆₁	C₂⁶	1	32	yes	—
37	C₄×C₆₁	C₂⁶	1	32	yes	complemented
38	Dic₆₁	C₂⁶	1	32	yes	complemented
39	C₂⁷	—	61	1	no	—
40	C₂⁵×C₄	—	61	1	no	—
41	C₂⁵×C₄	—	61	124	no	—
42	C₂⁵×C₄	D₆₁	1	1	yes	characteristic, direct product factor
43	C₂×C₆₁	C₂⁵×C₄	1	62	yes	complemented
44	C₂×C₆₁	C₂⁷	1	1	yes	characteristic
45	D₆₁	C₂⁵×C₄	1	64	yes	direct product factor
46	C₂⁶	—	61	64	no	—
47	C₂⁶	—	61	62	no	—
48	C₂⁶	C₂×D₆₁	1	1	yes	characteristic
49	C₂⁴×C₄	—	61	62	no	—
50	C₂⁴×C₄	—	61	2480	no	—
51	C₂⁴×C₄	C₂×D₆₁	1	62	yes	direct product factor
52	C₆₁	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
53	C₂⁵	—	61	1984	no	—
54	C₂⁵	—	61	620	no	—
55	C₂⁵	C₄×D₆₁	1	32	yes	direct product factor
56	C₂⁵	C₂²×D₆₁	1	31	yes	—
57	C₂³×C₄	—	61	620	no	—
58	C₂³×C₄	—	61	9920	no	—
59	C₂³×C₄	C₂²×D₆₁	1	620	yes	direct product factor
60	C₂⁴	—	61	9920	no	—
61	C₂⁴	—	61	1240	no	—
62	C₂⁴	C₂×C₄×D₆₁	1	496	yes	direct product factor
63	C₂⁴	C₂³×D₆₁	1	155	yes	—
64	C₂²×C₄	—	61	1240	no	—
65	C₂²×C₄	—	61	7936	no	—
66	C₂²×C₄	C₂³×D₆₁	1	1240	yes	direct product factor
67	C₂³	—	61	9920	no	—
68	C₂³	—	61	496	no	—
69	C₂³	C₂²×C₄×D₆₁	1	1240	yes	direct product factor
70	C₂³	C₂⁴×D₆₁	1	155	yes	—
71	C₂×C₄	—	61	496	no	—
72	C₂×C₄	—	61	1024	no	—
73	C₂×C₄	C₂⁴×D₆₁	1	496	yes	direct product factor
74	C₂²	—	61	1984	no	—
75	C₂²	—	61	32	no	—
76	C₂²	C₂³×C₄×D₆₁	1	620	yes	direct product factor
77	C₂²	C₂⁵×D₆₁	1	31	yes	—
78	C₄	—	61	32	no	—
79	C₄	C₂⁵×D₆₁	1	32	yes	direct product factor
80	C₂	—	61	64	no	—
81	C₂	C₂⁴×C₄×D₆₁	1	62	yes	direct product factor
82	C₂	C₂⁶×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₄	D₆₁
commutator, hypocenter	C₆₁	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₆₁
Fitting	C₂⁵×C₄×C₆₁	C₂
socle	C₂⁶×C₆₁	C₂²
prime radical	C₂⁶×D₆₁	C₂
cosocle	C₂×C₆₁	C₂⁷
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁵×Dic₆₁	C₂	semidirect
3. C₂⁴×C₄×D₆₁	C₂	direct (N × H)
4. C₂⁵×C₄×C₆₁	C₂	semidirect
5. C₂⁵×D₆₁	C₄	direct (N × H)
7. C₂⁴×Dic₆₁	C₂²	semidirect
8. C₂³×C₄×D₆₁	C₂²	direct (N × H)
10. C₂⁴×C₄×C₆₁	C₂²	semidirect
11. C₂⁴×D₆₁	C₂×C₄	direct (N × H)
13. C₂³×Dic₆₁	C₂³	semidirect
14. C₂²×C₄×D₆₁	C₂³	direct (N × H)
15. C₂⁵×C₆₁	C₂×C₄	semidirect
17. C₂³×C₄×C₆₁	C₂³	semidirect
18. C₂⁴×C₆₁	C₂²×C₄	semidirect
20. C₂³×D₆₁	C₂²×C₄	direct (N × H)
22. C₂²×C₄×C₆₁	C₂⁴	semidirect
23. C₂²×Dic₆₁	C₂⁴	semidirect
24. C₂×C₄×D₆₁	C₂⁴	direct (N × H)
25. C₂³×C₆₁	C₂³×C₄	semidirect
27. C₂²×D₆₁	C₂³×C₄	direct (N × H)
29. C₂×C₄×C₆₁	C₂⁵	semidirect
30. C₂×Dic₆₁	C₂⁵	semidirect
31. C₄×D₆₁	C₂⁵	direct (N × H)
33. C₂²×C₆₁	C₂⁴×C₄	semidirect
35. C₂×D₆₁	C₂⁴×C₄	direct (N × H)
37. C₄×C₆₁	C₂⁶	semidirect
38. Dic₆₁	C₂⁶	semidirect
42. C₂⁵×C₄	D₆₁	direct (N × H)
43. C₂×C₆₁	C₂⁵×C₄	semidirect
45. D₆₁	C₂⁵×C₄	direct (N × H)
51. C₂⁴×C₄	C₂×D₆₁	direct (N × H)
52. C₆₁	C₂⁶×C₄	semidirect
55. C₂⁵	C₄×D₆₁	direct (N × H)
59. C₂³×C₄	C₂²×D₆₁	direct (N × H)
62. C₂⁴	C₂×C₄×D₆₁	direct (N × H)
66. C₂²×C₄	C₂³×D₆₁	direct (N × H)
69. C₂³	C₂²×C₄×D₆₁	direct (N × H)
73. C₂×C₄	C₂⁴×D₆₁	direct (N × H)
76. C₂²	C₂³×C₄×D₆₁	direct (N × H)
79. C₄	C₂⁵×D₆₁	direct (N × H)
81. C₂	C₂⁴×C₄×D₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₆₁	2
C₂⁵×Dic₆₁	2
C₂⁴×C₄×D₆₁	2
C₂⁵×C₄×C₆₁	2
C₂⁶×C₄	61

Subgroups — C25×C4×D61 #30593887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₄×D₆₁ #30593887