Subgroups — C₂⁵×D₄×C₁₃ #15749434

Order 3328.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₄×C₁₃	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶×C₁₃	—	2	64	no	—
5	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
6	C₂⁶×C₁₃	C₂²	1	124	yes	complemented
7	C₂³×D₄×C₁₃	C₂²	1	2480	yes	direct product factor
8	C₂⁴×C₄×C₁₃	C₂²	1	62	yes	complemented
9	C₂⁵×C₁₃	—	2	1984	no	—
10	C₂⁵×C₁₃	D₄	1	32	yes	direct product factor
11	C₂⁵×C₁₃	C₂³	1	31	yes	—
12	C₂⁵×C₁₃	C₂³	1	1240	yes	complemented
13	C₂²×D₄×C₁₃	C₂³	1	9920	yes	direct product factor
14	C₂³×C₄×C₁₃	C₂³	1	620	yes	complemented
15	C₂⁵×D₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂⁴×C₁₃	—	2	9920	no	—
17	C₂⁴×C₁₃	C₂×D₄	1	496	yes	direct product factor
18	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
19	C₂⁴×C₁₃	C₂⁴	1	2480	yes	complemented
20	C₂×D₄×C₁₃	C₂⁴	1	7936	yes	direct product factor
21	C₂²×C₄×C₁₃	C₂⁴	1	1240	yes	complemented
22	C₂⁷	C₂×C₁₃	1	2	yes	complemented
23	C₂⁴×D₄	C₂×C₁₃	1	124	yes	direct product factor
24	C₂⁵×C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₂³×C₁₃	—	2	9920	no	—
26	C₂³×C₁₃	C₂²×D₄	1	1240	yes	direct product factor
27	C₂³×C₁₃	C₂⁵	1	155	yes	—
28	C₂³×C₁₃	C₂⁵	1	992	yes	complemented
29	D₄×C₁₃	C₂⁵	1	1024	yes	direct product factor
30	C₂×C₄×C₁₃	C₂⁵	1	496	yes	complemented
31	C₂⁶	—	2	64	no	—
32	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
33	C₂⁶	C₂²×C₁₃	1	124	yes	complemented
34	C₂³×D₄	C₂²×C₁₃	1	2480	yes	direct product factor
35	C₂⁴×C₄	C₂²×C₁₃	1	62	yes	complemented
36	C₂²×C₁₃	—	2	1984	no	—
37	C₂²×C₁₃	C₂³×D₄	1	620	yes	direct product factor
38	C₂²×C₁₃	C₂⁶	1	31	yes	—
39	C₂²×C₁₃	C₂⁶	1	64	yes	complemented
40	C₄×C₁₃	C₂⁶	1	32	yes	complemented
41	C₂⁵	—	2	1984	no	—
42	C₂⁵	D₄×C₁₃	1	32	yes	direct product factor
43	C₂⁵	C₂³×C₁₃	1	31	yes	—
44	C₂⁵	C₂³×C₁₃	1	1240	yes	complemented
45	C₂²×D₄	C₂³×C₁₃	1	9920	yes	direct product factor
46	C₂³×C₄	C₂³×C₁₃	1	620	yes	complemented
47	C₂×C₁₃	—	2	64	no	—
48	C₂×C₁₃	C₂⁴×D₄	1	62	yes	direct product factor
49	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
50	C₂⁴	—	2	9920	no	—
51	C₂⁴	C₂×D₄×C₁₃	1	496	yes	direct product factor
52	C₂⁴	C₂⁴×C₁₃	1	155	yes	—
53	C₂⁴	C₂⁴×C₁₃	1	2480	yes	complemented
54	C₂×D₄	C₂⁴×C₁₃	1	7936	yes	direct product factor
55	C₂²×C₄	C₂⁴×C₁₃	1	1240	yes	complemented
56	C₁₃	C₂⁵×D₄	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³	—	2	9920	no	—
58	C₂³	C₂²×D₄×C₁₃	1	1240	yes	direct product factor
59	C₂³	C₂⁵×C₁₃	1	155	yes	—
60	C₂³	C₂⁵×C₁₃	1	992	yes	complemented
61	D₄	C₂⁵×C₁₃	1	1024	yes	direct product factor
62	C₂×C₄	C₂⁵×C₁₃	1	496	yes	complemented
63	C₂²	—	2	1984	no	—
64	C₂²	C₂³×D₄×C₁₃	1	620	yes	direct product factor
65	C₂²	C₂⁶×C₁₃	1	31	yes	—
66	C₂²	C₂⁶×C₁₃	1	64	yes	complemented
67	C₄	C₂⁶×C₁₃	1	32	yes	complemented
68	C₂	—	2	64	no	—
69	C₂	C₂⁴×D₄×C₁₃	1	62	yes	direct product factor
70	C₂	C₂⁷×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶×C₁₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁷×C₁₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁷×C₁₃	C₂	semidirect
2. C₂⁴×D₄×C₁₃	C₂	direct (N × H)
3. C₂⁵×C₄×C₁₃	C₂	semidirect
6. C₂⁶×C₁₃	C₂²	semidirect
7. C₂³×D₄×C₁₃	C₂²	direct (N × H)
8. C₂⁴×C₄×C₁₃	C₂²	semidirect
10. C₂⁵×C₁₃	D₄	direct (N × H)
12. C₂⁵×C₁₃	C₂³	semidirect
13. C₂²×D₄×C₁₃	C₂³	direct (N × H)
14. C₂³×C₄×C₁₃	C₂³	semidirect
15. C₂⁵×D₄	C₁₃	direct (N × H)
17. C₂⁴×C₁₃	C₂×D₄	direct (N × H)
19. C₂⁴×C₁₃	C₂⁴	semidirect
20. C₂×D₄×C₁₃	C₂⁴	direct (N × H)
21. C₂²×C₄×C₁₃	C₂⁴	semidirect
22. C₂⁷	C₂×C₁₃	semidirect
23. C₂⁴×D₄	C₂×C₁₃	direct (N × H)
24. C₂⁵×C₄	C₂×C₁₃	semidirect
26. C₂³×C₁₃	C₂²×D₄	direct (N × H)
28. C₂³×C₁₃	C₂⁵	semidirect
29. D₄×C₁₃	C₂⁵	direct (N × H)
30. C₂×C₄×C₁₃	C₂⁵	semidirect
33. C₂⁶	C₂²×C₁₃	semidirect
34. C₂³×D₄	C₂²×C₁₃	direct (N × H)
35. C₂⁴×C₄	C₂²×C₁₃	semidirect
37. C₂²×C₁₃	C₂³×D₄	direct (N × H)
39. C₂²×C₁₃	C₂⁶	semidirect
40. C₄×C₁₃	C₂⁶	semidirect
42. C₂⁵	D₄×C₁₃	direct (N × H)
44. C₂⁵	C₂³×C₁₃	semidirect
45. C₂²×D₄	C₂³×C₁₃	direct (N × H)
46. C₂³×C₄	C₂³×C₁₃	semidirect
48. C₂×C₁₃	C₂⁴×D₄	direct (N × H)
51. C₂⁴	C₂×D₄×C₁₃	direct (N × H)
53. C₂⁴	C₂⁴×C₁₃	semidirect
54. C₂×D₄	C₂⁴×C₁₃	direct (N × H)
55. C₂²×C₄	C₂⁴×C₁₃	semidirect
56. C₁₃	C₂⁵×D₄	direct (N × H)
58. C₂³	C₂²×D₄×C₁₃	direct (N × H)
60. C₂³	C₂⁵×C₁₃	semidirect
61. D₄	C₂⁵×C₁₃	direct (N × H)
62. C₂×C₄	C₂⁵×C₁₃	semidirect
64. C₂²	C₂³×D₄×C₁₃	direct (N × H)
66. C₂²	C₂⁶×C₁₃	semidirect
67. C₄	C₂⁶×C₁₃	semidirect
69. C₂	C₂⁴×D₄×C₁₃	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×C₁₃	2
C₂⁴×D₄×C₁₃	2
C₂⁵×C₄×C₁₃	2
C₂⁵×D₄	13

Subgroups — C25×D4×C13 #15749434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₄×C₁₃ #15749434