Subgroups — C₂×C₃²×C₅²×D₁₃ #26043883

Order 11700.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅²×D₁₃	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₅×D₁₃	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₃×C₅²×C₁₃	C₂×C₃	1	4	yes	complemented
7	C₃×C₅²×D₁₃	C₂×C₃	1	8	yes	direct product factor
8	C₂×C₅²×D₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₅×C₁₃	C₂×C₅	1	6	yes	complemented
10	C₃²×C₅×D₁₃	C₂×C₅	1	12	yes	direct product factor
11	C₃×C₅²×C₁₃	C₂²×C₃	1	4	yes	complemented
12	C₂²×C₃²×C₅²	—	13	1	no	maximal, Hall
13	C₂×C₃×C₅×D₁₃	C₃×C₅	1	24	yes	direct product factor
14	C₂×C₅²×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₅²×D₁₃	C₂×C₃²	1	2	yes	direct product factor
16	C₃²×C₅×C₁₃	C₂²×C₅	1	6	yes	complemented
17	C₂×C₃²×D₁₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃²×C₅²	—	13	2	no	—
19	C₂×C₃²×C₅²	D₁₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₅×C₁₃	C₂×C₃×C₅	1	24	yes	complemented
21	C₃×C₅×D₁₃	C₂×C₃×C₅	1	48	yes	direct product factor
22	C₅²×C₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃×C₅²	—	13	4	no	—
24	C₂×C₅×D₁₃	C₃²×C₅	1	6	yes	direct product factor
25	C₂×C₃²×C₁₃	C₂×C₅²	1	1	yes	characteristic, complemented
26	C₃²×D₁₃	C₂×C₅²	1	2	yes	direct product factor
27	C₃²×C₅²	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅×C₁₃	C₂²×C₃×C₅	1	24	yes	complemented
29	C₂²×C₃²×C₅	—	13	6	no	—
30	C₂×C₃×D₁₃	C₃×C₅²	1	4	yes	direct product factor
31	C₂×C₃×C₅²	—	13	8	no	—
32	C₂×C₃×C₅²	C₃×D₁₃	1	4	yes	direct product factor
33	C₂×C₅×C₁₃	C₂×C₃²×C₅	1	6	yes	complemented
34	C₅×D₁₃	C₂×C₃²×C₅	1	12	yes	direct product factor
35	C₃²×C₁₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₅²	—	13	1	no	Hall
37	C₂×C₃²×C₅	—	13	12	no	—
38	C₂×C₃²×C₅	C₅×D₁₃	1	6	yes	direct product factor
39	C₂×C₃×C₁₃	C₂×C₃×C₅²	1	4	yes	complemented
40	C₃×D₁₃	C₂×C₃×C₅²	1	8	yes	direct product factor
41	C₃×C₅²	C₂×C₃×D₁₃	1	4	yes	direct product factor
42	C₅×C₁₃	C₂²×C₃²×C₅	1	6	yes	complemented
43	C₂²×C₃×C₅	—	13	24	no	—
44	C₂×D₁₃	C₃²×C₅²	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₅²	—	13	2	no	—
46	C₂×C₅²	C₃²×D₁₃	1	1	yes	characteristic, direct product factor
47	C₃²×C₅	C₂×C₅×D₁₃	1	6	yes	direct product factor
48	C₃×C₁₃	C₂²×C₃×C₅²	1	4	yes	complemented
49	C₂²×C₃²	—	13	1	no	Hall
50	C₂×C₃×C₅	—	13	48	no	—
51	C₂×C₃×C₅	C₃×C₅×D₁₃	1	24	yes	direct product factor
52	C₂×C₁₃	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented
53	D₁₃	C₂×C₃²×C₅²	1	2	yes	direct product factor
54	C₅²	C₂×C₃²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	—	13	6	no	—
56	C₂×C₃²	—	13	2	no	—
57	C₂×C₃²	C₅²×D₁₃	1	1	yes	characteristic, direct product factor
58	C₃×C₅	C₂×C₃×C₅×D₁₃	1	24	yes	direct product factor
59	C₁₃	C₂²×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₃	—	13	4	no	—
61	C₂×C₅	—	13	12	no	—
62	C₂×C₅	C₃²×C₅×D₁₃	1	6	yes	direct product factor
63	C₃²	C₂×C₅²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	13	8	no	—
65	C₂×C₃	C₃×C₅²×D₁₃	1	4	yes	direct product factor
66	C₅	C₂×C₃²×C₅×D₁₃	1	6	yes	direct product factor
67	C₂²	—	13	1	no	Sylow
68	C₃	C₂×C₃×C₅²×D₁₃	1	4	yes	direct product factor
69	C₂	—	13	2	no	—
70	C₂	C₃²×C₅²×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅²	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃²×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×D₁₃	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₃	C₂	semidirect
3. C₂×C₃×C₅²×D₁₃	C₃	direct (N × H)
4. C₃²×C₅²×C₁₃	C₂²	semidirect
5. C₂×C₃²×C₅×D₁₃	C₅	direct (N × H)
6. C₂×C₃×C₅²×C₁₃	C₂×C₃	semidirect
7. C₃×C₅²×D₁₃	C₂×C₃	direct (N × H)
8. C₂×C₅²×D₁₃	C₃²	direct (N × H)
9. C₂×C₃²×C₅×C₁₃	C₂×C₅	semidirect
10. C₃²×C₅×D₁₃	C₂×C₅	direct (N × H)
11. C₃×C₅²×C₁₃	C₂²×C₃	semidirect
13. C₂×C₃×C₅×D₁₃	C₃×C₅	direct (N × H)
14. C₂×C₅²×C₁₃	C₂×C₃²	semidirect
15. C₅²×D₁₃	C₂×C₃²	direct (N × H)
16. C₃²×C₅×C₁₃	C₂²×C₅	semidirect
17. C₂×C₃²×D₁₃	C₅²	direct (N × H)
19. C₂×C₃²×C₅²	D₁₃	direct (N × H)
20. C₂×C₃×C₅×C₁₃	C₂×C₃×C₅	semidirect
21. C₃×C₅×D₁₃	C₂×C₃×C₅	direct (N × H)
22. C₅²×C₁₃	C₂²×C₃²	semidirect
24. C₂×C₅×D₁₃	C₃²×C₅	direct (N × H)
25. C₂×C₃²×C₁₃	C₂×C₅²	semidirect
26. C₃²×D₁₃	C₂×C₅²	direct (N × H)
27. C₃²×C₅²	C₂×D₁₃	direct (N × H)
28. C₃×C₅×C₁₃	C₂²×C₃×C₅	semidirect
30. C₂×C₃×D₁₃	C₃×C₅²	direct (N × H)
32. C₂×C₃×C₅²	C₃×D₁₃	direct (N × H)
33. C₂×C₅×C₁₃	C₂×C₃²×C₅	semidirect
34. C₅×D₁₃	C₂×C₃²×C₅	direct (N × H)
35. C₃²×C₁₃	C₂²×C₅²	semidirect
38. C₂×C₃²×C₅	C₅×D₁₃	direct (N × H)
39. C₂×C₃×C₁₃	C₂×C₃×C₅²	semidirect
40. C₃×D₁₃	C₂×C₃×C₅²	direct (N × H)
41. C₃×C₅²	C₂×C₃×D₁₃	direct (N × H)
42. C₅×C₁₃	C₂²×C₃²×C₅	semidirect
44. C₂×D₁₃	C₃²×C₅²	direct (N × H)
46. C₂×C₅²	C₃²×D₁₃	direct (N × H)
47. C₃²×C₅	C₂×C₅×D₁₃	direct (N × H)
48. C₃×C₁₃	C₂²×C₃×C₅²	semidirect
51. C₂×C₃×C₅	C₃×C₅×D₁₃	direct (N × H)
52. C₂×C₁₃	C₂×C₃²×C₅²	semidirect
53. D₁₃	C₂×C₃²×C₅²	direct (N × H)
54. C₅²	C₂×C₃²×D₁₃	direct (N × H)
57. C₂×C₃²	C₅²×D₁₃	direct (N × H)
58. C₃×C₅	C₂×C₃×C₅×D₁₃	direct (N × H)
59. C₁₃	C₂²×C₃²×C₅²	semidirect
62. C₂×C₅	C₃²×C₅×D₁₃	direct (N × H)
63. C₃²	C₂×C₅²×D₁₃	direct (N × H)
65. C₂×C₃	C₃×C₅²×D₁₃	direct (N × H)
66. C₅	C₂×C₃²×C₅×D₁₃	direct (N × H)
68. C₃	C₂×C₃×C₅²×D₁₃	direct (N × H)
70. C₂	C₃²×C₅²×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅²×D₁₃	2
C₂×C₃²×C₅²×C₁₃	2
C₂×C₃×C₅²×D₁₃	3
C₂×C₃²×C₅×D₁₃	5
C₂²×C₃²×C₅²	13

Subgroups — C2×C32×C52×D13 #26043883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅²×D₁₃ #26043883