Subgroups — C₂×C₅×C₁₃²×C₃⋊D₃ #44478348

Order 30420.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₁₃²	—	3	4	no	maximal
4	C₃²×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₁₃²	—	3	8	no	—
7	C₂×C₃×C₅×C₁₃²	D₃	1	4	yes	complemented
8	C₂²×C₅×C₁₃²	—	9	1	no	Hall
9	C₁₃²×C₃⋊D₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃²×C₁₃²	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₃²	C₂×D₃	1	4	yes	complemented
12	C₂×C₅×C₁₃×C₃⋊D₃	C₁₃	1	14	yes	maximal, direct product factor
13	C₂×D₃×C₁₃²	—	3	4	no	—
14	C₂×C₅×C₁₃²	—	9	2	no	—
15	C₂×C₅×C₁₃²	C₃⋊D₃	1	1	yes	characteristic, direct product factor
16	C₃²×C₁₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₅×C₁₃	C₂×C₁₃	1	14	yes	complemented
18	C₅×C₁₃×C₃⋊D₃	C₂×C₁₃	1	28	yes	direct product factor
19	C₂×C₃×C₁₃²	C₅×D₃	1	4	yes	complemented
20	D₃×C₁₃²	—	3	8	no	—
21	C₅×C₁₃²	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×D₃×C₁₃	—	3	56	no	—
23	C₂²×C₁₃²	—	9	1	no	Hall
24	C₃²×C₅×C₁₃	C₂²×C₁₃	1	14	yes	complemented
25	C₃×C₁₃²	C₂×C₅×D₃	1	4	yes	complemented
26	C₂×C₁₃×C₃⋊D₃	C₅×C₁₃	1	14	yes	direct product factor
27	C₂×C₃×C₅×C₁₃	D₃×C₁₃	1	56	yes	complemented
28	C₅×D₃×C₁₃	—	3	112	no	—
29	C₂×C₁₃²	—	9	2	no	—
30	C₂×C₁₃²	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
31	C₂²×C₅×C₁₃	—	9	14	no	—
32	C₂×C₃²×C₁₃	C₂×C₅×C₁₃	1	14	yes	complemented
33	C₁₃×C₃⋊D₃	C₂×C₅×C₁₃	1	28	yes	direct product factor
34	C₃×C₅×C₁₃	C₂×D₃×C₁₃	1	56	yes	complemented
35	C₂×C₅×C₃⋊D₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
36	C₁₃²	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×D₃×C₁₃	—	3	56	no	—
38	C₂×C₅×C₁₃	—	9	28	no	—
39	C₂×C₅×C₁₃	C₁₃×C₃⋊D₃	1	14	yes	direct product factor
40	C₃²×C₁₃	C₂²×C₅×C₁₃	1	14	yes	complemented
41	C₂×C₃²×C₅	C₂×C₁₃²	1	1	yes	characteristic, complemented
42	C₅×C₃⋊D₃	C₂×C₁₃²	1	2	yes	direct product factor
43	C₂×C₃×C₁₃	C₅×D₃×C₁₃	1	56	yes	complemented
44	D₃×C₁₃	—	3	112	no	—
45	C₅×C₁₃	C₂×C₁₃×C₃⋊D₃	1	14	yes	direct product factor
46	C₂×C₅×D₃	—	3	4	no	—
47	C₂²×C₁₃	—	9	14	no	—
48	C₃²×C₅	C₂²×C₁₃²	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	C₂×C₅×D₃×C₁₃	1	56	yes	complemented
50	C₂×C₃⋊D₃	C₅×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₅	D₃×C₁₃²	1	4	yes	complemented
52	C₅×D₃	—	3	8	no	—
53	C₂×C₁₃	—	9	28	no	—
54	C₂×C₁₃	C₅×C₁₃×C₃⋊D₃	1	14	yes	direct product factor
55	C₂²×C₅	—	9	1	no	Hall
56	C₂×C₃²	C₂×C₅×C₁₃²	1	1	yes	characteristic, complemented
57	C₃⋊D₃	C₂×C₅×C₁₃²	1	2	yes	direct product factor
58	C₃×C₅	C₂×D₃×C₁₃²	1	4	yes	complemented
59	C₁₃	C₂×C₅×C₁₃×C₃⋊D₃	1	14	yes	direct product factor
60	C₂×D₃	—	3	4	no	—
61	C₂×C₅	—	9	2	no	—
62	C₂×C₅	C₁₃²×C₃⋊D₃	1	1	yes	characteristic, direct product factor
63	C₃²	C₂²×C₅×C₁₃²	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₅×D₃×C₁₃²	1	4	yes	complemented
65	D₃	—	3	8	no	—
66	C₅	C₂×C₁₃²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	9	1	no	Sylow
68	C₃	C₂×C₅×D₃×C₁₃²	1	4	yes	complemented
69	C₂	—	9	2	no	—
70	C₂	C₅×C₁₃²×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₁₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₃²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₁₃²

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃²×C₃⋊D₃	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₃²	C₂	semidirect
4. C₃²×C₅×C₁₃²	C₂²	semidirect
5. C₂×C₁₃²×C₃⋊D₃	C₅	direct (N × H)
7. C₂×C₃×C₅×C₁₃²	D₃	semidirect
9. C₁₃²×C₃⋊D₃	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₁₃²	C₂×C₅	semidirect
11. C₃×C₅×C₁₃²	C₂×D₃	semidirect
12. C₂×C₅×C₁₃×C₃⋊D₃	C₁₃	direct (N × H)
15. C₂×C₅×C₁₃²	C₃⋊D₃	direct (N × H)
16. C₃²×C₁₃²	C₂²×C₅	semidirect
17. C₂×C₃²×C₅×C₁₃	C₂×C₁₃	semidirect
18. C₅×C₁₃×C₃⋊D₃	C₂×C₁₃	direct (N × H)
19. C₂×C₃×C₁₃²	C₅×D₃	semidirect
21. C₅×C₁₃²	C₂×C₃⋊D₃	direct (N × H)
24. C₃²×C₅×C₁₃	C₂²×C₁₃	semidirect
25. C₃×C₁₃²	C₂×C₅×D₃	semidirect
26. C₂×C₁₃×C₃⋊D₃	C₅×C₁₃	direct (N × H)
27. C₂×C₃×C₅×C₁₃	D₃×C₁₃	semidirect
30. C₂×C₁₃²	C₅×C₃⋊D₃	direct (N × H)
32. C₂×C₃²×C₁₃	C₂×C₅×C₁₃	semidirect
33. C₁₃×C₃⋊D₃	C₂×C₅×C₁₃	direct (N × H)
34. C₃×C₅×C₁₃	C₂×D₃×C₁₃	semidirect
35. C₂×C₅×C₃⋊D₃	C₁₃²	direct (N × H)
36. C₁₃²	C₂×C₅×C₃⋊D₃	direct (N × H)
39. C₂×C₅×C₁₃	C₁₃×C₃⋊D₃	direct (N × H)
40. C₃²×C₁₃	C₂²×C₅×C₁₃	semidirect
41. C₂×C₃²×C₅	C₂×C₁₃²	semidirect
42. C₅×C₃⋊D₃	C₂×C₁₃²	direct (N × H)
43. C₂×C₃×C₁₃	C₅×D₃×C₁₃	semidirect
45. C₅×C₁₃	C₂×C₁₃×C₃⋊D₃	direct (N × H)
48. C₃²×C₅	C₂²×C₁₃²	semidirect
49. C₃×C₁₃	C₂×C₅×D₃×C₁₃	semidirect
50. C₂×C₃⋊D₃	C₅×C₁₃²	direct (N × H)
51. C₂×C₃×C₅	D₃×C₁₃²	semidirect
54. C₂×C₁₃	C₅×C₁₃×C₃⋊D₃	direct (N × H)
56. C₂×C₃²	C₂×C₅×C₁₃²	semidirect
57. C₃⋊D₃	C₂×C₅×C₁₃²	direct (N × H)
58. C₃×C₅	C₂×D₃×C₁₃²	semidirect
59. C₁₃	C₂×C₅×C₁₃×C₃⋊D₃	direct (N × H)
62. C₂×C₅	C₁₃²×C₃⋊D₃	direct (N × H)
63. C₃²	C₂²×C₅×C₁₃²	semidirect
64. C₂×C₃	C₅×D₃×C₁₃²	semidirect
66. C₅	C₂×C₁₃²×C₃⋊D₃	direct (N × H)
68. C₃	C₂×C₅×D₃×C₁₃²	semidirect
70. C₂	C₅×C₁₃²×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃²×C₃⋊D₃	2
C₂×C₃²×C₅×C₁₃²	2
C₂×C₅×D₃×C₁₃²	3
C₂×C₁₃²×C₃⋊D₃	5
C₂×C₅×C₁₃×C₃⋊D₃	13

Subgroups — C2×C5×C132×C3⋊D3 #44478348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃²×C₃⋊D₃ #44478348