Subgroups — C₂×D₅×C₁₃×C₁₃⋊C₃ #23778528

Order 10140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₃×C₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₁₃×C₁₃⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₁₃²	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃×C₁₃⋊C₃	—	5	2	no	—
9	C₂×C₁₃×C₁₃⋊C₃	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₅×C₁₃	—	13	1	no	maximal
12	C₂×D₅×C₁₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
13	C₂²×C₁₃²	—	5	1	no	Hall
14	C₁₃×C₁₃⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₅×C₁₃	—	13	1	no	—
16	C₃×D₅×C₁₃	—	13	2	no	—
17	C₂×C₅×C₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	D₅×C₁₃⋊C₃	C₂×C₁₃	1	2	yes	direct product factor
19	C₂×C₁₃²	—	5	2	no	—
20	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
21	C₂×D₅×C₁₃	—	3	4	no	—
22	C₂×D₅×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₂×D₅×C₁₃	C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₃	—	13	1	no	—
25	C₅×C₁₃⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
26	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃×C₁₃	—	65	1	no	—
28	C₂²×C₁₃⋊C₃	—	5	1	no	—
29	C₂×C₅×C₁₃	—	3	4	no	—
30	C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₅×C₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
32	D₅×C₁₃	—	3	8	no	—
33	D₅×C₁₃	C₂×C₁₃⋊C₃	1	2	yes	direct product factor
34	D₅×C₁₃	C₂×C₃×C₁₃	1	2	yes	complemented
35	C₂×C₃×C₁₃	—	13	1	no	—
36	C₂×C₃×C₁₃	—	65	2	no	—
37	C₂×C₁₃⋊C₃	—	5	2	no	—
38	C₂×C₁₃⋊C₃	D₅×C₁₃	1	1	yes	characteristic, direct product factor
39	C₅×C₁₃	—	3	4	no	—
40	C₅×C₁₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
41	C₅×C₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
42	C₂×C₃×D₅	—	13	1	no	Hall
43	C₂²×C₁₃	—	5	1	no	—
44	C₂²×C₁₃	—	5	1	no	—
45	C₂²×C₁₃	—	15	4	no	—
46	C₃×C₁₃	—	13	1	no	—
47	C₁₃⋊C₃	C₂×D₅×C₁₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₅	—	13	1	no	—
49	C₃×D₅	—	13	2	no	—
50	C₂×C₁₃	—	3	4	no	—
51	C₂×C₁₃	—	5	2	no	—
52	C₂×C₁₃	—	5	2	no	—
53	C₂×C₁₃	—	15	8	no	—
54	C₂×C₁₃	D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
55	C₂×C₁₃	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented
56	C₂×D₅	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
57	C₃×C₅	—	13	1	no	Hall
58	C₁₃	—	3	4	no	—
59	C₁₃	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
60	C₁₃	C₂×C₃×D₅×C₁₃	1	1	yes	characteristic, complemented
61	C₂²×C₃	—	65	1	no	Hall
62	C₂×C₅	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
63	D₅	C₂×C₁₃×C₁₃⋊C₃	1	2	yes	direct product factor
64	C₂×C₃	—	13	1	no	—
65	C₂×C₃	—	65	2	no	—
66	C₅	C₂²×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	5	1	no	Sylow
68	C₃	—	13	1	no	Sylow
69	C₂	—	5	2	no	—
70	C₂	D₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₅×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₃×C₁₃⋊C₃	C₂	semidirect
2. D₅×C₁₃×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂×D₅×C₁₃²	C₃	semidirect
4. C₅×C₁₃×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. D₅×C₁₃²	C₂×C₃	semidirect
9. C₂×C₁₃×C₁₃⋊C₃	D₅	direct (N × H)
10. C₅×C₁₃²	C₂²×C₃	semidirect
12. C₂×D₅×C₁₃⋊C₃	C₁₃	direct (N × H)
14. C₁₃×C₁₃⋊C₃	C₂×D₅	direct (N × H)
17. C₂×C₅×C₁₃⋊C₃	C₂×C₁₃	semidirect
18. D₅×C₁₃⋊C₃	C₂×C₁₃	direct (N × H)
20. C₂×C₁₃²	C₃×D₅	semidirect
22. C₂×D₅×C₁₃	C₁₃⋊C₃	direct (N × H)
23. C₂×D₅×C₁₃	C₃×C₁₃	semidirect
25. C₅×C₁₃⋊C₃	C₂²×C₁₃	semidirect
26. C₁₃²	C₂×C₃×D₅	semidirect
30. C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
31. C₂×C₅×C₁₃	C₂×C₃×C₁₃	semidirect
33. D₅×C₁₃	C₂×C₁₃⋊C₃	direct (N × H)
34. D₅×C₁₃	C₂×C₃×C₁₃	semidirect
38. C₂×C₁₃⋊C₃	D₅×C₁₃	direct (N × H)
40. C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
41. C₅×C₁₃	C₂²×C₃×C₁₃	semidirect
47. C₁₃⋊C₃	C₂×D₅×C₁₃	direct (N × H)
54. C₂×C₁₃	D₅×C₁₃⋊C₃	direct (N × H)
55. C₂×C₁₃	C₃×D₅×C₁₃	semidirect
56. C₂×D₅	C₁₃×C₁₃⋊C₃	direct (N × H)
59. C₁₃	C₂×D₅×C₁₃⋊C₃	direct (N × H)
60. C₁₃	C₂×C₃×D₅×C₁₃	semidirect
62. C₂×C₅	C₂×C₁₃×C₁₃⋊C₃	semidirect
63. D₅	C₂×C₁₃×C₁₃⋊C₃	direct (N × H)
66. C₅	C₂²×C₁₃×C₁₃⋊C₃	semidirect
70. C₂	D₅×C₁₃×C₁₃⋊C₃	direct (N × H)

Subgroups — C2×D5×C13×C13⋊C3 #23778528

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₅×C₁₃×C₁₃⋊C₃ #23778528