Subgroups — C₂×C₅⋊#11759818 #23778532

Order 10140.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#92789	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊#11759818	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#92789	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#11759818	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₆₅	C₂×C₃	1	2	yes	complemented
8	C₂×#92789	D₅	1	1	yes	characteristic, complemented
9	#11759818	—	5	2	no	—
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅⋊(D₁₃⋊C₃)	—	13	1	no	maximal
12	C₂×D₅×C₁₃⋊C₃	—	13	1	no	maximal
13	C₂×C₁₃×D₁₃	—	5	1	no	Hall
14	#92789	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₃⋊C₃	—	13	1	no	—
16	C₂×C₅×C₁₃⋊C₃	—	13	1	no	—
17	C₅⋊(D₁₃⋊C₃)	—	13	2	no	—
18	D₅×C₁₃⋊C₃	—	13	2	no	—
19	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
20	C₁₃×D₁₃	—	5	2	no	—
21	C₂×D₆₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented
22	C₂×D₅×C₁₃	—	13	1	no	—
23	C₅×C₁₃⋊C₃	—	13	1	no	—
24	C₅×C₁₃⋊C₃	—	13	1	no	—
25	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
26	C₂²×C₁₃⋊C₃	—	65	1	no	—
27	C₂×D₁₃⋊C₃	—	65	1	no	—
28	C₂×C₅×C₁₃	—	6	2	no	—
29	C₂×C₅×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	D₆₅	C₂×C₁₃⋊C₃	1	2	yes	complemented
32	D₅×C₁₃	—	13	2	no	—
33	C₂×C₁₃⋊C₃	—	13	1	no	—
34	C₂×C₁₃⋊C₃	—	13	1	no	—
35	C₂×C₁₃⋊C₃	—	65	2	no	—
36	D₁₃⋊C₃	—	65	2	no	—
37	C₅×C₁₃	—	6	2	no	—
38	C₅×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₅×C₁₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
40	C₂×C₃×D₅	—	169	1	no	Hall
41	C₂²×C₁₃	—	65	1	no	—
42	C₂×D₁₃	—	5	1	no	—
43	C₁₃⋊C₃	—	13	1	no	—
44	C₁₃⋊C₃	—	13	1	no	—
45	C₂×C₃×C₅	—	169	1	no	—
46	C₃×D₅	—	169	2	no	—
47	C₂×C₁₃	—	6	2	no	—
48	C₂×C₁₃	—	65	2	no	—
49	C₂×C₁₃	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
50	C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
51	D₁₃	—	5	2	no	—
52	C₂×D₅	—	13	1	no	Hall
53	C₃×C₅	—	169	1	no	Hall
54	C₁₃	—	6	2	no	—
55	C₁₃	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
56	C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
57	C₂²×C₃	—	845	1	no	Hall
58	C₂×C₅	#11759818	1	1	yes	characteristic, complemented
59	D₅	—	13	2	no	—
60	C₂×C₃	—	845	2	no	—
61	C₂×C₃	—	169	1	no	—
62	C₅	C₂×#11759818	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	65	1	no	Sylow
64	C₃	—	169	1	no	Sylow
65	C₂	—	65	2	no	—
66	C₂	C₅⋊#11759818	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#11759818
commutator, cosocle, hypocenter	C₅×C₁₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#92789	C₂	semidirect
2. C₅⋊#11759818	C₂	direct (N × H)
3. C₂×C₁₃×D₆₅	C₃	semidirect
4. C₅×#92789	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. C₁₃×D₆₅	C₂×C₃	semidirect
8. C₂×#92789	D₅	semidirect
10. C₅×C₁₃²	C₂²×C₃	semidirect
14. #92789	C₂×D₅	semidirect
19. C₂×C₁₃²	C₃×D₅	semidirect
21. C₂×D₆₅	C₁₃⋊C₃	semidirect
25. C₁₃²	C₂×C₃×D₅	semidirect
29. C₂×C₅×C₁₃	D₁₃⋊C₃	semidirect
30. C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
31. D₆₅	C₂×C₁₃⋊C₃	semidirect
38. C₅×C₁₃	C₂×D₁₃⋊C₃	semidirect
39. C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
49. C₂×C₁₃	D₅×C₁₃⋊C₃	semidirect
50. C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	semidirect
55. C₁₃	C₂×D₅×C₁₃⋊C₃	semidirect
56. C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
58. C₂×C₅	#11759818	semidirect
62. C₅	C₂×#11759818	semidirect
66. C₂	C₅⋊#11759818	direct (N × H)

Subgroups — C2×C5⋊#11759818 #23778532

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊#11759818 #23778532