Subgroups — C₂×C₅×#10587717 #19129792

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#10587717	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#63271	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#63271	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#10587717	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₇×D₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×D₁₃⋊C₃	—	7	1	no	maximal, Hall
9	C₂×#63271	C₂×C₅	1	1	yes	characteristic, complemented
10	#10587717	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₅×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
13	C₂×C₅×C₁₃⋊C₃	—	7	1	no	—
14	C₅×D₁₃⋊C₃	—	7	2	no	—
15	C₂×C₇×D₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	#63271	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×ΓL(1,𝔽₈)	—	13	2	no	—
19	C₂×C₅×ΓL(1,𝔽₈)	—	13	1	no	—
20	C₅×C₁₃⋊C₃	—	7	1	no	Hall
21	C₂×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₇×D₁₃	C₂×C₃×C₅	1	2	yes	complemented
23	C₂×D₁₃⋊C₃	—	7	1	no	Hall
24	C₂²×C₅×C₇	—	13	1	no	Hall
25	C₂×C₅×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₅×D₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
27	C₅×ΓL(1,𝔽₈)	—	13	1	no	Hall
28	C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
29	C₂²×ΓL(1,𝔽₈)	—	13	1	no	Hall
30	C₂×C₁₃⋊C₃	—	7	1	no	—
31	D₁₃⋊C₃	—	7	2	no	—
32	C₂×C₅×C₇	—	13	2	no	—
33	C₂×C₅×C₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₅×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₅	—	91	1	no	Hall
36	C₂×D₁₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
37	C₂×ΓL(1,𝔽₈)	—	13	2	no	—
38	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
39	C₁₃⋊C₃	—	7	1	no	Hall
40	C₅×C₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₅	—	91	2	no	—
42	C₂×C₃×C₅	—	91	1	no	—
43	C₂²×C₇	—	13	1	no	Hall
44	C₂×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
45	D₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	2	yes	complemented
46	ΓL(1,𝔽₈)	—	13	1	no	Hall
47	C₂²×C₅	—	13	1	no	Hall
48	C₃×C₅	—	91	1	no	Hall
49	C₂×C₇	—	13	2	no	—
50	C₂×C₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
51	C₁₃	C₂²×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	91	1	no	Hall
53	C₂×C₅	—	13	2	no	—
54	C₂×C₅	#10587717	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	91	2	no	—
57	C₂×C₃	—	91	1	no	—
58	C₅	C₂×#10587717	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	13	1	no	Sylow
60	C₃	—	91	1	no	Sylow
61	C₂	—	13	2	no	—
62	C₂	C₅×#10587717	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	#10587717
commutator, hypocenter	C₇×C₁₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#10587717	C₂	direct (N × H)
2. C₂×C₅×#63271	C₂	semidirect
3. C₂×C₅×C₇×D₁₃	C₃	semidirect
4. C₅×#63271	C₂²	semidirect
5. C₂×#10587717	C₅	direct (N × H)
6. C₂×C₅×C₇×C₁₃	C₂×C₃	semidirect
7. C₅×C₇×D₁₃	C₂×C₃	semidirect
9. C₂×#63271	C₂×C₅	semidirect
10. #10587717	C₂×C₅	direct (N × H)
11. C₅×C₇×C₁₃	C₂²×C₃	semidirect
15. C₂×C₇×D₁₃	C₃×C₅	semidirect
16. #63271	C₂²×C₅	semidirect
17. C₂×C₅×D₁₃	ΓL(1,𝔽₈)	semidirect
21. C₂×C₇×C₁₃	C₂×C₃×C₅	semidirect
22. C₇×D₁₃	C₂×C₃×C₅	semidirect
25. C₂×C₅×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
26. C₅×D₁₃	C₂×ΓL(1,𝔽₈)	semidirect
28. C₇×C₁₃	C₂²×C₃×C₅	semidirect
33. C₂×C₅×C₇	D₁₃⋊C₃	semidirect
34. C₅×C₁₃	C₂²×ΓL(1,𝔽₈)	semidirect
36. C₂×D₁₃	C₅×ΓL(1,𝔽₈)	semidirect
40. C₅×C₇	C₂×D₁₃⋊C₃	semidirect
44. C₂×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
45. D₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
50. C₂×C₇	C₅×D₁₃⋊C₃	semidirect
51. C₁₃	C₂²×C₅×ΓL(1,𝔽₈)	semidirect
54. C₂×C₅	#10587717	direct (N × H)
55. C₇	C₂×C₅×D₁₃⋊C₃	semidirect
58. C₅	C₂×#10587717	direct (N × H)
62. C₂	C₅×#10587717	direct (N × H)

Subgroups — C2×C5×#10587717 #19129792

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×#10587717 #19129792