Subgroups — C₂×D₅×#92789 #23778535

Order 10140.

120 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	D₅×#92789	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#92789	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×#92789	—	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×#92789	—	5	2	no	—
9	C₂×#92789	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₁₃⋊C₃	—	13	2	no	maximal
12	C₂²×C₁₃²	—	5	1	no	Hall
13	#92789	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₃⋊C₃	—	13	2	no	—
15	D₅×C₁₃⋊C₃	—	13	4	no	—
16	C₂×C₁₃²	—	5	2	no	—
17	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
18	C₂×D₅×C₁₃	—	3	4	no	—
19	C₂×D₅×C₁₃	C₁₃⋊C₃	1	2	yes	complemented
20	C₅×C₁₃⋊C₃	—	13	2	no	—
21	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₁₃⋊C₃	—	65	2	no	—
23	C₂×C₅×C₁₃	—	3	4	no	—
24	C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	1	2	yes	complemented
25	D₅×C₁₃	—	3	8	no	—
26	D₅×C₁₃	C₂×C₁₃⋊C₃	1	4	yes	complemented
27	C₂×C₁₃⋊C₃	—	13	2	no	—
28	C₂×C₁₃⋊C₃	—	65	4	no	—
29	C₅×C₁₃	—	3	4	no	—
30	C₅×C₁₃	C₂²×C₁₃⋊C₃	1	2	yes	complemented
31	C₂×C₃×D₅	—	169	1	no	Hall
32	C₂²×C₁₃	—	5	2	no	—
33	C₂²×C₁₃	—	15	4	no	—
34	C₁₃⋊C₃	—	13	2	no	—
35	C₂×C₃×C₅	—	169	1	no	—
36	C₃×D₅	—	169	2	no	—
37	C₂×C₁₃	—	3	4	no	—
38	C₂×C₁₃	—	5	4	no	—
39	C₂×C₁₃	—	15	8	no	—
40	C₂×C₁₃	D₅×C₁₃⋊C₃	1	2	yes	complemented
41	C₂×D₅	#92789	1	1	yes	characteristic, direct product factor, Hall
42	C₃×C₅	—	169	1	no	Hall
43	C₁₃	—	3	4	no	—
44	C₁₃	C₂×D₅×C₁₃⋊C₃	1	2	yes	complemented
45	C₂²×C₃	—	845	1	no	Hall
46	C₂×C₅	C₂×#92789	1	1	yes	characteristic, complemented
47	D₅	C₂×#92789	1	2	yes	direct product factor
48	C₂×C₃	—	845	2	no	—
49	C₂×C₃	—	169	1	no	—
50	C₅	C₂²×#92789	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	5	1	no	Sylow
52	C₃	—	169	1	no	Sylow
53	C₂	—	5	2	no	—
54	C₂	D₅×#92789	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×#92789
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. D₅×#92789	C₂	direct (N × H)
3. C₂×D₅×C₁₃²	C₃	semidirect
4. C₅×#92789	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. D₅×C₁₃²	C₂×C₃	semidirect
9. C₂×#92789	D₅	direct (N × H)
10. C₅×C₁₃²	C₂²×C₃	semidirect
13. #92789	C₂×D₅	direct (N × H)
17. C₂×C₁₃²	C₃×D₅	semidirect
19. C₂×D₅×C₁₃	C₁₃⋊C₃	semidirect
21. C₁₃²	C₂×C₃×D₅	semidirect
24. C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
26. D₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
30. C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
40. C₂×C₁₃	D₅×C₁₃⋊C₃	semidirect
41. C₂×D₅	#92789	direct (N × H)
44. C₁₃	C₂×D₅×C₁₃⋊C₃	semidirect
46. C₂×C₅	C₂×#92789	semidirect
47. D₅	C₂×#92789	direct (N × H)
50. C₅	C₂²×#92789	semidirect
54. C₂	D₅×#92789	direct (N × H)

Subgroups — C2×D5×#92789 #23778535

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₅×#92789 #23778535