Subgroups — C₂×C₅⋊#11759816 #23778530

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	C₅⋊#11759816	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#92789	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#11759816	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	1	2	yes	complemented
8	C₂×#92789	D₅	1	1	yes	characteristic, complemented
9	#11759816	—	5	2	no	—
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅⋊(D₁₃⋊C₃)	—	13	2	no	maximal
12	C₂×C₁₃⋊D₁₃	—	5	1	no	Hall
13	#92789	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₁₃⋊C₃	—	13	2	no	—
15	C₅⋊(D₁₃⋊C₃)	—	13	4	no	—
16	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
17	C₁₃⋊D₁₃	—	5	2	no	—
18	C₂×D₆₅	—	13	2	no	—
19	C₂×D₆₅	—	39	4	no	—
20	C₅×C₁₃⋊C₃	—	13	2	no	—
21	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×D₁₃⋊C₃	—	65	2	no	—
23	C₂×C₅×C₁₃	—	3	4	no	—
24	C₂×C₅×C₁₃	D₁₃⋊C₃	1	2	yes	complemented
25	D₆₅	—	13	4	no	—
26	D₆₅	—	39	8	no	—
27	C₂×C₁₃⋊C₃	—	13	2	no	—
28	D₁₃⋊C₃	—	65	4	no	—
29	C₅×C₁₃	—	3	4	no	—
30	C₅×C₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
31	C₂×C₃×D₅	—	169	1	no	Hall
32	C₂×D₁₃	—	65	2	no	—
33	C₂×D₁₃	—	195	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	C₅⋊(D₁₃⋊C₃)	1	2	yes	complemented
39	D₁₃	—	65	4	no	—
40	D₁₃	—	195	8	no	—
41	C₂×D₅	—	169	1	no	Hall
42	C₃×C₅	—	169	1	no	Hall
43	C₁₃	—	3	4	no	—
44	C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	1	2	yes	complemented
45	C₂²×C₃	—	845	1	no	Hall
46	C₂×C₅	#11759816	1	1	yes	characteristic, complemented
47	D₅	—	169	2	no	—
48	C₂×C₃	—	845	2	no	—
49	C₂×C₃	—	169	1	no	—
50	C₅	C₂×#11759816	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	845	1	no	Sylow
52	C₃	—	169	1	no	Sylow
53	C₂	—	845	2	no	—
54	C₂	C₅⋊#11759816	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#11759816
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⋊#11759816	C₂	direct (N × H)
3. C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	semidirect
4. C₅×#92789	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	semidirect
8. C₂×#92789	D₅	semidirect
10. C₅×C₁₃²	C₂²×C₃	semidirect
13. #92789	C₂×D₅	semidirect
16. C₂×C₁₃²	C₃×D₅	semidirect
21. C₁₃²	C₂×C₃×D₅	semidirect
24. C₂×C₅×C₁₃	D₁₃⋊C₃	semidirect
30. C₅×C₁₃	C₂×D₁₃⋊C₃	semidirect
38. C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	semidirect
44. C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
46. C₂×C₅	#11759816	semidirect
50. C₅	C₂×#11759816	semidirect
54. C₂	C₅⋊#11759816	direct (N × H)

Subgroups — C2×C5⋊#11759816 #23778530

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊#11759816 #23778530