Subgroups — C₂×C₅⋊#11759815 #23778529

Order 10140.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#92788	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊#11759815	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#92788	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#11759815	—	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×#92788	D₅	1	1	yes	characteristic, complemented
9	#11759815	—	5	2	no	—
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅⋊(D₁₃⋊C₃)	—	13	14	no	maximal
12	C₂×C₁₃⋊D₁₃	—	5	1	no	Hall
13	#92788	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₁₃⋊C₃	—	13	14	no	—
15	C₅⋊(D₁₃⋊C₃)	—	13	28	no	—
16	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
17	C₁₃⋊D₁₃	—	5	2	no	—
18	C₂×D₆₅	—	13	14	no	—
19	C₅×C₁₃⋊C₃	—	13	14	no	—
20	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂×D₁₃⋊C₃	—	65	14	no	—
22	C₂×C₅×C₁₃	D₁₃⋊C₃	1	14	yes	complemented
23	D₆₅	—	13	28	no	—
24	C₂×C₁₃⋊C₃	—	13	14	no	—
25	D₁₃⋊C₃	—	65	28	no	—
26	C₅×C₁₃	C₂×D₁₃⋊C₃	1	14	yes	complemented
27	C₂×C₃×D₅	—	169	1	no	Hall
28	C₂×D₁₃	—	65	14	no	—
29	C₁₃⋊C₃	—	13	14	no	—
30	C₂×C₃×C₅	—	169	1	no	—
31	C₃×D₅	—	169	2	no	—
32	C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
33	D₁₃	—	65	28	no	—
34	C₂×D₅	—	169	1	no	Hall
35	C₃×C₅	—	169	1	no	Hall
36	C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
37	C₂²×C₃	—	845	1	no	Hall
38	C₂×C₅	#11759815	1	1	yes	characteristic, complemented
39	D₅	—	169	2	no	—
40	C₂×C₃	—	845	2	no	—
41	C₂×C₃	—	169	1	no	—
42	C₅	C₂×#11759815	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	845	1	no	Sylow
44	C₃	—	169	1	no	Sylow
45	C₂	—	845	2	no	—
46	C₂	C₅⋊#11759815	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#11759815
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×#92788	C₂	semidirect
2. C₅⋊#11759815	C₂	direct (N × H)
3. C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	semidirect
4. C₅×#92788	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	semidirect
8. C₂×#92788	D₅	semidirect
10. C₅×C₁₃²	C₂²×C₃	semidirect
13. #92788	C₂×D₅	semidirect
16. C₂×C₁₃²	C₃×D₅	semidirect
20. C₁₃²	C₂×C₃×D₅	semidirect
22. C₂×C₅×C₁₃	D₁₃⋊C₃	semidirect
26. C₅×C₁₃	C₂×D₁₃⋊C₃	semidirect
32. C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	semidirect
36. C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
38. C₂×C₅	#11759815	semidirect
42. C₅	C₂×#11759815	semidirect
46. C₂	C₅⋊#11759815	direct (N × H)

Subgroups — C2×C5⋊#11759815 #23778529

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊#11759815 #23778529