Subgroups — C₂×D₅×#92788 #23778534

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	D₅×#92788	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#92788	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×#92788	—	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×#92788	—	5	2	no	—
9	C₂×#92788	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	14	no	maximal
12	C₂²×C₁₃²	—	5	1	no	Hall
13	#92788	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₃⋊C₃	—	13	14	no	—
15	D₅×C₁₃⋊C₃	—	13	28	no	—
16	C₂×C₁₃²	—	5	2	no	—
17	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
18	C₂×D₅×C₁₃	C₁₃⋊C₃	1	14	yes	complemented
19	C₅×C₁₃⋊C₃	—	13	14	no	—
20	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₁₃⋊C₃	—	65	14	no	—
22	C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	1	14	yes	complemented
23	D₅×C₁₃	C₂×C₁₃⋊C₃	1	28	yes	complemented
24	C₂×C₁₃⋊C₃	—	13	14	no	—
25	C₂×C₁₃⋊C₃	—	65	28	no	—
26	C₅×C₁₃	C₂²×C₁₃⋊C₃	1	14	yes	complemented
27	C₂×C₃×D₅	—	169	1	no	Hall
28	C₂²×C₁₃	—	5	14	no	—
29	C₁₃⋊C₃	—	13	14	no	—
30	C₂×C₃×C₅	—	169	1	no	—
31	C₃×D₅	—	169	2	no	—
32	C₂×C₁₃	—	5	28	no	—
33	C₂×C₁₃	D₅×C₁₃⋊C₃	1	14	yes	complemented
34	C₂×D₅	#92788	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₅	—	169	1	no	Hall
36	C₁₃	C₂×D₅×C₁₃⋊C₃	1	14	yes	complemented
37	C₂²×C₃	—	845	1	no	Hall
38	C₂×C₅	C₂×#92788	1	1	yes	characteristic, complemented
39	D₅	C₂×#92788	1	2	yes	direct product factor
40	C₂×C₃	—	845	2	no	—
41	C₂×C₃	—	169	1	no	—
42	C₅	C₂²×#92788	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	5	1	no	Sylow
44	C₃	—	169	1	no	Sylow
45	C₂	—	5	2	no	—
46	C₂	D₅×#92788	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×#92788
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. D₅×#92788	C₂	direct (N × H)
3. C₂×D₅×C₁₃²	C₃	semidirect
4. C₅×#92788	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. D₅×C₁₃²	C₂×C₃	semidirect
9. C₂×#92788	D₅	direct (N × H)
10. C₅×C₁₃²	C₂²×C₃	semidirect
13. #92788	C₂×D₅	direct (N × H)
17. C₂×C₁₃²	C₃×D₅	semidirect
18. C₂×D₅×C₁₃	C₁₃⋊C₃	semidirect
20. C₁₃²	C₂×C₃×D₅	semidirect
22. C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
23. D₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
26. C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
33. C₂×C₁₃	D₅×C₁₃⋊C₃	semidirect
34. C₂×D₅	#92788	direct (N × H)
36. C₁₃	C₂×D₅×C₁₃⋊C₃	semidirect
38. C₂×C₅	C₂×#92788	semidirect
39. D₅	C₂×#92788	direct (N × H)
42. C₅	C₂²×#92788	semidirect
46. C₂	D₅×#92788	direct (N × H)

Subgroups — C2×D5×#92788 #23778534

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₅×#92788 #23778534