Subgroups — C₂²×C₅×#92789 #23778601

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	3	yes	maximal, direct product factor
2	C₂²×C₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#92789	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×#92789	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃²	C₂×C₃	1	3	yes	complemented
6	C₂×#92789	C₂×C₅	1	3	yes	direct product factor
7	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₁₃⋊C₃	—	13	2	no	maximal
9	C₂²×C₁₃²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	#92789	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₃⋊C₃	—	13	6	no	—
12	C₂×C₁₃²	C₂×C₃×C₅	1	3	yes	complemented
13	C₂²×C₅×C₁₃	—	3	4	no	—
14	C₂²×C₅×C₁₃	C₁₃⋊C₃	1	2	yes	complemented
15	C₅×C₁₃⋊C₃	—	13	2	no	—
16	C₁₃²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₁₃⋊C₃	—	13	2	no	—
18	C₂×C₅×C₁₃	—	3	12	no	—
19	C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	1	6	yes	complemented
20	C₂×C₁₃⋊C₃	—	13	6	no	—
21	C₅×C₁₃	—	3	4	no	—
22	C₅×C₁₃	C₂²×C₁₃⋊C₃	1	2	yes	complemented
23	C₂²×C₃×C₅	—	169	1	no	Hall
24	C₂²×C₁₃	—	3	4	no	—
25	C₂²×C₁₃	C₅×C₁₃⋊C₃	1	2	yes	complemented
26	C₁₃⋊C₃	—	13	2	no	—
27	C₂×C₃×C₅	—	169	3	no	—
28	C₂×C₁₃	—	3	12	no	—
29	C₂×C₁₃	C₂×C₅×C₁₃⋊C₃	1	6	yes	complemented
30	C₂²×C₅	#92789	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₅	—	169	1	no	Hall
32	C₁₃	—	3	4	no	—
33	C₁₃	C₂²×C₅×C₁₃⋊C₃	1	2	yes	complemented
34	C₂²×C₃	—	169	1	no	Hall
35	C₂×C₅	C₂×#92789	1	3	yes	direct product factor
36	C₂×C₃	—	169	3	no	—
37	C₅	C₂²×#92789	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	C₅×#92789	1	1	yes	characteristic, direct product factor, Sylow
39	C₃	—	169	1	no	Sylow
40	C₂	C₂×C₅×#92789	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	#92789
commutator, cosocle, hypocenter	C₁₃²	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃²	C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#92789	C₂	direct (N × H)
2. C₂²×C₅×C₁₃²	C₃	semidirect
3. C₅×#92789	C₂²	direct (N × H)
4. C₂²×#92789	C₅	direct (N × H)
5. C₂×C₅×C₁₃²	C₂×C₃	semidirect
6. C₂×#92789	C₂×C₅	direct (N × H)
7. C₅×C₁₃²	C₂²×C₃	semidirect
9. C₂²×C₁₃²	C₃×C₅	semidirect
10. #92789	C₂²×C₅	direct (N × H)
12. C₂×C₁₃²	C₂×C₃×C₅	semidirect
14. C₂²×C₅×C₁₃	C₁₃⋊C₃	semidirect
16. C₁₃²	C₂²×C₃×C₅	semidirect
19. C₂×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
22. C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
25. C₂²×C₁₃	C₅×C₁₃⋊C₃	semidirect
29. C₂×C₁₃	C₂×C₅×C₁₃⋊C₃	semidirect
30. C₂²×C₅	#92789	direct (N × H)
33. C₁₃	C₂²×C₅×C₁₃⋊C₃	semidirect
35. C₂×C₅	C₂×#92789	direct (N × H)
37. C₅	C₂²×#92789	direct (N × H)
38. C₂²	C₅×#92789	direct (N × H)
40. C₂	C₂×C₅×#92789	direct (N × H)

Subgroups — C22×C5×#92789 #23778601

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₅×#92789 #23778601