Subgroups — C₅²×D₃×D₁₀₃ #44525515

Order 30900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₃₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×D₁₀₃	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×D₁₀₃	C₅	1	6	yes	maximal, direct product factor
7	C₅²×D₁₀₃	—	3	1	no	—
8	C₅²×D₁₀₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅²×C₁₀₃	—	3	1	no	—
10	C₅×D₃₀₉	C₂×C₅	1	6	yes	complemented
11	C₅×D₃×C₁₀₃	C₂×C₅	1	6	yes	complemented
12	C₃×C₅×D₁₀₃	C₂×C₅	1	6	yes	complemented
13	C₅²×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₁₀₃	—	3	6	no	—
15	C₃×C₅×C₁₀₃	C₂²×C₅	1	6	yes	complemented
16	D₃×D₁₀₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₀₃	—	3	6	no	—
18	C₅×D₁₀₃	—	3	6	no	—
19	C₅×D₁₀₃	C₅×D₃	1	6	yes	direct product factor
20	D₃₀₉	C₂×C₅²	1	1	yes	characteristic, complemented
21	C₃×D₁₀₃	C₂×C₅²	1	1	yes	characteristic, complemented
22	D₃×C₁₀₃	C₂×C₅²	1	1	yes	characteristic, complemented
23	C₅×C₁₀₃	C₂×C₅×D₃	1	6	yes	complemented
24	C₂×D₁₀₃	—	3	1	no	Hall
25	C₃×C₁₀₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅²×D₃	—	103	1	no	maximal, Hall
27	C₂×C₁₀₃	—	3	1	no	—
28	D₁₀₃	—	3	1	no	—
29	D₁₀₃	C₅²×D₃	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₅²	—	103	1	no	—
31	C₅²×D₃	—	103	1	no	—
32	C₅²×D₃	D₁₀₃	1	1	yes	characteristic, direct product factor
33	C₁₀₃	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₅²	—	309	1	no	Hall
35	C₃×C₅²	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×D₃	—	103	6	no	—
37	C₂×C₅²	—	3	1	no	—
38	C₂×C₅²	—	309	1	no	—
39	C₂×C₅²	—	103	1	no	—
40	C₂×C₃×C₅	—	103	6	no	—
41	C₅×D₃	—	103	6	no	—
42	C₅×D₃	C₅×D₁₀₃	1	6	yes	direct product factor
43	C₅²	D₃×D₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₅	—	309	6	no	—
45	C₃×C₅	C₂×C₅×D₁₀₃	1	6	yes	complemented
46	C₂×D₃	—	103	1	no	Hall
47	C₂×C₅	—	3	6	no	—
48	C₂×C₅	—	309	6	no	—
49	C₂×C₅	—	103	6	no	—
50	C₂×C₃	—	103	1	no	—
51	D₃	—	103	1	no	—
52	D₃	C₅²×D₁₀₃	1	1	yes	characteristic, direct product factor
53	C₅	C₅×D₃×D₁₀₃	1	6	yes	direct product factor
54	C₂²	—	309	1	no	Sylow
55	C₃	C₂×C₅²×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	309	1	no	—
58	C₂	—	103	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	D₃×D₁₀₃
commutator, cosocle, hypocenter	C₃×C₁₀₃	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₀₃	C₂²
LCS	G ▷ C₃×C₁₀₃
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×D₁₀₃	C₂	semidirect
2. C₅²×D₃×C₁₀₃	C₂	semidirect
3. C₅²×D₃₀₉	C₂	semidirect
5. C₃×C₅²×C₁₀₃	C₂²	semidirect
6. C₅×D₃×D₁₀₃	C₅	direct (N × H)
8. C₅²×D₁₀₃	D₃	direct (N × H)
10. C₅×D₃₀₉	C₂×C₅	semidirect
11. C₅×D₃×C₁₀₃	C₂×C₅	semidirect
12. C₃×C₅×D₁₀₃	C₂×C₅	semidirect
13. C₅²×C₁₀₃	C₂×D₃	semidirect
15. C₃×C₅×C₁₀₃	C₂²×C₅	semidirect
16. D₃×D₁₀₃	C₅²	direct (N × H)
19. C₅×D₁₀₃	C₅×D₃	direct (N × H)
20. D₃₀₉	C₂×C₅²	semidirect
21. C₃×D₁₀₃	C₂×C₅²	semidirect
22. D₃×C₁₀₃	C₂×C₅²	semidirect
23. C₅×C₁₀₃	C₂×C₅×D₃	semidirect
25. C₃×C₁₀₃	C₂²×C₅²	semidirect
29. D₁₀₃	C₅²×D₃	direct (N × H)
32. C₅²×D₃	D₁₀₃	direct (N × H)
33. C₁₀₃	C₂×C₅²×D₃	semidirect
35. C₃×C₅²	C₂×D₁₀₃	semidirect
42. C₅×D₃	C₅×D₁₀₃	direct (N × H)
43. C₅²	D₃×D₁₀₃	direct (N × H)
45. C₃×C₅	C₂×C₅×D₁₀₃	semidirect
52. D₃	C₅²×D₁₀₃	direct (N × H)
53. C₅	C₅×D₃×D₁₀₃	direct (N × H)
55. C₃	C₂×C₅²×D₁₀₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×D₁₀₃	2
C₅²×D₃×C₁₀₃	2
C₅²×D₃₀₉	2
C₂×C₅²×D₁₀₃	3
C₅×D₃×D₁₀₃	5
C₂×C₅²×D₃	103

Subgroups — C52×D3×D103 #44525515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×D₁₀₃ #44525515