Subgroups — C₃×D₅²×C₁₀₃ #44525507

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₁₀₃	C₂	1	2	yes	maximal, complemented
2	C₃×C₅⋊D₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅²×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅×C₁₀₃	—	5	2	no	maximal
6	C₅⋊D₅×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₁₀₃	C₂×C₃	1	2	yes	complemented
8	C₃×D₅×C₁₀₃	—	5	2	no	—
9	C₃×D₅×C₁₀₃	—	10	2	no	—
10	C₃×D₅×C₁₀₃	D₅	1	2	yes	direct product factor
11	C₂×C₃×C₅×C₁₀₃	—	5	2	no	—
12	C₅²×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₅×C₁₀₃	—	5	2	no	—
14	C₃×C₅×C₁₀₃	—	2	2	no	—
15	C₃×C₅×C₁₀₃	C₂×D₅	1	2	yes	complemented
16	C₂²×C₃×C₁₀₃	—	25	1	no	Hall
17	C₂×C₅×C₁₀₃	—	5	2	no	—
18	D₅×C₁₀₃	—	5	2	no	—
19	D₅×C₁₀₃	—	10	2	no	—
20	D₅×C₁₀₃	C₃×D₅	1	2	yes	direct product factor
21	C₂×C₃×C₁₀₃	—	5	2	no	—
22	C₂×C₃×C₁₀₃	—	25	1	no	—
23	C₅×C₁₀₃	—	2	2	no	—
24	C₅×C₁₀₃	C₂×C₃×D₅	1	2	yes	complemented
25	C₂²×C₁₀₃	—	25	1	no	Hall
26	C₃×C₁₀₃	D₅²	1	1	yes	characteristic, direct product factor, Hall
27	C₃×D₅²	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₁₀₃	—	5	2	no	—
29	C₂×C₁₀₃	—	25	1	no	—
30	C₃×C₅⋊D₅	C₂×C₁₀₃	1	1	yes	characteristic, complemented
31	C₃×C₅×D₅	C₂×C₁₀₃	1	2	yes	complemented
32	C₁₀₃	C₃×D₅²	1	1	yes	characteristic, direct product factor, Sylow
33	D₅²	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₅²	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×D₅	—	5	2	no	—
36	C₅⋊D₅	C₂×C₃×C₁₀₃	1	1	yes	characteristic, complemented
37	C₅×D₅	C₂×C₃×C₁₀₃	1	2	yes	complemented
38	C₂×C₃×C₅	—	5	2	no	—
39	C₃×D₅	—	5	2	no	—
40	C₃×D₅	—	10	2	no	—
41	C₃×D₅	D₅×C₁₀₃	1	2	yes	direct product factor
42	C₅²	C₂²×C₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	5	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	C₂×D₅×C₁₀₃	1	2	yes	complemented
46	C₂²×C₃	—	25	1	no	Hall
47	C₂×C₅	—	5	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	C₃×D₅×C₁₀₃	1	2	yes	direct product factor
51	C₂×C₃	—	5	2	no	—
52	C₂×C₃	—	25	1	no	—
53	C₅	—	2	2	no	—
54	C₅	C₂×C₃×D₅×C₁₀₃	1	2	yes	complemented
55	C₂²	—	25	1	no	Sylow
56	C₃	D₅²×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	5	2	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₀₃	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₀₃	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅×C₁₀₃	C₂	semidirect
2. C₃×C₅⋊D₅×C₁₀₃	C₂	semidirect
3. D₅²×C₁₀₃	C₃	direct (N × H)
4. C₃×C₅²×C₁₀₃	C₂²	semidirect
6. C₅⋊D₅×C₁₀₃	C₂×C₃	semidirect
7. C₅×D₅×C₁₀₃	C₂×C₃	semidirect
10. C₃×D₅×C₁₀₃	D₅	direct (N × H)
12. C₅²×C₁₀₃	C₂²×C₃	semidirect
15. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
20. D₅×C₁₀₃	C₃×D₅	direct (N × H)
24. C₅×C₁₀₃	C₂×C₃×D₅	semidirect
26. C₃×C₁₀₃	D₅²	direct (N × H)
27. C₃×D₅²	C₁₀₃	direct (N × H)
30. C₃×C₅⋊D₅	C₂×C₁₀₃	semidirect
31. C₃×C₅×D₅	C₂×C₁₀₃	semidirect
32. C₁₀₃	C₃×D₅²	direct (N × H)
33. D₅²	C₃×C₁₀₃	direct (N × H)
34. C₃×C₅²	C₂²×C₁₀₃	semidirect
36. C₅⋊D₅	C₂×C₃×C₁₀₃	semidirect
37. C₅×D₅	C₂×C₃×C₁₀₃	semidirect
41. C₃×D₅	D₅×C₁₀₃	direct (N × H)
42. C₅²	C₂²×C₃×C₁₀₃	semidirect
45. C₃×C₅	C₂×D₅×C₁₀₃	semidirect
50. D₅	C₃×D₅×C₁₀₃	direct (N × H)
54. C₅	C₂×C₃×D₅×C₁₀₃	semidirect
56. C₃	D₅²×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×D₅×C₁₀₃	2
C₃×C₅⋊D₅×C₁₀₃	2
D₅²×C₁₀₃	3
C₂×C₃×D₅×C₁₀₃	5
C₃×D₅²	103

Subgroups — C3×D52×C103 #44525507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅²×C₁₀₃ #44525507