Subgroups — C₂×C₅⋊D₅×C₁₀₃⋊C₃ #44525501

Order 30900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊D₅×C₁₀₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₅×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²×C₁₀₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅×C₁₀₃⋊C₃	—	5	6	no	maximal
6	C₅⋊D₅×C₁₀₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₅²×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₀₃⋊C₃	—	5	12	no	—
9	C₂×C₅×C₁₀₃⋊C₃	D₅	1	6	yes	complemented
10	C₅²×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₁₀₃	—	5	6	no	—
12	C₅×C₁₀₃⋊C₃	C₂×D₅	1	6	yes	complemented
13	C₂²×C₁₀₃⋊C₃	—	25	1	no	Hall
14	C₂×C₅×C₁₀₃	C₃×D₅	1	6	yes	complemented
15	D₅×C₁₀₃	—	5	12	no	—
16	C₂×C₁₀₃⋊C₃	—	25	2	no	—
17	C₂×C₁₀₃⋊C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
18	C₅×C₁₀₃	C₂×C₃×D₅	1	6	yes	complemented
19	C₂²×C₁₀₃	—	25	1	no	Hall
20	C₁₀₃⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅⋊D₅	—	103	1	no	maximal, Hall
22	C₂×C₁₀₃	—	25	2	no	—
23	C₂×C₁₀₃	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅²	—	103	1	no	—
25	C₃×C₅⋊D₅	—	103	2	no	—
26	C₁₀₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅⋊D₅	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅²	—	103	1	no	Hall
29	C₂×C₃×D₅	—	515	6	no	—
30	C₂×C₅²	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
31	C₅⋊D₅	C₂×C₁₀₃⋊C₃	1	2	yes	direct product factor
32	C₂×C₃×C₅	—	103	6	no	—
33	C₃×D₅	—	515	12	no	—
34	C₅²	C₂²×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	5	6	no	—
36	C₃×C₅	—	103	6	no	—
37	C₂²×C₃	—	2575	1	no	Hall
38	C₂×C₅	D₅×C₁₀₃⋊C₃	1	6	yes	complemented
39	D₅	—	5	12	no	—
40	C₂×C₃	—	2575	2	no	—
41	C₂×C₃	—	103	1	no	—
42	C₅	C₂×D₅×C₁₀₃⋊C₃	1	6	yes	complemented
43	C₂²	—	25	1	no	Sylow
44	C₃	—	103	1	no	Sylow
45	C₂	—	25	2	no	—
46	C₂	C₅⋊D₅×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₅×C₁₀₃⋊C₃
commutator, cosocle, hypocenter	C₅²×C₁₀₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₀₃	C₂×C₃
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×C₁₀₃⋊C₃	C₂	semidirect
2. C₅⋊D₅×C₁₀₃⋊C₃	C₂	direct (N × H)
3. C₂×C₅⋊D₅×C₁₀₃	C₃	semidirect
4. C₅²×C₁₀₃⋊C₃	C₂²	semidirect
6. C₅⋊D₅×C₁₀₃	C₂×C₃	semidirect
7. C₂×C₅²×C₁₀₃	C₂×C₃	semidirect
9. C₂×C₅×C₁₀₃⋊C₃	D₅	semidirect
10. C₅²×C₁₀₃	C₂²×C₃	semidirect
12. C₅×C₁₀₃⋊C₃	C₂×D₅	semidirect
14. C₂×C₅×C₁₀₃	C₃×D₅	semidirect
17. C₂×C₁₀₃⋊C₃	C₅⋊D₅	direct (N × H)
18. C₅×C₁₀₃	C₂×C₃×D₅	semidirect
20. C₁₀₃⋊C₃	C₂×C₅⋊D₅	direct (N × H)
23. C₂×C₁₀₃	C₃×C₅⋊D₅	semidirect
26. C₁₀₃	C₂×C₃×C₅⋊D₅	semidirect
27. C₂×C₅⋊D₅	C₁₀₃⋊C₃	direct (N × H)
30. C₂×C₅²	C₂×C₁₀₃⋊C₃	semidirect
31. C₅⋊D₅	C₂×C₁₀₃⋊C₃	direct (N × H)
34. C₅²	C₂²×C₁₀₃⋊C₃	semidirect
38. C₂×C₅	D₅×C₁₀₃⋊C₃	semidirect
42. C₅	C₂×D₅×C₁₀₃⋊C₃	semidirect
46. C₂	C₅⋊D₅×C₁₀₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₁₀₃⋊C₃	2
C₅⋊D₅×C₁₀₃⋊C₃	2
C₂×C₅⋊D₅×C₁₀₃	3
C₂×D₅×C₁₀₃⋊C₃	5
C₂×C₃×C₅⋊D₅	103

Subgroups — C2×C5⋊D5×C103⋊C3 #44525501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊D₅×C₁₀₃⋊C₃ #44525501