Subgroups — C₂×C₅²⋊C₃×D₁₀₃ #44525490

Order 30900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊C₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²⋊C₃×D₁₀₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²⋊C₃×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅²×D₁₀₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₅²×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×D₁₀₃	—	3	2	no	—
9	C₂×C₃×D₁₀₃	—	25	1	no	maximal, Hall
10	C₂×C₅×C₁₀₃	—	3	2	no	—
11	C₅×D₁₀₃	—	3	4	no	—
12	C₂×C₃×C₁₀₃	—	25	1	no	—
13	C₃×D₁₀₃	—	25	2	no	—
14	C₅×C₁₀₃	—	3	2	no	—
15	C₂×D₁₀₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₀₃	—	25	1	no	Hall
17	C₂²×C₅²⋊C₃	—	103	1	no	maximal, Hall
18	C₂×C₁₀₃	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
19	D₁₀₃	C₂×C₅²⋊C₃	1	2	yes	direct product factor
20	C₂×C₅²⋊C₃	—	103	2	no	—
21	C₂×C₅²⋊C₃	D₁₀₃	1	1	yes	characteristic, direct product factor
22	C₁₀₃	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₅²	—	103	1	no	Hall
24	C₅²⋊C₃	C₂×D₁₀₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅²	—	103	2	no	—
26	C₂×C₅²	C₃×D₁₀₃	1	1	yes	characteristic, complemented
27	C₅²	C₂×C₃×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₅	—	309	2	no	—
29	C₂²×C₃	—	2575	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	C₂×C₅	—	309	4	no	—
32	C₂×C₃	—	2575	2	no	—
33	C₂×C₃	—	25	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	103	1	no	Sylow
36	C₃	—	25	1	no	Sylow
37	C₂	—	103	2	no	—
38	C₂	C₅²⋊C₃×D₁₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅²⋊C₃×D₁₀₃
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⋊C₃×C₁₀₃	C₂	semidirect
2. C₅²⋊C₃×D₁₀₃	C₂	direct (N × H)
3. C₂×C₅²×D₁₀₃	C₃	semidirect
4. C₅²⋊C₃×C₁₀₃	C₂²	semidirect
5. C₅²×D₁₀₃	C₂×C₃	semidirect
6. C₂×C₅²×C₁₀₃	C₂×C₃	semidirect
7. C₅²×C₁₀₃	C₂²×C₃	semidirect
15. C₂×D₁₀₃	C₅²⋊C₃	direct (N × H)
18. C₂×C₁₀₃	C₂×C₅²⋊C₃	semidirect
19. D₁₀₃	C₂×C₅²⋊C₃	direct (N × H)
21. C₂×C₅²⋊C₃	D₁₀₃	direct (N × H)
22. C₁₀₃	C₂²×C₅²⋊C₃	semidirect
24. C₅²⋊C₃	C₂×D₁₀₃	direct (N × H)
26. C₂×C₅²	C₃×D₁₀₃	semidirect
27. C₅²	C₂×C₃×D₁₀₃	semidirect
38. C₂	C₅²⋊C₃×D₁₀₃	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⋊C₃×C₁₀₃	2
C₅²⋊C₃×D₁₀₃	2
C₂×C₅²×D₁₀₃	3
C₂×C₃×D₁₀₃	25
C₂²×C₅²⋊C₃	103

Subgroups — C2×C52⋊C3×D103 #44525490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²⋊C₃×D₁₀₃ #44525490