Subgroups — #1039×C₁₀₃⋊C₃ #44525440

Order 30900.

96 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
2	#1039×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₀₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₅×C₁₀₃⋊C₃	—	5	6	no	maximal
5	C₂×C₅²×C₁₀₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₅×C₁₀₃⋊C₃	D₅	1	6	yes	—
7	C₅²×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₅×C₁₀₃	—	5	6	no	—
9	C₅×C₁₀₃⋊C₃	Dic₅	1	6	yes	complemented
10	C₄×C₁₀₃⋊C₃	—	25	1	no	Hall
11	C₂×C₅×C₁₀₃	C₃×D₅	1	6	yes	—
12	C₂×C₁₀₃⋊C₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅×C₁₀₃	C₃×Dic₅	1	6	yes	complemented
14	C₄×C₁₀₃	—	25	1	no	Hall
15	C₁₀₃⋊C₃	#1039	1	1	yes	characteristic, direct product factor, Hall
16	C₃×#1039	—	103	1	no	maximal, Hall
17	C₂×C₁₀₃	C₃×C₅⋊D₅	1	1	yes	characteristic
18	C₂×C₃×C₅²	—	103	1	no	—
19	C₁₀₃	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
20	#1039	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅²	—	103	1	no	Hall
22	C₃×Dic₅	—	515	6	no	—
23	C₂×C₅²	C₂×C₁₀₃⋊C₃	1	1	yes	characteristic
24	C₂×C₃×C₅	—	103	6	no	—
25	C₅²	C₄×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	5	6	no	—
27	C₃×C₅	—	103	6	no	—
28	C₃×C₄	—	2575	1	no	Hall
29	C₂×C₅	D₅×C₁₀₃⋊C₃	1	6	yes	—
30	C₂×C₃	—	103	1	no	—
31	C₅	Dic₅×C₁₀₃⋊C₃	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	—	103	1	no	Sylow
34	C₂	C₅⋊D₅×C₁₀₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₅×C₁₀₃⋊C₃
commutator, hypocenter	C₅²×C₁₀₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₁₀₃	C₂×C₃
prime radical	C₂×C₅²×C₁₀₃⋊C₃	C₂
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #1039×C₁₀₃	C₃	semidirect
3. C₅²×C₁₀₃⋊C₃	C₄	semidirect
7. C₅²×C₁₀₃	C₃×C₄	semidirect
9. C₅×C₁₀₃⋊C₃	Dic₅	semidirect
13. C₅×C₁₀₃	C₃×Dic₅	semidirect
15. C₁₀₃⋊C₃	#1039	direct (N × H)
19. C₁₀₃	C₃×#1039	semidirect
20. #1039	C₁₀₃⋊C₃	direct (N × H)
25. C₅²	C₄×C₁₀₃⋊C₃	semidirect
31. C₅	Dic₅×C₁₀₃⋊C₃	semidirect

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
#1039×C₁₀₃	3
Dic₅×C₁₀₃⋊C₃	5
C₃×#1039	103

Subgroups — #1039×C103⋊C3 #44525440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1039×C₁₀₃⋊C₃ #44525440