Subgroups — C₃×C₂₅×Dic₁₀₃ #44525397

Order 30900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂₅×Dic₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×Dic₁₀₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×C₁₀₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₁₀₃	C₂×C₅	1	1	yes	characteristic
7	C₂₅×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₅×Dic₁₀₃	C₃×C₅	1	1	yes	characteristic
9	C₃×C₅×C₁₀₃	C₄×C₅	1	1	yes	characteristic
10	C₃×Dic₁₀₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₀₃	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₃×C₁₀₃	C₂×C₂₅	1	1	yes	characteristic
13	C₅×C₁₀₃	C₃×C₄×C₅	1	1	yes	characteristic
14	Dic₁₀₃	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₀₃	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₂₅	—	103	1	no	maximal, Hall
17	C₂×C₁₀₃	C₂×C₃×C₂₅	1	1	yes	characteristic
18	C₂×C₃×C₂₅	D₁₀₃	1	1	yes	characteristic
19	C₁₀₃	C₃×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₄×C₂₅	—	103	1	no	Hall
21	C₃×C₂₅	Dic₁₀₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₄×C₅	—	103	1	no	—
23	C₂×C₂₅	C₃×D₁₀₃	1	1	yes	characteristic
24	C₂×C₃×C₅	C₅×D₁₀₃	1	1	yes	characteristic
25	C₂₅	C₃×Dic₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	—	103	1	no	—
27	C₃×C₅	C₅×Dic₁₀₃	1	1	yes	characteristic
28	C₃×C₄	—	103	1	no	Hall
29	C₂×C₅	C₃×C₅×D₁₀₃	1	1	yes	characteristic
30	C₂×C₃	C₂₅×D₁₀₃	1	1	yes	characteristic
31	C₅	C₃×C₅×Dic₁₀₃	1	1	yes	characteristic
32	C₄	—	103	1	no	Sylow
33	C₃	C₂₅×Dic₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₂₅×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₅	D₁₀₃
commutator, hypocenter	C₁₀₃	C₃×C₄×C₂₅
Frattini	C₂×C₅	C₃×C₅×D₁₀₃
Fitting	C₂×C₃×C₂₅×C₁₀₃	C₂
socle, prime radical	C₂×C₃×C₅×C₁₀₃	C₂×C₅
cosocle	C₂×C₅×C₁₀₃	C₂×C₃×C₅
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₃×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₂₅×Dic₁₀₃	C₃	direct (N × H)
3. C₃×C₂₅×C₁₀₃	C₄	semidirect
7. C₂₅×C₁₀₃	C₃×C₄	semidirect
10. C₃×Dic₁₀₃	C₂₅	direct (N × H)
14. Dic₁₀₃	C₃×C₂₅	direct (N × H)
15. C₃×C₁₀₃	C₄×C₂₅	semidirect
19. C₁₀₃	C₃×C₄×C₂₅	semidirect
21. C₃×C₂₅	Dic₁₀₃	direct (N × H)
25. C₂₅	C₃×Dic₁₀₃	direct (N × H)
33. C₃	C₂₅×Dic₁₀₃	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×C₃×C₂₅×C₁₀₃	2
C₂₅×Dic₁₀₃	3
C₃×C₅×Dic₁₀₃	5
C₃×C₄×C₂₅	103

Subgroups — C3×C25×Dic103 #44525397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₅×Dic₁₀₃ #44525397