Subgroups — D₃×C₂₅×D₁₀₃ #44525417

Order 30900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×D₃₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₅×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₅×D₁₀₃	—	3	1	no	maximal, Hall
5	C₃×C₂₅×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×D₁₀₃	C₅	1	1	yes	maximal, characteristic
7	C₂₅×D₁₀₃	—	3	1	no	—
8	C₂₅×D₁₀₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₂₅×C₁₀₃	—	3	1	no	—
10	C₅×D₃₀₉	C₂×C₅	1	1	yes	characteristic
11	C₅×D₃×C₁₀₃	C₂×C₅	1	1	yes	characteristic
12	C₃×C₅×D₁₀₃	C₂×C₅	1	1	yes	characteristic
13	C₂₅×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₁₀₃	—	3	1	no	—
15	C₃×C₅×C₁₀₃	C₂²×C₅	1	1	yes	characteristic
16	D₃×D₁₀₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₀₃	—	3	1	no	—
18	C₅×D₁₀₃	—	3	1	no	—
19	C₅×D₁₀₃	C₅×D₃	1	1	yes	characteristic
20	D₃₀₉	C₂×C₂₅	1	1	yes	characteristic, complemented
21	C₃×D₁₀₃	C₂×C₂₅	1	1	yes	characteristic, complemented
22	D₃×C₁₀₃	C₂×C₂₅	1	1	yes	characteristic, complemented
23	C₅×C₁₀₃	C₂×C₅×D₃	1	1	yes	characteristic
24	C₂×D₁₀₃	—	3	1	no	Hall
25	C₃×C₁₀₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₂₅	—	103	1	no	maximal, Hall
27	C₂×C₁₀₃	—	3	1	no	—
28	D₁₀₃	—	3	1	no	—
29	D₁₀₃	D₃×C₂₅	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₂₅	—	103	1	no	—
31	D₃×C₂₅	—	103	1	no	—
32	D₃×C₂₅	D₁₀₃	1	1	yes	characteristic, direct product factor
33	C₁₀₃	C₂×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₂₅	—	309	1	no	Hall
35	C₃×C₂₅	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×D₃	—	103	1	no	—
37	C₂×C₂₅	—	3	1	no	—
38	C₂×C₂₅	—	309	1	no	—
39	C₂×C₂₅	—	103	1	no	—
40	C₂×C₃×C₅	—	103	1	no	—
41	C₅×D₃	—	103	1	no	—
42	C₅×D₃	C₅×D₁₀₃	1	1	yes	characteristic
43	C₂₅	D₃×D₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₅	—	309	1	no	—
45	C₃×C₅	C₂×C₅×D₁₀₃	1	1	yes	characteristic
46	C₂×D₃	—	103	1	no	Hall
47	C₂×C₅	—	3	1	no	—
48	C₂×C₅	—	309	1	no	—
49	C₂×C₅	—	103	1	no	—
50	C₂×C₃	—	103	1	no	—
51	D₃	—	103	1	no	—
52	D₃	C₂₅×D₁₀₃	1	1	yes	characteristic, direct product factor
53	C₅	C₅×D₃×D₁₀₃	1	1	yes	characteristic
54	C₂²	—	309	1	no	Sylow
55	C₃	C₂×C₂₅×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	309	1	no	—
58	C₂	—	103	1	no	—

	subgroup	G/H
center, hypercenter	C₂₅	D₃×D₁₀₃
commutator, hypocenter	C₃×C₁₀₃	C₂²×C₂₅
Frattini	C₅	C₅×D₃×D₁₀₃
Fitting	C₃×C₂₅×C₁₀₃	C₂²
socle, cosocle	C₃×C₅×C₁₀₃	C₂²×C₅
prime radical	C₅×D₃×D₁₀₃	C₅
LCS	G ▷ C₃×C₁₀₃
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×D₃₀₉	C₂	semidirect
2. D₃×C₂₅×C₁₀₃	C₂	semidirect
3. C₃×C₂₅×D₁₀₃	C₂	semidirect
5. C₃×C₂₅×C₁₀₃	C₂²	semidirect
8. C₂₅×D₁₀₃	D₃	direct (N × H)
13. C₂₅×C₁₀₃	C₂×D₃	semidirect
16. D₃×D₁₀₃	C₂₅	direct (N × H)
20. D₃₀₉	C₂×C₂₅	semidirect
21. C₃×D₁₀₃	C₂×C₂₅	semidirect
22. D₃×C₁₀₃	C₂×C₂₅	semidirect
25. C₃×C₁₀₃	C₂²×C₂₅	semidirect
29. D₁₀₃	D₃×C₂₅	direct (N × H)
32. D₃×C₂₅	D₁₀₃	direct (N × H)
33. C₁₀₃	C₂×D₃×C₂₅	semidirect
35. C₃×C₂₅	C₂×D₁₀₃	semidirect
43. C₂₅	D₃×D₁₀₃	direct (N × H)
52. D₃	C₂₅×D₁₀₃	direct (N × H)
55. C₃	C₂×C₂₅×D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×D₃₀₉	2
D₃×C₂₅×C₁₀₃	2
C₃×C₂₅×D₁₀₃	2
C₂×C₂₅×D₁₀₃	3
C₅×D₃×D₁₀₃	5
C₂×D₃×C₂₅	103

Subgroups — D3×C25×D103 #44525417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂₅×D₁₀₃ #44525417