Subgroups — C₃×D₂₅×D₄₁ #27134166

Order 12300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₀₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄₁×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₅×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₅×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅×D₄₁	—	5	1	no	maximal
7	D₁₀₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₅×D₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₄₁×D₂₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₂₀₅	—	5	1	no	—
11	C₃×D₅×C₄₁	—	5	1	no	—
12	C₃×C₅×D₄₁	D₅	1	1	yes	characteristic
13	C₂₅×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₄₁	—	5	1	no	—
15	C₃×C₅×C₄₁	C₂×D₅	1	1	yes	characteristic
16	C₂×C₃×D₄₁	—	25	1	no	Hall
17	D₂₀₅	—	5	1	no	—
18	C₅×D₄₁	C₃×D₅	1	1	yes	characteristic
19	D₅×C₄₁	—	5	1	no	—
20	C₂×C₃×D₂₅	—	41	1	no	maximal, Hall
21	C₂×C₃×C₄₁	—	25	1	no	—
22	C₃×D₄₁	—	25	1	no	—
23	C₃×D₄₁	D₂₅	1	1	yes	characteristic, direct product factor
24	C₅×C₄₁	C₂×C₃×D₅	1	1	yes	characteristic
25	C₂×D₄₁	—	25	1	no	Hall
26	C₂×C₃×C₂₅	—	41	1	no	—
27	C₃×D₂₅	—	41	1	no	—
28	C₃×D₂₅	D₄₁	1	1	yes	characteristic, direct product factor
29	C₃×C₄₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
30	C₂×D₂₅	—	41	1	no	Hall
31	C₂×C₄₁	—	25	1	no	—
32	D₄₁	—	25	1	no	—
33	D₄₁	C₃×D₂₅	1	1	yes	characteristic, direct product factor
34	C₃×C₂₅	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×D₅	—	205	1	no	—
36	C₂×C₂₅	—	41	1	no	—
37	D₂₅	—	41	1	no	—
38	D₂₅	C₃×D₄₁	1	1	yes	characteristic, direct product factor
39	C₄₁	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	—	41	1	no	—
41	C₃×D₅	—	5	1	no	—
42	C₃×D₅	—	205	1	no	—
43	C₂₅	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	205	1	no	—
45	C₃×C₅	D₅×D₄₁	1	1	yes	characteristic
46	C₂²×C₃	—	1025	1	no	Hall
47	C₂×C₅	—	41	1	no	—
48	D₅	—	5	1	no	—
49	D₅	—	205	1	no	—
50	C₂×C₃	—	1025	1	no	—
51	C₂×C₃	—	25	1	no	—
52	C₂×C₃	—	41	1	no	—
53	C₅	C₃×D₅×D₄₁	1	1	yes	characteristic
54	C₂²	—	1025	1	no	Sylow
55	C₃	D₂₅×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	1025	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₂₅×D₄₁
commutator, cosocle, hypocenter	C₂₅×C₄₁	C₂²×C₃
Frattini	C₅	C₃×D₅×D₄₁
Fitting	C₃×C₂₅×C₄₁	C₂²
socle	C₃×C₅×C₄₁	C₂×D₅
LCS	G ▷ C₂₅×C₄₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₀₂₅	C₂	semidirect
2. C₃×C₄₁×D₂₅	C₂	semidirect
3. C₃×C₂₅×D₄₁	C₂	semidirect
4. D₂₅×D₄₁	C₃	direct (N × H)
5. C₃×C₂₅×C₄₁	C₂²	semidirect
7. D₁₀₂₅	C₂×C₃	semidirect
8. C₂₅×D₄₁	C₂×C₃	semidirect
9. C₄₁×D₂₅	C₂×C₃	semidirect
13. C₂₅×C₄₁	C₂²×C₃	semidirect
23. C₃×D₄₁	D₂₅	direct (N × H)
28. C₃×D₂₅	D₄₁	direct (N × H)
29. C₃×C₄₁	C₂×D₂₅	semidirect
33. D₄₁	C₃×D₂₅	direct (N × H)
34. C₃×C₂₅	C₂×D₄₁	semidirect
38. D₂₅	C₃×D₄₁	direct (N × H)
39. C₄₁	C₂×C₃×D₂₅	semidirect
43. C₂₅	C₂×C₃×D₄₁	semidirect
55. C₃	D₂₅×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₁₀₂₅	2
C₃×C₄₁×D₂₅	2
C₃×C₂₅×D₄₁	2
D₂₅×D₄₁	3
C₃×D₅×D₄₁	5
C₂×C₃×D₂₅	41

Subgroups — C3×D25×D41 #27134166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₂₅×D₄₁ #27134166