Subgroups — C₂×C₃×D₂₀₃₅ #37567639

Order 24420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₀₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₄₀₇	—	5	1	no	maximal, Hall
6	D₂₀₃₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₄₀₇	—	5	2	no	—
9	C₂×C₃×C₁₁×C₃₇	D₅	1	1	yes	characteristic, complemented
10	C₂×C₃×D₁₈₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₄₀₇	—	5	1	no	Hall
13	C₃×C₁₁×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₃₇	D₁₁	1	1	yes	characteristic, complemented
15	C₃×D₁₈₅	—	11	2	no	—
16	C₂×C₁₁×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented
17	D₄₀₇	—	5	2	no	—
18	C₂×D₁₈₅	—	11	1	no	Hall
19	C₂×C₃×D₅₅	—	37	1	no	maximal, Hall
20	C₃×C₅×C₃₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×D₃₇	—	55	1	no	Hall
22	C₁₁×C₃₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₃₇	C₃×D₁₁	1	1	yes	characteristic, complemented
24	D₁₈₅	—	11	2	no	—
25	C₂×C₃×C₅×C₁₁	D₃₇	1	1	yes	characteristic, complemented
26	C₃×D₅₅	—	37	2	no	—
27	C₂×C₃×C₃₇	D₅₅	1	1	yes	characteristic, complemented
28	C₃×D₃₇	—	55	2	no	—
29	C₂×D₅₅	—	37	1	no	Hall
30	C₅×C₃₇	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₁	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
32	C₂×D₃₇	—	55	1	no	Hall
33	C₂×C₃×D₁₁	—	185	1	no	Hall
34	C₃×C₃₇	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₁	C₃×D₃₇	1	1	yes	characteristic, complemented
36	D₅₅	—	37	2	no	—
37	C₂×C₃₇	C₃×D₅₅	1	1	yes	characteristic, complemented
38	D₃₇	—	55	2	no	—
39	C₂×C₃×C₁₁	D₁₈₅	1	1	yes	characteristic, complemented
40	C₃×D₁₁	—	185	2	no	—
41	C₂×C₃×D₅	—	407	1	no	Hall
42	C₅×C₁₁	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
43	C₂×D₁₁	—	185	1	no	Hall
44	C₃₇	C₂×C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
45	C₃×C₁₁	C₂×D₁₈₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₅	D₄₀₇	1	1	yes	characteristic, complemented
47	C₃×D₅	—	407	2	no	—
48	C₂×C₁₁	C₃×D₁₈₅	1	1	yes	characteristic, complemented
49	D₁₁	—	185	2	no	—
50	C₂×D₅	—	407	1	no	Hall
51	C₃×C₅	C₂×D₄₀₇	1	1	yes	characteristic, complemented, Hall
52	C₂²×C₃	—	2035	1	no	Hall
53	C₁₁	C₂×C₃×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	C₃×D₄₀₇	1	1	yes	characteristic, complemented
55	D₅	—	407	2	no	—
56	C₂×C₃	—	2035	2	no	—
57	C₂×C₃	D₂₀₃₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₄₀₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2035	1	no	Sylow
60	C₃	C₂×D₂₀₃₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2035	2	no	—
62	C₂	C₃×D₂₀₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₀₃₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₃₇	C₂
LCS	G ▷ C₅×C₁₁×C₃₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₀₃₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₃₇	C₂	semidirect
3. C₂×D₂₀₃₅	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₃₇	C₂²	semidirect
6. D₂₀₃₅	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₁×C₃₇	C₂×C₃	semidirect
9. C₂×C₃×C₁₁×C₃₇	D₅	semidirect
11. C₅×C₁₁×C₃₇	C₂²×C₃	semidirect
13. C₃×C₁₁×C₃₇	C₂×D₅	semidirect
14. C₂×C₃×C₅×C₃₇	D₁₁	semidirect
16. C₂×C₁₁×C₃₇	C₃×D₅	semidirect
20. C₃×C₅×C₃₇	C₂×D₁₁	semidirect
22. C₁₁×C₃₇	C₂×C₃×D₅	semidirect
23. C₂×C₅×C₃₇	C₃×D₁₁	semidirect
25. C₂×C₃×C₅×C₁₁	D₃₇	semidirect
27. C₂×C₃×C₃₇	D₅₅	semidirect
30. C₅×C₃₇	C₂×C₃×D₁₁	semidirect
31. C₃×C₅×C₁₁	C₂×D₃₇	semidirect
34. C₃×C₃₇	C₂×D₅₅	semidirect
35. C₂×C₅×C₁₁	C₃×D₃₇	semidirect
37. C₂×C₃₇	C₃×D₅₅	semidirect
39. C₂×C₃×C₁₁	D₁₈₅	semidirect
42. C₅×C₁₁	C₂×C₃×D₃₇	semidirect
44. C₃₇	C₂×C₃×D₅₅	semidirect
45. C₃×C₁₁	C₂×D₁₈₅	semidirect
46. C₂×C₃×C₅	D₄₀₇	semidirect
48. C₂×C₁₁	C₃×D₁₈₅	semidirect
51. C₃×C₅	C₂×D₄₀₇	semidirect
53. C₁₁	C₂×C₃×D₁₈₅	semidirect
54. C₂×C₅	C₃×D₄₀₇	semidirect
57. C₂×C₃	D₂₀₃₅	direct (N × H)
58. C₅	C₂×C₃×D₄₀₇	semidirect
60. C₃	C₂×D₂₀₃₅	direct (N × H)
62. C₂	C₃×D₂₀₃₅	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×D₂₀₃₅	2
C₂×C₃×C₅×C₁₁×C₃₇	2
C₂×D₂₀₃₅	3
C₂×C₃×D₄₀₇	5
C₂×C₃×D₁₈₅	11
C₂×C₃×D₅₅	37

Subgroups — C2×C3×D2035 #37567639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₀₃₅ #37567639