Subgroups — C₂×C₅×D₇₄₁ #28414940

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₂₄₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₂₄₇	—	3	2	no	—
7	C₂×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₃×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
9	D₇₄₁	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₅₇	—	13	1	no	maximal, Hall
12	C₂×D₂₄₇	—	3	1	no	Hall
13	C₂×C₅×D₃₉	—	19	1	no	maximal, Hall
14	C₃×C₁₃×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₉	D₁₃	1	1	yes	characteristic, complemented
16	C₅×D₅₇	—	13	2	no	—
17	C₂×C₁₃×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
18	D₂₄₇	—	3	2	no	—
19	C₂×C₃×C₅×C₁₃	D₁₉	1	1	yes	characteristic, complemented
20	C₅×D₃₉	—	19	2	no	—
21	C₂×C₅×D₁₉	—	39	1	no	Hall
22	C₃×C₅×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×D₁₃	—	57	1	no	Hall
24	C₁₃×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₅₇	—	13	1	no	Hall
26	C₃×C₅×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₉	D₃₉	1	1	yes	characteristic, complemented
28	C₅×D₁₉	—	39	2	no	—
29	C₂×D₃₉	—	19	1	no	Hall
30	C₂×C₅×C₁₃	D₅₇	1	1	yes	characteristic, complemented
31	C₅×D₁₃	—	57	2	no	—
32	C₂×C₃×C₁₉	C₅×D₁₃	1	1	yes	characteristic, complemented
33	D₅₇	—	13	2	no	—
34	C₅×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₁₃	C₅×D₁₉	1	1	yes	characteristic, complemented
36	D₃₉	—	19	2	no	—
37	C₂×D₁₉	—	39	1	no	Hall
38	C₅×C₁₃	C₂×D₅₇	1	1	yes	characteristic, complemented, Hall
39	C₂×C₅×D₃	—	247	1	no	Hall
40	C₃×C₁₉	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×D₁₃	—	57	1	no	Hall
42	C₃×C₁₃	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₁₉	C₅×D₃₉	1	1	yes	characteristic, complemented
44	D₁₉	—	39	2	no	—
45	C₂×C₃×C₅	D₂₄₇	1	1	yes	characteristic, complemented
46	C₅×D₃	—	247	2	no	—
47	C₂×C₁₃	C₅×D₅₇	1	1	yes	characteristic, complemented
48	D₁₃	—	57	2	no	—
49	C₂²×C₅	—	741	1	no	Hall
50	C₁₉	C₂×C₅×D₃₉	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₅	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Hall
52	C₁₃	C₂×C₅×D₅₇	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₃	—	247	1	no	Hall
54	C₂×C₅	—	741	2	no	—
55	C₂×C₅	D₇₄₁	1	1	yes	characteristic, direct product factor
56	C₂×C₃	C₅×D₂₄₇	1	1	yes	characteristic, complemented
57	D₃	—	247	2	no	—
58	C₅	C₂×D₇₄₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	741	1	no	Sylow
60	C₃	C₂×C₅×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	741	2	no	—
62	C₂	C₅×D₇₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇₄₁
commutator, cosocle, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₇₄₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₃×C₁₉	C₂²	semidirect
5. C₂×D₇₄₁	C₅	direct (N × H)
7. C₂×C₅×C₁₃×C₁₉	D₃	semidirect
8. C₂×C₃×C₁₃×C₁₉	C₂×C₅	semidirect
9. D₇₄₁	C₂×C₅	direct (N × H)
10. C₅×C₁₃×C₁₉	C₂×D₃	semidirect
14. C₃×C₁₃×C₁₉	C₂²×C₅	semidirect
15. C₂×C₃×C₅×C₁₉	D₁₃	semidirect
17. C₂×C₁₃×C₁₉	C₅×D₃	semidirect
19. C₂×C₃×C₅×C₁₃	D₁₉	semidirect
22. C₃×C₅×C₁₉	C₂×D₁₃	semidirect
24. C₁₃×C₁₉	C₂×C₅×D₃	semidirect
26. C₃×C₅×C₁₃	C₂×D₁₉	semidirect
27. C₂×C₅×C₁₉	D₃₉	semidirect
30. C₂×C₅×C₁₃	D₅₇	semidirect
32. C₂×C₃×C₁₉	C₅×D₁₃	semidirect
34. C₅×C₁₉	C₂×D₃₉	semidirect
35. C₂×C₃×C₁₃	C₅×D₁₉	semidirect
38. C₅×C₁₃	C₂×D₅₇	semidirect
40. C₃×C₁₉	C₂×C₅×D₁₃	semidirect
42. C₃×C₁₃	C₂×C₅×D₁₉	semidirect
43. C₂×C₁₉	C₅×D₃₉	semidirect
45. C₂×C₃×C₅	D₂₄₇	semidirect
47. C₂×C₁₃	C₅×D₅₇	semidirect
50. C₁₉	C₂×C₅×D₃₉	semidirect
51. C₃×C₅	C₂×D₂₄₇	semidirect
52. C₁₃	C₂×C₅×D₅₇	semidirect
55. C₂×C₅	D₇₄₁	direct (N × H)
56. C₂×C₃	C₅×D₂₄₇	semidirect
58. C₅	C₂×D₇₄₁	direct (N × H)
60. C₃	C₂×C₅×D₂₄₇	semidirect
62. C₂	C₅×D₇₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₇₄₁	2
C₂×C₃×C₅×C₁₃×C₁₉	2
C₂×C₅×D₂₄₇	3
C₂×D₇₄₁	5
C₂×C₅×D₅₇	13
C₂×C₅×D₃₉	19

Subgroups — C2×C5×D741 #28414940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₇₄₁ #28414940