Subgroups — C₃×D₅₁₈₇ #44528037

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₇₂₉	—	3	1	no	maximal
4	C₃×C₇×C₁₃×C₁₉	—	2	1	no	—
5	C₃×C₇×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₇₄₁	—	7	1	no	maximal, Hall
8	D₁₇₂₉	—	3	1	no	Hall
9	C₃×D₃₉₉	—	13	1	no	maximal, Hall
10	C₃²×C₁₃×C₁₉	D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₂₇₃	—	19	1	no	maximal, Hall
13	D₇₄₁	—	7	1	no	—
14	C₃×D₂₄₇	—	21	1	no	—
15	C₃²×C₇×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
17	D₃₉₉	—	13	1	no	—
18	C₃×D₁₃₃	—	39	1	no	—
19	C₃×C₁₃×C₁₉	—	2	1	no	—
20	C₃×C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×C₁₃×C₁₉	D₂₁	1	1	yes	characteristic, complemented
22	D₂₇₃	—	19	1	no	—
23	C₃×D₉₁	—	57	1	no	—
24	D₂₄₇	—	21	1	no	Hall
25	C₃×C₇×C₁₉	—	2	1	no	—
26	C₃×C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₉	D₃₉	1	1	yes	characteristic, complemented
28	C₃×D₅₇	—	91	1	no	Hall
29	C₃×C₇×C₁₃	—	2	1	no	—
30	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₃	D₅₇	1	1	yes	characteristic, complemented
32	D₁₃₃	—	39	1	no	Hall
33	C₁₃×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
34	C₃×D₃₉	—	133	1	no	Hall
35	D₉₁	—	57	1	no	Hall
36	C₃²×C₁₉	D₉₁	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₉	C₃×D₃₉	1	1	yes	characteristic, complemented, Hall
38	C₃×D₂₁	—	247	1	no	Hall
39	C₃²×C₁₃	D₁₃₃	1	1	yes	characteristic, complemented, Hall
40	D₅₇	—	91	1	no	—
41	C₃×D₁₉	—	273	1	no	—
42	C₇×C₁₃	C₃×D₅₇	1	1	yes	characteristic, complemented, Hall
43	D₃₉	—	133	1	no	—
44	C₃×D₁₃	—	399	1	no	—
45	C₃²×C₇	D₂₄₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₉	—	2	1	no	—
47	C₃×C₁₉	C₃×D₉₁	1	1	yes	characteristic, complemented
48	C₃×C₁₉	D₂₇₃	1	1	yes	characteristic, complemented
49	D₂₁	—	247	1	no	—
50	C₃×D₇	—	741	1	no	—
51	C₃×C₁₃	—	2	1	no	—
52	C₃×C₁₃	C₃×D₁₃₃	1	1	yes	characteristic, complemented
53	C₃×C₁₃	D₃₉₉	1	1	yes	characteristic, complemented
54	D₁₉	—	273	1	no	Hall
55	D₁₃	—	399	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	C₃×D₂₄₇	1	1	yes	characteristic, complemented
58	C₃×C₇	D₇₄₁	1	1	yes	characteristic, complemented
59	C₁₉	C₃×D₂₇₃	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	1729	1	no	Hall
61	D₇	—	741	1	no	Hall
62	C₁₃	C₃×D₃₉₉	1	1	yes	characteristic, complemented, Sylow
63	C₃²	D₁₇₂₉	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×D₇₄₁	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	5187	1	no	—
66	D₃	—	1729	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×D₁₇₂₉	1	1	yes	characteristic, complemented
69	C₃	D₅₁₈₇	1	1	yes	characteristic, direct product factor
70	C₂	—	5187	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₁₈₇
commutator, cosocle, hypocenter	C₃×C₇×C₁₃×C₁₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
2. D₅₁₈₇	C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₁₉	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
10. C₃²×C₁₃×C₁₉	D₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
15. C₃²×C₇×C₁₉	D₁₃	semidirect
16. C₃²×C₇×C₁₃	D₁₉	semidirect
20. C₃×C₁₃×C₁₉	C₃×D₇	semidirect
21. C₃×C₁₃×C₁₉	D₂₁	semidirect
26. C₃×C₇×C₁₉	C₃×D₁₃	semidirect
27. C₃×C₇×C₁₉	D₃₉	semidirect
30. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
31. C₃×C₇×C₁₃	D₅₇	semidirect
33. C₁₃×C₁₉	C₃×D₂₁	semidirect
36. C₃²×C₁₉	D₉₁	semidirect
37. C₇×C₁₉	C₃×D₃₉	semidirect
39. C₃²×C₁₃	D₁₃₃	semidirect
42. C₇×C₁₃	C₃×D₅₇	semidirect
45. C₃²×C₇	D₂₄₇	semidirect
47. C₃×C₁₉	C₃×D₉₁	semidirect
48. C₃×C₁₉	D₂₇₃	semidirect
52. C₃×C₁₃	C₃×D₁₃₃	semidirect
53. C₃×C₁₃	D₃₉₉	semidirect
57. C₃×C₇	C₃×D₂₄₇	semidirect
58. C₃×C₇	D₇₄₁	semidirect
59. C₁₉	C₃×D₂₇₃	semidirect
62. C₁₃	C₃×D₃₉₉	semidirect
63. C₃²	D₁₇₂₉	semidirect
64. C₇	C₃×D₇₄₁	semidirect
68. C₃	C₃×D₁₇₂₉	semidirect
69. C₃	D₅₁₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₃×C₁₉	2
D₅₁₈₇	3
C₃×D₁₇₂₉	3
C₃×D₇₄₁	7
C₃×D₃₉₉	13
C₃×D₂₇₃	19

Subgroups — C3×D5187 #44528037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₁₈₇ #44528037